Dark Energy

[nc]

My understanding is that the Universe is expanding and that this expansion
is speeding up. What is fuelling this expansion rate increase that is
working against the force of gravity?

The answer seems to be Dark Energy. Whatever that is!

The question in my mind is where does this energy come from and it would
seem that more and more of it is needed in order to increase the expansion
rate.


Now I know that this is purely speculation and is not backed up by any
mathematics or observation but I wondered if there was a connection between
energy / matter falling past the event horizon of black holes.

As the universe gets older more black holes form. These black holes consume
matter and energy from the universe. Hence the total energy consumed by
black holes across the universe is increasing.

Therefore, is it possible that the energy that has fallen into a black hole
is some how making a re-appearance as this "dark energy".


Wondered if anyone had calculated the number of black holes (and their
energy consumption) at various points in time since the creation of the
universe and attempted to correlate this with the amount of dark energy
required at each of these times?

I know that this may be nonsense but its just a very very speculative
thought that I thought I would mention.

Any comment?

Best Regards,

N

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Phillip Helbig---remove CLOTHES to reply]

In article <dfvq9s$9m8$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com>, "nc"
<colosimo@btinternet.com> writes:

> My understanding is that the Universe is expanding and that this expansion
> is speeding up. What is fuelling this expansion rate increase that is
> working against the force of gravity?
>
> The answer seems to be Dark Energy. Whatever that is!
>
> The question in my mind is where does this energy come from and it would
> seem that more and more of it is needed in order to increase the expansion
> rate.

It doesn't have to come from anywhere. The Friedmann-Lemaître equations
allow for such a term, and apparently it has been observed. Note that
there is not a problem with energy conservation, since energy isn't
conserved in general relativity anyway. (Imagine a universe consisting
only of radiation. It expands. The number of photons remains the same,
but the energy of each decreases due to the redshift. No, this lost
energy does not do the work of expanding the universe.)

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Lou Pecora]

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to
reply) wrote:

> > The question in my mind is where does this energy come from and it would
> > seem that more and more of it is needed in order to increase the expansion
> > rate.
>
> It doesn't have to come from anywhere. The Friedmann-Lemaître equations
> allow for such a term, and apparently it has been observed. Note that
> there is not a problem with energy conservation, since energy isn't
> conserved in general relativity anyway. (Imagine a universe consisting
> only of radiation. It expands. The number of photons remains the same,
> but the energy of each decreases due to the redshift. No, this lost
> energy does not do the work of expanding the universe.)
>

What, if any, conserved quantities are there in General Relativity? I
recall there is an Energy-Momentum tensor, but I know little beyond
that. Is that conserved or involved in a conservation law? If so, what
does it mean?

thanks.

-- Lou Pecora (my views are my own) REMOVE THIS to email me.

[Michael C Price]

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion
>> rate increase that is working against the force of gravity?
>>
>> The answer seems to be Dark Energy.

Correct.

> Whatever that is!

Dark energy may be modelled by adding a constant to Einstein's
equations; hence the term "cosmological constant".

>> The question in my mind is where does this energy come from
>> and it would seem that more and more of it is needed in order
>> to increase the expansion rate.

Correct. The energy comes from the expansion (a form of
gravitational or geometric energy) which is negative. As the
universe expands the positive energy locked as dark energy
increases (density is constant, but volume increases); this is
offset by the negative energy in the Hubble expansion which
decreases (becomes more negative).

In the case of dark energy this process can continue for ever;
it's a slow form of inflation.

>
> It doesn't have to come from anywhere. The Friedmann-Lemaître
> equations allow for such a term, and apparently it has been observed.
> Note that there is not a problem with energy conservation, since
> energy isn't conserved in general relativity anyway.

That is not true. Energy is conserved in GR, with the obvious
caveat that we have to adopt a sensible definition of energy.
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

> (Imagine a universe consisting only of radiation. It expands.
> The number of photons remains the same, but the energy of each
> decreases due to the redshift. No, this lost energy does not do
> the work of expanding the universe.)

Then why does a radiant-filled universe decelerate faster than
a matter-filled universe? Because the energy lost in the redshift
cancels some of the negative energy tied up in the Hubble
expansion.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion
>> rate increase that is working against the force of gravity?
>>
>> The answer seems to be Dark Energy.

Correct.

> Whatever that is!

Dark energy may be modelled by adding a constant to Einstein's
equations; hence the term "cosmological constant".

>> The question in my mind is where does this energy come from
>> and it would seem that more and more of it is needed in order
>> to increase the expansion rate.

Correct. The energy comes from the expansion (a form of
gravitational or geometric energy) which is negative. As the
universe expands the positive energy locked as dark energy
increases (density is constant, but volume increases); this is
offset by the negative energy in the Hubble expansion which
decreases (becomes more negative).

In the case of dark energy this process can continue for ever;
it's a slow form of inflation.

>
> It doesn't have to come from anywhere. The Friedmann-Lemaître
> equations allow for such a term, and apparently it has been observed.
> Note that there is not a problem with energy conservation, since
> energy isn't conserved in general relativity anyway.

That is not true. Energy is conserved in GR, with the obvious
caveat that we have to adopt a sensible definition of energy.
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

> (Imagine a universe consisting only of radiation. It expands.
> The number of photons remains the same, but the energy of each
> decreases due to the redshift. No, this lost energy does not do
> the work of expanding the universe.)

Then why does a radiant-filled universe decelerate faster than
a matter-filled universe? Because the energy lost in the redshift
cancels some of the negative energy tied up in the Hubble
expansion.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion
>> rate increase that is working against the force of gravity?
>>
>> The answer seems to be Dark Energy.

Correct.

> Whatever that is!

Dark energy may be modelled by adding a constant to Einstein's
equations; hence the term "cosmological constant".

>> The question in my mind is where does this energy come from
>> and it would seem that more and more of it is needed in order
>> to increase the expansion rate.

Correct. The energy comes from the expansion (a form of
gravitational or geometric energy) which is negative. As the
universe expands the positive energy locked as dark energy
increases (density is constant, but volume increases); this is
offset by the negative energy in the Hubble expansion which
decreases (becomes more negative).

In the case of dark energy this process can continue for ever;
it's a slow form of inflation.

>
> It doesn't have to come from anywhere. The Friedmann-Lemaître
> equations allow for such a term, and apparently it has been observed.
> Note that there is not a problem with energy conservation, since
> energy isn't conserved in general relativity anyway.

That is not true. Energy is conserved in GR, with the obvious
caveat that we have to adopt a sensible definition of energy.
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

> (Imagine a universe consisting only of radiation. It expands.
> The number of photons remains the same, but the energy of each
> decreases due to the redshift. No, this lost energy does not do
> the work of expanding the universe.)

Then why does a radiant-filled universe decelerate faster than
a matter-filled universe? Because the energy lost in the redshift
cancels some of the negative energy tied up in the Hubble
expansion.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion
>> rate increase that is working against the force of gravity?
>>
>> The answer seems to be Dark Energy.

Correct.

> Whatever that is!

Dark energy may be modelled by adding a constant to Einstein's
equations; hence the term "cosmological constant".

>> The question in my mind is where does this energy come from
>> and it would seem that more and more of it is needed in order
>> to increase the expansion rate.

Correct. The energy comes from the expansion (a form of
gravitational or geometric energy) which is negative. As the
universe expands the positive energy locked as dark energy
increases (density is constant, but volume increases); this is
offset by the negative energy in the Hubble expansion which
decreases (becomes more negative).

In the case of dark energy this process can continue for ever;
it's a slow form of inflation.

>
> It doesn't have to come from anywhere. The Friedmann-Lemaître
> equations allow for such a term, and apparently it has been observed.
> Note that there is not a problem with energy conservation, since
> energy isn't conserved in general relativity anyway.

That is not true. Energy is conserved in GR, with the obvious
caveat that we have to adopt a sensible definition of energy.
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

> (Imagine a universe consisting only of radiation. It expands.
> The number of photons remains the same, but the energy of each
> decreases due to the redshift. No, this lost energy does not do
> the work of expanding the universe.)

Then why does a radiant-filled universe decelerate faster than
a matter-filled universe? Because the energy lost in the redshift
cancels some of the negative energy tied up in the Hubble
expansion.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion
>> rate increase that is working against the force of gravity?
>>
>> The answer seems to be Dark Energy.

Correct.

> Whatever that is!

Dark energy may be modelled by adding a constant to Einstein's
equations; hence the term "cosmological constant".

>> The question in my mind is where does this energy come from
>> and it would seem that more and more of it is needed in order
>> to increase the expansion rate.

Correct. The energy comes from the expansion (a form of
gravitational or geometric energy) which is negative. As the
universe expands the positive energy locked as dark energy
increases (density is constant, but volume increases); this is
offset by the negative energy in the Hubble expansion which
decreases (becomes more negative).

In the case of dark energy this process can continue for ever;
it's a slow form of inflation.

>
> It doesn't have to come from anywhere. The Friedmann-Lemaître
> equations allow for such a term, and apparently it has been observed.
> Note that there is not a problem with energy conservation, since
> energy isn't conserved in general relativity anyway.

That is not true. Energy is conserved in GR, with the obvious
caveat that we have to adopt a sensible definition of energy.
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

> (Imagine a universe consisting only of radiation. It expands.
> The number of photons remains the same, but the energy of each
> decreases due to the redshift. No, this lost energy does not do
> the work of expanding the universe.)

Then why does a radiant-filled universe decelerate faster than
a matter-filled universe? Because the energy lost in the redshift
cancels some of the negative energy tied up in the Hubble
expansion.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion
>> rate increase that is working against the force of gravity?
>>
>> The answer seems to be Dark Energy.

Correct.

> Whatever that is!

Dark energy may be modelled by adding a constant to Einstein's
equations; hence the term "cosmological constant".

>> The question in my mind is where does this energy come from
>> and it would seem that more and more of it is needed in order
>> to increase the expansion rate.

Correct. The energy comes from the expansion (a form of
gravitational or geometric energy) which is negative. As the
universe expands the positive energy locked as dark energy
increases (density is constant, but volume increases); this is
offset by the negative energy in the Hubble expansion which
decreases (becomes more negative).

In the case of dark energy this process can continue for ever;
it's a slow form of inflation.

>
> It doesn't have to come from anywhere. The Friedmann-Lemaître
> equations allow for such a term, and apparently it has been observed.
> Note that there is not a problem with energy conservation, since
> energy isn't conserved in general relativity anyway.

That is not true. Energy is conserved in GR, with the obvious
caveat that we have to adopt a sensible definition of energy.
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

> (Imagine a universe consisting only of radiation. It expands.
> The number of photons remains the same, but the energy of each
> decreases due to the redshift. No, this lost energy does not do
> the work of expanding the universe.)

Then why does a radiant-filled universe decelerate faster than
a matter-filled universe? Because the energy lost in the redshift
cancels some of the negative energy tied up in the Hubble
expansion.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion
>> rate increase that is working against the force of gravity?
>>
>> The answer seems to be Dark Energy.

Correct.

> Whatever that is!

Dark energy may be modelled by adding a constant to Einstein's
equations; hence the term "cosmological constant".

>> The question in my mind is where does this energy come from
>> and it would seem that more and more of it is needed in order
>> to increase the expansion rate.

Correct. The energy comes from the expansion (a form of
gravitational or geometric energy) which is negative. As the
universe expands the positive energy locked as dark energy
increases (density is constant, but volume increases); this is
offset by the negative energy in the Hubble expansion which
decreases (becomes more negative).

In the case of dark energy this process can continue for ever;
it's a slow form of inflation.

>
> It doesn't have to come from anywhere. The Friedmann-Lemaître
> equations allow for such a term, and apparently it has been observed.
> Note that there is not a problem with energy conservation, since
> energy isn't conserved in general relativity anyway.

That is not true. Energy is conserved in GR, with the obvious
caveat that we have to adopt a sensible definition of energy.
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

> (Imagine a universe consisting only of radiation. It expands.
> The number of photons remains the same, but the energy of each
> decreases due to the redshift. No, this lost energy does not do
> the work of expanding the universe.)

Then why does a radiant-filled universe decelerate faster than
a matter-filled universe? Because the energy lost in the redshift
cancels some of the negative energy tied up in the Hubble
expansion.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion
>> rate increase that is working against the force of gravity?
>>
>> The answer seems to be Dark Energy.

Correct.

> Whatever that is!

Dark energy may be modelled by adding a constant to Einstein's
equations; hence the term "cosmological constant".

>> The question in my mind is where does this energy come from
>> and it would seem that more and more of it is needed in order
>> to increase the expansion rate.

Correct. The energy comes from the expansion (a form of
gravitational or geometric energy) which is negative. As the
universe expands the positive energy locked as dark energy
increases (density is constant, but volume increases); this is
offset by the negative energy in the Hubble expansion which
decreases (becomes more negative).

In the case of dark energy this process can continue for ever;
it's a slow form of inflation.

>
> It doesn't have to come from anywhere. The Friedmann-Lemaître
> equations allow for such a term, and apparently it has been observed.
> Note that there is not a problem with energy conservation, since
> energy isn't conserved in general relativity anyway.

That is not true. Energy is conserved in GR, with the obvious
caveat that we have to adopt a sensible definition of energy.
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

> (Imagine a universe consisting only of radiation. It expands.
> The number of photons remains the same, but the energy of each
> decreases due to the redshift. No, this lost energy does not do
> the work of expanding the universe.)

Then why does a radiant-filled universe decelerate faster than
a matter-filled universe? Because the energy lost in the redshift
cancels some of the negative energy tied up in the Hubble
expansion.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion
>> rate increase that is working against the force of gravity?
>>
>> The answer seems to be Dark Energy.

Correct.

> Whatever that is!

Dark energy may be modelled by adding a constant to Einstein's
equations; hence the term "cosmological constant".

>> The question in my mind is where does this energy come from
>> and it would seem that more and more of it is needed in order
>> to increase the expansion rate.

Correct. The energy comes from the expansion (a form of
gravitational or geometric energy) which is negative. As the
universe expands the positive energy locked as dark energy
increases (density is constant, but volume increases); this is
offset by the negative energy in the Hubble expansion which
decreases (becomes more negative).

In the case of dark energy this process can continue for ever;
it's a slow form of inflation.

>
> It doesn't have to come from anywhere. The Friedmann-Lemaître
> equations allow for such a term, and apparently it has been observed.
> Note that there is not a problem with energy conservation, since
> energy isn't conserved in general relativity anyway.

That is not true. Energy is conserved in GR, with the obvious
caveat that we have to adopt a sensible definition of energy.
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

> (Imagine a universe consisting only of radiation. It expands.
> The number of photons remains the same, but the energy of each
> decreases due to the redshift. No, this lost energy does not do
> the work of expanding the universe.)

Then why does a radiant-filled universe decelerate faster than
a matter-filled universe? Because the energy lost in the redshift
cancels some of the negative energy tied up in the Hubble
expansion.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Phillip Helbig---remove CLOTHES to reply]

In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> >> My understanding is that the Universe is expanding and that
> >> this expansion is speeding up. What is fuelling this expansion
> >> rate increase that is working against the force of gravity?
> >>
> >> The answer seems to be Dark Energy.
>
> Correct.
>
> > Whatever that is!
>
> Dark energy may be modelled by adding a constant to Einstein's
> equations; hence the term "cosmological constant".
>
> >> The question in my mind is where does this energy come from
> >> and it would seem that more and more of it is needed in order
> >> to increase the expansion rate.
>
> Correct. The energy comes from the expansion (a form of
> gravitational or geometric energy) which is negative. As the
> universe expands the positive energy locked as dark energy
> increases (density is constant, but volume increases); this is
> offset by the negative energy in the Hubble expansion which
> decreases (becomes more negative).

Where did you get this idea from? Explain how the energy of the
cosmological constant "comes from" the expansion. The stuff about "dark
energy" is OK, but the claim that it is "offset by the negative energy
in the Hubble expansion" is completely bogus. Actually, gravitational
energy is such that the closer two gravitating objects are, the more
negative the energy, thus with expansion it would become more positive,
not become more negative.

Also, imagine a universe with NO cosmological constant. There would
thus be no "offset". Are you claiming that such a universe is
impossible?

> > It doesn't have to come from anywhere. The Friedmann-Lemaître
> > equations allow for such a term, and apparently it has been observed.
> > Note that there is not a problem with energy conservation, since
> > energy isn't conserved in general relativity anyway.
>
> That is not true. Energy is conserved in GR, with the obvious
> caveat that we have to adopt a sensible definition of energy.
> http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

Quoting from this:

The Cosmic Background Radiation (CBR) has red-shifted over billions
of years. Each photon gets redder and redder. What happens to this
energy? Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding
balloon speckled with galaxies" belongs to this class of models.) The
FRW spacetimes are neither static nor asymptotically flat. Those who
harbor no qualms about pseudo -tensors will say that radiant energy
becomes gravitational energy. Others will say that the energy is
simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^

The issue is much more complicated than the "this link proves that
energy is conserved" you claim.

> > (Imagine a universe consisting only of radiation. It expands.
> > The number of photons remains the same, but the energy of each
> > decreases due to the redshift. No, this lost energy does not do
> > the work of expanding the universe.)

Give a "sensible definition of energy", which is not ad-hoc, which is
conserved in this case.

> Then why does a radiant-filled universe decelerate faster than
> a matter-filled universe? Because the energy lost in the redshift
> cancels some of the negative energy tied up in the Hubble
> expansion.

I think you need to spell out exactly what you mean by "decelerate
faster". Presumably, two universes which are otherwise equivalent
decelerate differently. What does "otherwise equivalent" mean here?
The expansion histories are obviously different; WHEN does it
"decelerate faster"?

[Phillip Helbig---remove CLOTHES to reply]

In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> >> My understanding is that the Universe is expanding and that
> >> this expansion is speeding up. What is fuelling this expansion
> >> rate increase that is working against the force of gravity?
> >>
> >> The answer seems to be Dark Energy.
>
> Correct.
>
> > Whatever that is!
>
> Dark energy may be modelled by adding a constant to Einstein's
> equations; hence the term "cosmological constant".
>
> >> The question in my mind is where does this energy come from
> >> and it would seem that more and more of it is needed in order
> >> to increase the expansion rate.
>
> Correct. The energy comes from the expansion (a form of
> gravitational or geometric energy) which is negative. As the
> universe expands the positive energy locked as dark energy
> increases (density is constant, but volume increases); this is
> offset by the negative energy in the Hubble expansion which
> decreases (becomes more negative).

Where did you get this idea from? Explain how the energy of the
cosmological constant "comes from" the expansion. The stuff about "dark
energy" is OK, but the claim that it is "offset by the negative energy
in the Hubble expansion" is completely bogus. Actually, gravitational
energy is such that the closer two gravitating objects are, the more
negative the energy, thus with expansion it would become more positive,
not become more negative.

Also, imagine a universe with NO cosmological constant. There would
thus be no "offset". Are you claiming that such a universe is
impossible?

> > It doesn't have to come from anywhere. The Friedmann-Lemaître
> > equations allow for such a term, and apparently it has been observed.
> > Note that there is not a problem with energy conservation, since
> > energy isn't conserved in general relativity anyway.
>
> That is not true. Energy is conserved in GR, with the obvious
> caveat that we have to adopt a sensible definition of energy.
> http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

Quoting from this:

The Cosmic Background Radiation (CBR) has red-shifted over billions
of years. Each photon gets redder and redder. What happens to this
energy? Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding
balloon speckled with galaxies" belongs to this class of models.) The
FRW spacetimes are neither static nor asymptotically flat. Those who
harbor no qualms about pseudo -tensors will say that radiant energy
becomes gravitational energy. Others will say that the energy is
simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^

The issue is much more complicated than the "this link proves that
energy is conserved" you claim.

> > (Imagine a universe consisting only of radiation. It expands.
> > The number of photons remains the same, but the energy of each
> > decreases due to the redshift. No, this lost energy does not do
> > the work of expanding the universe.)

Give a "sensible definition of energy", which is not ad-hoc, which is
conserved in this case.

> Then why does a radiant-filled universe decelerate faster than
> a matter-filled universe? Because the energy lost in the redshift
> cancels some of the negative energy tied up in the Hubble
> expansion.

I think you need to spell out exactly what you mean by "decelerate
faster". Presumably, two universes which are otherwise equivalent
decelerate differently. What does "otherwise equivalent" mean here?
The expansion histories are obviously different; WHEN does it
"decelerate faster"?

[Phillip Helbig---remove CLOTHES to reply]

In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> >> My understanding is that the Universe is expanding and that
> >> this expansion is speeding up. What is fuelling this expansion
> >> rate increase that is working against the force of gravity?
> >>
> >> The answer seems to be Dark Energy.
>
> Correct.
>
> > Whatever that is!
>
> Dark energy may be modelled by adding a constant to Einstein's
> equations; hence the term "cosmological constant".
>
> >> The question in my mind is where does this energy come from
> >> and it would seem that more and more of it is needed in order
> >> to increase the expansion rate.
>
> Correct. The energy comes from the expansion (a form of
> gravitational or geometric energy) which is negative. As the
> universe expands the positive energy locked as dark energy
> increases (density is constant, but volume increases); this is
> offset by the negative energy in the Hubble expansion which
> decreases (becomes more negative).

Where did you get this idea from? Explain how the energy of the
cosmological constant "comes from" the expansion. The stuff about "dark
energy" is OK, but the claim that it is "offset by the negative energy
in the Hubble expansion" is completely bogus. Actually, gravitational
energy is such that the closer two gravitating objects are, the more
negative the energy, thus with expansion it would become more positive,
not become more negative.

Also, imagine a universe with NO cosmological constant. There would
thus be no "offset". Are you claiming that such a universe is
impossible?

> > It doesn't have to come from anywhere. The Friedmann-Lemaître
> > equations allow for such a term, and apparently it has been observed.
> > Note that there is not a problem with energy conservation, since
> > energy isn't conserved in general relativity anyway.
>
> That is not true. Energy is conserved in GR, with the obvious
> caveat that we have to adopt a sensible definition of energy.
> http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

Quoting from this:

The Cosmic Background Radiation (CBR) has red-shifted over billions
of years. Each photon gets redder and redder. What happens to this
energy? Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding
balloon speckled with galaxies" belongs to this class of models.) The
FRW spacetimes are neither static nor asymptotically flat. Those who
harbor no qualms about pseudo -tensors will say that radiant energy
becomes gravitational energy. Others will say that the energy is
simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^

The issue is much more complicated than the "this link proves that
energy is conserved" you claim.

> > (Imagine a universe consisting only of radiation. It expands.
> > The number of photons remains the same, but the energy of each
> > decreases due to the redshift. No, this lost energy does not do
> > the work of expanding the universe.)

Give a "sensible definition of energy", which is not ad-hoc, which is
conserved in this case.

> Then why does a radiant-filled universe decelerate faster than
> a matter-filled universe? Because the energy lost in the redshift
> cancels some of the negative energy tied up in the Hubble
> expansion.

I think you need to spell out exactly what you mean by "decelerate
faster". Presumably, two universes which are otherwise equivalent
decelerate differently. What does "otherwise equivalent" mean here?
The expansion histories are obviously different; WHEN does it
"decelerate faster"?

[Phillip Helbig---remove CLOTHES to reply]

In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> >> My understanding is that the Universe is expanding and that
> >> this expansion is speeding up. What is fuelling this expansion
> >> rate increase that is working against the force of gravity?
> >>
> >> The answer seems to be Dark Energy.
>
> Correct.
>
> > Whatever that is!
>
> Dark energy may be modelled by adding a constant to Einstein's
> equations; hence the term "cosmological constant".
>
> >> The question in my mind is where does this energy come from
> >> and it would seem that more and more of it is needed in order
> >> to increase the expansion rate.
>
> Correct. The energy comes from the expansion (a form of
> gravitational or geometric energy) which is negative. As the
> universe expands the positive energy locked as dark energy
> increases (density is constant, but volume increases); this is
> offset by the negative energy in the Hubble expansion which
> decreases (becomes more negative).

Where did you get this idea from? Explain how the energy of the
cosmological constant "comes from" the expansion. The stuff about "dark
energy" is OK, but the claim that it is "offset by the negative energy
in the Hubble expansion" is completely bogus. Actually, gravitational
energy is such that the closer two gravitating objects are, the more
negative the energy, thus with expansion it would become more positive,
not become more negative.

Also, imagine a universe with NO cosmological constant. There would
thus be no "offset". Are you claiming that such a universe is
impossible?

> > It doesn't have to come from anywhere. The Friedmann-Lemaître
> > equations allow for such a term, and apparently it has been observed.
> > Note that there is not a problem with energy conservation, since
> > energy isn't conserved in general relativity anyway.
>
> That is not true. Energy is conserved in GR, with the obvious
> caveat that we have to adopt a sensible definition of energy.
> http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

Quoting from this:

The Cosmic Background Radiation (CBR) has red-shifted over billions
of years. Each photon gets redder and redder. What happens to this
energy? Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding
balloon speckled with galaxies" belongs to this class of models.) The
FRW spacetimes are neither static nor asymptotically flat. Those who
harbor no qualms about pseudo -tensors will say that radiant energy
becomes gravitational energy. Others will say that the energy is
simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^

The issue is much more complicated than the "this link proves that
energy is conserved" you claim.

> > (Imagine a universe consisting only of radiation. It expands.
> > The number of photons remains the same, but the energy of each
> > decreases due to the redshift. No, this lost energy does not do
> > the work of expanding the universe.)

Give a "sensible definition of energy", which is not ad-hoc, which is
conserved in this case.

> Then why does a radiant-filled universe decelerate faster than
> a matter-filled universe? Because the energy lost in the redshift
> cancels some of the negative energy tied up in the Hubble
> expansion.

I think you need to spell out exactly what you mean by "decelerate
faster". Presumably, two universes which are otherwise equivalent
decelerate differently. What does "otherwise equivalent" mean here?
The expansion histories are obviously different; WHEN does it
"decelerate faster"?

[Phillip Helbig---remove CLOTHES to reply]

In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> >> My understanding is that the Universe is expanding and that
> >> this expansion is speeding up. What is fuelling this expansion
> >> rate increase that is working against the force of gravity?
> >>
> >> The answer seems to be Dark Energy.
>
> Correct.
>
> > Whatever that is!
>
> Dark energy may be modelled by adding a constant to Einstein's
> equations; hence the term "cosmological constant".
>
> >> The question in my mind is where does this energy come from
> >> and it would seem that more and more of it is needed in order
> >> to increase the expansion rate.
>
> Correct. The energy comes from the expansion (a form of
> gravitational or geometric energy) which is negative. As the
> universe expands the positive energy locked as dark energy
> increases (density is constant, but volume increases); this is
> offset by the negative energy in the Hubble expansion which
> decreases (becomes more negative).

Where did you get this idea from? Explain how the energy of the
cosmological constant "comes from" the expansion. The stuff about "dark
energy" is OK, but the claim that it is "offset by the negative energy
in the Hubble expansion" is completely bogus. Actually, gravitational
energy is such that the closer two gravitating objects are, the more
negative the energy, thus with expansion it would become more positive,
not become more negative.

Also, imagine a universe with NO cosmological constant. There would
thus be no "offset". Are you claiming that such a universe is
impossible?

> > It doesn't have to come from anywhere. The Friedmann-Lemaître
> > equations allow for such a term, and apparently it has been observed.
> > Note that there is not a problem with energy conservation, since
> > energy isn't conserved in general relativity anyway.
>
> That is not true. Energy is conserved in GR, with the obvious
> caveat that we have to adopt a sensible definition of energy.
> http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

Quoting from this:

The Cosmic Background Radiation (CBR) has red-shifted over billions
of years. Each photon gets redder and redder. What happens to this
energy? Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding
balloon speckled with galaxies" belongs to this class of models.) The
FRW spacetimes are neither static nor asymptotically flat. Those who
harbor no qualms about pseudo -tensors will say that radiant energy
becomes gravitational energy. Others will say that the energy is
simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^

The issue is much more complicated than the "this link proves that
energy is conserved" you claim.

> > (Imagine a universe consisting only of radiation. It expands.
> > The number of photons remains the same, but the energy of each
> > decreases due to the redshift. No, this lost energy does not do
> > the work of expanding the universe.)

Give a "sensible definition of energy", which is not ad-hoc, which is
conserved in this case.

> Then why does a radiant-filled universe decelerate faster than
> a matter-filled universe? Because the energy lost in the redshift
> cancels some of the negative energy tied up in the Hubble
> expansion.

I think you need to spell out exactly what you mean by "decelerate
faster". Presumably, two universes which are otherwise equivalent
decelerate differently. What does "otherwise equivalent" mean here?
The expansion histories are obviously different; WHEN does it
"decelerate faster"?

[Phillip Helbig---remove CLOTHES to reply]

In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> >> My understanding is that the Universe is expanding and that
> >> this expansion is speeding up. What is fuelling this expansion
> >> rate increase that is working against the force of gravity?
> >>
> >> The answer seems to be Dark Energy.
>
> Correct.
>
> > Whatever that is!
>
> Dark energy may be modelled by adding a constant to Einstein's
> equations; hence the term "cosmological constant".
>
> >> The question in my mind is where does this energy come from
> >> and it would seem that more and more of it is needed in order
> >> to increase the expansion rate.
>
> Correct. The energy comes from the expansion (a form of
> gravitational or geometric energy) which is negative. As the
> universe expands the positive energy locked as dark energy
> increases (density is constant, but volume increases); this is
> offset by the negative energy in the Hubble expansion which
> decreases (becomes more negative).

Where did you get this idea from? Explain how the energy of the
cosmological constant "comes from" the expansion. The stuff about "dark
energy" is OK, but the claim that it is "offset by the negative energy
in the Hubble expansion" is completely bogus. Actually, gravitational
energy is such that the closer two gravitating objects are, the more
negative the energy, thus with expansion it would become more positive,
not become more negative.

Also, imagine a universe with NO cosmological constant. There would
thus be no "offset". Are you claiming that such a universe is
impossible?

> > It doesn't have to come from anywhere. The Friedmann-Lemaître
> > equations allow for such a term, and apparently it has been observed.
> > Note that there is not a problem with energy conservation, since
> > energy isn't conserved in general relativity anyway.
>
> That is not true. Energy is conserved in GR, with the obvious
> caveat that we have to adopt a sensible definition of energy.
> http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

Quoting from this:

The Cosmic Background Radiation (CBR) has red-shifted over billions
of years. Each photon gets redder and redder. What happens to this
energy? Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding
balloon speckled with galaxies" belongs to this class of models.) The
FRW spacetimes are neither static nor asymptotically flat. Those who
harbor no qualms about pseudo -tensors will say that radiant energy
becomes gravitational energy. Others will say that the energy is
simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^

The issue is much more complicated than the "this link proves that
energy is conserved" you claim.

> > (Imagine a universe consisting only of radiation. It expands.
> > The number of photons remains the same, but the energy of each
> > decreases due to the redshift. No, this lost energy does not do
> > the work of expanding the universe.)

Give a "sensible definition of energy", which is not ad-hoc, which is
conserved in this case.

> Then why does a radiant-filled universe decelerate faster than
> a matter-filled universe? Because the energy lost in the redshift
> cancels some of the negative energy tied up in the Hubble
> expansion.

I think you need to spell out exactly what you mean by "decelerate
faster". Presumably, two universes which are otherwise equivalent
decelerate differently. What does "otherwise equivalent" mean here?
The expansion histories are obviously different; WHEN does it
"decelerate faster"?

[Phillip Helbig---remove CLOTHES to reply]

In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> >> My understanding is that the Universe is expanding and that
> >> this expansion is speeding up. What is fuelling this expansion
> >> rate increase that is working against the force of gravity?
> >>
> >> The answer seems to be Dark Energy.
>
> Correct.
>
> > Whatever that is!
>
> Dark energy may be modelled by adding a constant to Einstein's
> equations; hence the term "cosmological constant".
>
> >> The question in my mind is where does this energy come from
> >> and it would seem that more and more of it is needed in order
> >> to increase the expansion rate.
>
> Correct. The energy comes from the expansion (a form of
> gravitational or geometric energy) which is negative. As the
> universe expands the positive energy locked as dark energy
> increases (density is constant, but volume increases); this is
> offset by the negative energy in the Hubble expansion which
> decreases (becomes more negative).

Where did you get this idea from? Explain how the energy of the
cosmological constant "comes from" the expansion. The stuff about "dark
energy" is OK, but the claim that it is "offset by the negative energy
in the Hubble expansion" is completely bogus. Actually, gravitational
energy is such that the closer two gravitating objects are, the more
negative the energy, thus with expansion it would become more positive,
not become more negative.

Also, imagine a universe with NO cosmological constant. There would
thus be no "offset". Are you claiming that such a universe is
impossible?

> > It doesn't have to come from anywhere. The Friedmann-Lemaître
> > equations allow for such a term, and apparently it has been observed.
> > Note that there is not a problem with energy conservation, since
> > energy isn't conserved in general relativity anyway.
>
> That is not true. Energy is conserved in GR, with the obvious
> caveat that we have to adopt a sensible definition of energy.
> http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

Quoting from this:

The Cosmic Background Radiation (CBR) has red-shifted over billions
of years. Each photon gets redder and redder. What happens to this
energy? Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding
balloon speckled with galaxies" belongs to this class of models.) The
FRW spacetimes are neither static nor asymptotically flat. Those who
harbor no qualms about pseudo -tensors will say that radiant energy
becomes gravitational energy. Others will say that the energy is
simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^

The issue is much more complicated than the "this link proves that
energy is conserved" you claim.

> > (Imagine a universe consisting only of radiation. It expands.
> > The number of photons remains the same, but the energy of each
> > decreases due to the redshift. No, this lost energy does not do
> > the work of expanding the universe.)

Give a "sensible definition of energy", which is not ad-hoc, which is
conserved in this case.

> Then why does a radiant-filled universe decelerate faster than
> a matter-filled universe? Because the energy lost in the redshift
> cancels some of the negative energy tied up in the Hubble
> expansion.

I think you need to spell out exactly what you mean by "decelerate
faster". Presumably, two universes which are otherwise equivalent
decelerate differently. What does "otherwise equivalent" mean here?
The expansion histories are obviously different; WHEN does it
"decelerate faster"?

[Phillip Helbig---remove CLOTHES to reply]

In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> >> My understanding is that the Universe is expanding and that
> >> this expansion is speeding up. What is fuelling this expansion
> >> rate increase that is working against the force of gravity?
> >>
> >> The answer seems to be Dark Energy.
>
> Correct.
>
> > Whatever that is!
>
> Dark energy may be modelled by adding a constant to Einstein's
> equations; hence the term "cosmological constant".
>
> >> The question in my mind is where does this energy come from
> >> and it would seem that more and more of it is needed in order
> >> to increase the expansion rate.
>
> Correct. The energy comes from the expansion (a form of
> gravitational or geometric energy) which is negative. As the
> universe expands the positive energy locked as dark energy
> increases (density is constant, but volume increases); this is
> offset by the negative energy in the Hubble expansion which
> decreases (becomes more negative).

Where did you get this idea from? Explain how the energy of the
cosmological constant "comes from" the expansion. The stuff about "dark
energy" is OK, but the claim that it is "offset by the negative energy
in the Hubble expansion" is completely bogus. Actually, gravitational
energy is such that the closer two gravitating objects are, the more
negative the energy, thus with expansion it would become more positive,
not become more negative.

Also, imagine a universe with NO cosmological constant. There would
thus be no "offset". Are you claiming that such a universe is
impossible?

> > It doesn't have to come from anywhere. The Friedmann-Lemaître
> > equations allow for such a term, and apparently it has been observed.
> > Note that there is not a problem with energy conservation, since
> > energy isn't conserved in general relativity anyway.
>
> That is not true. Energy is conserved in GR, with the obvious
> caveat that we have to adopt a sensible definition of energy.
> http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

Quoting from this:

The Cosmic Background Radiation (CBR) has red-shifted over billions
of years. Each photon gets redder and redder. What happens to this
energy? Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding
balloon speckled with galaxies" belongs to this class of models.) The
FRW spacetimes are neither static nor asymptotically flat. Those who
harbor no qualms about pseudo -tensors will say that radiant energy
becomes gravitational energy. Others will say that the energy is
simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^

The issue is much more complicated than the "this link proves that
energy is conserved" you claim.

> > (Imagine a universe consisting only of radiation. It expands.
> > The number of photons remains the same, but the energy of each
> > decreases due to the redshift. No, this lost energy does not do
> > the work of expanding the universe.)

Give a "sensible definition of energy", which is not ad-hoc, which is
conserved in this case.

> Then why does a radiant-filled universe decelerate faster than
> a matter-filled universe? Because the energy lost in the redshift
> cancels some of the negative energy tied up in the Hubble
> expansion.

I think you need to spell out exactly what you mean by "decelerate
faster". Presumably, two universes which are otherwise equivalent
decelerate differently. What does "otherwise equivalent" mean here?
The expansion histories are obviously different; WHEN does it
"decelerate faster"?

[Phillip Helbig---remove CLOTHES to reply]

In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> >> My understanding is that the Universe is expanding and that
> >> this expansion is speeding up. What is fuelling this expansion
> >> rate increase that is working against the force of gravity?
> >>
> >> The answer seems to be Dark Energy.
>
> Correct.
>
> > Whatever that is!
>
> Dark energy may be modelled by adding a constant to Einstein's
> equations; hence the term "cosmological constant".
>
> >> The question in my mind is where does this energy come from
> >> and it would seem that more and more of it is needed in order
> >> to increase the expansion rate.
>
> Correct. The energy comes from the expansion (a form of
> gravitational or geometric energy) which is negative. As the
> universe expands the positive energy locked as dark energy
> increases (density is constant, but volume increases); this is
> offset by the negative energy in the Hubble expansion which
> decreases (becomes more negative).

Where did you get this idea from? Explain how the energy of the
cosmological constant "comes from" the expansion. The stuff about "dark
energy" is OK, but the claim that it is "offset by the negative energy
in the Hubble expansion" is completely bogus. Actually, gravitational
energy is such that the closer two gravitating objects are, the more
negative the energy, thus with expansion it would become more positive,
not become more negative.

Also, imagine a universe with NO cosmological constant. There would
thus be no "offset". Are you claiming that such a universe is
impossible?

> > It doesn't have to come from anywhere. The Friedmann-Lemaître
> > equations allow for such a term, and apparently it has been observed.
> > Note that there is not a problem with energy conservation, since
> > energy isn't conserved in general relativity anyway.
>
> That is not true. Energy is conserved in GR, with the obvious
> caveat that we have to adopt a sensible definition of energy.
> http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

Quoting from this:

The Cosmic Background Radiation (CBR) has red-shifted over billions
of years. Each photon gets redder and redder. What happens to this
energy? Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding
balloon speckled with galaxies" belongs to this class of models.) The
FRW spacetimes are neither static nor asymptotically flat. Those who
harbor no qualms about pseudo -tensors will say that radiant energy
becomes gravitational energy. Others will say that the energy is
simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^

The issue is much more complicated than the "this link proves that
energy is conserved" you claim.

> > (Imagine a universe consisting only of radiation. It expands.
> > The number of photons remains the same, but the energy of each
> > decreases due to the redshift. No, this lost energy does not do
> > the work of expanding the universe.)

Give a "sensible definition of energy", which is not ad-hoc, which is
conserved in this case.

> Then why does a radiant-filled universe decelerate faster than
> a matter-filled universe? Because the energy lost in the redshift
> cancels some of the negative energy tied up in the Hubble
> expansion.

I think you need to spell out exactly what you mean by "decelerate
faster". Presumably, two universes which are otherwise equivalent
decelerate differently. What does "otherwise equivalent" mean here?
The expansion histories are obviously different; WHEN does it
"decelerate faster"?

[Michael C Price]

"Phillip Helbig---remove CLOTHES to reply" <helbig@astro.multiCLOTHESvax.de>
wrote in message news:diqsgh$ppl$1@online.de...
> In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
> <michaelEXCISESPAMprice917@tesco.net> writes:
>
>>>> My understanding is that the Universe is expanding and that
>>>> this expansion is speeding up. What is fuelling this expansion
>>>> rate increase that is working against the force of gravity?
>>>>
>>>> The answer seems to be Dark Energy.
>>
>> Correct.
>>
>>> Whatever that is!
>>
>> Dark energy may be modelled by adding a constant to Einstein's
>> equations; hence the term "cosmological constant".
>>
>>>> The question in my mind is where does this energy come from
>>>> and it would seem that more and more of it is needed in order
>>>> to increase the expansion rate.
>>
>> Correct. The energy comes from the expansion (a form of
>> gravitational or geometric energy) which is negative. As the
>> universe expands the positive energy locked as dark energy
>> increases (density is constant, but volume increases); this is
>> offset by the negative energy in the Hubble expansion which
>> decreases (becomes more negative).
>
> Where did you get this idea from?

I presume we both agree that in a post-inflationary, homogenous,
isotropic universe:

8 pi G rho + gamma + -3H^2 = 0

( gamma = cosmological constant, a form of dark energy.
rho = average matter density
G = Newton's constant
H = Hubble's expansion factor. )

The question is: how do we interpret this equation?

Since the first two terms are proportional to energy density then
it is a reasonable inference that we have an expression of energy
conservation if the last term is also proportional to energy density;
in this case the energy of the dynamic geometry.

> Explain how the energy of the
> cosmological constant "comes from" the expansion. The stuff about
> "dark energy" is OK, but the claim that it is "offset by the negative
> energy in the Hubble expansion" is completely bogus.

Yet the above equation shows that the offset is exact with
complete cancellation or conservation.

> Actually,
> gravitational energy is such that the closer two gravitating objects are,
> the more negative the energy, thus with expansion it would become
> more positive, not become more negative.

That may be true if it were a potential energy term, but the Hubble
factor term appears a square and looks more like a kinetic term.

> Also, imagine a universe with NO cosmological constant. There
> would thus be no "offset".

Correct.

> Are you claiming that such a universe is impossible?

No, at this stage I was only talking about how the dark energy/
cosmological constant was handled, which was what the original
query related to. If there is no cosmological constant then set
gamma = 0 in the above equation.

>>> It doesn't have to come from anywhere. The Friedmann-Lemaître
>>> equations allow for such a term, and apparently it has been observed.
>>> Note that there is not a problem with energy conservation, since
>>> energy isn't conserved in general relativity anyway.
>>
>> That is not true. Energy is conserved in GR, with the obvious
>> caveat that we have to adopt a sensible definition of energy.
>>
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html
>
> Quoting from this:
>
> The Cosmic Background Radiation (CBR) has red-shifted over billions
> of years. Each photon gets redder and redder. What happens to this
> energy? Cosmologists model the expanding universe with Friedmann
> -Robertson-Walker (FRW) spacetimes. (The familiar "expanding
> balloon speckled with galaxies" belongs to this class of models.) The
> FRW spacetimes are neither static nor asymptotically flat. Those who
> harbor no qualms about pseudo -tensors will say that radiant energy
> becomes gravitational energy. Others will say that the energy is
> simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> ^^^^^^^^^^^
>
> The issue is much more complicated than the "this link proves that
> energy is conserved" you claim.

It doesn't say the "others" are correct :-)

Note that the link starts by saying:
> In special cases, yes [energy is conserved]. In general -- it depends
> on what you mean by "energy", and what you mean by "conserved".
which I interpret as consistent with and supportive of energy being
conserved in GR with the caveat I mentioned that we have to adopt
sensible definitions of energy. Obviously you can adopt incomplete
and flawed definitions of energy which will not be conserved, but
what's the point of that? Why violate the first law of thermodynamics
when we don't have to?

>>> (Imagine a universe consisting only of radiation. It expands.
>>> The number of photons remains the same, but the energy of each
>>> decreases due to the redshift. No, this lost energy does not do
>>> the work of expanding the universe.)
>
> Give a "sensible definition of energy", which is not ad-hoc, which is
> conserved in this case.

8piG rho + gamma - 3H^2 .

>> Then why does a radiant-filled universe decelerate faster than
>> a matter-filled universe? Because the energy lost in the redshift
>> cancels some of the negative energy tied up in the Hubble
>> expansion.
>
> I think you need to spell out exactly what you mean by "decelerate
> faster". Presumably, two universes which are otherwise equivalent
> decelerate differently. What does "otherwise equivalent" mean here?
> The expansion histories are obviously different; WHEN does it
> "decelerate faster"?

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Phillip Helbig---remove CLOTHES to reply" <helbig@astro.multiCLOTHESvax.de>
wrote in message news:diqsgh$ppl$1@online.de...
> In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
> <michaelEXCISESPAMprice917@tesco.net> writes:
>
>>>> My understanding is that the Universe is expanding and that
>>>> this expansion is speeding up. What is fuelling this expansion
>>>> rate increase that is working against the force of gravity?
>>>>
>>>> The answer seems to be Dark Energy.
>>
>> Correct.
>>
>>> Whatever that is!
>>
>> Dark energy may be modelled by adding a constant to Einstein's
>> equations; hence the term "cosmological constant".
>>
>>>> The question in my mind is where does this energy come from
>>>> and it would seem that more and more of it is needed in order
>>>> to increase the expansion rate.
>>
>> Correct. The energy comes from the expansion (a form of
>> gravitational or geometric energy) which is negative. As the
>> universe expands the positive energy locked as dark energy
>> increases (density is constant, but volume increases); this is
>> offset by the negative energy in the Hubble expansion which
>> decreases (becomes more negative).
>
> Where did you get this idea from?

I presume we both agree that in a post-inflationary, homogenous,
isotropic universe:

8 pi G rho + gamma + -3H^2 = 0

( gamma = cosmological constant, a form of dark energy.
rho = average matter density
G = Newton's constant
H = Hubble's expansion factor. )

The question is: how do we interpret this equation?

Since the first two terms are proportional to energy density then
it is a reasonable inference that we have an expression of energy
conservation if the last term is also proportional to energy density;
in this case the energy of the dynamic geometry.

> Explain how the energy of the
> cosmological constant "comes from" the expansion. The stuff about
> "dark energy" is OK, but the claim that it is "offset by the negative
> energy in the Hubble expansion" is completely bogus.

Yet the above equation shows that the offset is exact with
complete cancellation or conservation.

> Actually,
> gravitational energy is such that the closer two gravitating objects are,
> the more negative the energy, thus with expansion it would become
> more positive, not become more negative.

That may be true if it were a potential energy term, but the Hubble
factor term appears a square and looks more like a kinetic term.

> Also, imagine a universe with NO cosmological constant. There
> would thus be no "offset".

Correct.

> Are you claiming that such a universe is impossible?

No, at this stage I was only talking about how the dark energy/
cosmological constant was handled, which was what the original
query related to. If there is no cosmological constant then set
gamma = 0 in the above equation.

>>> It doesn't have to come from anywhere. The Friedmann-Lemaître
>>> equations allow for such a term, and apparently it has been observed.
>>> Note that there is not a problem with energy conservation, since
>>> energy isn't conserved in general relativity anyway.
>>
>> That is not true. Energy is conserved in GR, with the obvious
>> caveat that we have to adopt a sensible definition of energy.
>>
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html
>
> Quoting from this:
>
> The Cosmic Background Radiation (CBR) has red-shifted over billions
> of years. Each photon gets redder and redder. What happens to this
> energy? Cosmologists model the expanding universe with Friedmann
> -Robertson-Walker (FRW) spacetimes. (The familiar "expanding
> balloon speckled with galaxies" belongs to this class of models.) The
> FRW spacetimes are neither static nor asymptotically flat. Those who
> harbor no qualms about pseudo -tensors will say that radiant energy
> becomes gravitational energy. Others will say that the energy is
> simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> ^^^^^^^^^^^
>
> The issue is much more complicated than the "this link proves that
> energy is conserved" you claim.

It doesn't say the "others" are correct :-)

Note that the link starts by saying:
> In special cases, yes [energy is conserved]. In general -- it depends
> on what you mean by "energy", and what you mean by "conserved".
which I interpret as consistent with and supportive of energy being
conserved in GR with the caveat I mentioned that we have to adopt
sensible definitions of energy. Obviously you can adopt incomplete
and flawed definitions of energy which will not be conserved, but
what's the point of that? Why violate the first law of thermodynamics
when we don't have to?

>>> (Imagine a universe consisting only of radiation. It expands.
>>> The number of photons remains the same, but the energy of each
>>> decreases due to the redshift. No, this lost energy does not do
>>> the work of expanding the universe.)
>
> Give a "sensible definition of energy", which is not ad-hoc, which is
> conserved in this case.

8piG rho + gamma - 3H^2 .

>> Then why does a radiant-filled universe decelerate faster than
>> a matter-filled universe? Because the energy lost in the redshift
>> cancels some of the negative energy tied up in the Hubble
>> expansion.
>
> I think you need to spell out exactly what you mean by "decelerate
> faster". Presumably, two universes which are otherwise equivalent
> decelerate differently. What does "otherwise equivalent" mean here?
> The expansion histories are obviously different; WHEN does it
> "decelerate faster"?

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Phillip Helbig---remove CLOTHES to reply" <helbig@astro.multiCLOTHESvax.de>
wrote in message news:diqsgh$ppl$1@online.de...
> In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
> <michaelEXCISESPAMprice917@tesco.net> writes:
>
>>>> My understanding is that the Universe is expanding and that
>>>> this expansion is speeding up. What is fuelling this expansion
>>>> rate increase that is working against the force of gravity?
>>>>
>>>> The answer seems to be Dark Energy.
>>
>> Correct.
>>
>>> Whatever that is!
>>
>> Dark energy may be modelled by adding a constant to Einstein's
>> equations; hence the term "cosmological constant".
>>
>>>> The question in my mind is where does this energy come from
>>>> and it would seem that more and more of it is needed in order
>>>> to increase the expansion rate.
>>
>> Correct. The energy comes from the expansion (a form of
>> gravitational or geometric energy) which is negative. As the
>> universe expands the positive energy locked as dark energy
>> increases (density is constant, but volume increases); this is
>> offset by the negative energy in the Hubble expansion which
>> decreases (becomes more negative).
>
> Where did you get this idea from?

I presume we both agree that in a post-inflationary, homogenous,
isotropic universe:

8 pi G rho + gamma + -3H^2 = 0

( gamma = cosmological constant, a form of dark energy.
rho = average matter density
G = Newton's constant
H = Hubble's expansion factor. )

The question is: how do we interpret this equation?

Since the first two terms are proportional to energy density then
it is a reasonable inference that we have an expression of energy
conservation if the last term is also proportional to energy density;
in this case the energy of the dynamic geometry.

> Explain how the energy of the
> cosmological constant "comes from" the expansion. The stuff about
> "dark energy" is OK, but the claim that it is "offset by the negative
> energy in the Hubble expansion" is completely bogus.

Yet the above equation shows that the offset is exact with
complete cancellation or conservation.

> Actually,
> gravitational energy is such that the closer two gravitating objects are,
> the more negative the energy, thus with expansion it would become
> more positive, not become more negative.

That may be true if it were a potential energy term, but the Hubble
factor term appears a square and looks more like a kinetic term.

> Also, imagine a universe with NO cosmological constant. There
> would thus be no "offset".

Correct.

> Are you claiming that such a universe is impossible?

No, at this stage I was only talking about how the dark energy/
cosmological constant was handled, which was what the original
query related to. If there is no cosmological constant then set
gamma = 0 in the above equation.

>>> It doesn't have to come from anywhere. The Friedmann-Lemaître
>>> equations allow for such a term, and apparently it has been observed.
>>> Note that there is not a problem with energy conservation, since
>>> energy isn't conserved in general relativity anyway.
>>
>> That is not true. Energy is conserved in GR, with the obvious
>> caveat that we have to adopt a sensible definition of energy.
>>
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html
>
> Quoting from this:
>
> The Cosmic Background Radiation (CBR) has red-shifted over billions
> of years. Each photon gets redder and redder. What happens to this
> energy? Cosmologists model the expanding universe with Friedmann
> -Robertson-Walker (FRW) spacetimes. (The familiar "expanding
> balloon speckled with galaxies" belongs to this class of models.) The
> FRW spacetimes are neither static nor asymptotically flat. Those who
> harbor no qualms about pseudo -tensors will say that radiant energy
> becomes gravitational energy. Others will say that the energy is
> simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> ^^^^^^^^^^^
>
> The issue is much more complicated than the "this link proves that
> energy is conserved" you claim.

It doesn't say the "others" are correct :-)

Note that the link starts by saying:
> In special cases, yes [energy is conserved]. In general -- it depends
> on what you mean by "energy", and what you mean by "conserved".
which I interpret as consistent with and supportive of energy being
conserved in GR with the caveat I mentioned that we have to adopt
sensible definitions of energy. Obviously you can adopt incomplete
and flawed definitions of energy which will not be conserved, but
what's the point of that? Why violate the first law of thermodynamics
when we don't have to?

>>> (Imagine a universe consisting only of radiation. It expands.
>>> The number of photons remains the same, but the energy of each
>>> decreases due to the redshift. No, this lost energy does not do
>>> the work of expanding the universe.)
>
> Give a "sensible definition of energy", which is not ad-hoc, which is
> conserved in this case.

8piG rho + gamma - 3H^2 .

>> Then why does a radiant-filled universe decelerate faster than
>> a matter-filled universe? Because the energy lost in the redshift
>> cancels some of the negative energy tied up in the Hubble
>> expansion.
>
> I think you need to spell out exactly what you mean by "decelerate
> faster". Presumably, two universes which are otherwise equivalent
> decelerate differently. What does "otherwise equivalent" mean here?
> The expansion histories are obviously different; WHEN does it
> "decelerate faster"?

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Phillip Helbig---remove CLOTHES to reply" <helbig@astro.multiCLOTHESvax.de>
wrote in message news:diqsgh$ppl$1@online.de...
> In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
> <michaelEXCISESPAMprice917@tesco.net> writes:
>
>>>> My understanding is that the Universe is expanding and that
>>>> this expansion is speeding up. What is fuelling this expansion
>>>> rate increase that is working against the force of gravity?
>>>>
>>>> The answer seems to be Dark Energy.
>>
>> Correct.
>>
>>> Whatever that is!
>>
>> Dark energy may be modelled by adding a constant to Einstein's
>> equations; hence the term "cosmological constant".
>>
>>>> The question in my mind is where does this energy come from
>>>> and it would seem that more and more of it is needed in order
>>>> to increase the expansion rate.
>>
>> Correct. The energy comes from the expansion (a form of
>> gravitational or geometric energy) which is negative. As the
>> universe expands the positive energy locked as dark energy
>> increases (density is constant, but volume increases); this is
>> offset by the negative energy in the Hubble expansion which
>> decreases (becomes more negative).
>
> Where did you get this idea from?

I presume we both agree that in a post-inflationary, homogenous,
isotropic universe:

8 pi G rho + gamma + -3H^2 = 0

( gamma = cosmological constant, a form of dark energy.
rho = average matter density
G = Newton's constant
H = Hubble's expansion factor. )

The question is: how do we interpret this equation?

Since the first two terms are proportional to energy density then
it is a reasonable inference that we have an expression of energy
conservation if the last term is also proportional to energy density;
in this case the energy of the dynamic geometry.

> Explain how the energy of the
> cosmological constant "comes from" the expansion. The stuff about
> "dark energy" is OK, but the claim that it is "offset by the negative
> energy in the Hubble expansion" is completely bogus.

Yet the above equation shows that the offset is exact with
complete cancellation or conservation.

> Actually,
> gravitational energy is such that the closer two gravitating objects are,
> the more negative the energy, thus with expansion it would become
> more positive, not become more negative.

That may be true if it were a potential energy term, but the Hubble
factor term appears a square and looks more like a kinetic term.

> Also, imagine a universe with NO cosmological constant. There
> would thus be no "offset".

Correct.

> Are you claiming that such a universe is impossible?

No, at this stage I was only talking about how the dark energy/
cosmological constant was handled, which was what the original
query related to. If there is no cosmological constant then set
gamma = 0 in the above equation.

>>> It doesn't have to come from anywhere. The Friedmann-Lemaître
>>> equations allow for such a term, and apparently it has been observed.
>>> Note that there is not a problem with energy conservation, since
>>> energy isn't conserved in general relativity anyway.
>>
>> That is not true. Energy is conserved in GR, with the obvious
>> caveat that we have to adopt a sensible definition of energy.
>>
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html
>
> Quoting from this:
>
> The Cosmic Background Radiation (CBR) has red-shifted over billions
> of years. Each photon gets redder and redder. What happens to this
> energy? Cosmologists model the expanding universe with Friedmann
> -Robertson-Walker (FRW) spacetimes. (The familiar "expanding
> balloon speckled with galaxies" belongs to this class of models.) The
> FRW spacetimes are neither static nor asymptotically flat. Those who
> harbor no qualms about pseudo -tensors will say that radiant energy
> becomes gravitational energy. Others will say that the energy is
> simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> ^^^^^^^^^^^
>
> The issue is much more complicated than the "this link proves that
> energy is conserved" you claim.

It doesn't say the "others" are correct :-)

Note that the link starts by saying:
> In special cases, yes [energy is conserved]. In general -- it depends
> on what you mean by "energy", and what you mean by "conserved".
which I interpret as consistent with and supportive of energy being
conserved in GR with the caveat I mentioned that we have to adopt
sensible definitions of energy. Obviously you can adopt incomplete
and flawed definitions of energy which will not be conserved, but
what's the point of that? Why violate the first law of thermodynamics
when we don't have to?

>>> (Imagine a universe consisting only of radiation. It expands.
>>> The number of photons remains the same, but the energy of each
>>> decreases due to the redshift. No, this lost energy does not do
>>> the work of expanding the universe.)
>
> Give a "sensible definition of energy", which is not ad-hoc, which is
> conserved in this case.

8piG rho + gamma - 3H^2 .

>> Then why does a radiant-filled universe decelerate faster than
>> a matter-filled universe? Because the energy lost in the redshift
>> cancels some of the negative energy tied up in the Hubble
>> expansion.
>
> I think you need to spell out exactly what you mean by "decelerate
> faster". Presumably, two universes which are otherwise equivalent
> decelerate differently. What does "otherwise equivalent" mean here?
> The expansion histories are obviously different; WHEN does it
> "decelerate faster"?

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Phillip Helbig---remove CLOTHES to reply" <helbig@astro.multiCLOTHESvax.de>
wrote in message news:diqsgh$ppl$1@online.de...
> In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
> <michaelEXCISESPAMprice917@tesco.net> writes:
>
>>>> My understanding is that the Universe is expanding and that
>>>> this expansion is speeding up. What is fuelling this expansion
>>>> rate increase that is working against the force of gravity?
>>>>
>>>> The answer seems to be Dark Energy.
>>
>> Correct.
>>
>>> Whatever that is!
>>
>> Dark energy may be modelled by adding a constant to Einstein's
>> equations; hence the term "cosmological constant".
>>
>>>> The question in my mind is where does this energy come from
>>>> and it would seem that more and more of it is needed in order
>>>> to increase the expansion rate.
>>
>> Correct. The energy comes from the expansion (a form of
>> gravitational or geometric energy) which is negative. As the
>> universe expands the positive energy locked as dark energy
>> increases (density is constant, but volume increases); this is
>> offset by the negative energy in the Hubble expansion which
>> decreases (becomes more negative).
>
> Where did you get this idea from?

I presume we both agree that in a post-inflationary, homogenous,
isotropic universe:

8 pi G rho + gamma + -3H^2 = 0

( gamma = cosmological constant, a form of dark energy.
rho = average matter density
G = Newton's constant
H = Hubble's expansion factor. )

The question is: how do we interpret this equation?

Since the first two terms are proportional to energy density then
it is a reasonable inference that we have an expression of energy
conservation if the last term is also proportional to energy density;
in this case the energy of the dynamic geometry.

> Explain how the energy of the
> cosmological constant "comes from" the expansion. The stuff about
> "dark energy" is OK, but the claim that it is "offset by the negative
> energy in the Hubble expansion" is completely bogus.

Yet the above equation shows that the offset is exact with
complete cancellation or conservation.

> Actually,
> gravitational energy is such that the closer two gravitating objects are,
> the more negative the energy, thus with expansion it would become
> more positive, not become more negative.

That may be true if it were a potential energy term, but the Hubble
factor term appears a square and looks more like a kinetic term.

> Also, imagine a universe with NO cosmological constant. There
> would thus be no "offset".

Correct.

> Are you claiming that such a universe is impossible?

No, at this stage I was only talking about how the dark energy/
cosmological constant was handled, which was what the original
query related to. If there is no cosmological constant then set
gamma = 0 in the above equation.

>>> It doesn't have to come from anywhere. The Friedmann-Lemaître
>>> equations allow for such a term, and apparently it has been observed.
>>> Note that there is not a problem with energy conservation, since
>>> energy isn't conserved in general relativity anyway.
>>
>> That is not true. Energy is conserved in GR, with the obvious
>> caveat that we have to adopt a sensible definition of energy.
>>
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html
>
> Quoting from this:
>
> The Cosmic Background Radiation (CBR) has red-shifted over billions
> of years. Each photon gets redder and redder. What happens to this
> energy? Cosmologists model the expanding universe with Friedmann
> -Robertson-Walker (FRW) spacetimes. (The familiar "expanding
> balloon speckled with galaxies" belongs to this class of models.) The
> FRW spacetimes are neither static nor asymptotically flat. Those who
> harbor no qualms about pseudo -tensors will say that radiant energy
> becomes gravitational energy. Others will say that the energy is
> simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> ^^^^^^^^^^^
>
> The issue is much more complicated than the "this link proves that
> energy is conserved" you claim.

It doesn't say the "others" are correct :-)

Note that the link starts by saying:
> In special cases, yes [energy is conserved]. In general -- it depends
> on what you mean by "energy", and what you mean by "conserved".
which I interpret as consistent with and supportive of energy being
conserved in GR with the caveat I mentioned that we have to adopt
sensible definitions of energy. Obviously you can adopt incomplete
and flawed definitions of energy which will not be conserved, but
what's the point of that? Why violate the first law of thermodynamics
when we don't have to?

>>> (Imagine a universe consisting only of radiation. It expands.
>>> The number of photons remains the same, but the energy of each
>>> decreases due to the redshift. No, this lost energy does not do
>>> the work of expanding the universe.)
>
> Give a "sensible definition of energy", which is not ad-hoc, which is
> conserved in this case.

8piG rho + gamma - 3H^2 .

>> Then why does a radiant-filled universe decelerate faster than
>> a matter-filled universe? Because the energy lost in the redshift
>> cancels some of the negative energy tied up in the Hubble
>> expansion.
>
> I think you need to spell out exactly what you mean by "decelerate
> faster". Presumably, two universes which are otherwise equivalent
> decelerate differently. What does "otherwise equivalent" mean here?
> The expansion histories are obviously different; WHEN does it
> "decelerate faster"?

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Phillip Helbig---remove CLOTHES to reply" <helbig@astro.multiCLOTHESvax.de>
wrote in message news:diqsgh$ppl$1@online.de...
> In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
> <michaelEXCISESPAMprice917@tesco.net> writes:
>
>>>> My understanding is that the Universe is expanding and that
>>>> this expansion is speeding up. What is fuelling this expansion
>>>> rate increase that is working against the force of gravity?
>>>>
>>>> The answer seems to be Dark Energy.
>>
>> Correct.
>>
>>> Whatever that is!
>>
>> Dark energy may be modelled by adding a constant to Einstein's
>> equations; hence the term "cosmological constant".
>>
>>>> The question in my mind is where does this energy come from
>>>> and it would seem that more and more of it is needed in order
>>>> to increase the expansion rate.
>>
>> Correct. The energy comes from the expansion (a form of
>> gravitational or geometric energy) which is negative. As the
>> universe expands the positive energy locked as dark energy
>> increases (density is constant, but volume increases); this is
>> offset by the negative energy in the Hubble expansion which
>> decreases (becomes more negative).
>
> Where did you get this idea from?

I presume we both agree that in a post-inflationary, homogenous,
isotropic universe:

8 pi G rho + gamma + -3H^2 = 0

( gamma = cosmological constant, a form of dark energy.
rho = average matter density
G = Newton's constant
H = Hubble's expansion factor. )

The question is: how do we interpret this equation?

Since the first two terms are proportional to energy density then
it is a reasonable inference that we have an expression of energy
conservation if the last term is also proportional to energy density;
in this case the energy of the dynamic geometry.

> Explain how the energy of the
> cosmological constant "comes from" the expansion. The stuff about
> "dark energy" is OK, but the claim that it is "offset by the negative
> energy in the Hubble expansion" is completely bogus.

Yet the above equation shows that the offset is exact with
complete cancellation or conservation.

> Actually,
> gravitational energy is such that the closer two gravitating objects are,
> the more negative the energy, thus with expansion it would become
> more positive, not become more negative.

That may be true if it were a potential energy term, but the Hubble
factor term appears a square and looks more like a kinetic term.

> Also, imagine a universe with NO cosmological constant. There
> would thus be no "offset".

Correct.

> Are you claiming that such a universe is impossible?

No, at this stage I was only talking about how the dark energy/
cosmological constant was handled, which was what the original
query related to. If there is no cosmological constant then set
gamma = 0 in the above equation.

>>> It doesn't have to come from anywhere. The Friedmann-Lemaître
>>> equations allow for such a term, and apparently it has been observed.
>>> Note that there is not a problem with energy conservation, since
>>> energy isn't conserved in general relativity anyway.
>>
>> That is not true. Energy is conserved in GR, with the obvious
>> caveat that we have to adopt a sensible definition of energy.
>>
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html
>
> Quoting from this:
>
> The Cosmic Background Radiation (CBR) has red-shifted over billions
> of years. Each photon gets redder and redder. What happens to this
> energy? Cosmologists model the expanding universe with Friedmann
> -Robertson-Walker (FRW) spacetimes. (The familiar "expanding
> balloon speckled with galaxies" belongs to this class of models.) The
> FRW spacetimes are neither static nor asymptotically flat. Those who
> harbor no qualms about pseudo -tensors will say that radiant energy
> becomes gravitational energy. Others will say that the energy is
> simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> ^^^^^^^^^^^
>
> The issue is much more complicated than the "this link proves that
> energy is conserved" you claim.

It doesn't say the "others" are correct :-)

Note that the link starts by saying:
> In special cases, yes [energy is conserved]. In general -- it depends
> on what you mean by "energy", and what you mean by "conserved".
which I interpret as consistent with and supportive of energy being
conserved in GR with the caveat I mentioned that we have to adopt
sensible definitions of energy. Obviously you can adopt incomplete
and flawed definitions of energy which will not be conserved, but
what's the point of that? Why violate the first law of thermodynamics
when we don't have to?

>>> (Imagine a universe consisting only of radiation. It expands.
>>> The number of photons remains the same, but the energy of each
>>> decreases due to the redshift. No, this lost energy does not do
>>> the work of expanding the universe.)
>
> Give a "sensible definition of energy", which is not ad-hoc, which is
> conserved in this case.

8piG rho + gamma - 3H^2 .

>> Then why does a radiant-filled universe decelerate faster than
>> a matter-filled universe? Because the energy lost in the redshift
>> cancels some of the negative energy tied up in the Hubble
>> expansion.
>
> I think you need to spell out exactly what you mean by "decelerate
> faster". Presumably, two universes which are otherwise equivalent
> decelerate differently. What does "otherwise equivalent" mean here?
> The expansion histories are obviously different; WHEN does it
> "decelerate faster"?

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Phillip Helbig---remove CLOTHES to reply" <helbig@astro.multiCLOTHESvax.de>
wrote in message news:diqsgh$ppl$1@online.de...
> In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
> <michaelEXCISESPAMprice917@tesco.net> writes:
>
>>>> My understanding is that the Universe is expanding and that
>>>> this expansion is speeding up. What is fuelling this expansion
>>>> rate increase that is working against the force of gravity?
>>>>
>>>> The answer seems to be Dark Energy.
>>
>> Correct.
>>
>>> Whatever that is!
>>
>> Dark energy may be modelled by adding a constant to Einstein's
>> equations; hence the term "cosmological constant".
>>
>>>> The question in my mind is where does this energy come from
>>>> and it would seem that more and more of it is needed in order
>>>> to increase the expansion rate.
>>
>> Correct. The energy comes from the expansion (a form of
>> gravitational or geometric energy) which is negative. As the
>> universe expands the positive energy locked as dark energy
>> increases (density is constant, but volume increases); this is
>> offset by the negative energy in the Hubble expansion which
>> decreases (becomes more negative).
>
> Where did you get this idea from?

I presume we both agree that in a post-inflationary, homogenous,
isotropic universe:

8 pi G rho + gamma + -3H^2 = 0

( gamma = cosmological constant, a form of dark energy.
rho = average matter density
G = Newton's constant
H = Hubble's expansion factor. )

The question is: how do we interpret this equation?

Since the first two terms are proportional to energy density then
it is a reasonable inference that we have an expression of energy
conservation if the last term is also proportional to energy density;
in this case the energy of the dynamic geometry.

> Explain how the energy of the
> cosmological constant "comes from" the expansion. The stuff about
> "dark energy" is OK, but the claim that it is "offset by the negative
> energy in the Hubble expansion" is completely bogus.

Yet the above equation shows that the offset is exact with
complete cancellation or conservation.

> Actually,
> gravitational energy is such that the closer two gravitating objects are,
> the more negative the energy, thus with expansion it would become
> more positive, not become more negative.

That may be true if it were a potential energy term, but the Hubble
factor term appears a square and looks more like a kinetic term.

> Also, imagine a universe with NO cosmological constant. There
> would thus be no "offset".

Correct.

> Are you claiming that such a universe is impossible?

No, at this stage I was only talking about how the dark energy/
cosmological constant was handled, which was what the original
query related to. If there is no cosmological constant then set
gamma = 0 in the above equation.

>>> It doesn't have to come from anywhere. The Friedmann-Lemaître
>>> equations allow for such a term, and apparently it has been observed.
>>> Note that there is not a problem with energy conservation, since
>>> energy isn't conserved in general relativity anyway.
>>
>> That is not true. Energy is conserved in GR, with the obvious
>> caveat that we have to adopt a sensible definition of energy.
>>
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html
>
> Quoting from this:
>
> The Cosmic Background Radiation (CBR) has red-shifted over billions
> of years. Each photon gets redder and redder. What happens to this
> energy? Cosmologists model the expanding universe with Friedmann
> -Robertson-Walker (FRW) spacetimes. (The familiar "expanding
> balloon speckled with galaxies" belongs to this class of models.) The
> FRW spacetimes are neither static nor asymptotically flat. Those who
> harbor no qualms about pseudo -tensors will say that radiant energy
> becomes gravitational energy. Others will say that the energy is
> simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> ^^^^^^^^^^^
>
> The issue is much more complicated than the "this link proves that
> energy is conserved" you claim.

It doesn't say the "others" are correct :-)

Note that the link starts by saying:
> In special cases, yes [energy is conserved]. In general -- it depends
> on what you mean by "energy", and what you mean by "conserved".
which I interpret as consistent with and supportive of energy being
conserved in GR with the caveat I mentioned that we have to adopt
sensible definitions of energy. Obviously you can adopt incomplete
and flawed definitions of energy which will not be conserved, but
what's the point of that? Why violate the first law of thermodynamics
when we don't have to?

>>> (Imagine a universe consisting only of radiation. It expands.
>>> The number of photons remains the same, but the energy of each
>>> decreases due to the redshift. No, this lost energy does not do
>>> the work of expanding the universe.)
>
> Give a "sensible definition of energy", which is not ad-hoc, which is
> conserved in this case.

8piG rho + gamma - 3H^2 .

>> Then why does a radiant-filled universe decelerate faster than
>> a matter-filled universe? Because the energy lost in the redshift
>> cancels some of the negative energy tied up in the Hubble
>> expansion.
>
> I think you need to spell out exactly what you mean by "decelerate
> faster". Presumably, two universes which are otherwise equivalent
> decelerate differently. What does "otherwise equivalent" mean here?
> The expansion histories are obviously different; WHEN does it
> "decelerate faster"?

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Phillip Helbig---remove CLOTHES to reply" <helbig@astro.multiCLOTHESvax.de>
wrote in message news:diqsgh$ppl$1@online.de...
> In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
> <michaelEXCISESPAMprice917@tesco.net> writes:
>
>>>> My understanding is that the Universe is expanding and that
>>>> this expansion is speeding up. What is fuelling this expansion
>>>> rate increase that is working against the force of gravity?
>>>>
>>>> The answer seems to be Dark Energy.
>>
>> Correct.
>>
>>> Whatever that is!
>>
>> Dark energy may be modelled by adding a constant to Einstein's
>> equations; hence the term "cosmological constant".
>>
>>>> The question in my mind is where does this energy come from
>>>> and it would seem that more and more of it is needed in order
>>>> to increase the expansion rate.
>>
>> Correct. The energy comes from the expansion (a form of
>> gravitational or geometric energy) which is negative. As the
>> universe expands the positive energy locked as dark energy
>> increases (density is constant, but volume increases); this is
>> offset by the negative energy in the Hubble expansion which
>> decreases (becomes more negative).
>
> Where did you get this idea from?

I presume we both agree that in a post-inflationary, homogenous,
isotropic universe:

8 pi G rho + gamma + -3H^2 = 0

( gamma = cosmological constant, a form of dark energy.
rho = average matter density
G = Newton's constant
H = Hubble's expansion factor. )

The question is: how do we interpret this equation?

Since the first two terms are proportional to energy density then
it is a reasonable inference that we have an expression of energy
conservation if the last term is also proportional to energy density;
in this case the energy of the dynamic geometry.

> Explain how the energy of the
> cosmological constant "comes from" the expansion. The stuff about
> "dark energy" is OK, but the claim that it is "offset by the negative
> energy in the Hubble expansion" is completely bogus.

Yet the above equation shows that the offset is exact with
complete cancellation or conservation.

> Actually,
> gravitational energy is such that the closer two gravitating objects are,
> the more negative the energy, thus with expansion it would become
> more positive, not become more negative.

That may be true if it were a potential energy term, but the Hubble
factor term appears a square and looks more like a kinetic term.

> Also, imagine a universe with NO cosmological constant. There
> would thus be no "offset".

Correct.

> Are you claiming that such a universe is impossible?

No, at this stage I was only talking about how the dark energy/
cosmological constant was handled, which was what the original
query related to. If there is no cosmological constant then set
gamma = 0 in the above equation.

>>> It doesn't have to come from anywhere. The Friedmann-Lemaître
>>> equations allow for such a term, and apparently it has been observed.
>>> Note that there is not a problem with energy conservation, since
>>> energy isn't conserved in general relativity anyway.
>>
>> That is not true. Energy is conserved in GR, with the obvious
>> caveat that we have to adopt a sensible definition of energy.
>>
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html
>
> Quoting from this:
>
> The Cosmic Background Radiation (CBR) has red-shifted over billions
> of years. Each photon gets redder and redder. What happens to this
> energy? Cosmologists model the expanding universe with Friedmann
> -Robertson-Walker (FRW) spacetimes. (The familiar "expanding
> balloon speckled with galaxies" belongs to this class of models.) The
> FRW spacetimes are neither static nor asymptotically flat. Those who
> harbor no qualms about pseudo -tensors will say that radiant energy
> becomes gravitational energy. Others will say that the energy is
> simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> ^^^^^^^^^^^
>
> The issue is much more complicated than the "this link proves that
> energy is conserved" you claim.

It doesn't say the "others" are correct :-)

Note that the link starts by saying:
> In special cases, yes [energy is conserved]. In general -- it depends
> on what you mean by "energy", and what you mean by "conserved".
which I interpret as consistent with and supportive of energy being
conserved in GR with the caveat I mentioned that we have to adopt
sensible definitions of energy. Obviously you can adopt incomplete
and flawed definitions of energy which will not be conserved, but
what's the point of that? Why violate the first law of thermodynamics
when we don't have to?

>>> (Imagine a universe consisting only of radiation. It expands.
>>> The number of photons remains the same, but the energy of each
>>> decreases due to the redshift. No, this lost energy does not do
>>> the work of expanding the universe.)
>
> Give a "sensible definition of energy", which is not ad-hoc, which is
> conserved in this case.

8piG rho + gamma - 3H^2 .

>> Then why does a radiant-filled universe decelerate faster than
>> a matter-filled universe? Because the energy lost in the redshift
>> cancels some of the negative energy tied up in the Hubble
>> expansion.
>
> I think you need to spell out exactly what you mean by "decelerate
> faster". Presumably, two universes which are otherwise equivalent
> decelerate differently. What does "otherwise equivalent" mean here?
> The expansion histories are obviously different; WHEN does it
> "decelerate faster"?

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Phillip Helbig---remove CLOTHES to reply" <helbig@astro.multiCLOTHESvax.de>
wrote in message news:diqsgh$ppl$1@online.de...
> In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price"
> <michaelEXCISESPAMprice917@tesco.net> writes:
>
>>>> My understanding is that the Universe is expanding and that
>>>> this expansion is speeding up. What is fuelling this expansion
>>>> rate increase that is working against the force of gravity?
>>>>
>>>> The answer seems to be Dark Energy.
>>
>> Correct.
>>
>>> Whatever that is!
>>
>> Dark energy may be modelled by adding a constant to Einstein's
>> equations; hence the term "cosmological constant".
>>
>>>> The question in my mind is where does this energy come from
>>>> and it would seem that more and more of it is needed in order
>>>> to increase the expansion rate.
>>
>> Correct. The energy comes from the expansion (a form of
>> gravitational or geometric energy) which is negative. As the
>> universe expands the positive energy locked as dark energy
>> increases (density is constant, but volume increases); this is
>> offset by the negative energy in the Hubble expansion which
>> decreases (becomes more negative).
>
> Where did you get this idea from?

I presume we both agree that in a post-inflationary, homogenous,
isotropic universe:

8 pi G rho + gamma + -3H^2 = 0

( gamma = cosmological constant, a form of dark energy.
rho = average matter density
G = Newton's constant
H = Hubble's expansion factor. )

The question is: how do we interpret this equation?

Since the first two terms are proportional to energy density then
it is a reasonable inference that we have an expression of energy
conservation if the last term is also proportional to energy density;
in this case the energy of the dynamic geometry.

> Explain how the energy of the
> cosmological constant "comes from" the expansion. The stuff about
> "dark energy" is OK, but the claim that it is "offset by the negative
> energy in the Hubble expansion" is completely bogus.

Yet the above equation shows that the offset is exact with
complete cancellation or conservation.

> Actually,
> gravitational energy is such that the closer two gravitating objects are,
> the more negative the energy, thus with expansion it would become
> more positive, not become more negative.

That may be true if it were a potential energy term, but the Hubble
factor term appears a square and looks more like a kinetic term.

> Also, imagine a universe with NO cosmological constant. There
> would thus be no "offset".

Correct.

> Are you claiming that such a universe is impossible?

No, at this stage I was only talking about how the dark energy/
cosmological constant was handled, which was what the original
query related to. If there is no cosmological constant then set
gamma = 0 in the above equation.

>>> It doesn't have to come from anywhere. The Friedmann-Lemaître
>>> equations allow for such a term, and apparently it has been observed.
>>> Note that there is not a problem with energy conservation, since
>>> energy isn't conserved in general relativity anyway.
>>
>> That is not true. Energy is conserved in GR, with the obvious
>> caveat that we have to adopt a sensible definition of energy.
>>
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html
>
> Quoting from this:
>
> The Cosmic Background Radiation (CBR) has red-shifted over billions
> of years. Each photon gets redder and redder. What happens to this
> energy? Cosmologists model the expanding universe with Friedmann
> -Robertson-Walker (FRW) spacetimes. (The familiar "expanding
> balloon speckled with galaxies" belongs to this class of models.) The
> FRW spacetimes are neither static nor asymptotically flat. Those who
> harbor no qualms about pseudo -tensors will say that radiant energy
> becomes gravitational energy. Others will say that the energy is
> simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> ^^^^^^^^^^^
>
> The issue is much more complicated than the "this link proves that
> energy is conserved" you claim.

It doesn't say the "others" are correct :-)

Note that the link starts by saying:
> In special cases, yes [energy is conserved]. In general -- it depends
> on what you mean by "energy", and what you mean by "conserved".
which I interpret as consistent with and supportive of energy being
conserved in GR with the caveat I mentioned that we have to adopt
sensible definitions of energy. Obviously you can adopt incomplete
and flawed definitions of energy which will not be conserved, but
what's the point of that? Why violate the first law of thermodynamics
when we don't have to?

>>> (Imagine a universe consisting only of radiation. It expands.
>>> The number of photons remains the same, but the energy of each
>>> decreases due to the redshift. No, this lost energy does not do
>>> the work of expanding the universe.)
>
> Give a "sensible definition of energy", which is not ad-hoc, which is
> conserved in this case.

8piG rho + gamma - 3H^2 .

>> Then why does a radiant-filled universe decelerate faster than
>> a matter-filled universe? Because the energy lost in the redshift
>> cancels some of the negative energy tied up in the Hubble
>> expansion.
>
> I think you need to spell out exactly what you mean by "decelerate
> faster". Presumably, two universes which are otherwise equivalent
> decelerate differently. What does "otherwise equivalent" mean here?
> The expansion histories are obviously different; WHEN does it
> "decelerate faster"?

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Phillip Helbig---remove CLOTHES to reply]

In article <%ZD4f.3782$cA4.3019@newsfe3-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>>> My understanding is that the Universe is expanding and that
> >>>> this expansion is speeding up. What is fuelling this expansion
> >>>> rate increase that is working against the force of gravity?
> >>>>
> >>>> The answer seems to be Dark Energy.

> >>>> The question in my mind is where does this energy come from
> >>>> and it would seem that more and more of it is needed in order
> >>>> to increase the expansion rate.
> >>
> >> Correct. The energy comes from the expansion (a form of
> >> gravitational or geometric energy) which is negative. As the
> >> universe expands the positive energy locked as dark energy
> >> increases (density is constant, but volume increases); this is
> >> offset by the negative energy in the Hubble expansion which
> >> decreases (becomes more negative).
> >
> > Where did you get this idea from?

> 8 pi G rho + gamma + -3H^2 = 0
>
> ( gamma = cosmological constant, a form of dark energy.
> rho = average matter density
> G = Newton's constant
> H = Hubble's expansion factor. )
>
> The question is: how do we interpret this equation?
>
> Since the first two terms are proportional to energy density then
> it is a reasonable inference that we have an expression of energy
> conservation if the last term is also proportional to energy density;
> in this case the energy of the dynamic geometry.
>
> > Explain how the energy of the
> > cosmological constant "comes from" the expansion. The stuff about
> > "dark energy" is OK, but the claim that it is "offset by the negative
> > energy in the Hubble expansion" is completely bogus.
>
> Yet the above equation shows that the offset is exact with
> complete cancellation or conservation.

> > Also, imagine a universe with NO cosmological constant. There
> > would thus be no "offset".
>
> Correct.
>
> > Are you claiming that such a universe is impossible?
>
> No, at this stage I was only talking about how the dark energy/
> cosmological constant was handled, which was what the original
> query related to. If there is no cosmological constant then set
> gamma = 0 in the above equation.

> >>> (Imagine a universe consisting only of radiation. It expands.
> >>> The number of photons remains the same, but the energy of each
> >>> decreases due to the redshift. No, this lost energy does not do
> >>> the work of expanding the universe.)
> >
> > Give a "sensible definition of energy", which is not ad-hoc, which is
> > conserved in this case.
>
> 8piG rho + gamma - 3H^2 .

Let me rephrase my criticism. You say that there is a conservation
equation, and say that the energy of the cosmological constant "comes
from" the expansion and also that the equation is valid if there is no
cosmological constant. So, my question is, if there is no cosmological
constant, then, in the case of no cosmological constant, where does the
energy go which, in the case of a cosmological constant, is transformed
into the cosmological constant?

Imagin the Einstein static universe. There is no expansion. Yet there
is an energy density due to the cosmological constant. How does it
"come from" the (non-existent) expansion in this case? What about a
negative cosmological constant?

I'll reply in more detail later.

Perhaps we are merely using completely different terminology. However,
I think that what you are saying is misleading, or at least confusingly
phrased. You seem to be saying "no mystery where the dark energy comes
from, it comes from expansion". Of course if there is an equation which
holds while the universe expands, then something is conserved; the
question is how this relates to commonly used usages of the term.

I think Edward Harrison has explained rather well what is meant by
"energy is not conserved in the expanding universe". Do you disagree
with his analysis?

This argument might be similar to "cosmological redshift is a Doppler
redshift, and at large redshift one must use the relativistic Doppler
formula". This is not the case if the words have their normal meaning.
One can of course DEFINE a velocity such that it is given by the
relativistic Doppler formula, but I don't see how that is useful.
(Narlikar, in an American Journal of Physics article which Ted Bunn
mentioned here a while back, shows how this can be perhaps useful in a
very unorthodox sense; this might be interesting to experts, but
certainly not to the casual layman interested in cosmology and trying to
get around elementary misunderstandings about Olbers's paradox, what was
before the big bang, where was the big bang etc.)

[Phillip Helbig---remove CLOTHES to reply]

In article <%ZD4f.3782$cA4.3019@newsfe3-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>>> My understanding is that the Universe is expanding and that
> >>>> this expansion is speeding up. What is fuelling this expansion
> >>>> rate increase that is working against the force of gravity?
> >>>>
> >>>> The answer seems to be Dark Energy.

> >>>> The question in my mind is where does this energy come from
> >>>> and it would seem that more and more of it is needed in order
> >>>> to increase the expansion rate.
> >>
> >> Correct. The energy comes from the expansion (a form of
> >> gravitational or geometric energy) which is negative. As the
> >> universe expands the positive energy locked as dark energy
> >> increases (density is constant, but volume increases); this is
> >> offset by the negative energy in the Hubble expansion which
> >> decreases (becomes more negative).
> >
> > Where did you get this idea from?

> 8 pi G rho + gamma + -3H^2 = 0
>
> ( gamma = cosmological constant, a form of dark energy.
> rho = average matter density
> G = Newton's constant
> H = Hubble's expansion factor. )
>
> The question is: how do we interpret this equation?
>
> Since the first two terms are proportional to energy density then
> it is a reasonable inference that we have an expression of energy
> conservation if the last term is also proportional to energy density;
> in this case the energy of the dynamic geometry.
>
> > Explain how the energy of the
> > cosmological constant "comes from" the expansion. The stuff about
> > "dark energy" is OK, but the claim that it is "offset by the negative
> > energy in the Hubble expansion" is completely bogus.
>
> Yet the above equation shows that the offset is exact with
> complete cancellation or conservation.

> > Also, imagine a universe with NO cosmological constant. There
> > would thus be no "offset".
>
> Correct.
>
> > Are you claiming that such a universe is impossible?
>
> No, at this stage I was only talking about how the dark energy/
> cosmological constant was handled, which was what the original
> query related to. If there is no cosmological constant then set
> gamma = 0 in the above equation.

> >>> (Imagine a universe consisting only of radiation. It expands.
> >>> The number of photons remains the same, but the energy of each
> >>> decreases due to the redshift. No, this lost energy does not do
> >>> the work of expanding the universe.)
> >
> > Give a "sensible definition of energy", which is not ad-hoc, which is
> > conserved in this case.
>
> 8piG rho + gamma - 3H^2 .

Let me rephrase my criticism. You say that there is a conservation
equation, and say that the energy of the cosmological constant "comes
from" the expansion and also that the equation is valid if there is no
cosmological constant. So, my question is, if there is no cosmological
constant, then, in the case of no cosmological constant, where does the
energy go which, in the case of a cosmological constant, is transformed
into the cosmological constant?

Imagin the Einstein static universe. There is no expansion. Yet there
is an energy density due to the cosmological constant. How does it
"come from" the (non-existent) expansion in this case? What about a
negative cosmological constant?

I'll reply in more detail later.

Perhaps we are merely using completely different terminology. However,
I think that what you are saying is misleading, or at least confusingly
phrased. You seem to be saying "no mystery where the dark energy comes
from, it comes from expansion". Of course if there is an equation which
holds while the universe expands, then something is conserved; the
question is how this relates to commonly used usages of the term.

I think Edward Harrison has explained rather well what is meant by
"energy is not conserved in the expanding universe". Do you disagree
with his analysis?

This argument might be similar to "cosmological redshift is a Doppler
redshift, and at large redshift one must use the relativistic Doppler
formula". This is not the case if the words have their normal meaning.
One can of course DEFINE a velocity such that it is given by the
relativistic Doppler formula, but I don't see how that is useful.
(Narlikar, in an American Journal of Physics article which Ted Bunn
mentioned here a while back, shows how this can be perhaps useful in a
very unorthodox sense; this might be interesting to experts, but
certainly not to the casual layman interested in cosmology and trying to
get around elementary misunderstandings about Olbers's paradox, what was
before the big bang, where was the big bang etc.)

[Phillip Helbig---remove CLOTHES to reply]

In article <%ZD4f.3782$cA4.3019@newsfe3-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>>> My understanding is that the Universe is expanding and that
> >>>> this expansion is speeding up. What is fuelling this expansion
> >>>> rate increase that is working against the force of gravity?
> >>>>
> >>>> The answer seems to be Dark Energy.

> >>>> The question in my mind is where does this energy come from
> >>>> and it would seem that more and more of it is needed in order
> >>>> to increase the expansion rate.
> >>
> >> Correct. The energy comes from the expansion (a form of
> >> gravitational or geometric energy) which is negative. As the
> >> universe expands the positive energy locked as dark energy
> >> increases (density is constant, but volume increases); this is
> >> offset by the negative energy in the Hubble expansion which
> >> decreases (becomes more negative).
> >
> > Where did you get this idea from?

> 8 pi G rho + gamma + -3H^2 = 0
>
> ( gamma = cosmological constant, a form of dark energy.
> rho = average matter density
> G = Newton's constant
> H = Hubble's expansion factor. )
>
> The question is: how do we interpret this equation?
>
> Since the first two terms are proportional to energy density then
> it is a reasonable inference that we have an expression of energy
> conservation if the last term is also proportional to energy density;
> in this case the energy of the dynamic geometry.
>
> > Explain how the energy of the
> > cosmological constant "comes from" the expansion. The stuff about
> > "dark energy" is OK, but the claim that it is "offset by the negative
> > energy in the Hubble expansion" is completely bogus.
>
> Yet the above equation shows that the offset is exact with
> complete cancellation or conservation.

> > Also, imagine a universe with NO cosmological constant. There
> > would thus be no "offset".
>
> Correct.
>
> > Are you claiming that such a universe is impossible?
>
> No, at this stage I was only talking about how the dark energy/
> cosmological constant was handled, which was what the original
> query related to. If there is no cosmological constant then set
> gamma = 0 in the above equation.

> >>> (Imagine a universe consisting only of radiation. It expands.
> >>> The number of photons remains the same, but the energy of each
> >>> decreases due to the redshift. No, this lost energy does not do
> >>> the work of expanding the universe.)
> >
> > Give a "sensible definition of energy", which is not ad-hoc, which is
> > conserved in this case.
>
> 8piG rho + gamma - 3H^2 .

Let me rephrase my criticism. You say that there is a conservation
equation, and say that the energy of the cosmological constant "comes
from" the expansion and also that the equation is valid if there is no
cosmological constant. So, my question is, if there is no cosmological
constant, then, in the case of no cosmological constant, where does the
energy go which, in the case of a cosmological constant, is transformed
into the cosmological constant?

Imagin the Einstein static universe. There is no expansion. Yet there
is an energy density due to the cosmological constant. How does it
"come from" the (non-existent) expansion in this case? What about a
negative cosmological constant?

I'll reply in more detail later.

Perhaps we are merely using completely different terminology. However,
I think that what you are saying is misleading, or at least confusingly
phrased. You seem to be saying "no mystery where the dark energy comes
from, it comes from expansion". Of course if there is an equation which
holds while the universe expands, then something is conserved; the
question is how this relates to commonly used usages of the term.

I think Edward Harrison has explained rather well what is meant by
"energy is not conserved in the expanding universe". Do you disagree
with his analysis?

This argument might be similar to "cosmological redshift is a Doppler
redshift, and at large redshift one must use the relativistic Doppler
formula". This is not the case if the words have their normal meaning.
One can of course DEFINE a velocity such that it is given by the
relativistic Doppler formula, but I don't see how that is useful.
(Narlikar, in an American Journal of Physics article which Ted Bunn
mentioned here a while back, shows how this can be perhaps useful in a
very unorthodox sense; this might be interesting to experts, but
certainly not to the casual layman interested in cosmology and trying to
get around elementary misunderstandings about Olbers's paradox, what was
before the big bang, where was the big bang etc.)

[Phillip Helbig---remove CLOTHES to reply]

In article <%ZD4f.3782$cA4.3019@newsfe3-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>>> My understanding is that the Universe is expanding and that
> >>>> this expansion is speeding up. What is fuelling this expansion
> >>>> rate increase that is working against the force of gravity?
> >>>>
> >>>> The answer seems to be Dark Energy.

> >>>> The question in my mind is where does this energy come from
> >>>> and it would seem that more and more of it is needed in order
> >>>> to increase the expansion rate.
> >>
> >> Correct. The energy comes from the expansion (a form of
> >> gravitational or geometric energy) which is negative. As the
> >> universe expands the positive energy locked as dark energy
> >> increases (density is constant, but volume increases); this is
> >> offset by the negative energy in the Hubble expansion which
> >> decreases (becomes more negative).
> >
> > Where did you get this idea from?

> 8 pi G rho + gamma + -3H^2 = 0
>
> ( gamma = cosmological constant, a form of dark energy.
> rho = average matter density
> G = Newton's constant
> H = Hubble's expansion factor. )
>
> The question is: how do we interpret this equation?
>
> Since the first two terms are proportional to energy density then
> it is a reasonable inference that we have an expression of energy
> conservation if the last term is also proportional to energy density;
> in this case the energy of the dynamic geometry.
>
> > Explain how the energy of the
> > cosmological constant "comes from" the expansion. The stuff about
> > "dark energy" is OK, but the claim that it is "offset by the negative
> > energy in the Hubble expansion" is completely bogus.
>
> Yet the above equation shows that the offset is exact with
> complete cancellation or conservation.

> > Also, imagine a universe with NO cosmological constant. There
> > would thus be no "offset".
>
> Correct.
>
> > Are you claiming that such a universe is impossible?
>
> No, at this stage I was only talking about how the dark energy/
> cosmological constant was handled, which was what the original
> query related to. If there is no cosmological constant then set
> gamma = 0 in the above equation.

> >>> (Imagine a universe consisting only of radiation. It expands.
> >>> The number of photons remains the same, but the energy of each
> >>> decreases due to the redshift. No, this lost energy does not do
> >>> the work of expanding the universe.)
> >
> > Give a "sensible definition of energy", which is not ad-hoc, which is
> > conserved in this case.
>
> 8piG rho + gamma - 3H^2 .

Let me rephrase my criticism. You say that there is a conservation
equation, and say that the energy of the cosmological constant "comes
from" the expansion and also that the equation is valid if there is no
cosmological constant. So, my question is, if there is no cosmological
constant, then, in the case of no cosmological constant, where does the
energy go which, in the case of a cosmological constant, is transformed
into the cosmological constant?

Imagin the Einstein static universe. There is no expansion. Yet there
is an energy density due to the cosmological constant. How does it
"come from" the (non-existent) expansion in this case? What about a
negative cosmological constant?

I'll reply in more detail later.

Perhaps we are merely using completely different terminology. However,
I think that what you are saying is misleading, or at least confusingly
phrased. You seem to be saying "no mystery where the dark energy comes
from, it comes from expansion". Of course if there is an equation which
holds while the universe expands, then something is conserved; the
question is how this relates to commonly used usages of the term.

I think Edward Harrison has explained rather well what is meant by
"energy is not conserved in the expanding universe". Do you disagree
with his analysis?

This argument might be similar to "cosmological redshift is a Doppler
redshift, and at large redshift one must use the relativistic Doppler
formula". This is not the case if the words have their normal meaning.
One can of course DEFINE a velocity such that it is given by the
relativistic Doppler formula, but I don't see how that is useful.
(Narlikar, in an American Journal of Physics article which Ted Bunn
mentioned here a while back, shows how this can be perhaps useful in a
very unorthodox sense; this might be interesting to experts, but
certainly not to the casual layman interested in cosmology and trying to
get around elementary misunderstandings about Olbers's paradox, what was
before the big bang, where was the big bang etc.)

[Phillip Helbig---remove CLOTHES to reply]

In article <%ZD4f.3782$cA4.3019@newsfe3-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>>> My understanding is that the Universe is expanding and that
> >>>> this expansion is speeding up. What is fuelling this expansion
> >>>> rate increase that is working against the force of gravity?
> >>>>
> >>>> The answer seems to be Dark Energy.

> >>>> The question in my mind is where does this energy come from
> >>>> and it would seem that more and more of it is needed in order
> >>>> to increase the expansion rate.
> >>
> >> Correct. The energy comes from the expansion (a form of
> >> gravitational or geometric energy) which is negative. As the
> >> universe expands the positive energy locked as dark energy
> >> increases (density is constant, but volume increases); this is
> >> offset by the negative energy in the Hubble expansion which
> >> decreases (becomes more negative).
> >
> > Where did you get this idea from?

> 8 pi G rho + gamma + -3H^2 = 0
>
> ( gamma = cosmological constant, a form of dark energy.
> rho = average matter density
> G = Newton's constant
> H = Hubble's expansion factor. )
>
> The question is: how do we interpret this equation?
>
> Since the first two terms are proportional to energy density then
> it is a reasonable inference that we have an expression of energy
> conservation if the last term is also proportional to energy density;
> in this case the energy of the dynamic geometry.
>
> > Explain how the energy of the
> > cosmological constant "comes from" the expansion. The stuff about
> > "dark energy" is OK, but the claim that it is "offset by the negative
> > energy in the Hubble expansion" is completely bogus.
>
> Yet the above equation shows that the offset is exact with
> complete cancellation or conservation.

> > Also, imagine a universe with NO cosmological constant. There
> > would thus be no "offset".
>
> Correct.
>
> > Are you claiming that such a universe is impossible?
>
> No, at this stage I was only talking about how the dark energy/
> cosmological constant was handled, which was what the original
> query related to. If there is no cosmological constant then set
> gamma = 0 in the above equation.

> >>> (Imagine a universe consisting only of radiation. It expands.
> >>> The number of photons remains the same, but the energy of each
> >>> decreases due to the redshift. No, this lost energy does not do
> >>> the work of expanding the universe.)
> >
> > Give a "sensible definition of energy", which is not ad-hoc, which is
> > conserved in this case.
>
> 8piG rho + gamma - 3H^2 .

Let me rephrase my criticism. You say that there is a conservation
equation, and say that the energy of the cosmological constant "comes
from" the expansion and also that the equation is valid if there is no
cosmological constant. So, my question is, if there is no cosmological
constant, then, in the case of no cosmological constant, where does the
energy go which, in the case of a cosmological constant, is transformed
into the cosmological constant?

Imagin the Einstein static universe. There is no expansion. Yet there
is an energy density due to the cosmological constant. How does it
"come from" the (non-existent) expansion in this case? What about a
negative cosmological constant?

I'll reply in more detail later.

Perhaps we are merely using completely different terminology. However,
I think that what you are saying is misleading, or at least confusingly
phrased. You seem to be saying "no mystery where the dark energy comes
from, it comes from expansion". Of course if there is an equation which
holds while the universe expands, then something is conserved; the
question is how this relates to commonly used usages of the term.

I think Edward Harrison has explained rather well what is meant by
"energy is not conserved in the expanding universe". Do you disagree
with his analysis?

This argument might be similar to "cosmological redshift is a Doppler
redshift, and at large redshift one must use the relativistic Doppler
formula". This is not the case if the words have their normal meaning.
One can of course DEFINE a velocity such that it is given by the
relativistic Doppler formula, but I don't see how that is useful.
(Narlikar, in an American Journal of Physics article which Ted Bunn
mentioned here a while back, shows how this can be perhaps useful in a
very unorthodox sense; this might be interesting to experts, but
certainly not to the casual layman interested in cosmology and trying to
get around elementary misunderstandings about Olbers's paradox, what was
before the big bang, where was the big bang etc.)

[Phillip Helbig---remove CLOTHES to reply]

In article <%ZD4f.3782$cA4.3019@newsfe3-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>>> My understanding is that the Universe is expanding and that
> >>>> this expansion is speeding up. What is fuelling this expansion
> >>>> rate increase that is working against the force of gravity?
> >>>>
> >>>> The answer seems to be Dark Energy.

> >>>> The question in my mind is where does this energy come from
> >>>> and it would seem that more and more of it is needed in order
> >>>> to increase the expansion rate.
> >>
> >> Correct. The energy comes from the expansion (a form of
> >> gravitational or geometric energy) which is negative. As the
> >> universe expands the positive energy locked as dark energy
> >> increases (density is constant, but volume increases); this is
> >> offset by the negative energy in the Hubble expansion which
> >> decreases (becomes more negative).
> >
> > Where did you get this idea from?

> 8 pi G rho + gamma + -3H^2 = 0
>
> ( gamma = cosmological constant, a form of dark energy.
> rho = average matter density
> G = Newton's constant
> H = Hubble's expansion factor. )
>
> The question is: how do we interpret this equation?
>
> Since the first two terms are proportional to energy density then
> it is a reasonable inference that we have an expression of energy
> conservation if the last term is also proportional to energy density;
> in this case the energy of the dynamic geometry.
>
> > Explain how the energy of the
> > cosmological constant "comes from" the expansion. The stuff about
> > "dark energy" is OK, but the claim that it is "offset by the negative
> > energy in the Hubble expansion" is completely bogus.
>
> Yet the above equation shows that the offset is exact with
> complete cancellation or conservation.

> > Also, imagine a universe with NO cosmological constant. There
> > would thus be no "offset".
>
> Correct.
>
> > Are you claiming that such a universe is impossible?
>
> No, at this stage I was only talking about how the dark energy/
> cosmological constant was handled, which was what the original
> query related to. If there is no cosmological constant then set
> gamma = 0 in the above equation.

> >>> (Imagine a universe consisting only of radiation. It expands.
> >>> The number of photons remains the same, but the energy of each
> >>> decreases due to the redshift. No, this lost energy does not do
> >>> the work of expanding the universe.)
> >
> > Give a "sensible definition of energy", which is not ad-hoc, which is
> > conserved in this case.
>
> 8piG rho + gamma - 3H^2 .

Let me rephrase my criticism. You say that there is a conservation
equation, and say that the energy of the cosmological constant "comes
from" the expansion and also that the equation is valid if there is no
cosmological constant. So, my question is, if there is no cosmological
constant, then, in the case of no cosmological constant, where does the
energy go which, in the case of a cosmological constant, is transformed
into the cosmological constant?

Imagin the Einstein static universe. There is no expansion. Yet there
is an energy density due to the cosmological constant. How does it
"come from" the (non-existent) expansion in this case? What about a
negative cosmological constant?

I'll reply in more detail later.

Perhaps we are merely using completely different terminology. However,
I think that what you are saying is misleading, or at least confusingly
phrased. You seem to be saying "no mystery where the dark energy comes
from, it comes from expansion". Of course if there is an equation which
holds while the universe expands, then something is conserved; the
question is how this relates to commonly used usages of the term.

I think Edward Harrison has explained rather well what is meant by
"energy is not conserved in the expanding universe". Do you disagree
with his analysis?

This argument might be similar to "cosmological redshift is a Doppler
redshift, and at large redshift one must use the relativistic Doppler
formula". This is not the case if the words have their normal meaning.
One can of course DEFINE a velocity such that it is given by the
relativistic Doppler formula, but I don't see how that is useful.
(Narlikar, in an American Journal of Physics article which Ted Bunn
mentioned here a while back, shows how this can be perhaps useful in a
very unorthodox sense; this might be interesting to experts, but
certainly not to the casual layman interested in cosmology and trying to
get around elementary misunderstandings about Olbers's paradox, what was
before the big bang, where was the big bang etc.)

[Phillip Helbig---remove CLOTHES to reply]

In article <%ZD4f.3782$cA4.3019@newsfe3-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>>> My understanding is that the Universe is expanding and that
> >>>> this expansion is speeding up. What is fuelling this expansion
> >>>> rate increase that is working against the force of gravity?
> >>>>
> >>>> The answer seems to be Dark Energy.

> >>>> The question in my mind is where does this energy come from
> >>>> and it would seem that more and more of it is needed in order
> >>>> to increase the expansion rate.
> >>
> >> Correct. The energy comes from the expansion (a form of
> >> gravitational or geometric energy) which is negative. As the
> >> universe expands the positive energy locked as dark energy
> >> increases (density is constant, but volume increases); this is
> >> offset by the negative energy in the Hubble expansion which
> >> decreases (becomes more negative).
> >
> > Where did you get this idea from?

> 8 pi G rho + gamma + -3H^2 = 0
>
> ( gamma = cosmological constant, a form of dark energy.
> rho = average matter density
> G = Newton's constant
> H = Hubble's expansion factor. )
>
> The question is: how do we interpret this equation?
>
> Since the first two terms are proportional to energy density then
> it is a reasonable inference that we have an expression of energy
> conservation if the last term is also proportional to energy density;
> in this case the energy of the dynamic geometry.
>
> > Explain how the energy of the
> > cosmological constant "comes from" the expansion. The stuff about
> > "dark energy" is OK, but the claim that it is "offset by the negative
> > energy in the Hubble expansion" is completely bogus.
>
> Yet the above equation shows that the offset is exact with
> complete cancellation or conservation.

> > Also, imagine a universe with NO cosmological constant. There
> > would thus be no "offset".
>
> Correct.
>
> > Are you claiming that such a universe is impossible?
>
> No, at this stage I was only talking about how the dark energy/
> cosmological constant was handled, which was what the original
> query related to. If there is no cosmological constant then set
> gamma = 0 in the above equation.

> >>> (Imagine a universe consisting only of radiation. It expands.
> >>> The number of photons remains the same, but the energy of each
> >>> decreases due to the redshift. No, this lost energy does not do
> >>> the work of expanding the universe.)
> >
> > Give a "sensible definition of energy", which is not ad-hoc, which is
> > conserved in this case.
>
> 8piG rho + gamma - 3H^2 .

Let me rephrase my criticism. You say that there is a conservation
equation, and say that the energy of the cosmological constant "comes
from" the expansion and also that the equation is valid if there is no
cosmological constant. So, my question is, if there is no cosmological
constant, then, in the case of no cosmological constant, where does the
energy go which, in the case of a cosmological constant, is transformed
into the cosmological constant?

Imagin the Einstein static universe. There is no expansion. Yet there
is an energy density due to the cosmological constant. How does it
"come from" the (non-existent) expansion in this case? What about a
negative cosmological constant?

I'll reply in more detail later.

Perhaps we are merely using completely different terminology. However,
I think that what you are saying is misleading, or at least confusingly
phrased. You seem to be saying "no mystery where the dark energy comes
from, it comes from expansion". Of course if there is an equation which
holds while the universe expands, then something is conserved; the
question is how this relates to commonly used usages of the term.

I think Edward Harrison has explained rather well what is meant by
"energy is not conserved in the expanding universe". Do you disagree
with his analysis?

This argument might be similar to "cosmological redshift is a Doppler
redshift, and at large redshift one must use the relativistic Doppler
formula". This is not the case if the words have their normal meaning.
One can of course DEFINE a velocity such that it is given by the
relativistic Doppler formula, but I don't see how that is useful.
(Narlikar, in an American Journal of Physics article which Ted Bunn
mentioned here a while back, shows how this can be perhaps useful in a
very unorthodox sense; this might be interesting to experts, but
certainly not to the casual layman interested in cosmology and trying to
get around elementary misunderstandings about Olbers's paradox, what was
before the big bang, where was the big bang etc.)

[Phillip Helbig---remove CLOTHES to reply]

In article <%ZD4f.3782$cA4.3019@newsfe3-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>>> My understanding is that the Universe is expanding and that
> >>>> this expansion is speeding up. What is fuelling this expansion
> >>>> rate increase that is working against the force of gravity?
> >>>>
> >>>> The answer seems to be Dark Energy.

> >>>> The question in my mind is where does this energy come from
> >>>> and it would seem that more and more of it is needed in order
> >>>> to increase the expansion rate.
> >>
> >> Correct. The energy comes from the expansion (a form of
> >> gravitational or geometric energy) which is negative. As the
> >> universe expands the positive energy locked as dark energy
> >> increases (density is constant, but volume increases); this is
> >> offset by the negative energy in the Hubble expansion which
> >> decreases (becomes more negative).
> >
> > Where did you get this idea from?

> 8 pi G rho + gamma + -3H^2 = 0
>
> ( gamma = cosmological constant, a form of dark energy.
> rho = average matter density
> G = Newton's constant
> H = Hubble's expansion factor. )
>
> The question is: how do we interpret this equation?
>
> Since the first two terms are proportional to energy density then
> it is a reasonable inference that we have an expression of energy
> conservation if the last term is also proportional to energy density;
> in this case the energy of the dynamic geometry.
>
> > Explain how the energy of the
> > cosmological constant "comes from" the expansion. The stuff about
> > "dark energy" is OK, but the claim that it is "offset by the negative
> > energy in the Hubble expansion" is completely bogus.
>
> Yet the above equation shows that the offset is exact with
> complete cancellation or conservation.

> > Also, imagine a universe with NO cosmological constant. There
> > would thus be no "offset".
>
> Correct.
>
> > Are you claiming that such a universe is impossible?
>
> No, at this stage I was only talking about how the dark energy/
> cosmological constant was handled, which was what the original
> query related to. If there is no cosmological constant then set
> gamma = 0 in the above equation.

> >>> (Imagine a universe consisting only of radiation. It expands.
> >>> The number of photons remains the same, but the energy of each
> >>> decreases due to the redshift. No, this lost energy does not do
> >>> the work of expanding the universe.)
> >
> > Give a "sensible definition of energy", which is not ad-hoc, which is
> > conserved in this case.
>
> 8piG rho + gamma - 3H^2 .

Let me rephrase my criticism. You say that there is a conservation
equation, and say that the energy of the cosmological constant "comes
from" the expansion and also that the equation is valid if there is no
cosmological constant. So, my question is, if there is no cosmological
constant, then, in the case of no cosmological constant, where does the
energy go which, in the case of a cosmological constant, is transformed
into the cosmological constant?

Imagin the Einstein static universe. There is no expansion. Yet there
is an energy density due to the cosmological constant. How does it
"come from" the (non-existent) expansion in this case? What about a
negative cosmological constant?

I'll reply in more detail later.

Perhaps we are merely using completely different terminology. However,
I think that what you are saying is misleading, or at least confusingly
phrased. You seem to be saying "no mystery where the dark energy comes
from, it comes from expansion". Of course if there is an equation which
holds while the universe expands, then something is conserved; the
question is how this relates to commonly used usages of the term.

I think Edward Harrison has explained rather well what is meant by
"energy is not conserved in the expanding universe". Do you disagree
with his analysis?

This argument might be similar to "cosmological redshift is a Doppler
redshift, and at large redshift one must use the relativistic Doppler
formula". This is not the case if the words have their normal meaning.
One can of course DEFINE a velocity such that it is given by the
relativistic Doppler formula, but I don't see how that is useful.
(Narlikar, in an American Journal of Physics article which Ted Bunn
mentioned here a while back, shows how this can be perhaps useful in a
very unorthodox sense; this might be interesting to experts, but
certainly not to the casual layman interested in cosmology and trying to
get around elementary misunderstandings about Olbers's paradox, what was
before the big bang, where was the big bang etc.)

[Phillip Helbig---remove CLOTHES to reply]

In article <%ZD4f.3782$cA4.3019@newsfe3-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>>> My understanding is that the Universe is expanding and that
> >>>> this expansion is speeding up. What is fuelling this expansion
> >>>> rate increase that is working against the force of gravity?
> >>>>
> >>>> The answer seems to be Dark Energy.

> >>>> The question in my mind is where does this energy come from
> >>>> and it would seem that more and more of it is needed in order
> >>>> to increase the expansion rate.
> >>
> >> Correct. The energy comes from the expansion (a form of
> >> gravitational or geometric energy) which is negative. As the
> >> universe expands the positive energy locked as dark energy
> >> increases (density is constant, but volume increases); this is
> >> offset by the negative energy in the Hubble expansion which
> >> decreases (becomes more negative).
> >
> > Where did you get this idea from?

> 8 pi G rho + gamma + -3H^2 = 0
>
> ( gamma = cosmological constant, a form of dark energy.
> rho = average matter density
> G = Newton's constant
> H = Hubble's expansion factor. )
>
> The question is: how do we interpret this equation?
>
> Since the first two terms are proportional to energy density then
> it is a reasonable inference that we have an expression of energy
> conservation if the last term is also proportional to energy density;
> in this case the energy of the dynamic geometry.
>
> > Explain how the energy of the
> > cosmological constant "comes from" the expansion. The stuff about
> > "dark energy" is OK, but the claim that it is "offset by the negative
> > energy in the Hubble expansion" is completely bogus.
>
> Yet the above equation shows that the offset is exact with
> complete cancellation or conservation.

> > Also, imagine a universe with NO cosmological constant. There
> > would thus be no "offset".
>
> Correct.
>
> > Are you claiming that such a universe is impossible?
>
> No, at this stage I was only talking about how the dark energy/
> cosmological constant was handled, which was what the original
> query related to. If there is no cosmological constant then set
> gamma = 0 in the above equation.

> >>> (Imagine a universe consisting only of radiation. It expands.
> >>> The number of photons remains the same, but the energy of each
> >>> decreases due to the redshift. No, this lost energy does not do
> >>> the work of expanding the universe.)
> >
> > Give a "sensible definition of energy", which is not ad-hoc, which is
> > conserved in this case.
>
> 8piG rho + gamma - 3H^2 .

Let me rephrase my criticism. You say that there is a conservation
equation, and say that the energy of the cosmological constant "comes
from" the expansion and also that the equation is valid if there is no
cosmological constant. So, my question is, if there is no cosmological
constant, then, in the case of no cosmological constant, where does the
energy go which, in the case of a cosmological constant, is transformed
into the cosmological constant?

Imagin the Einstein static universe. There is no expansion. Yet there
is an energy density due to the cosmological constant. How does it
"come from" the (non-existent) expansion in this case? What about a
negative cosmological constant?

I'll reply in more detail later.

Perhaps we are merely using completely different terminology. However,
I think that what you are saying is misleading, or at least confusingly
phrased. You seem to be saying "no mystery where the dark energy comes
from, it comes from expansion". Of course if there is an equation which
holds while the universe expands, then something is conserved; the
question is how this relates to commonly used usages of the term.

I think Edward Harrison has explained rather well what is meant by
"energy is not conserved in the expanding universe". Do you disagree
with his analysis?

This argument might be similar to "cosmological redshift is a Doppler
redshift, and at large redshift one must use the relativistic Doppler
formula". This is not the case if the words have their normal meaning.
One can of course DEFINE a velocity such that it is given by the
relativistic Doppler formula, but I don't see how that is useful.
(Narlikar, in an American Journal of Physics article which Ted Bunn
mentioned here a while back, shows how this can be perhaps useful in a
very unorthodox sense; this might be interesting to experts, but
certainly not to the casual layman interested in cosmology and trying to
get around elementary misunderstandings about Olbers's paradox, what was
before the big bang, where was the big bang etc.)

[Michael C Price]

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Phillip Helbig---remove CLOTHES to reply]

In article <ovh5f.5505$cA4.1338@newsfe3-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> Let me answer it this way: the cosmological constant currently dominates
> the expansion of the universe. The matter and photons are just being
> carried along for the ride. (This wasn't always the case. Earlier the
> matter dominated, and before that the photons.) The dominant flow of
> energy, today, is from the Hubble expansion to the cosmological constant,
> each one growing in magnitude although of opposite sign. Without a
> cosmological constant the presently insignificant flow from the photons
> (via the red shift) to the Hubble factor would dominate, as it did in the
> early universe. i.e. the direction of the energy flow would be reversed.

You seem to think that this "flow" is some sort of physical
transformation. Can you explain this in more detail?

> > Imagine the Einstein static universe. There is no expansion. Yet there
> > is an energy density due to the cosmological constant. How does it
> > "come from" the (non-existent) expansion in this case? What about a
> > negative cosmological constant?
>
> Indeed, as you point out, in Einstein's original static universe the
> cosmological constant was negative

The cosmological constant in the Einstein static universe is positive.
I was providing two examples: one in which there can be no "flow" since
there is no expansion, and in addition mentioning that the cosmological
constant can, theoretically, be negative while the expansion has the
same sign as it has today. I don't see how you can say that there is a
"flow" in all three cases (static, negative cosmological constant,
positive cosmological constant) or, if you don't claim this (which seems
to be the case), how you can say that in some cases (like the one which
corresponds to our universe), there IS a flow.

Let me EXAGGERATE. Fewer children are born where fewer storks nest.
Does this prove that storks bring children? No. It is due to a common
cause (fewer children are born in industrialised societies, and storks
are less common here as well). Historically, global warming is also
negatively correlated with the number of pirates sailing the seven seas,
but that doesn't mean that pirates prevent global warming. You seem to
be saying a) there is expansion and b) there is a cosmological constant
and then claiming that one "causes" the other in some sense.

> > I think Edward Harrison has explained rather well what is meant by
> > "energy is not conserved in the expanding universe". Do you disagree
> > with his analysis?
>
> Yes. If I understand Harrison's argument it is that pressure and pressure
> gradients mediate the transfer of energy in the thermodynamic dE = -P dV
> equation (which has a cosmological equivalent), which describes the
> expansion of, say, a pressurised gas against its environment. But in the
> universe there is no exterior system to push against and hence no transfer
> of energy. Instead he concludes the red-shift energy is lost and not
> transferred. I think he is being lead astray by the thermodynamic
> analogy with pressure. Pressure is the result of particles (including
> photons) with momenta, which have de Broglie wavelengths. It is the
> stretching of the wavelengths by the Hubble expansion which causes the
> loss of momenta and the red-shift. The loss of radiation pressure is a
> consequence of this stretching and not a mediating mechanism; no
> pressure gradient or exterior system is required.

Harrison (in his textbook) explicitly states that the universe is not
like a steam engine, so I think the disagreement has another cause.

[Phillip Helbig---remove CLOTHES to reply]

In article <ovh5f.5505$cA4.1338@newsfe3-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> Let me answer it this way: the cosmological constant currently dominates
> the expansion of the universe. The matter and photons are just being
> carried along for the ride. (This wasn't always the case. Earlier the
> matter dominated, and before that the photons.) The dominant flow of
> energy, today, is from the Hubble expansion to the cosmological constant,
> each one growing in magnitude although of opposite sign. Without a
> cosmological constant the presently insignificant flow from the photons
> (via the red shift) to the Hubble factor would dominate, as it did in the
> early universe. i.e. the direction of the energy flow would be reversed.

You seem to think that this "flow" is some sort of physical
transformation. Can you explain this in more detail?

> > Imagine the Einstein static universe. There is no expansion. Yet there
> > is an energy density due to the cosmological constant. How does it
> > "come from" the (non-existent) expansion in this case? What about a
> > negative cosmological constant?
>
> Indeed, as you point out, in Einstein's original static universe the
> cosmological constant was negative

The cosmological constant in the Einstein static universe is positive.
I was providing two examples: one in which there can be no "flow" since
there is no expansion, and in addition mentioning that the cosmological
constant can, theoretically, be negative while the expansion has the
same sign as it has today. I don't see how you can say that there is a
"flow" in all three cases (static, negative cosmological constant,
positive cosmological constant) or, if you don't claim this (which seems
to be the case), how you can say that in some cases (like the one which
corresponds to our universe), there IS a flow.

Let me EXAGGERATE. Fewer children are born where fewer storks nest.
Does this prove that storks bring children? No. It is due to a common
cause (fewer children are born in industrialised societies, and storks
are less common here as well). Historically, global warming is also
negatively correlated with the number of pirates sailing the seven seas,
but that doesn't mean that pirates prevent global warming. You seem to
be saying a) there is expansion and b) there is a cosmological constant
and then claiming that one "causes" the other in some sense.

> > I think Edward Harrison has explained rather well what is meant by
> > "energy is not conserved in the expanding universe". Do you disagree
> > with his analysis?
>
> Yes. If I understand Harrison's argument it is that pressure and pressure
> gradients mediate the transfer of energy in the thermodynamic dE = -P dV
> equation (which has a cosmological equivalent), which describes the
> expansion of, say, a pressurised gas against its environment. But in the
> universe there is no exterior system to push against and hence no transfer
> of energy. Instead he concludes the red-shift energy is lost and not
> transferred. I think he is being lead astray by the thermodynamic
> analogy with pressure. Pressure is the result of particles (including
> photons) with momenta, which have de Broglie wavelengths. It is the
> stretching of the wavelengths by the Hubble expansion which causes the
> loss of momenta and the red-shift. The loss of radiation pressure is a
> consequence of this stretching and not a mediating mechanism; no
> pressure gradient or exterior system is required.

Harrison (in his textbook) explicitly states that the universe is not
like a steam engine, so I think the disagreement has another cause.

[Phillip Helbig---remove CLOTHES to reply]

In article <ovh5f.5505$cA4.1338@newsfe3-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> Let me answer it this way: the cosmological constant currently dominates
> the expansion of the universe. The matter and photons are just being
> carried along for the ride. (This wasn't always the case. Earlier the
> matter dominated, and before that the photons.) The dominant flow of
> energy, today, is from the Hubble expansion to the cosmological constant,
> each one growing in magnitude although of opposite sign. Without a
> cosmological constant the presently insignificant flow from the photons
> (via the red shift) to the Hubble factor would dominate, as it did in the
> early universe. i.e. the direction of the energy flow would be reversed.

You seem to think that this "flow" is some sort of physical
transformation. Can you explain this in more detail?

> > Imagine the Einstein static universe. There is no expansion. Yet there
> > is an energy density due to the cosmological constant. How does it
> > "come from" the (non-existent) expansion in this case? What about a
> > negative cosmological constant?
>
> Indeed, as you point out, in Einstein's original static universe the
> cosmological constant was negative

The cosmological constant in the Einstein static universe is positive.
I was providing two examples: one in which there can be no "flow" since
there is no expansion, and in addition mentioning that the cosmological
constant can, theoretically, be negative while the expansion has the
same sign as it has today. I don't see how you can say that there is a
"flow" in all three cases (static, negative cosmological constant,
positive cosmological constant) or, if you don't claim this (which seems
to be the case), how you can say that in some cases (like the one which
corresponds to our universe), there IS a flow.

Let me EXAGGERATE. Fewer children are born where fewer storks nest.
Does this prove that storks bring children? No. It is due to a common
cause (fewer children are born in industrialised societies, and storks
are less common here as well). Historically, global warming is also
negatively correlated with the number of pirates sailing the seven seas,
but that doesn't mean that pirates prevent global warming. You seem to
be saying a) there is expansion and b) there is a cosmological constant
and then claiming that one "causes" the other in some sense.

> > I think Edward Harrison has explained rather well what is meant by
> > "energy is not conserved in the expanding universe". Do you disagree
> > with his analysis?
>
> Yes. If I understand Harrison's argument it is that pressure and pressure
> gradients mediate the transfer of energy in the thermodynamic dE = -P dV
> equation (which has a cosmological equivalent), which describes the
> expansion of, say, a pressurised gas against its environment. But in the
> universe there is no exterior system to push against and hence no transfer
> of energy. Instead he concludes the red-shift energy is lost and not
> transferred. I think he is being lead astray by the thermodynamic
> analogy with pressure. Pressure is the result of particles (including
> photons) with momenta, which have de Broglie wavelengths. It is the
> stretching of the wavelengths by the Hubble expansion which causes the
> loss of momenta and the red-shift. The loss of radiation pressure is a
> consequence of this stretching and not a mediating mechanism; no
> pressure gradient or exterior system is required.

Harrison (in his textbook) explicitly states that the universe is not
like a steam engine, so I think the disagreement has another cause.

[Phillip Helbig---remove CLOTHES to reply]

In article <ovh5f.5505$cA4.1338@newsfe3-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> Let me answer it this way: the cosmological constant currently dominates
> the expansion of the universe. The matter and photons are just being
> carried along for the ride. (This wasn't always the case. Earlier the
> matter dominated, and before that the photons.) The dominant flow of
> energy, today, is from the Hubble expansion to the cosmological constant,
> each one growing in magnitude although of opposite sign. Without a
> cosmological constant the presently insignificant flow from the photons
> (via the red shift) to the Hubble factor would dominate, as it did in the
> early universe. i.e. the direction of the energy flow would be reversed.

You seem to think that this "flow" is some sort of physical
transformation. Can you explain this in more detail?

> > Imagine the Einstein static universe. There is no expansion. Yet there
> > is an energy density due to the cosmological constant. How does it
> > "come from" the (non-existent) expansion in this case? What about a
> > negative cosmological constant?
>
> Indeed, as you point out, in Einstein's original static universe the
> cosmological constant was negative

The cosmological constant in the Einstein static universe is positive.
I was providing two examples: one in which there can be no "flow" since
there is no expansion, and in addition mentioning that the cosmological
constant can, theoretically, be negative while the expansion has the
same sign as it has today. I don't see how you can say that there is a
"flow" in all three cases (static, negative cosmological constant,
positive cosmological constant) or, if you don't claim this (which seems
to be the case), how you can say that in some cases (like the one which
corresponds to our universe), there IS a flow.

Let me EXAGGERATE. Fewer children are born where fewer storks nest.
Does this prove that storks bring children? No. It is due to a common
cause (fewer children are born in industrialised societies, and storks
are less common here as well). Historically, global warming is also
negatively correlated with the number of pirates sailing the seven seas,
but that doesn't mean that pirates prevent global warming. You seem to
be saying a) there is expansion and b) there is a cosmological constant
and then claiming that one "causes" the other in some sense.

> > I think Edward Harrison has explained rather well what is meant by
> > "energy is not conserved in the expanding universe". Do you disagree
> > with his analysis?
>
> Yes. If I understand Harrison's argument it is that pressure and pressure
> gradients mediate the transfer of energy in the thermodynamic dE = -P dV
> equation (which has a cosmological equivalent), which describes the
> expansion of, say, a pressurised gas against its environment. But in the
> universe there is no exterior system to push against and hence no transfer
> of energy. Instead he concludes the red-shift energy is lost and not
> transferred. I think he is being lead astray by the thermodynamic
> analogy with pressure. Pressure is the result of particles (including
> photons) with momenta, which have de Broglie wavelengths. It is the
> stretching of the wavelengths by the Hubble expansion which causes the
> loss of momenta and the red-shift. The loss of radiation pressure is a
> consequence of this stretching and not a mediating mechanism; no
> pressure gradient or exterior system is required.

Harrison (in his textbook) explicitly states that the universe is not
like a steam engine, so I think the disagreement has another cause.

[Phillip Helbig---remove CLOTHES to reply]

In article <ovh5f.5505$cA4.1338@newsfe3-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> Let me answer it this way: the cosmological constant currently dominates
> the expansion of the universe. The matter and photons are just being
> carried along for the ride. (This wasn't always the case. Earlier the
> matter dominated, and before that the photons.) The dominant flow of
> energy, today, is from the Hubble expansion to the cosmological constant,
> each one growing in magnitude although of opposite sign. Without a
> cosmological constant the presently insignificant flow from the photons
> (via the red shift) to the Hubble factor would dominate, as it did in the
> early universe. i.e. the direction of the energy flow would be reversed.

You seem to think that this "flow" is some sort of physical
transformation. Can you explain this in more detail?

> > Imagine the Einstein static universe. There is no expansion. Yet there
> > is an energy density due to the cosmological constant. How does it
> > "come from" the (non-existent) expansion in this case? What about a
> > negative cosmological constant?
>
> Indeed, as you point out, in Einstein's original static universe the
> cosmological constant was negative

The cosmological constant in the Einstein static universe is positive.
I was providing two examples: one in which there can be no "flow" since
there is no expansion, and in addition mentioning that the cosmological
constant can, theoretically, be negative while the expansion has the
same sign as it has today. I don't see how you can say that there is a
"flow" in all three cases (static, negative cosmological constant,
positive cosmological constant) or, if you don't claim this (which seems
to be the case), how you can say that in some cases (like the one which
corresponds to our universe), there IS a flow.

Let me EXAGGERATE. Fewer children are born where fewer storks nest.
Does this prove that storks bring children? No. It is due to a common
cause (fewer children are born in industrialised societies, and storks
are less common here as well). Historically, global warming is also
negatively correlated with the number of pirates sailing the seven seas,
but that doesn't mean that pirates prevent global warming. You seem to
be saying a) there is expansion and b) there is a cosmological constant
and then claiming that one "causes" the other in some sense.

> > I think Edward Harrison has explained rather well what is meant by
> > "energy is not conserved in the expanding universe". Do you disagree
> > with his analysis?
>
> Yes. If I understand Harrison's argument it is that pressure and pressure
> gradients mediate the transfer of energy in the thermodynamic dE = -P dV
> equation (which has a cosmological equivalent), which describes the
> expansion of, say, a pressurised gas against its environment. But in the
> universe there is no exterior system to push against and hence no transfer
> of energy. Instead he concludes the red-shift energy is lost and not
> transferred. I think he is being lead astray by the thermodynamic
> analogy with pressure. Pressure is the result of particles (including
> photons) with momenta, which have de Broglie wavelengths. It is the
> stretching of the wavelengths by the Hubble expansion which causes the
> loss of momenta and the red-shift. The loss of radiation pressure is a
> consequence of this stretching and not a mediating mechanism; no
> pressure gradient or exterior system is required.

Harrison (in his textbook) explicitly states that the universe is not
like a steam engine, so I think the disagreement has another cause.

[Phillip Helbig---remove CLOTHES to reply]

In article <ovh5f.5505$cA4.1338@newsfe3-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> Let me answer it this way: the cosmological constant currently dominates
> the expansion of the universe. The matter and photons are just being
> carried along for the ride. (This wasn't always the case. Earlier the
> matter dominated, and before that the photons.) The dominant flow of
> energy, today, is from the Hubble expansion to the cosmological constant,
> each one growing in magnitude although of opposite sign. Without a
> cosmological constant the presently insignificant flow from the photons
> (via the red shift) to the Hubble factor would dominate, as it did in the
> early universe. i.e. the direction of the energy flow would be reversed.

You seem to think that this "flow" is some sort of physical
transformation. Can you explain this in more detail?

> > Imagine the Einstein static universe. There is no expansion. Yet there
> > is an energy density due to the cosmological constant. How does it
> > "come from" the (non-existent) expansion in this case? What about a
> > negative cosmological constant?
>
> Indeed, as you point out, in Einstein's original static universe the
> cosmological constant was negative

The cosmological constant in the Einstein static universe is positive.
I was providing two examples: one in which there can be no "flow" since
there is no expansion, and in addition mentioning that the cosmological
constant can, theoretically, be negative while the expansion has the
same sign as it has today. I don't see how you can say that there is a
"flow" in all three cases (static, negative cosmological constant,
positive cosmological constant) or, if you don't claim this (which seems
to be the case), how you can say that in some cases (like the one which
corresponds to our universe), there IS a flow.

Let me EXAGGERATE. Fewer children are born where fewer storks nest.
Does this prove that storks bring children? No. It is due to a common
cause (fewer children are born in industrialised societies, and storks
are less common here as well). Historically, global warming is also
negatively correlated with the number of pirates sailing the seven seas,
but that doesn't mean that pirates prevent global warming. You seem to
be saying a) there is expansion and b) there is a cosmological constant
and then claiming that one "causes" the other in some sense.

> > I think Edward Harrison has explained rather well what is meant by
> > "energy is not conserved in the expanding universe". Do you disagree
> > with his analysis?
>
> Yes. If I understand Harrison's argument it is that pressure and pressure
> gradients mediate the transfer of energy in the thermodynamic dE = -P dV
> equation (which has a cosmological equivalent), which describes the
> expansion of, say, a pressurised gas against its environment. But in the
> universe there is no exterior system to push against and hence no transfer
> of energy. Instead he concludes the red-shift energy is lost and not
> transferred. I think he is being lead astray by the thermodynamic
> analogy with pressure. Pressure is the result of particles (including
> photons) with momenta, which have de Broglie wavelengths. It is the
> stretching of the wavelengths by the Hubble expansion which causes the
> loss of momenta and the red-shift. The loss of radiation pressure is a
> consequence of this stretching and not a mediating mechanism; no
> pressure gradient or exterior system is required.

Harrison (in his textbook) explicitly states that the universe is not
like a steam engine, so I think the disagreement has another cause.

[Phillip Helbig---remove CLOTHES to reply]

In article <ovh5f.5505$cA4.1338@newsfe3-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> Let me answer it this way: the cosmological constant currently dominates
> the expansion of the universe. The matter and photons are just being
> carried along for the ride. (This wasn't always the case. Earlier the
> matter dominated, and before that the photons.) The dominant flow of
> energy, today, is from the Hubble expansion to the cosmological constant,
> each one growing in magnitude although of opposite sign. Without a
> cosmological constant the presently insignificant flow from the photons
> (via the red shift) to the Hubble factor would dominate, as it did in the
> early universe. i.e. the direction of the energy flow would be reversed.

You seem to think that this "flow" is some sort of physical
transformation. Can you explain this in more detail?

> > Imagine the Einstein static universe. There is no expansion. Yet there
> > is an energy density due to the cosmological constant. How does it
> > "come from" the (non-existent) expansion in this case? What about a
> > negative cosmological constant?
>
> Indeed, as you point out, in Einstein's original static universe the
> cosmological constant was negative

The cosmological constant in the Einstein static universe is positive.
I was providing two examples: one in which there can be no "flow" since
there is no expansion, and in addition mentioning that the cosmological
constant can, theoretically, be negative while the expansion has the
same sign as it has today. I don't see how you can say that there is a
"flow" in all three cases (static, negative cosmological constant,
positive cosmological constant) or, if you don't claim this (which seems
to be the case), how you can say that in some cases (like the one which
corresponds to our universe), there IS a flow.

Let me EXAGGERATE. Fewer children are born where fewer storks nest.
Does this prove that storks bring children? No. It is due to a common
cause (fewer children are born in industrialised societies, and storks
are less common here as well). Historically, global warming is also
negatively correlated with the number of pirates sailing the seven seas,
but that doesn't mean that pirates prevent global warming. You seem to
be saying a) there is expansion and b) there is a cosmological constant
and then claiming that one "causes" the other in some sense.

> > I think Edward Harrison has explained rather well what is meant by
> > "energy is not conserved in the expanding universe". Do you disagree
> > with his analysis?
>
> Yes. If I understand Harrison's argument it is that pressure and pressure
> gradients mediate the transfer of energy in the thermodynamic dE = -P dV
> equation (which has a cosmological equivalent), which describes the
> expansion of, say, a pressurised gas against its environment. But in the
> universe there is no exterior system to push against and hence no transfer
> of energy. Instead he concludes the red-shift energy is lost and not
> transferred. I think he is being lead astray by the thermodynamic
> analogy with pressure. Pressure is the result of particles (including
> photons) with momenta, which have de Broglie wavelengths. It is the
> stretching of the wavelengths by the Hubble expansion which causes the
> loss of momenta and the red-shift. The loss of radiation pressure is a
> consequence of this stretching and not a mediating mechanism; no
> pressure gradient or exterior system is required.

Harrison (in his textbook) explicitly states that the universe is not
like a steam engine, so I think the disagreement has another cause.

[Phillip Helbig---remove CLOTHES to reply]

In article <ovh5f.5505$cA4.1338@newsfe3-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> Let me answer it this way: the cosmological constant currently dominates
> the expansion of the universe. The matter and photons are just being
> carried along for the ride. (This wasn't always the case. Earlier the
> matter dominated, and before that the photons.) The dominant flow of
> energy, today, is from the Hubble expansion to the cosmological constant,
> each one growing in magnitude although of opposite sign. Without a
> cosmological constant the presently insignificant flow from the photons
> (via the red shift) to the Hubble factor would dominate, as it did in the
> early universe. i.e. the direction of the energy flow would be reversed.

You seem to think that this "flow" is some sort of physical
transformation. Can you explain this in more detail?

> > Imagine the Einstein static universe. There is no expansion. Yet there
> > is an energy density due to the cosmological constant. How does it
> > "come from" the (non-existent) expansion in this case? What about a
> > negative cosmological constant?
>
> Indeed, as you point out, in Einstein's original static universe the
> cosmological constant was negative

The cosmological constant in the Einstein static universe is positive.
I was providing two examples: one in which there can be no "flow" since
there is no expansion, and in addition mentioning that the cosmological
constant can, theoretically, be negative while the expansion has the
same sign as it has today. I don't see how you can say that there is a
"flow" in all three cases (static, negative cosmological constant,
positive cosmological constant) or, if you don't claim this (which seems
to be the case), how you can say that in some cases (like the one which
corresponds to our universe), there IS a flow.

Let me EXAGGERATE. Fewer children are born where fewer storks nest.
Does this prove that storks bring children? No. It is due to a common
cause (fewer children are born in industrialised societies, and storks
are less common here as well). Historically, global warming is also
negatively correlated with the number of pirates sailing the seven seas,
but that doesn't mean that pirates prevent global warming. You seem to
be saying a) there is expansion and b) there is a cosmological constant
and then claiming that one "causes" the other in some sense.

> > I think Edward Harrison has explained rather well what is meant by
> > "energy is not conserved in the expanding universe". Do you disagree
> > with his analysis?
>
> Yes. If I understand Harrison's argument it is that pressure and pressure
> gradients mediate the transfer of energy in the thermodynamic dE = -P dV
> equation (which has a cosmological equivalent), which describes the
> expansion of, say, a pressurised gas against its environment. But in the
> universe there is no exterior system to push against and hence no transfer
> of energy. Instead he concludes the red-shift energy is lost and not
> transferred. I think he is being lead astray by the thermodynamic
> analogy with pressure. Pressure is the result of particles (including
> photons) with momenta, which have de Broglie wavelengths. It is the
> stretching of the wavelengths by the Hubble expansion which causes the
> loss of momenta and the red-shift. The loss of radiation pressure is a
> consequence of this stretching and not a mediating mechanism; no
> pressure gradient or exterior system is required.

Harrison (in his textbook) explicitly states that the universe is not
like a steam engine, so I think the disagreement has another cause.

[Phillip Helbig---remove CLOTHES to reply]

In article <ovh5f.5505$cA4.1338@newsfe3-gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes:

> Let me answer it this way: the cosmological constant currently dominates
> the expansion of the universe. The matter and photons are just being
> carried along for the ride. (This wasn't always the case. Earlier the
> matter dominated, and before that the photons.) The dominant flow of
> energy, today, is from the Hubble expansion to the cosmological constant,
> each one growing in magnitude although of opposite sign. Without a
> cosmological constant the presently insignificant flow from the photons
> (via the red shift) to the Hubble factor would dominate, as it did in the
> early universe. i.e. the direction of the energy flow would be reversed.

You seem to think that this "flow" is some sort of physical
transformation. Can you explain this in more detail?

> > Imagine the Einstein static universe. There is no expansion. Yet there
> > is an energy density due to the cosmological constant. How does it
> > "come from" the (non-existent) expansion in this case? What about a
> > negative cosmological constant?
>
> Indeed, as you point out, in Einstein's original static universe the
> cosmological constant was negative

The cosmological constant in the Einstein static universe is positive.
I was providing two examples: one in which there can be no "flow" since
there is no expansion, and in addition mentioning that the cosmological
constant can, theoretically, be negative while the expansion has the
same sign as it has today. I don't see how you can say that there is a
"flow" in all three cases (static, negative cosmological constant,
positive cosmological constant) or, if you don't claim this (which seems
to be the case), how you can say that in some cases (like the one which
corresponds to our universe), there IS a flow.

Let me EXAGGERATE. Fewer children are born where fewer storks nest.
Does this prove that storks bring children? No. It is due to a common
cause (fewer children are born in industrialised societies, and storks
are less common here as well). Historically, global warming is also
negatively correlated with the number of pirates sailing the seven seas,
but that doesn't mean that pirates prevent global warming. You seem to
be saying a) there is expansion and b) there is a cosmological constant
and then claiming that one "causes" the other in some sense.

> > I think Edward Harrison has explained rather well what is meant by
> > "energy is not conserved in the expanding universe". Do you disagree
> > with his analysis?
>
> Yes. If I understand Harrison's argument it is that pressure and pressure
> gradients mediate the transfer of energy in the thermodynamic dE = -P dV
> equation (which has a cosmological equivalent), which describes the
> expansion of, say, a pressurised gas against its environment. But in the
> universe there is no exterior system to push against and hence no transfer
> of energy. Instead he concludes the red-shift energy is lost and not
> transferred. I think he is being lead astray by the thermodynamic
> analogy with pressure. Pressure is the result of particles (including
> photons) with momenta, which have de Broglie wavelengths. It is the
> stretching of the wavelengths by the Hubble expansion which causes the
> loss of momenta and the red-shift. The loss of radiation pressure is a
> consequence of this stretching and not a mediating mechanism; no
> pressure gradient or exterior system is required.

Harrison (in his textbook) explicitly states that the universe is not
like a steam engine, so I think the disagreement has another cause.

[Michael C Price]

Me:
>> The dominant flow of energy, today, is from the Hubble expansion
>> to the cosmological constant, each one growing in magnitude
>> although of opposite sign. Without a cosmological constant
>> the presently insignificant flow from the photons (via the red shift)
>> to the Hubble factor would dominate, as it did in the early
>> universe. i.e. the direction of the energy flow would be reversed.
>
Phillip:
> You seem to think that this "flow" is some sort of physical
> transformation. Can you explain this in more detail?

For the cosmological constant, no. For the red-shift (about which
we know more) yes. I would say that the photons are doing work
on the Hubble expansion, resulting in a loss of photonic energy
and a corresponding increase in Hubble energy/ decrease in Hubble
factor.

>>> Imagine the Einstein static universe. There is no expansion.
>>> Yet there is an energy density due to the cosmological constant.
>>> How does it "come from" the (non-existent) expansion in this
>>> case? What about a negative cosmological constant?
>>
>> Indeed, as you point out, in Einstein's original static universe the
>> cosmological constant was negative
>
> The cosmological constant in the Einstein static universe is
> positive.

Perhaps -- but not if we wish to have a spatially flat static universe.
Granted that Einstein was modelling a spatially closed static universe
which has an extra curvature term to mess with. I made the
assumption of flatness without really thinking about it -- probably as
result of assuming a post-inflationary scenario.

> I was providing two examples: one in which there can be no "flow"
> since there is no expansion, and in addition mentioning that the
> cosmological constant can, theoretically, be negative while the
> expansion has the same sign as it has today. I don't see how you
> can say that there is a "flow" in all three cases (static, negative
> cosmological constant, positive cosmological constant)

Neither do I, which is why I didn't say it.

> or, if you don't claim this (which seems to be the case), how
> you can say that in some cases (like the one which
> corresponds to our universe), there IS a flow.

Well, it's quite simple. The lack of flow in the static case has no
bearing on the dynamic case which pertains to our universe.

> [..........] You seem to be saying a) there is expansion and
> b) there is a cosmological constant and then claiming that one
> "causes" the other in some sense.

I'm more interested in the red-shift, which was the example you raised
to demonstrate non-conservation of energy; the issue of causality is
strongly suggested by modelling universes which only differ in the
amount of radiation *or* in the ratio of hot to cold matter. As I
previously said:

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Comments?

>
>>> I think Edward Harrison has explained rather well what is meant
>>> by "energy is not conserved in the expanding universe". Do you
>>> disagree with his analysis?
>>
>> Yes. If I understand Harrison's argument it is that pressure and
>> pressure gradients mediate the transfer of energy in the
>> thermodynamic dE = -P dV equation (which has a cosmological
>> equivalent), which describes the expansion of, say, a pressurised
>> gas against its environment. But in the universe there is no exterior
>> system to push against and hence no transfer of energy. Instead
>> he concludes the red-shift energy is lost and not transferred. I think
>> he is being lead astray by the thermodynamic analogy with pressure.
>> Pressure is the result of particles (including photons) with momenta,
>> which have de Broglie wavelengths. It is the stretching of the
>> wavelengths by the Hubble expansion which causes the loss of
>> momenta and the red-shift. The loss of radiation pressure is a
> > consequence of this stretching and not a mediating mechanism; no
> > pressure gradient or exterior system is required.
>
> Harrison (in his textbook) explicitly states that the universe is not
> like a steam engine, so I think the disagreement has another cause.

You're missing the point if you think that counters my explanation.
Of course the universe is not like a steam engine -- for one thing
there is no exterior system. Since you have the textbook, please
explain Harrison's more subtle argument. BTW the stuff about
Harrison and pressure gradients I took from your May 9 1995 post
here on s.p.r, entitled "Question posed in Discover Magazine".

Here's what you said:
***************************************
The question of energy conservation in cosmology is a more
complex issue. Edward Harrison gives an excellent discussion
in his COSMOLOGY: THE SCIENCE OF THE UNIVERSE,
which I highly recommend. Especially those interested in
more philosophic issues involving basic principles and those
wanting to find more detailed information on issues which are
given short shrift in most cosmology books should read this book.
The mathematics is kept to a minimum. There is no simplification
of difficult topics, but rather explanation. This makes the book
longer than most while still remaining more an introductory work
than a reference for the working cosmologist, but makes it
ideal for the armchair cosmologist.

Basically, energy is NOT conserved in an expanding universe.

Consider radiation. The number of photons is constant, but they
are redshifted, reducing the individual and hence the total energy.
The (rest)energy of matter doesn't change. Where does the
energy go? It certainly doesn't do work in the expansion, as is
sometimes claimed, since there is no pressure gradient.
***************************************
Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> The dominant flow of energy, today, is from the Hubble expansion
>> to the cosmological constant, each one growing in magnitude
>> although of opposite sign. Without a cosmological constant
>> the presently insignificant flow from the photons (via the red shift)
>> to the Hubble factor would dominate, as it did in the early
>> universe. i.e. the direction of the energy flow would be reversed.
>
Phillip:
> You seem to think that this "flow" is some sort of physical
> transformation. Can you explain this in more detail?

For the cosmological constant, no. For the red-shift (about which
we know more) yes. I would say that the photons are doing work
on the Hubble expansion, resulting in a loss of photonic energy
and a corresponding increase in Hubble energy/ decrease in Hubble
factor.

>>> Imagine the Einstein static universe. There is no expansion.
>>> Yet there is an energy density due to the cosmological constant.
>>> How does it "come from" the (non-existent) expansion in this
>>> case? What about a negative cosmological constant?
>>
>> Indeed, as you point out, in Einstein's original static universe the
>> cosmological constant was negative
>
> The cosmological constant in the Einstein static universe is
> positive.

Perhaps -- but not if we wish to have a spatially flat static universe.
Granted that Einstein was modelling a spatially closed static universe
which has an extra curvature term to mess with. I made the
assumption of flatness without really thinking about it -- probably as
result of assuming a post-inflationary scenario.

> I was providing two examples: one in which there can be no "flow"
> since there is no expansion, and in addition mentioning that the
> cosmological constant can, theoretically, be negative while the
> expansion has the same sign as it has today. I don't see how you
> can say that there is a "flow" in all three cases (static, negative
> cosmological constant, positive cosmological constant)

Neither do I, which is why I didn't say it.

> or, if you don't claim this (which seems to be the case), how
> you can say that in some cases (like the one which
> corresponds to our universe), there IS a flow.

Well, it's quite simple. The lack of flow in the static case has no
bearing on the dynamic case which pertains to our universe.

> [..........] You seem to be saying a) there is expansion and
> b) there is a cosmological constant and then claiming that one
> "causes" the other in some sense.

I'm more interested in the red-shift, which was the example you raised
to demonstrate non-conservation of energy; the issue of causality is
strongly suggested by modelling universes which only differ in the
amount of radiation *or* in the ratio of hot to cold matter. As I
previously said:

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Comments?

>
>>> I think Edward Harrison has explained rather well what is meant
>>> by "energy is not conserved in the expanding universe". Do you
>>> disagree with his analysis?
>>
>> Yes. If I understand Harrison's argument it is that pressure and
>> pressure gradients mediate the transfer of energy in the
>> thermodynamic dE = -P dV equation (which has a cosmological
>> equivalent), which describes the expansion of, say, a pressurised
>> gas against its environment. But in the universe there is no exterior
>> system to push against and hence no transfer of energy. Instead
>> he concludes the red-shift energy is lost and not transferred. I think
>> he is being lead astray by the thermodynamic analogy with pressure.
>> Pressure is the result of particles (including photons) with momenta,
>> which have de Broglie wavelengths. It is the stretching of the
>> wavelengths by the Hubble expansion which causes the loss of
>> momenta and the red-shift. The loss of radiation pressure is a
> > consequence of this stretching and not a mediating mechanism; no
> > pressure gradient or exterior system is required.
>
> Harrison (in his textbook) explicitly states that the universe is not
> like a steam engine, so I think the disagreement has another cause.

You're missing the point if you think that counters my explanation.
Of course the universe is not like a steam engine -- for one thing
there is no exterior system. Since you have the textbook, please
explain Harrison's more subtle argument. BTW the stuff about
Harrison and pressure gradients I took from your May 9 1995 post
here on s.p.r, entitled "Question posed in Discover Magazine".

Here's what you said:
***************************************
The question of energy conservation in cosmology is a more
complex issue. Edward Harrison gives an excellent discussion
in his COSMOLOGY: THE SCIENCE OF THE UNIVERSE,
which I highly recommend. Especially those interested in
more philosophic issues involving basic principles and those
wanting to find more detailed information on issues which are
given short shrift in most cosmology books should read this book.
The mathematics is kept to a minimum. There is no simplification
of difficult topics, but rather explanation. This makes the book
longer than most while still remaining more an introductory work
than a reference for the working cosmologist, but makes it
ideal for the armchair cosmologist.

Basically, energy is NOT conserved in an expanding universe.

Consider radiation. The number of photons is constant, but they
are redshifted, reducing the individual and hence the total energy.
The (rest)energy of matter doesn't change. Where does the
energy go? It certainly doesn't do work in the expansion, as is
sometimes claimed, since there is no pressure gradient.
***************************************
Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> The dominant flow of energy, today, is from the Hubble expansion
>> to the cosmological constant, each one growing in magnitude
>> although of opposite sign. Without a cosmological constant
>> the presently insignificant flow from the photons (via the red shift)
>> to the Hubble factor would dominate, as it did in the early
>> universe. i.e. the direction of the energy flow would be reversed.
>
Phillip:
> You seem to think that this "flow" is some sort of physical
> transformation. Can you explain this in more detail?

For the cosmological constant, no. For the red-shift (about which
we know more) yes. I would say that the photons are doing work
on the Hubble expansion, resulting in a loss of photonic energy
and a corresponding increase in Hubble energy/ decrease in Hubble
factor.

>>> Imagine the Einstein static universe. There is no expansion.
>>> Yet there is an energy density due to the cosmological constant.
>>> How does it "come from" the (non-existent) expansion in this
>>> case? What about a negative cosmological constant?
>>
>> Indeed, as you point out, in Einstein's original static universe the
>> cosmological constant was negative
>
> The cosmological constant in the Einstein static universe is
> positive.

Perhaps -- but not if we wish to have a spatially flat static universe.
Granted that Einstein was modelling a spatially closed static universe
which has an extra curvature term to mess with. I made the
assumption of flatness without really thinking about it -- probably as
result of assuming a post-inflationary scenario.

> I was providing two examples: one in which there can be no "flow"
> since there is no expansion, and in addition mentioning that the
> cosmological constant can, theoretically, be negative while the
> expansion has the same sign as it has today. I don't see how you
> can say that there is a "flow" in all three cases (static, negative
> cosmological constant, positive cosmological constant)

Neither do I, which is why I didn't say it.

> or, if you don't claim this (which seems to be the case), how
> you can say that in some cases (like the one which
> corresponds to our universe), there IS a flow.

Well, it's quite simple. The lack of flow in the static case has no
bearing on the dynamic case which pertains to our universe.

> [..........] You seem to be saying a) there is expansion and
> b) there is a cosmological constant and then claiming that one
> "causes" the other in some sense.

I'm more interested in the red-shift, which was the example you raised
to demonstrate non-conservation of energy; the issue of causality is
strongly suggested by modelling universes which only differ in the
amount of radiation *or* in the ratio of hot to cold matter. As I
previously said:

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Comments?

>
>>> I think Edward Harrison has explained rather well what is meant
>>> by "energy is not conserved in the expanding universe". Do you
>>> disagree with his analysis?
>>
>> Yes. If I understand Harrison's argument it is that pressure and
>> pressure gradients mediate the transfer of energy in the
>> thermodynamic dE = -P dV equation (which has a cosmological
>> equivalent), which describes the expansion of, say, a pressurised
>> gas against its environment. But in the universe there is no exterior
>> system to push against and hence no transfer of energy. Instead
>> he concludes the red-shift energy is lost and not transferred. I think
>> he is being lead astray by the thermodynamic analogy with pressure.
>> Pressure is the result of particles (including photons) with momenta,
>> which have de Broglie wavelengths. It is the stretching of the
>> wavelengths by the Hubble expansion which causes the loss of
>> momenta and the red-shift. The loss of radiation pressure is a
> > consequence of this stretching and not a mediating mechanism; no
> > pressure gradient or exterior system is required.
>
> Harrison (in his textbook) explicitly states that the universe is not
> like a steam engine, so I think the disagreement has another cause.

You're missing the point if you think that counters my explanation.
Of course the universe is not like a steam engine -- for one thing
there is no exterior system. Since you have the textbook, please
explain Harrison's more subtle argument. BTW the stuff about
Harrison and pressure gradients I took from your May 9 1995 post
here on s.p.r, entitled "Question posed in Discover Magazine".

Here's what you said:
***************************************
The question of energy conservation in cosmology is a more
complex issue. Edward Harrison gives an excellent discussion
in his COSMOLOGY: THE SCIENCE OF THE UNIVERSE,
which I highly recommend. Especially those interested in
more philosophic issues involving basic principles and those
wanting to find more detailed information on issues which are
given short shrift in most cosmology books should read this book.
The mathematics is kept to a minimum. There is no simplification
of difficult topics, but rather explanation. This makes the book
longer than most while still remaining more an introductory work
than a reference for the working cosmologist, but makes it
ideal for the armchair cosmologist.

Basically, energy is NOT conserved in an expanding universe.

Consider radiation. The number of photons is constant, but they
are redshifted, reducing the individual and hence the total energy.
The (rest)energy of matter doesn't change. Where does the
energy go? It certainly doesn't do work in the expansion, as is
sometimes claimed, since there is no pressure gradient.
***************************************
Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> The dominant flow of energy, today, is from the Hubble expansion
>> to the cosmological constant, each one growing in magnitude
>> although of opposite sign. Without a cosmological constant
>> the presently insignificant flow from the photons (via the red shift)
>> to the Hubble factor would dominate, as it did in the early
>> universe. i.e. the direction of the energy flow would be reversed.
>
Phillip:
> You seem to think that this "flow" is some sort of physical
> transformation. Can you explain this in more detail?

For the cosmological constant, no. For the red-shift (about which
we know more) yes. I would say that the photons are doing work
on the Hubble expansion, resulting in a loss of photonic energy
and a corresponding increase in Hubble energy/ decrease in Hubble
factor.

>>> Imagine the Einstein static universe. There is no expansion.
>>> Yet there is an energy density due to the cosmological constant.
>>> How does it "come from" the (non-existent) expansion in this
>>> case? What about a negative cosmological constant?
>>
>> Indeed, as you point out, in Einstein's original static universe the
>> cosmological constant was negative
>
> The cosmological constant in the Einstein static universe is
> positive.

Perhaps -- but not if we wish to have a spatially flat static universe.
Granted that Einstein was modelling a spatially closed static universe
which has an extra curvature term to mess with. I made the
assumption of flatness without really thinking about it -- probably as
result of assuming a post-inflationary scenario.

> I was providing two examples: one in which there can be no "flow"
> since there is no expansion, and in addition mentioning that the
> cosmological constant can, theoretically, be negative while the
> expansion has the same sign as it has today. I don't see how you
> can say that there is a "flow" in all three cases (static, negative
> cosmological constant, positive cosmological constant)

Neither do I, which is why I didn't say it.

> or, if you don't claim this (which seems to be the case), how
> you can say that in some cases (like the one which
> corresponds to our universe), there IS a flow.

Well, it's quite simple. The lack of flow in the static case has no
bearing on the dynamic case which pertains to our universe.

> [..........] You seem to be saying a) there is expansion and
> b) there is a cosmological constant and then claiming that one
> "causes" the other in some sense.

I'm more interested in the red-shift, which was the example you raised
to demonstrate non-conservation of energy; the issue of causality is
strongly suggested by modelling universes which only differ in the
amount of radiation *or* in the ratio of hot to cold matter. As I
previously said:

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Comments?

>
>>> I think Edward Harrison has explained rather well what is meant
>>> by "energy is not conserved in the expanding universe". Do you
>>> disagree with his analysis?
>>
>> Yes. If I understand Harrison's argument it is that pressure and
>> pressure gradients mediate the transfer of energy in the
>> thermodynamic dE = -P dV equation (which has a cosmological
>> equivalent), which describes the expansion of, say, a pressurised
>> gas against its environment. But in the universe there is no exterior
>> system to push against and hence no transfer of energy. Instead
>> he concludes the red-shift energy is lost and not transferred. I think
>> he is being lead astray by the thermodynamic analogy with pressure.
>> Pressure is the result of particles (including photons) with momenta,
>> which have de Broglie wavelengths. It is the stretching of the
>> wavelengths by the Hubble expansion which causes the loss of
>> momenta and the red-shift. The loss of radiation pressure is a
> > consequence of this stretching and not a mediating mechanism; no
> > pressure gradient or exterior system is required.
>
> Harrison (in his textbook) explicitly states that the universe is not
> like a steam engine, so I think the disagreement has another cause.

You're missing the point if you think that counters my explanation.
Of course the universe is not like a steam engine -- for one thing
there is no exterior system. Since you have the textbook, please
explain Harrison's more subtle argument. BTW the stuff about
Harrison and pressure gradients I took from your May 9 1995 post
here on s.p.r, entitled "Question posed in Discover Magazine".

Here's what you said:
***************************************
The question of energy conservation in cosmology is a more
complex issue. Edward Harrison gives an excellent discussion
in his COSMOLOGY: THE SCIENCE OF THE UNIVERSE,
which I highly recommend. Especially those interested in
more philosophic issues involving basic principles and those
wanting to find more detailed information on issues which are
given short shrift in most cosmology books should read this book.
The mathematics is kept to a minimum. There is no simplification
of difficult topics, but rather explanation. This makes the book
longer than most while still remaining more an introductory work
than a reference for the working cosmologist, but makes it
ideal for the armchair cosmologist.

Basically, energy is NOT conserved in an expanding universe.

Consider radiation. The number of photons is constant, but they
are redshifted, reducing the individual and hence the total energy.
The (rest)energy of matter doesn't change. Where does the
energy go? It certainly doesn't do work in the expansion, as is
sometimes claimed, since there is no pressure gradient.
***************************************
Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> The dominant flow of energy, today, is from the Hubble expansion
>> to the cosmological constant, each one growing in magnitude
>> although of opposite sign. Without a cosmological constant
>> the presently insignificant flow from the photons (via the red shift)
>> to the Hubble factor would dominate, as it did in the early
>> universe. i.e. the direction of the energy flow would be reversed.
>
Phillip:
> You seem to think that this "flow" is some sort of physical
> transformation. Can you explain this in more detail?

For the cosmological constant, no. For the red-shift (about which
we know more) yes. I would say that the photons are doing work
on the Hubble expansion, resulting in a loss of photonic energy
and a corresponding increase in Hubble energy/ decrease in Hubble
factor.

>>> Imagine the Einstein static universe. There is no expansion.
>>> Yet there is an energy density due to the cosmological constant.
>>> How does it "come from" the (non-existent) expansion in this
>>> case? What about a negative cosmological constant?
>>
>> Indeed, as you point out, in Einstein's original static universe the
>> cosmological constant was negative
>
> The cosmological constant in the Einstein static universe is
> positive.

Perhaps -- but not if we wish to have a spatially flat static universe.
Granted that Einstein was modelling a spatially closed static universe
which has an extra curvature term to mess with. I made the
assumption of flatness without really thinking about it -- probably as
result of assuming a post-inflationary scenario.

> I was providing two examples: one in which there can be no "flow"
> since there is no expansion, and in addition mentioning that the
> cosmological constant can, theoretically, be negative while the
> expansion has the same sign as it has today. I don't see how you
> can say that there is a "flow" in all three cases (static, negative
> cosmological constant, positive cosmological constant)

Neither do I, which is why I didn't say it.

> or, if you don't claim this (which seems to be the case), how
> you can say that in some cases (like the one which
> corresponds to our universe), there IS a flow.

Well, it's quite simple. The lack of flow in the static case has no
bearing on the dynamic case which pertains to our universe.

> [..........] You seem to be saying a) there is expansion and
> b) there is a cosmological constant and then claiming that one
> "causes" the other in some sense.

I'm more interested in the red-shift, which was the example you raised
to demonstrate non-conservation of energy; the issue of causality is
strongly suggested by modelling universes which only differ in the
amount of radiation *or* in the ratio of hot to cold matter. As I
previously said:

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Comments?

>
>>> I think Edward Harrison has explained rather well what is meant
>>> by "energy is not conserved in the expanding universe". Do you
>>> disagree with his analysis?
>>
>> Yes. If I understand Harrison's argument it is that pressure and
>> pressure gradients mediate the transfer of energy in the
>> thermodynamic dE = -P dV equation (which has a cosmological
>> equivalent), which describes the expansion of, say, a pressurised
>> gas against its environment. But in the universe there is no exterior
>> system to push against and hence no transfer of energy. Instead
>> he concludes the red-shift energy is lost and not transferred. I think
>> he is being lead astray by the thermodynamic analogy with pressure.
>> Pressure is the result of particles (including photons) with momenta,
>> which have de Broglie wavelengths. It is the stretching of the
>> wavelengths by the Hubble expansion which causes the loss of
>> momenta and the red-shift. The loss of radiation pressure is a
> > consequence of this stretching and not a mediating mechanism; no
> > pressure gradient or exterior system is required.
>
> Harrison (in his textbook) explicitly states that the universe is not
> like a steam engine, so I think the disagreement has another cause.

You're missing the point if you think that counters my explanation.
Of course the universe is not like a steam engine -- for one thing
there is no exterior system. Since you have the textbook, please
explain Harrison's more subtle argument. BTW the stuff about
Harrison and pressure gradients I took from your May 9 1995 post
here on s.p.r, entitled "Question posed in Discover Magazine".

Here's what you said:
***************************************
The question of energy conservation in cosmology is a more
complex issue. Edward Harrison gives an excellent discussion
in his COSMOLOGY: THE SCIENCE OF THE UNIVERSE,
which I highly recommend. Especially those interested in
more philosophic issues involving basic principles and those
wanting to find more detailed information on issues which are
given short shrift in most cosmology books should read this book.
The mathematics is kept to a minimum. There is no simplification
of difficult topics, but rather explanation. This makes the book
longer than most while still remaining more an introductory work
than a reference for the working cosmologist, but makes it
ideal for the armchair cosmologist.

Basically, energy is NOT conserved in an expanding universe.

Consider radiation. The number of photons is constant, but they
are redshifted, reducing the individual and hence the total energy.
The (rest)energy of matter doesn't change. Where does the
energy go? It certainly doesn't do work in the expansion, as is
sometimes claimed, since there is no pressure gradient.
***************************************
Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> The dominant flow of energy, today, is from the Hubble expansion
>> to the cosmological constant, each one growing in magnitude
>> although of opposite sign. Without a cosmological constant
>> the presently insignificant flow from the photons (via the red shift)
>> to the Hubble factor would dominate, as it did in the early
>> universe. i.e. the direction of the energy flow would be reversed.
>
Phillip:
> You seem to think that this "flow" is some sort of physical
> transformation. Can you explain this in more detail?

For the cosmological constant, no. For the red-shift (about which
we know more) yes. I would say that the photons are doing work
on the Hubble expansion, resulting in a loss of photonic energy
and a corresponding increase in Hubble energy/ decrease in Hubble
factor.

>>> Imagine the Einstein static universe. There is no expansion.
>>> Yet there is an energy density due to the cosmological constant.
>>> How does it "come from" the (non-existent) expansion in this
>>> case? What about a negative cosmological constant?
>>
>> Indeed, as you point out, in Einstein's original static universe the
>> cosmological constant was negative
>
> The cosmological constant in the Einstein static universe is
> positive.

Perhaps -- but not if we wish to have a spatially flat static universe.
Granted that Einstein was modelling a spatially closed static universe
which has an extra curvature term to mess with. I made the
assumption of flatness without really thinking about it -- probably as
result of assuming a post-inflationary scenario.

> I was providing two examples: one in which there can be no "flow"
> since there is no expansion, and in addition mentioning that the
> cosmological constant can, theoretically, be negative while the
> expansion has the same sign as it has today. I don't see how you
> can say that there is a "flow" in all three cases (static, negative
> cosmological constant, positive cosmological constant)

Neither do I, which is why I didn't say it.

> or, if you don't claim this (which seems to be the case), how
> you can say that in some cases (like the one which
> corresponds to our universe), there IS a flow.

Well, it's quite simple. The lack of flow in the static case has no
bearing on the dynamic case which pertains to our universe.

> [..........] You seem to be saying a) there is expansion and
> b) there is a cosmological constant and then claiming that one
> "causes" the other in some sense.

I'm more interested in the red-shift, which was the example you raised
to demonstrate non-conservation of energy; the issue of causality is
strongly suggested by modelling universes which only differ in the
amount of radiation *or* in the ratio of hot to cold matter. As I
previously said:

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Comments?

>
>>> I think Edward Harrison has explained rather well what is meant
>>> by "energy is not conserved in the expanding universe". Do you
>>> disagree with his analysis?
>>
>> Yes. If I understand Harrison's argument it is that pressure and
>> pressure gradients mediate the transfer of energy in the
>> thermodynamic dE = -P dV equation (which has a cosmological
>> equivalent), which describes the expansion of, say, a pressurised
>> gas against its environment. But in the universe there is no exterior
>> system to push against and hence no transfer of energy. Instead
>> he concludes the red-shift energy is lost and not transferred. I think
>> he is being lead astray by the thermodynamic analogy with pressure.
>> Pressure is the result of particles (including photons) with momenta,
>> which have de Broglie wavelengths. It is the stretching of the
>> wavelengths by the Hubble expansion which causes the loss of
>> momenta and the red-shift. The loss of radiation pressure is a
> > consequence of this stretching and not a mediating mechanism; no
> > pressure gradient or exterior system is required.
>
> Harrison (in his textbook) explicitly states that the universe is not
> like a steam engine, so I think the disagreement has another cause.

You're missing the point if you think that counters my explanation.
Of course the universe is not like a steam engine -- for one thing
there is no exterior system. Since you have the textbook, please
explain Harrison's more subtle argument. BTW the stuff about
Harrison and pressure gradients I took from your May 9 1995 post
here on s.p.r, entitled "Question posed in Discover Magazine".

Here's what you said:
***************************************
The question of energy conservation in cosmology is a more
complex issue. Edward Harrison gives an excellent discussion
in his COSMOLOGY: THE SCIENCE OF THE UNIVERSE,
which I highly recommend. Especially those interested in
more philosophic issues involving basic principles and those
wanting to find more detailed information on issues which are
given short shrift in most cosmology books should read this book.
The mathematics is kept to a minimum. There is no simplification
of difficult topics, but rather explanation. This makes the book
longer than most while still remaining more an introductory work
than a reference for the working cosmologist, but makes it
ideal for the armchair cosmologist.

Basically, energy is NOT conserved in an expanding universe.

Consider radiation. The number of photons is constant, but they
are redshifted, reducing the individual and hence the total energy.
The (rest)energy of matter doesn't change. Where does the
energy go? It certainly doesn't do work in the expansion, as is
sometimes claimed, since there is no pressure gradient.
***************************************
Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> The dominant flow of energy, today, is from the Hubble expansion
>> to the cosmological constant, each one growing in magnitude
>> although of opposite sign. Without a cosmological constant
>> the presently insignificant flow from the photons (via the red shift)
>> to the Hubble factor would dominate, as it did in the early
>> universe. i.e. the direction of the energy flow would be reversed.
>
Phillip:
> You seem to think that this "flow" is some sort of physical
> transformation. Can you explain this in more detail?

For the cosmological constant, no. For the red-shift (about which
we know more) yes. I would say that the photons are doing work
on the Hubble expansion, resulting in a loss of photonic energy
and a corresponding increase in Hubble energy/ decrease in Hubble
factor.

>>> Imagine the Einstein static universe. There is no expansion.
>>> Yet there is an energy density due to the cosmological constant.
>>> How does it "come from" the (non-existent) expansion in this
>>> case? What about a negative cosmological constant?
>>
>> Indeed, as you point out, in Einstein's original static universe the
>> cosmological constant was negative
>
> The cosmological constant in the Einstein static universe is
> positive.

Perhaps -- but not if we wish to have a spatially flat static universe.
Granted that Einstein was modelling a spatially closed static universe
which has an extra curvature term to mess with. I made the
assumption of flatness without really thinking about it -- probably as
result of assuming a post-inflationary scenario.

> I was providing two examples: one in which there can be no "flow"
> since there is no expansion, and in addition mentioning that the
> cosmological constant can, theoretically, be negative while the
> expansion has the same sign as it has today. I don't see how you
> can say that there is a "flow" in all three cases (static, negative
> cosmological constant, positive cosmological constant)

Neither do I, which is why I didn't say it.

> or, if you don't claim this (which seems to be the case), how
> you can say that in some cases (like the one which
> corresponds to our universe), there IS a flow.

Well, it's quite simple. The lack of flow in the static case has no
bearing on the dynamic case which pertains to our universe.

> [..........] You seem to be saying a) there is expansion and
> b) there is a cosmological constant and then claiming that one
> "causes" the other in some sense.

I'm more interested in the red-shift, which was the example you raised
to demonstrate non-conservation of energy; the issue of causality is
strongly suggested by modelling universes which only differ in the
amount of radiation *or* in the ratio of hot to cold matter. As I
previously said:

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Comments?

>
>>> I think Edward Harrison has explained rather well what is meant
>>> by "energy is not conserved in the expanding universe". Do you
>>> disagree with his analysis?
>>
>> Yes. If I understand Harrison's argument it is that pressure and
>> pressure gradients mediate the transfer of energy in the
>> thermodynamic dE = -P dV equation (which has a cosmological
>> equivalent), which describes the expansion of, say, a pressurised
>> gas against its environment. But in the universe there is no exterior
>> system to push against and hence no transfer of energy. Instead
>> he concludes the red-shift energy is lost and not transferred. I think
>> he is being lead astray by the thermodynamic analogy with pressure.
>> Pressure is the result of particles (including photons) with momenta,
>> which have de Broglie wavelengths. It is the stretching of the
>> wavelengths by the Hubble expansion which causes the loss of
>> momenta and the red-shift. The loss of radiation pressure is a
> > consequence of this stretching and not a mediating mechanism; no
> > pressure gradient or exterior system is required.
>
> Harrison (in his textbook) explicitly states that the universe is not
> like a steam engine, so I think the disagreement has another cause.

You're missing the point if you think that counters my explanation.
Of course the universe is not like a steam engine -- for one thing
there is no exterior system. Since you have the textbook, please
explain Harrison's more subtle argument. BTW the stuff about
Harrison and pressure gradients I took from your May 9 1995 post
here on s.p.r, entitled "Question posed in Discover Magazine".

Here's what you said:
***************************************
The question of energy conservation in cosmology is a more
complex issue. Edward Harrison gives an excellent discussion
in his COSMOLOGY: THE SCIENCE OF THE UNIVERSE,
which I highly recommend. Especially those interested in
more philosophic issues involving basic principles and those
wanting to find more detailed information on issues which are
given short shrift in most cosmology books should read this book.
The mathematics is kept to a minimum. There is no simplification
of difficult topics, but rather explanation. This makes the book
longer than most while still remaining more an introductory work
than a reference for the working cosmologist, but makes it
ideal for the armchair cosmologist.

Basically, energy is NOT conserved in an expanding universe.

Consider radiation. The number of photons is constant, but they
are redshifted, reducing the individual and hence the total energy.
The (rest)energy of matter doesn't change. Where does the
energy go? It certainly doesn't do work in the expansion, as is
sometimes claimed, since there is no pressure gradient.
***************************************
Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> The dominant flow of energy, today, is from the Hubble expansion
>> to the cosmological constant, each one growing in magnitude
>> although of opposite sign. Without a cosmological constant
>> the presently insignificant flow from the photons (via the red shift)
>> to the Hubble factor would dominate, as it did in the early
>> universe. i.e. the direction of the energy flow would be reversed.
>
Phillip:
> You seem to think that this "flow" is some sort of physical
> transformation. Can you explain this in more detail?

For the cosmological constant, no. For the red-shift (about which
we know more) yes. I would say that the photons are doing work
on the Hubble expansion, resulting in a loss of photonic energy
and a corresponding increase in Hubble energy/ decrease in Hubble
factor.

>>> Imagine the Einstein static universe. There is no expansion.
>>> Yet there is an energy density due to the cosmological constant.
>>> How does it "come from" the (non-existent) expansion in this
>>> case? What about a negative cosmological constant?
>>
>> Indeed, as you point out, in Einstein's original static universe the
>> cosmological constant was negative
>
> The cosmological constant in the Einstein static universe is
> positive.

Perhaps -- but not if we wish to have a spatially flat static universe.
Granted that Einstein was modelling a spatially closed static universe
which has an extra curvature term to mess with. I made the
assumption of flatness without really thinking about it -- probably as
result of assuming a post-inflationary scenario.

> I was providing two examples: one in which there can be no "flow"
> since there is no expansion, and in addition mentioning that the
> cosmological constant can, theoretically, be negative while the
> expansion has the same sign as it has today. I don't see how you
> can say that there is a "flow" in all three cases (static, negative
> cosmological constant, positive cosmological constant)

Neither do I, which is why I didn't say it.

> or, if you don't claim this (which seems to be the case), how
> you can say that in some cases (like the one which
> corresponds to our universe), there IS a flow.

Well, it's quite simple. The lack of flow in the static case has no
bearing on the dynamic case which pertains to our universe.

> [..........] You seem to be saying a) there is expansion and
> b) there is a cosmological constant and then claiming that one
> "causes" the other in some sense.

I'm more interested in the red-shift, which was the example you raised
to demonstrate non-conservation of energy; the issue of causality is
strongly suggested by modelling universes which only differ in the
amount of radiation *or* in the ratio of hot to cold matter. As I
previously said:

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Comments?

>
>>> I think Edward Harrison has explained rather well what is meant
>>> by "energy is not conserved in the expanding universe". Do you
>>> disagree with his analysis?
>>
>> Yes. If I understand Harrison's argument it is that pressure and
>> pressure gradients mediate the transfer of energy in the
>> thermodynamic dE = -P dV equation (which has a cosmological
>> equivalent), which describes the expansion of, say, a pressurised
>> gas against its environment. But in the universe there is no exterior
>> system to push against and hence no transfer of energy. Instead
>> he concludes the red-shift energy is lost and not transferred. I think
>> he is being lead astray by the thermodynamic analogy with pressure.
>> Pressure is the result of particles (including photons) with momenta,
>> which have de Broglie wavelengths. It is the stretching of the
>> wavelengths by the Hubble expansion which causes the loss of
>> momenta and the red-shift. The loss of radiation pressure is a
> > consequence of this stretching and not a mediating mechanism; no
> > pressure gradient or exterior system is required.
>
> Harrison (in his textbook) explicitly states that the universe is not
> like a steam engine, so I think the disagreement has another cause.

You're missing the point if you think that counters my explanation.
Of course the universe is not like a steam engine -- for one thing
there is no exterior system. Since you have the textbook, please
explain Harrison's more subtle argument. BTW the stuff about
Harrison and pressure gradients I took from your May 9 1995 post
here on s.p.r, entitled "Question posed in Discover Magazine".

Here's what you said:
***************************************
The question of energy conservation in cosmology is a more
complex issue. Edward Harrison gives an excellent discussion
in his COSMOLOGY: THE SCIENCE OF THE UNIVERSE,
which I highly recommend. Especially those interested in
more philosophic issues involving basic principles and those
wanting to find more detailed information on issues which are
given short shrift in most cosmology books should read this book.
The mathematics is kept to a minimum. There is no simplification
of difficult topics, but rather explanation. This makes the book
longer than most while still remaining more an introductory work
than a reference for the working cosmologist, but makes it
ideal for the armchair cosmologist.

Basically, energy is NOT conserved in an expanding universe.

Consider radiation. The number of photons is constant, but they
are redshifted, reducing the individual and hence the total energy.
The (rest)energy of matter doesn't change. Where does the
energy go? It certainly doesn't do work in the expansion, as is
sometimes claimed, since there is no pressure gradient.
***************************************
Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> The dominant flow of energy, today, is from the Hubble expansion
>> to the cosmological constant, each one growing in magnitude
>> although of opposite sign. Without a cosmological constant
>> the presently insignificant flow from the photons (via the red shift)
>> to the Hubble factor would dominate, as it did in the early
>> universe. i.e. the direction of the energy flow would be reversed.
>
Phillip:
> You seem to think that this "flow" is some sort of physical
> transformation. Can you explain this in more detail?

For the cosmological constant, no. For the red-shift (about which
we know more) yes. I would say that the photons are doing work
on the Hubble expansion, resulting in a loss of photonic energy
and a corresponding increase in Hubble energy/ decrease in Hubble
factor.

>>> Imagine the Einstein static universe. There is no expansion.
>>> Yet there is an energy density due to the cosmological constant.
>>> How does it "come from" the (non-existent) expansion in this
>>> case? What about a negative cosmological constant?
>>
>> Indeed, as you point out, in Einstein's original static universe the
>> cosmological constant was negative
>
> The cosmological constant in the Einstein static universe is
> positive.

Perhaps -- but not if we wish to have a spatially flat static universe.
Granted that Einstein was modelling a spatially closed static universe
which has an extra curvature term to mess with. I made the
assumption of flatness without really thinking about it -- probably as
result of assuming a post-inflationary scenario.

> I was providing two examples: one in which there can be no "flow"
> since there is no expansion, and in addition mentioning that the
> cosmological constant can, theoretically, be negative while the
> expansion has the same sign as it has today. I don't see how you
> can say that there is a "flow" in all three cases (static, negative
> cosmological constant, positive cosmological constant)

Neither do I, which is why I didn't say it.

> or, if you don't claim this (which seems to be the case), how
> you can say that in some cases (like the one which
> corresponds to our universe), there IS a flow.

Well, it's quite simple. The lack of flow in the static case has no
bearing on the dynamic case which pertains to our universe.

> [..........] You seem to be saying a) there is expansion and
> b) there is a cosmological constant and then claiming that one
> "causes" the other in some sense.

I'm more interested in the red-shift, which was the example you raised
to demonstrate non-conservation of energy; the issue of causality is
strongly suggested by modelling universes which only differ in the
amount of radiation *or* in the ratio of hot to cold matter. As I
previously said:

Look at the early evolution of the scale factor in a radiation-filled or
"hot" universe vs a matter-dominated or "cold" universe:
Hot: scale factor grows as t^1/2
Cold: scale factor grows as t^2/3

Comments?

>
>>> I think Edward Harrison has explained rather well what is meant
>>> by "energy is not conserved in the expanding universe". Do you
>>> disagree with his analysis?
>>
>> Yes. If I understand Harrison's argument it is that pressure and
>> pressure gradients mediate the transfer of energy in the
>> thermodynamic dE = -P dV equation (which has a cosmological
>> equivalent), which describes the expansion of, say, a pressurised
>> gas against its environment. But in the universe there is no exterior
>> system to push against and hence no transfer of energy. Instead
>> he concludes the red-shift energy is lost and not transferred. I think
>> he is being lead astray by the thermodynamic analogy with pressure.
>> Pressure is the result of particles (including photons) with momenta,
>> which have de Broglie wavelengths. It is the stretching of the
>> wavelengths by the Hubble expansion which causes the loss of
>> momenta and the red-shift. The loss of radiation pressure is a
> > consequence of this stretching and not a mediating mechanism; no
> > pressure gradient or exterior system is required.
>
> Harrison (in his textbook) explicitly states that the universe is not
> like a steam engine, so I think the disagreement has another cause.

You're missing the point if you think that counters my explanation.
Of course the universe is not like a steam engine -- for one thing
there is no exterior system. Since you have the textbook, please
explain Harrison's more subtle argument. BTW the stuff about
Harrison and pressure gradients I took from your May 9 1995 post
here on s.p.r, entitled "Question posed in Discover Magazine".

Here's what you said:
***************************************
The question of energy conservation in cosmology is a more
complex issue. Edward Harrison gives an excellent discussion
in his COSMOLOGY: THE SCIENCE OF THE UNIVERSE,
which I highly recommend. Especially those interested in
more philosophic issues involving basic principles and those
wanting to find more detailed information on issues which are
given short shrift in most cosmology books should read this book.
The mathematics is kept to a minimum. There is no simplification
of difficult topics, but rather explanation. This makes the book
longer than most while still remaining more an introductory work
than a reference for the working cosmologist, but makes it
ideal for the armchair cosmologist.

Basically, energy is NOT conserved in an expanding universe.

Consider radiation. The number of photons is constant, but they
are redshifted, reducing the individual and hence the total energy.
The (rest)energy of matter doesn't change. Where does the
energy go? It certainly doesn't do work in the expansion, as is
sometimes claimed, since there is no pressure gradient.
***************************************
Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Nick Maclaren]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Basically, energy is NOT conserved in an expanding universe.
|>
|> Consider radiation. The number of photons is constant, but they
|> are redshifted, reducing the individual and hence the total energy.
|> The (rest)energy of matter doesn't change. Where does the
|> energy go? It certainly doesn't do work in the expansion, as is
|> sometimes claimed, since there is no pressure gradient.

OK. But only provided that there is no compensatory factor we
don't know about. For example, people have speculated that there
is some 'dark matter' with ill-defined characteristics - can we
be sure that the energy isn't being transferred to that?

Personally, I think that is a daft hypothesis, but no dafter than
many that have been proposed in all seriousness by very eminent
scientists :-)

You have a good point in that the conservation of energy isn't
known to be true on a cosmological scale, and isn't a direct
consequence of any currently primary theory. But exactly the
same is true for the invariance of physical constants, and many
other cherished beliefs.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Basically, energy is NOT conserved in an expanding universe.
|>
|> Consider radiation. The number of photons is constant, but they
|> are redshifted, reducing the individual and hence the total energy.
|> The (rest)energy of matter doesn't change. Where does the
|> energy go? It certainly doesn't do work in the expansion, as is
|> sometimes claimed, since there is no pressure gradient.

OK. But only provided that there is no compensatory factor we
don't know about. For example, people have speculated that there
is some 'dark matter' with ill-defined characteristics - can we
be sure that the energy isn't being transferred to that?

Personally, I think that is a daft hypothesis, but no dafter than
many that have been proposed in all seriousness by very eminent
scientists :-)

You have a good point in that the conservation of energy isn't
known to be true on a cosmological scale, and isn't a direct
consequence of any currently primary theory. But exactly the
same is true for the invariance of physical constants, and many
other cherished beliefs.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Basically, energy is NOT conserved in an expanding universe.
|>
|> Consider radiation. The number of photons is constant, but they
|> are redshifted, reducing the individual and hence the total energy.
|> The (rest)energy of matter doesn't change. Where does the
|> energy go? It certainly doesn't do work in the expansion, as is
|> sometimes claimed, since there is no pressure gradient.

OK. But only provided that there is no compensatory factor we
don't know about. For example, people have speculated that there
is some 'dark matter' with ill-defined characteristics - can we
be sure that the energy isn't being transferred to that?

Personally, I think that is a daft hypothesis, but no dafter than
many that have been proposed in all seriousness by very eminent
scientists :-)

You have a good point in that the conservation of energy isn't
known to be true on a cosmological scale, and isn't a direct
consequence of any currently primary theory. But exactly the
same is true for the invariance of physical constants, and many
other cherished beliefs.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Basically, energy is NOT conserved in an expanding universe.
|>
|> Consider radiation. The number of photons is constant, but they
|> are redshifted, reducing the individual and hence the total energy.
|> The (rest)energy of matter doesn't change. Where does the
|> energy go? It certainly doesn't do work in the expansion, as is
|> sometimes claimed, since there is no pressure gradient.

OK. But only provided that there is no compensatory factor we
don't know about. For example, people have speculated that there
is some 'dark matter' with ill-defined characteristics - can we
be sure that the energy isn't being transferred to that?

Personally, I think that is a daft hypothesis, but no dafter than
many that have been proposed in all seriousness by very eminent
scientists :-)

You have a good point in that the conservation of energy isn't
known to be true on a cosmological scale, and isn't a direct
consequence of any currently primary theory. But exactly the
same is true for the invariance of physical constants, and many
other cherished beliefs.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Basically, energy is NOT conserved in an expanding universe.
|>
|> Consider radiation. The number of photons is constant, but they
|> are redshifted, reducing the individual and hence the total energy.
|> The (rest)energy of matter doesn't change. Where does the
|> energy go? It certainly doesn't do work in the expansion, as is
|> sometimes claimed, since there is no pressure gradient.

OK. But only provided that there is no compensatory factor we
don't know about. For example, people have speculated that there
is some 'dark matter' with ill-defined characteristics - can we
be sure that the energy isn't being transferred to that?

Personally, I think that is a daft hypothesis, but no dafter than
many that have been proposed in all seriousness by very eminent
scientists :-)

You have a good point in that the conservation of energy isn't
known to be true on a cosmological scale, and isn't a direct
consequence of any currently primary theory. But exactly the
same is true for the invariance of physical constants, and many
other cherished beliefs.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Basically, energy is NOT conserved in an expanding universe.
|>
|> Consider radiation. The number of photons is constant, but they
|> are redshifted, reducing the individual and hence the total energy.
|> The (rest)energy of matter doesn't change. Where does the
|> energy go? It certainly doesn't do work in the expansion, as is
|> sometimes claimed, since there is no pressure gradient.

OK. But only provided that there is no compensatory factor we
don't know about. For example, people have speculated that there
is some 'dark matter' with ill-defined characteristics - can we
be sure that the energy isn't being transferred to that?

Personally, I think that is a daft hypothesis, but no dafter than
many that have been proposed in all seriousness by very eminent
scientists :-)

You have a good point in that the conservation of energy isn't
known to be true on a cosmological scale, and isn't a direct
consequence of any currently primary theory. But exactly the
same is true for the invariance of physical constants, and many
other cherished beliefs.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Basically, energy is NOT conserved in an expanding universe.
|>
|> Consider radiation. The number of photons is constant, but they
|> are redshifted, reducing the individual and hence the total energy.
|> The (rest)energy of matter doesn't change. Where does the
|> energy go? It certainly doesn't do work in the expansion, as is
|> sometimes claimed, since there is no pressure gradient.

OK. But only provided that there is no compensatory factor we
don't know about. For example, people have speculated that there
is some 'dark matter' with ill-defined characteristics - can we
be sure that the energy isn't being transferred to that?

Personally, I think that is a daft hypothesis, but no dafter than
many that have been proposed in all seriousness by very eminent
scientists :-)

You have a good point in that the conservation of energy isn't
known to be true on a cosmological scale, and isn't a direct
consequence of any currently primary theory. But exactly the
same is true for the invariance of physical constants, and many
other cherished beliefs.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Basically, energy is NOT conserved in an expanding universe.
|>
|> Consider radiation. The number of photons is constant, but they
|> are redshifted, reducing the individual and hence the total energy.
|> The (rest)energy of matter doesn't change. Where does the
|> energy go? It certainly doesn't do work in the expansion, as is
|> sometimes claimed, since there is no pressure gradient.

OK. But only provided that there is no compensatory factor we
don't know about. For example, people have speculated that there
is some 'dark matter' with ill-defined characteristics - can we
be sure that the energy isn't being transferred to that?

Personally, I think that is a daft hypothesis, but no dafter than
many that have been proposed in all seriousness by very eminent
scientists :-)

You have a good point in that the conservation of energy isn't
known to be true on a cosmological scale, and isn't a direct
consequence of any currently primary theory. But exactly the
same is true for the invariance of physical constants, and many
other cherished beliefs.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Basically, energy is NOT conserved in an expanding universe.
|>
|> Consider radiation. The number of photons is constant, but they
|> are redshifted, reducing the individual and hence the total energy.
|> The (rest)energy of matter doesn't change. Where does the
|> energy go? It certainly doesn't do work in the expansion, as is
|> sometimes claimed, since there is no pressure gradient.

OK. But only provided that there is no compensatory factor we
don't know about. For example, people have speculated that there
is some 'dark matter' with ill-defined characteristics - can we
be sure that the energy isn't being transferred to that?

Personally, I think that is a daft hypothesis, but no dafter than
many that have been proposed in all seriousness by very eminent
scientists :-)

You have a good point in that the conservation of energy isn't
known to be true on a cosmological scale, and isn't a direct
consequence of any currently primary theory. But exactly the
same is true for the invariance of physical constants, and many
other cherished beliefs.


Regards,
Nick Maclaren.

[Michael C Price]

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
>
> In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
> Michael C Price <michaelEXCISESPAMprice917@tesco.net>
> writes:
> |>
> |> Basically, energy is NOT conserved in an expanding universe.
> |>
> |> Consider radiation. The number of photons is constant, but they
> |> are redshifted, reducing the individual and hence the total energy.
> |> The (rest)energy of matter doesn't change. Where does the
> |> energy go? It certainly doesn't do work in the expansion, as is
> |> sometimes claimed, since there is no pressure gradient.
>
> OK. But only provided that there is no compensatory factor we
> don't know about. For example, people have speculated that there
> is some 'dark matter' with ill-defined characteristics - can we
> be sure that the energy isn't being transferred to that?
>
> Personally, I think that is a daft hypothesis, but no dafter than
> many that have been proposed in all seriousness by very eminent
> scientists :-)
>
> You have a good point in that the conservation of energy isn't
> known to be true on a cosmological scale, and isn't a direct
> consequence of any currently primary theory. But exactly the
> same is true for the invariance of physical constants, and many
> other cherished beliefs.
>
>
> Regards,
> Nick Maclaren.

Nick's quoting style makes it look like I was the author
of the text he quotes (I wasn't) and that I agreed with
his observation that energy may not be conserved on
the cosmological scale (I don't agree).

To add a new point about energy conservation in this thread;
Noether's theorem. Energy, as we know, is the conserved
Noether charge implied by the invariance of physical law with
time. Ergo the universe obeys energy conservation or
physical law is a function of time..... and who would be happy
with the latter?

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
>
> In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
> Michael C Price <michaelEXCISESPAMprice917@tesco.net>
> writes:
> |>
> |> Basically, energy is NOT conserved in an expanding universe.
> |>
> |> Consider radiation. The number of photons is constant, but they
> |> are redshifted, reducing the individual and hence the total energy.
> |> The (rest)energy of matter doesn't change. Where does the
> |> energy go? It certainly doesn't do work in the expansion, as is
> |> sometimes claimed, since there is no pressure gradient.
>
> OK. But only provided that there is no compensatory factor we
> don't know about. For example, people have speculated that there
> is some 'dark matter' with ill-defined characteristics - can we
> be sure that the energy isn't being transferred to that?
>
> Personally, I think that is a daft hypothesis, but no dafter than
> many that have been proposed in all seriousness by very eminent
> scientists :-)
>
> You have a good point in that the conservation of energy isn't
> known to be true on a cosmological scale, and isn't a direct
> consequence of any currently primary theory. But exactly the
> same is true for the invariance of physical constants, and many
> other cherished beliefs.
>
>
> Regards,
> Nick Maclaren.

Nick's quoting style makes it look like I was the author
of the text he quotes (I wasn't) and that I agreed with
his observation that energy may not be conserved on
the cosmological scale (I don't agree).

To add a new point about energy conservation in this thread;
Noether's theorem. Energy, as we know, is the conserved
Noether charge implied by the invariance of physical law with
time. Ergo the universe obeys energy conservation or
physical law is a function of time..... and who would be happy
with the latter?

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
>
> In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
> Michael C Price <michaelEXCISESPAMprice917@tesco.net>
> writes:
> |>
> |> Basically, energy is NOT conserved in an expanding universe.
> |>
> |> Consider radiation. The number of photons is constant, but they
> |> are redshifted, reducing the individual and hence the total energy.
> |> The (rest)energy of matter doesn't change. Where does the
> |> energy go? It certainly doesn't do work in the expansion, as is
> |> sometimes claimed, since there is no pressure gradient.
>
> OK. But only provided that there is no compensatory factor we
> don't know about. For example, people have speculated that there
> is some 'dark matter' with ill-defined characteristics - can we
> be sure that the energy isn't being transferred to that?
>
> Personally, I think that is a daft hypothesis, but no dafter than
> many that have been proposed in all seriousness by very eminent
> scientists :-)
>
> You have a good point in that the conservation of energy isn't
> known to be true on a cosmological scale, and isn't a direct
> consequence of any currently primary theory. But exactly the
> same is true for the invariance of physical constants, and many
> other cherished beliefs.
>
>
> Regards,
> Nick Maclaren.

Nick's quoting style makes it look like I was the author
of the text he quotes (I wasn't) and that I agreed with
his observation that energy may not be conserved on
the cosmological scale (I don't agree).

To add a new point about energy conservation in this thread;
Noether's theorem. Energy, as we know, is the conserved
Noether charge implied by the invariance of physical law with
time. Ergo the universe obeys energy conservation or
physical law is a function of time..... and who would be happy
with the latter?

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
>
> In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
> Michael C Price <michaelEXCISESPAMprice917@tesco.net>
> writes:
> |>
> |> Basically, energy is NOT conserved in an expanding universe.
> |>
> |> Consider radiation. The number of photons is constant, but they
> |> are redshifted, reducing the individual and hence the total energy.
> |> The (rest)energy of matter doesn't change. Where does the
> |> energy go? It certainly doesn't do work in the expansion, as is
> |> sometimes claimed, since there is no pressure gradient.
>
> OK. But only provided that there is no compensatory factor we
> don't know about. For example, people have speculated that there
> is some 'dark matter' with ill-defined characteristics - can we
> be sure that the energy isn't being transferred to that?
>
> Personally, I think that is a daft hypothesis, but no dafter than
> many that have been proposed in all seriousness by very eminent
> scientists :-)
>
> You have a good point in that the conservation of energy isn't
> known to be true on a cosmological scale, and isn't a direct
> consequence of any currently primary theory. But exactly the
> same is true for the invariance of physical constants, and many
> other cherished beliefs.
>
>
> Regards,
> Nick Maclaren.

Nick's quoting style makes it look like I was the author
of the text he quotes (I wasn't) and that I agreed with
his observation that energy may not be conserved on
the cosmological scale (I don't agree).

To add a new point about energy conservation in this thread;
Noether's theorem. Energy, as we know, is the conserved
Noether charge implied by the invariance of physical law with
time. Ergo the universe obeys energy conservation or
physical law is a function of time..... and who would be happy
with the latter?

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
>
> In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
> Michael C Price <michaelEXCISESPAMprice917@tesco.net>
> writes:
> |>
> |> Basically, energy is NOT conserved in an expanding universe.
> |>
> |> Consider radiation. The number of photons is constant, but they
> |> are redshifted, reducing the individual and hence the total energy.
> |> The (rest)energy of matter doesn't change. Where does the
> |> energy go? It certainly doesn't do work in the expansion, as is
> |> sometimes claimed, since there is no pressure gradient.
>
> OK. But only provided that there is no compensatory factor we
> don't know about. For example, people have speculated that there
> is some 'dark matter' with ill-defined characteristics - can we
> be sure that the energy isn't being transferred to that?
>
> Personally, I think that is a daft hypothesis, but no dafter than
> many that have been proposed in all seriousness by very eminent
> scientists :-)
>
> You have a good point in that the conservation of energy isn't
> known to be true on a cosmological scale, and isn't a direct
> consequence of any currently primary theory. But exactly the
> same is true for the invariance of physical constants, and many
> other cherished beliefs.
>
>
> Regards,
> Nick Maclaren.

Nick's quoting style makes it look like I was the author
of the text he quotes (I wasn't) and that I agreed with
his observation that energy may not be conserved on
the cosmological scale (I don't agree).

To add a new point about energy conservation in this thread;
Noether's theorem. Energy, as we know, is the conserved
Noether charge implied by the invariance of physical law with
time. Ergo the universe obeys energy conservation or
physical law is a function of time..... and who would be happy
with the latter?

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
>
> In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
> Michael C Price <michaelEXCISESPAMprice917@tesco.net>
> writes:
> |>
> |> Basically, energy is NOT conserved in an expanding universe.
> |>
> |> Consider radiation. The number of photons is constant, but they
> |> are redshifted, reducing the individual and hence the total energy.
> |> The (rest)energy of matter doesn't change. Where does the
> |> energy go? It certainly doesn't do work in the expansion, as is
> |> sometimes claimed, since there is no pressure gradient.
>
> OK. But only provided that there is no compensatory factor we
> don't know about. For example, people have speculated that there
> is some 'dark matter' with ill-defined characteristics - can we
> be sure that the energy isn't being transferred to that?
>
> Personally, I think that is a daft hypothesis, but no dafter than
> many that have been proposed in all seriousness by very eminent
> scientists :-)
>
> You have a good point in that the conservation of energy isn't
> known to be true on a cosmological scale, and isn't a direct
> consequence of any currently primary theory. But exactly the
> same is true for the invariance of physical constants, and many
> other cherished beliefs.
>
>
> Regards,
> Nick Maclaren.

Nick's quoting style makes it look like I was the author
of the text he quotes (I wasn't) and that I agreed with
his observation that energy may not be conserved on
the cosmological scale (I don't agree).

To add a new point about energy conservation in this thread;
Noether's theorem. Energy, as we know, is the conserved
Noether charge implied by the invariance of physical law with
time. Ergo the universe obeys energy conservation or
physical law is a function of time..... and who would be happy
with the latter?

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
>
> In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
> Michael C Price <michaelEXCISESPAMprice917@tesco.net>
> writes:
> |>
> |> Basically, energy is NOT conserved in an expanding universe.
> |>
> |> Consider radiation. The number of photons is constant, but they
> |> are redshifted, reducing the individual and hence the total energy.
> |> The (rest)energy of matter doesn't change. Where does the
> |> energy go? It certainly doesn't do work in the expansion, as is
> |> sometimes claimed, since there is no pressure gradient.
>
> OK. But only provided that there is no compensatory factor we
> don't know about. For example, people have speculated that there
> is some 'dark matter' with ill-defined characteristics - can we
> be sure that the energy isn't being transferred to that?
>
> Personally, I think that is a daft hypothesis, but no dafter than
> many that have been proposed in all seriousness by very eminent
> scientists :-)
>
> You have a good point in that the conservation of energy isn't
> known to be true on a cosmological scale, and isn't a direct
> consequence of any currently primary theory. But exactly the
> same is true for the invariance of physical constants, and many
> other cherished beliefs.
>
>
> Regards,
> Nick Maclaren.

Nick's quoting style makes it look like I was the author
of the text he quotes (I wasn't) and that I agreed with
his observation that energy may not be conserved on
the cosmological scale (I don't agree).

To add a new point about energy conservation in this thread;
Noether's theorem. Energy, as we know, is the conserved
Noether charge implied by the invariance of physical law with
time. Ergo the universe obeys energy conservation or
physical law is a function of time..... and who would be happy
with the latter?

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
>
> In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
> Michael C Price <michaelEXCISESPAMprice917@tesco.net>
> writes:
> |>
> |> Basically, energy is NOT conserved in an expanding universe.
> |>
> |> Consider radiation. The number of photons is constant, but they
> |> are redshifted, reducing the individual and hence the total energy.
> |> The (rest)energy of matter doesn't change. Where does the
> |> energy go? It certainly doesn't do work in the expansion, as is
> |> sometimes claimed, since there is no pressure gradient.
>
> OK. But only provided that there is no compensatory factor we
> don't know about. For example, people have speculated that there
> is some 'dark matter' with ill-defined characteristics - can we
> be sure that the energy isn't being transferred to that?
>
> Personally, I think that is a daft hypothesis, but no dafter than
> many that have been proposed in all seriousness by very eminent
> scientists :-)
>
> You have a good point in that the conservation of energy isn't
> known to be true on a cosmological scale, and isn't a direct
> consequence of any currently primary theory. But exactly the
> same is true for the invariance of physical constants, and many
> other cherished beliefs.
>
>
> Regards,
> Nick Maclaren.

Nick's quoting style makes it look like I was the author
of the text he quotes (I wasn't) and that I agreed with
his observation that energy may not be conserved on
the cosmological scale (I don't agree).

To add a new point about energy conservation in this thread;
Noether's theorem. Energy, as we know, is the conserved
Noether charge implied by the invariance of physical law with
time. Ergo the universe obeys energy conservation or
physical law is a function of time..... and who would be happy
with the latter?

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
>
> In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>,
> Michael C Price <michaelEXCISESPAMprice917@tesco.net>
> writes:
> |>
> |> Basically, energy is NOT conserved in an expanding universe.
> |>
> |> Consider radiation. The number of photons is constant, but they
> |> are redshifted, reducing the individual and hence the total energy.
> |> The (rest)energy of matter doesn't change. Where does the
> |> energy go? It certainly doesn't do work in the expansion, as is
> |> sometimes claimed, since there is no pressure gradient.
>
> OK. But only provided that there is no compensatory factor we
> don't know about. For example, people have speculated that there
> is some 'dark matter' with ill-defined characteristics - can we
> be sure that the energy isn't being transferred to that?
>
> Personally, I think that is a daft hypothesis, but no dafter than
> many that have been proposed in all seriousness by very eminent
> scientists :-)
>
> You have a good point in that the conservation of energy isn't
> known to be true on a cosmological scale, and isn't a direct
> consequence of any currently primary theory. But exactly the
> same is true for the invariance of physical constants, and many
> other cherished beliefs.
>
>
> Regards,
> Nick Maclaren.

Nick's quoting style makes it look like I was the author
of the text he quotes (I wasn't) and that I agreed with
his observation that energy may not be conserved on
the cosmological scale (I don't agree).

To add a new point about energy conservation in this thread;
Noether's theorem. Energy, as we know, is the conserved
Noether charge implied by the invariance of physical law with
time. Ergo the universe obeys energy conservation or
physical law is a function of time..... and who would be happy
with the latter?

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[ebunn@lfa221051.richmond.edu]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:

>To add a new point about energy conservation in this thread;
>Noether's theorem. Energy, as we know, is the conserved
>Noether charge implied by the invariance of physical law with
>time. Ergo the universe obeys energy conservation or
>physical law is a function of time..... and who would be happy
>with the latter?

Noether's theorem gives you a way to construct a local conservation
law from a local symmetry. It does indeed apply in this case, and
energy is locally conserved in general relativity. The problem comes
when you try to integrate that up to get a global conservation law.
That can't be done for energy in general relativity.

Compare the situation with that of charge conservation. You
can express charge conservation locally this way:

d rho / dt = -div j

(rate of change of charge density at a given point is related to
the current flow into or out of that point). If you like, you
can integrate that over some volume to get

(d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

In a situation where there is no boundary, or where you know
there's no current flow across the boundary, you get global
conservation of charge.

The first version is the version that pops out of Noether's theorem,
and it has an analogue for energy conservation in general relatitivity
(the 4-dimensional divergence of the stress-energy tensor equals zero).
But the step where you integrate that up to get a global
law doesn't work in a nice way, so there's no nice law of
global energy conservation.

(To see what "nice" means in this context, see the FAQ.)

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[ebunn@lfa221051.richmond.edu]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:

>To add a new point about energy conservation in this thread;
>Noether's theorem. Energy, as we know, is the conserved
>Noether charge implied by the invariance of physical law with
>time. Ergo the universe obeys energy conservation or
>physical law is a function of time..... and who would be happy
>with the latter?

Noether's theorem gives you a way to construct a local conservation
law from a local symmetry. It does indeed apply in this case, and
energy is locally conserved in general relativity. The problem comes
when you try to integrate that up to get a global conservation law.
That can't be done for energy in general relativity.

Compare the situation with that of charge conservation. You
can express charge conservation locally this way:

d rho / dt = -div j

(rate of change of charge density at a given point is related to
the current flow into or out of that point). If you like, you
can integrate that over some volume to get

(d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

In a situation where there is no boundary, or where you know
there's no current flow across the boundary, you get global
conservation of charge.

The first version is the version that pops out of Noether's theorem,
and it has an analogue for energy conservation in general relatitivity
(the 4-dimensional divergence of the stress-energy tensor equals zero).
But the step where you integrate that up to get a global
law doesn't work in a nice way, so there's no nice law of
global energy conservation.

(To see what "nice" means in this context, see the FAQ.)

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[ebunn@lfa221051.richmond.edu]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:

>To add a new point about energy conservation in this thread;
>Noether's theorem. Energy, as we know, is the conserved
>Noether charge implied by the invariance of physical law with
>time. Ergo the universe obeys energy conservation or
>physical law is a function of time..... and who would be happy
>with the latter?

Noether's theorem gives you a way to construct a local conservation
law from a local symmetry. It does indeed apply in this case, and
energy is locally conserved in general relativity. The problem comes
when you try to integrate that up to get a global conservation law.
That can't be done for energy in general relativity.

Compare the situation with that of charge conservation. You
can express charge conservation locally this way:

d rho / dt = -div j

(rate of change of charge density at a given point is related to
the current flow into or out of that point). If you like, you
can integrate that over some volume to get

(d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

In a situation where there is no boundary, or where you know
there's no current flow across the boundary, you get global
conservation of charge.

The first version is the version that pops out of Noether's theorem,
and it has an analogue for energy conservation in general relatitivity
(the 4-dimensional divergence of the stress-energy tensor equals zero).
But the step where you integrate that up to get a global
law doesn't work in a nice way, so there's no nice law of
global energy conservation.

(To see what "nice" means in this context, see the FAQ.)

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[ebunn@lfa221051.richmond.edu]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:

>To add a new point about energy conservation in this thread;
>Noether's theorem. Energy, as we know, is the conserved
>Noether charge implied by the invariance of physical law with
>time. Ergo the universe obeys energy conservation or
>physical law is a function of time..... and who would be happy
>with the latter?

Noether's theorem gives you a way to construct a local conservation
law from a local symmetry. It does indeed apply in this case, and
energy is locally conserved in general relativity. The problem comes
when you try to integrate that up to get a global conservation law.
That can't be done for energy in general relativity.

Compare the situation with that of charge conservation. You
can express charge conservation locally this way:

d rho / dt = -div j

(rate of change of charge density at a given point is related to
the current flow into or out of that point). If you like, you
can integrate that over some volume to get

(d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

In a situation where there is no boundary, or where you know
there's no current flow across the boundary, you get global
conservation of charge.

The first version is the version that pops out of Noether's theorem,
and it has an analogue for energy conservation in general relatitivity
(the 4-dimensional divergence of the stress-energy tensor equals zero).
But the step where you integrate that up to get a global
law doesn't work in a nice way, so there's no nice law of
global energy conservation.

(To see what "nice" means in this context, see the FAQ.)

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[ebunn@lfa221051.richmond.edu]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:

>To add a new point about energy conservation in this thread;
>Noether's theorem. Energy, as we know, is the conserved
>Noether charge implied by the invariance of physical law with
>time. Ergo the universe obeys energy conservation or
>physical law is a function of time..... and who would be happy
>with the latter?

Noether's theorem gives you a way to construct a local conservation
law from a local symmetry. It does indeed apply in this case, and
energy is locally conserved in general relativity. The problem comes
when you try to integrate that up to get a global conservation law.
That can't be done for energy in general relativity.

Compare the situation with that of charge conservation. You
can express charge conservation locally this way:

d rho / dt = -div j

(rate of change of charge density at a given point is related to
the current flow into or out of that point). If you like, you
can integrate that over some volume to get

(d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

In a situation where there is no boundary, or where you know
there's no current flow across the boundary, you get global
conservation of charge.

The first version is the version that pops out of Noether's theorem,
and it has an analogue for energy conservation in general relatitivity
(the 4-dimensional divergence of the stress-energy tensor equals zero).
But the step where you integrate that up to get a global
law doesn't work in a nice way, so there's no nice law of
global energy conservation.

(To see what "nice" means in this context, see the FAQ.)

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[ebunn@lfa221051.richmond.edu]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:

>To add a new point about energy conservation in this thread;
>Noether's theorem. Energy, as we know, is the conserved
>Noether charge implied by the invariance of physical law with
>time. Ergo the universe obeys energy conservation or
>physical law is a function of time..... and who would be happy
>with the latter?

Noether's theorem gives you a way to construct a local conservation
law from a local symmetry. It does indeed apply in this case, and
energy is locally conserved in general relativity. The problem comes
when you try to integrate that up to get a global conservation law.
That can't be done for energy in general relativity.

Compare the situation with that of charge conservation. You
can express charge conservation locally this way:

d rho / dt = -div j

(rate of change of charge density at a given point is related to
the current flow into or out of that point). If you like, you
can integrate that over some volume to get

(d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

In a situation where there is no boundary, or where you know
there's no current flow across the boundary, you get global
conservation of charge.

The first version is the version that pops out of Noether's theorem,
and it has an analogue for energy conservation in general relatitivity
(the 4-dimensional divergence of the stress-energy tensor equals zero).
But the step where you integrate that up to get a global
law doesn't work in a nice way, so there's no nice law of
global energy conservation.

(To see what "nice" means in this context, see the FAQ.)

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[ebunn@lfa221051.richmond.edu]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:

>To add a new point about energy conservation in this thread;
>Noether's theorem. Energy, as we know, is the conserved
>Noether charge implied by the invariance of physical law with
>time. Ergo the universe obeys energy conservation or
>physical law is a function of time..... and who would be happy
>with the latter?

Noether's theorem gives you a way to construct a local conservation
law from a local symmetry. It does indeed apply in this case, and
energy is locally conserved in general relativity. The problem comes
when you try to integrate that up to get a global conservation law.
That can't be done for energy in general relativity.

Compare the situation with that of charge conservation. You
can express charge conservation locally this way:

d rho / dt = -div j

(rate of change of charge density at a given point is related to
the current flow into or out of that point). If you like, you
can integrate that over some volume to get

(d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

In a situation where there is no boundary, or where you know
there's no current flow across the boundary, you get global
conservation of charge.

The first version is the version that pops out of Noether's theorem,
and it has an analogue for energy conservation in general relatitivity
(the 4-dimensional divergence of the stress-energy tensor equals zero).
But the step where you integrate that up to get a global
law doesn't work in a nice way, so there's no nice law of
global energy conservation.

(To see what "nice" means in this context, see the FAQ.)

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[ebunn@lfa221051.richmond.edu]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:

>To add a new point about energy conservation in this thread;
>Noether's theorem. Energy, as we know, is the conserved
>Noether charge implied by the invariance of physical law with
>time. Ergo the universe obeys energy conservation or
>physical law is a function of time..... and who would be happy
>with the latter?

Noether's theorem gives you a way to construct a local conservation
law from a local symmetry. It does indeed apply in this case, and
energy is locally conserved in general relativity. The problem comes
when you try to integrate that up to get a global conservation law.
That can't be done for energy in general relativity.

Compare the situation with that of charge conservation. You
can express charge conservation locally this way:

d rho / dt = -div j

(rate of change of charge density at a given point is related to
the current flow into or out of that point). If you like, you
can integrate that over some volume to get

(d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

In a situation where there is no boundary, or where you know
there's no current flow across the boundary, you get global
conservation of charge.

The first version is the version that pops out of Noether's theorem,
and it has an analogue for energy conservation in general relatitivity
(the 4-dimensional divergence of the stress-energy tensor equals zero).
But the step where you integrate that up to get a global
law doesn't work in a nice way, so there's no nice law of
global energy conservation.

(To see what "nice" means in this context, see the FAQ.)

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[ebunn@lfa221051.richmond.edu]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:

>To add a new point about energy conservation in this thread;
>Noether's theorem. Energy, as we know, is the conserved
>Noether charge implied by the invariance of physical law with
>time. Ergo the universe obeys energy conservation or
>physical law is a function of time..... and who would be happy
>with the latter?

Noether's theorem gives you a way to construct a local conservation
law from a local symmetry. It does indeed apply in this case, and
energy is locally conserved in general relativity. The problem comes
when you try to integrate that up to get a global conservation law.
That can't be done for energy in general relativity.

Compare the situation with that of charge conservation. You
can express charge conservation locally this way:

d rho / dt = -div j

(rate of change of charge density at a given point is related to
the current flow into or out of that point). If you like, you
can integrate that over some volume to get

(d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

In a situation where there is no boundary, or where you know
there's no current flow across the boundary, you get global
conservation of charge.

The first version is the version that pops out of Noether's theorem,
and it has an analogue for energy conservation in general relatitivity
(the 4-dimensional divergence of the stress-energy tensor equals zero).
But the step where you integrate that up to get a global
law doesn't work in a nice way, so there's no nice law of
global energy conservation.

(To see what "nice" means in this context, see the FAQ.)

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[DRLunsford]

ebunn@lfa221051.richmond.edu wrote:

> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

Sharper: d/dt (Charge inside convected volume) = integral over
convected volume (Lie derivative along the convection)

or

d/dt integral Rho dV = integral L_v Rho dV

> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.

Actually there is no local conservation law strictly speaking, without
additional input, because

Tmn;n = 0

is not a conservation law. Only if the covariant divergence can be
converted to an ordinary divergence of a density, can you get a strict
conservation law, and these are what come out of Noether's (abused)
theorem. (I say abused because it would be better for students to first
understand flows, and derivatives with respect to them.) The best you
can do in GR is

(Tmn[matter] + tmn),n = 0

where tmn (pseudo energy density of gravity alone) is not a tensor - no
tensor, no locality. This IMO is the simplest evidence that GR is a
first-order approximation to an actual theory.

-drl

[DRLunsford]

ebunn@lfa221051.richmond.edu wrote:

> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

Sharper: d/dt (Charge inside convected volume) = integral over
convected volume (Lie derivative along the convection)

or

d/dt integral Rho dV = integral L_v Rho dV

> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.

Actually there is no local conservation law strictly speaking, without
additional input, because

Tmn;n = 0

is not a conservation law. Only if the covariant divergence can be
converted to an ordinary divergence of a density, can you get a strict
conservation law, and these are what come out of Noether's (abused)
theorem. (I say abused because it would be better for students to first
understand flows, and derivatives with respect to them.) The best you
can do in GR is

(Tmn[matter] + tmn),n = 0

where tmn (pseudo energy density of gravity alone) is not a tensor - no
tensor, no locality. This IMO is the simplest evidence that GR is a
first-order approximation to an actual theory.

-drl

[DRLunsford]

ebunn@lfa221051.richmond.edu wrote:

> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

Sharper: d/dt (Charge inside convected volume) = integral over
convected volume (Lie derivative along the convection)

or

d/dt integral Rho dV = integral L_v Rho dV

> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.

Actually there is no local conservation law strictly speaking, without
additional input, because

Tmn;n = 0

is not a conservation law. Only if the covariant divergence can be
converted to an ordinary divergence of a density, can you get a strict
conservation law, and these are what come out of Noether's (abused)
theorem. (I say abused because it would be better for students to first
understand flows, and derivatives with respect to them.) The best you
can do in GR is

(Tmn[matter] + tmn),n = 0

where tmn (pseudo energy density of gravity alone) is not a tensor - no
tensor, no locality. This IMO is the simplest evidence that GR is a
first-order approximation to an actual theory.

-drl

[DRLunsford]

ebunn@lfa221051.richmond.edu wrote:

> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

Sharper: d/dt (Charge inside convected volume) = integral over
convected volume (Lie derivative along the convection)

or

d/dt integral Rho dV = integral L_v Rho dV

> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.

Actually there is no local conservation law strictly speaking, without
additional input, because

Tmn;n = 0

is not a conservation law. Only if the covariant divergence can be
converted to an ordinary divergence of a density, can you get a strict
conservation law, and these are what come out of Noether's (abused)
theorem. (I say abused because it would be better for students to first
understand flows, and derivatives with respect to them.) The best you
can do in GR is

(Tmn[matter] + tmn),n = 0

where tmn (pseudo energy density of gravity alone) is not a tensor - no
tensor, no locality. This IMO is the simplest evidence that GR is a
first-order approximation to an actual theory.

-drl

[DRLunsford]

ebunn@lfa221051.richmond.edu wrote:

> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

Sharper: d/dt (Charge inside convected volume) = integral over
convected volume (Lie derivative along the convection)

or

d/dt integral Rho dV = integral L_v Rho dV

> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.

Actually there is no local conservation law strictly speaking, without
additional input, because

Tmn;n = 0

is not a conservation law. Only if the covariant divergence can be
converted to an ordinary divergence of a density, can you get a strict
conservation law, and these are what come out of Noether's (abused)
theorem. (I say abused because it would be better for students to first
understand flows, and derivatives with respect to them.) The best you
can do in GR is

(Tmn[matter] + tmn),n = 0

where tmn (pseudo energy density of gravity alone) is not a tensor - no
tensor, no locality. This IMO is the simplest evidence that GR is a
first-order approximation to an actual theory.

-drl

[DRLunsford]

ebunn@lfa221051.richmond.edu wrote:

> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

Sharper: d/dt (Charge inside convected volume) = integral over
convected volume (Lie derivative along the convection)

or

d/dt integral Rho dV = integral L_v Rho dV

> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.

Actually there is no local conservation law strictly speaking, without
additional input, because

Tmn;n = 0

is not a conservation law. Only if the covariant divergence can be
converted to an ordinary divergence of a density, can you get a strict
conservation law, and these are what come out of Noether's (abused)
theorem. (I say abused because it would be better for students to first
understand flows, and derivatives with respect to them.) The best you
can do in GR is

(Tmn[matter] + tmn),n = 0

where tmn (pseudo energy density of gravity alone) is not a tensor - no
tensor, no locality. This IMO is the simplest evidence that GR is a
first-order approximation to an actual theory.

-drl

[DRLunsford]

ebunn@lfa221051.richmond.edu wrote:

> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

Sharper: d/dt (Charge inside convected volume) = integral over
convected volume (Lie derivative along the convection)

or

d/dt integral Rho dV = integral L_v Rho dV

> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.

Actually there is no local conservation law strictly speaking, without
additional input, because

Tmn;n = 0

is not a conservation law. Only if the covariant divergence can be
converted to an ordinary divergence of a density, can you get a strict
conservation law, and these are what come out of Noether's (abused)
theorem. (I say abused because it would be better for students to first
understand flows, and derivatives with respect to them.) The best you
can do in GR is

(Tmn[matter] + tmn),n = 0

where tmn (pseudo energy density of gravity alone) is not a tensor - no
tensor, no locality. This IMO is the simplest evidence that GR is a
first-order approximation to an actual theory.

-drl

[DRLunsford]

ebunn@lfa221051.richmond.edu wrote:

> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

Sharper: d/dt (Charge inside convected volume) = integral over
convected volume (Lie derivative along the convection)

or

d/dt integral Rho dV = integral L_v Rho dV

> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.

Actually there is no local conservation law strictly speaking, without
additional input, because

Tmn;n = 0

is not a conservation law. Only if the covariant divergence can be
converted to an ordinary divergence of a density, can you get a strict
conservation law, and these are what come out of Noether's (abused)
theorem. (I say abused because it would be better for students to first
understand flows, and derivatives with respect to them.) The best you
can do in GR is

(Tmn[matter] + tmn),n = 0

where tmn (pseudo energy density of gravity alone) is not a tensor - no
tensor, no locality. This IMO is the simplest evidence that GR is a
first-order approximation to an actual theory.

-drl

[DRLunsford]

ebunn@lfa221051.richmond.edu wrote:

> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)

Sharper: d/dt (Charge inside convected volume) = integral over
convected volume (Lie derivative along the convection)

or

d/dt integral Rho dV = integral L_v Rho dV

> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.

Actually there is no local conservation law strictly speaking, without
additional input, because

Tmn;n = 0

is not a conservation law. Only if the covariant divergence can be
converted to an ordinary divergence of a density, can you get a strict
conservation law, and these are what come out of Noether's (abused)
theorem. (I say abused because it would be better for students to first
understand flows, and derivatives with respect to them.) The best you
can do in GR is

(Tmn[matter] + tmn),n = 0

where tmn (pseudo energy density of gravity alone) is not a tensor - no
tensor, no locality. This IMO is the simplest evidence that GR is a
first-order approximation to an actual theory.

-drl

[Phillip Helbig---remove CLOTHES to reply]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>> Imagine the Einstein static universe. There is no expansion.
> >>> Yet there is an energy density due to the cosmological constant.
> >>> How does it "come from" the (non-existent) expansion in this
> >>> case? What about a negative cosmological constant?
> >>
> >> Indeed, as you point out, in Einstein's original static universe the
> >> cosmological constant was negative
> >
> > The cosmological constant in the Einstein static universe is
> > positive.
>
> Perhaps -- but not if we wish to have a spatially flat static universe.
> Granted that Einstein was modelling a spatially closed static universe
> which has an extra curvature term to mess with. I made the
> assumption of flatness without really thinking about it -- probably as
> result of assuming a post-inflationary scenario.

Within the context of general relativity, if a static universe contains
matter and a cosmological constant, then it cannot be spatially flat.

[Phillip Helbig---remove CLOTHES to reply]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>> Imagine the Einstein static universe. There is no expansion.
> >>> Yet there is an energy density due to the cosmological constant.
> >>> How does it "come from" the (non-existent) expansion in this
> >>> case? What about a negative cosmological constant?
> >>
> >> Indeed, as you point out, in Einstein's original static universe the
> >> cosmological constant was negative
> >
> > The cosmological constant in the Einstein static universe is
> > positive.
>
> Perhaps -- but not if we wish to have a spatially flat static universe.
> Granted that Einstein was modelling a spatially closed static universe
> which has an extra curvature term to mess with. I made the
> assumption of flatness without really thinking about it -- probably as
> result of assuming a post-inflationary scenario.

Within the context of general relativity, if a static universe contains
matter and a cosmological constant, then it cannot be spatially flat.

[Phillip Helbig---remove CLOTHES to reply]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>> Imagine the Einstein static universe. There is no expansion.
> >>> Yet there is an energy density due to the cosmological constant.
> >>> How does it "come from" the (non-existent) expansion in this
> >>> case? What about a negative cosmological constant?
> >>
> >> Indeed, as you point out, in Einstein's original static universe the
> >> cosmological constant was negative
> >
> > The cosmological constant in the Einstein static universe is
> > positive.
>
> Perhaps -- but not if we wish to have a spatially flat static universe.
> Granted that Einstein was modelling a spatially closed static universe
> which has an extra curvature term to mess with. I made the
> assumption of flatness without really thinking about it -- probably as
> result of assuming a post-inflationary scenario.

Within the context of general relativity, if a static universe contains
matter and a cosmological constant, then it cannot be spatially flat.

[Phillip Helbig---remove CLOTHES to reply]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>> Imagine the Einstein static universe. There is no expansion.
> >>> Yet there is an energy density due to the cosmological constant.
> >>> How does it "come from" the (non-existent) expansion in this
> >>> case? What about a negative cosmological constant?
> >>
> >> Indeed, as you point out, in Einstein's original static universe the
> >> cosmological constant was negative
> >
> > The cosmological constant in the Einstein static universe is
> > positive.
>
> Perhaps -- but not if we wish to have a spatially flat static universe.
> Granted that Einstein was modelling a spatially closed static universe
> which has an extra curvature term to mess with. I made the
> assumption of flatness without really thinking about it -- probably as
> result of assuming a post-inflationary scenario.

Within the context of general relativity, if a static universe contains
matter and a cosmological constant, then it cannot be spatially flat.

[Phillip Helbig---remove CLOTHES to reply]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>> Imagine the Einstein static universe. There is no expansion.
> >>> Yet there is an energy density due to the cosmological constant.
> >>> How does it "come from" the (non-existent) expansion in this
> >>> case? What about a negative cosmological constant?
> >>
> >> Indeed, as you point out, in Einstein's original static universe the
> >> cosmological constant was negative
> >
> > The cosmological constant in the Einstein static universe is
> > positive.
>
> Perhaps -- but not if we wish to have a spatially flat static universe.
> Granted that Einstein was modelling a spatially closed static universe
> which has an extra curvature term to mess with. I made the
> assumption of flatness without really thinking about it -- probably as
> result of assuming a post-inflationary scenario.

Within the context of general relativity, if a static universe contains
matter and a cosmological constant, then it cannot be spatially flat.

[Phillip Helbig---remove CLOTHES to reply]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>> Imagine the Einstein static universe. There is no expansion.
> >>> Yet there is an energy density due to the cosmological constant.
> >>> How does it "come from" the (non-existent) expansion in this
> >>> case? What about a negative cosmological constant?
> >>
> >> Indeed, as you point out, in Einstein's original static universe the
> >> cosmological constant was negative
> >
> > The cosmological constant in the Einstein static universe is
> > positive.
>
> Perhaps -- but not if we wish to have a spatially flat static universe.
> Granted that Einstein was modelling a spatially closed static universe
> which has an extra curvature term to mess with. I made the
> assumption of flatness without really thinking about it -- probably as
> result of assuming a post-inflationary scenario.

Within the context of general relativity, if a static universe contains
matter and a cosmological constant, then it cannot be spatially flat.

[Phillip Helbig---remove CLOTHES to reply]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>> Imagine the Einstein static universe. There is no expansion.
> >>> Yet there is an energy density due to the cosmological constant.
> >>> How does it "come from" the (non-existent) expansion in this
> >>> case? What about a negative cosmological constant?
> >>
> >> Indeed, as you point out, in Einstein's original static universe the
> >> cosmological constant was negative
> >
> > The cosmological constant in the Einstein static universe is
> > positive.
>
> Perhaps -- but not if we wish to have a spatially flat static universe.
> Granted that Einstein was modelling a spatially closed static universe
> which has an extra curvature term to mess with. I made the
> assumption of flatness without really thinking about it -- probably as
> result of assuming a post-inflationary scenario.

Within the context of general relativity, if a static universe contains
matter and a cosmological constant, then it cannot be spatially flat.

[Phillip Helbig---remove CLOTHES to reply]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>> Imagine the Einstein static universe. There is no expansion.
> >>> Yet there is an energy density due to the cosmological constant.
> >>> How does it "come from" the (non-existent) expansion in this
> >>> case? What about a negative cosmological constant?
> >>
> >> Indeed, as you point out, in Einstein's original static universe the
> >> cosmological constant was negative
> >
> > The cosmological constant in the Einstein static universe is
> > positive.
>
> Perhaps -- but not if we wish to have a spatially flat static universe.
> Granted that Einstein was modelling a spatially closed static universe
> which has an extra curvature term to mess with. I made the
> assumption of flatness without really thinking about it -- probably as
> result of assuming a post-inflationary scenario.

Within the context of general relativity, if a static universe contains
matter and a cosmological constant, then it cannot be spatially flat.

[Phillip Helbig---remove CLOTHES to reply]

In article <BHP5f.249$Ce5.137@newsfe1-gui.ntli.net>, Michael C Price
<michaelEXCISESPAMprice917@tesco.net> writes:

> >>> Imagine the Einstein static universe. There is no expansion.
> >>> Yet there is an energy density due to the cosmological constant.
> >>> How does it "come from" the (non-existent) expansion in this
> >>> case? What about a negative cosmological constant?
> >>
> >> Indeed, as you point out, in Einstein's original static universe the
> >> cosmological constant was negative
> >
> > The cosmological constant in the Einstein static universe is
> > positive.
>
> Perhaps -- but not if we wish to have a spatially flat static universe.
> Granted that Einstein was modelling a spatially closed static universe
> which has an extra curvature term to mess with. I made the
> assumption of flatness without really thinking about it -- probably as
> result of assuming a post-inflationary scenario.

Within the context of general relativity, if a static universe contains
matter and a cosmological constant, then it cannot be spatially flat.

[Nick Maclaren]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Nick's quoting style makes it look like I was the author
|> of the text he quotes (I wasn't) and that I agreed with
|> his observation that energy may not be conserved on
|> the cosmological scale (I don't agree).

Sorry, I was confused by your somewhat unusual quoting style.
My quoting style is 'standard' (i.e. the most common) - I forgot
that you use one of the rarer ones.

But back to the physics. Do you have any reason to say that
energy must NECESSARILY be conserved? I.e. why is this a
fundamental principle?

My point is that it is a derivative principle, just as the law
that entropy increases is, and there is no obvious reason why
exact conservation should be required on a cosmological scale.
Equally, there is no reason why it shouldn't be, and I agree
that most evidence is that it probably is conserved :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Nick's quoting style makes it look like I was the author
|> of the text he quotes (I wasn't) and that I agreed with
|> his observation that energy may not be conserved on
|> the cosmological scale (I don't agree).

Sorry, I was confused by your somewhat unusual quoting style.
My quoting style is 'standard' (i.e. the most common) - I forgot
that you use one of the rarer ones.

But back to the physics. Do you have any reason to say that
energy must NECESSARILY be conserved? I.e. why is this a
fundamental principle?

My point is that it is a derivative principle, just as the law
that entropy increases is, and there is no obvious reason why
exact conservation should be required on a cosmological scale.
Equally, there is no reason why it shouldn't be, and I agree
that most evidence is that it probably is conserved :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Nick's quoting style makes it look like I was the author
|> of the text he quotes (I wasn't) and that I agreed with
|> his observation that energy may not be conserved on
|> the cosmological scale (I don't agree).

Sorry, I was confused by your somewhat unusual quoting style.
My quoting style is 'standard' (i.e. the most common) - I forgot
that you use one of the rarer ones.

But back to the physics. Do you have any reason to say that
energy must NECESSARILY be conserved? I.e. why is this a
fundamental principle?

My point is that it is a derivative principle, just as the law
that entropy increases is, and there is no obvious reason why
exact conservation should be required on a cosmological scale.
Equally, there is no reason why it shouldn't be, and I agree
that most evidence is that it probably is conserved :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Nick's quoting style makes it look like I was the author
|> of the text he quotes (I wasn't) and that I agreed with
|> his observation that energy may not be conserved on
|> the cosmological scale (I don't agree).

Sorry, I was confused by your somewhat unusual quoting style.
My quoting style is 'standard' (i.e. the most common) - I forgot
that you use one of the rarer ones.

But back to the physics. Do you have any reason to say that
energy must NECESSARILY be conserved? I.e. why is this a
fundamental principle?

My point is that it is a derivative principle, just as the law
that entropy increases is, and there is no obvious reason why
exact conservation should be required on a cosmological scale.
Equally, there is no reason why it shouldn't be, and I agree
that most evidence is that it probably is conserved :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Nick's quoting style makes it look like I was the author
|> of the text he quotes (I wasn't) and that I agreed with
|> his observation that energy may not be conserved on
|> the cosmological scale (I don't agree).

Sorry, I was confused by your somewhat unusual quoting style.
My quoting style is 'standard' (i.e. the most common) - I forgot
that you use one of the rarer ones.

But back to the physics. Do you have any reason to say that
energy must NECESSARILY be conserved? I.e. why is this a
fundamental principle?

My point is that it is a derivative principle, just as the law
that entropy increases is, and there is no obvious reason why
exact conservation should be required on a cosmological scale.
Equally, there is no reason why it shouldn't be, and I agree
that most evidence is that it probably is conserved :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Nick's quoting style makes it look like I was the author
|> of the text he quotes (I wasn't) and that I agreed with
|> his observation that energy may not be conserved on
|> the cosmological scale (I don't agree).

Sorry, I was confused by your somewhat unusual quoting style.
My quoting style is 'standard' (i.e. the most common) - I forgot
that you use one of the rarer ones.

But back to the physics. Do you have any reason to say that
energy must NECESSARILY be conserved? I.e. why is this a
fundamental principle?

My point is that it is a derivative principle, just as the law
that entropy increases is, and there is no obvious reason why
exact conservation should be required on a cosmological scale.
Equally, there is no reason why it shouldn't be, and I agree
that most evidence is that it probably is conserved :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Nick's quoting style makes it look like I was the author
|> of the text he quotes (I wasn't) and that I agreed with
|> his observation that energy may not be conserved on
|> the cosmological scale (I don't agree).

Sorry, I was confused by your somewhat unusual quoting style.
My quoting style is 'standard' (i.e. the most common) - I forgot
that you use one of the rarer ones.

But back to the physics. Do you have any reason to say that
energy must NECESSARILY be conserved? I.e. why is this a
fundamental principle?

My point is that it is a derivative principle, just as the law
that entropy increases is, and there is no obvious reason why
exact conservation should be required on a cosmological scale.
Equally, there is no reason why it shouldn't be, and I agree
that most evidence is that it probably is conserved :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Nick's quoting style makes it look like I was the author
|> of the text he quotes (I wasn't) and that I agreed with
|> his observation that energy may not be conserved on
|> the cosmological scale (I don't agree).

Sorry, I was confused by your somewhat unusual quoting style.
My quoting style is 'standard' (i.e. the most common) - I forgot
that you use one of the rarer ones.

But back to the physics. Do you have any reason to say that
energy must NECESSARILY be conserved? I.e. why is this a
fundamental principle?

My point is that it is a derivative principle, just as the law
that entropy increases is, and there is no obvious reason why
exact conservation should be required on a cosmological scale.
Equally, there is no reason why it shouldn't be, and I agree
that most evidence is that it probably is conserved :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <g4z8f.5304$iZ4.2901@newsfe2-gui.ntli.net>,
Michael C Price <michaelEXCISESPAMprice917@tesco.net> writes:
|>
|> Nick's quoting style makes it look like I was the author
|> of the text he quotes (I wasn't) and that I agreed with
|> his observation that energy may not be conserved on
|> the cosmological scale (I don't agree).

Sorry, I was confused by your somewhat unusual quoting style.
My quoting style is 'standard' (i.e. the most common) - I forgot
that you use one of the rarer ones.

But back to the physics. Do you have any reason to say that
energy must NECESSARILY be conserved? I.e. why is this a
fundamental principle?

My point is that it is a derivative principle, just as the law
that entropy increases is, and there is no obvious reason why
exact conservation should be required on a cosmological scale.
Equally, there is no reason why it shouldn't be, and I agree
that most evidence is that it probably is conserved :-)


Regards,
Nick Maclaren.

[Eugene Stefanovich]

Nick Maclaren wrote:

> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

In quantum physics, any system is described by a Hilbert space.
The principle of relativity demands that this Hilbert space carries
a unitary representation of the Poincare group. For example, if F
is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
is operator of this observable at time t, where H is the generator of
time translations that is identified with the observable of the
total energy of the system. Apparently

H(t) = exp(iHt)H exp(-iHt)
= H

which means that the total energy is exactly conserved.
The same is true in non-relativistic physics (the Poincare group
changes to the Galilei group). The same is true in classical physics,
i.e., in the limit hbar -> 0.

Eugene.

[Eugene Stefanovich]

Nick Maclaren wrote:

> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

In quantum physics, any system is described by a Hilbert space.
The principle of relativity demands that this Hilbert space carries
a unitary representation of the Poincare group. For example, if F
is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
is operator of this observable at time t, where H is the generator of
time translations that is identified with the observable of the
total energy of the system. Apparently

H(t) = exp(iHt)H exp(-iHt)
= H

which means that the total energy is exactly conserved.
The same is true in non-relativistic physics (the Poincare group
changes to the Galilei group). The same is true in classical physics,
i.e., in the limit hbar -> 0.

Eugene.

[Eugene Stefanovich]

Nick Maclaren wrote:

> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

In quantum physics, any system is described by a Hilbert space.
The principle of relativity demands that this Hilbert space carries
a unitary representation of the Poincare group. For example, if F
is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
is operator of this observable at time t, where H is the generator of
time translations that is identified with the observable of the
total energy of the system. Apparently

H(t) = exp(iHt)H exp(-iHt)
= H

which means that the total energy is exactly conserved.
The same is true in non-relativistic physics (the Poincare group
changes to the Galilei group). The same is true in classical physics,
i.e., in the limit hbar -> 0.

Eugene.

[Eugene Stefanovich]

Nick Maclaren wrote:

> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

In quantum physics, any system is described by a Hilbert space.
The principle of relativity demands that this Hilbert space carries
a unitary representation of the Poincare group. For example, if F
is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
is operator of this observable at time t, where H is the generator of
time translations that is identified with the observable of the
total energy of the system. Apparently

H(t) = exp(iHt)H exp(-iHt)
= H

which means that the total energy is exactly conserved.
The same is true in non-relativistic physics (the Poincare group
changes to the Galilei group). The same is true in classical physics,
i.e., in the limit hbar -> 0.

Eugene.

[Eugene Stefanovich]

Nick Maclaren wrote:

> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

In quantum physics, any system is described by a Hilbert space.
The principle of relativity demands that this Hilbert space carries
a unitary representation of the Poincare group. For example, if F
is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
is operator of this observable at time t, where H is the generator of
time translations that is identified with the observable of the
total energy of the system. Apparently

H(t) = exp(iHt)H exp(-iHt)
= H

which means that the total energy is exactly conserved.
The same is true in non-relativistic physics (the Poincare group
changes to the Galilei group). The same is true in classical physics,
i.e., in the limit hbar -> 0.

Eugene.

[Eugene Stefanovich]

Nick Maclaren wrote:

> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

In quantum physics, any system is described by a Hilbert space.
The principle of relativity demands that this Hilbert space carries
a unitary representation of the Poincare group. For example, if F
is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
is operator of this observable at time t, where H is the generator of
time translations that is identified with the observable of the
total energy of the system. Apparently

H(t) = exp(iHt)H exp(-iHt)
= H

which means that the total energy is exactly conserved.
The same is true in non-relativistic physics (the Poincare group
changes to the Galilei group). The same is true in classical physics,
i.e., in the limit hbar -> 0.

Eugene.

[Eugene Stefanovich]

Nick Maclaren wrote:

> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

In quantum physics, any system is described by a Hilbert space.
The principle of relativity demands that this Hilbert space carries
a unitary representation of the Poincare group. For example, if F
is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
is operator of this observable at time t, where H is the generator of
time translations that is identified with the observable of the
total energy of the system. Apparently

H(t) = exp(iHt)H exp(-iHt)
= H

which means that the total energy is exactly conserved.
The same is true in non-relativistic physics (the Poincare group
changes to the Galilei group). The same is true in classical physics,
i.e., in the limit hbar -> 0.

Eugene.

[Eugene Stefanovich]

Nick Maclaren wrote:

> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

In quantum physics, any system is described by a Hilbert space.
The principle of relativity demands that this Hilbert space carries
a unitary representation of the Poincare group. For example, if F
is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
is operator of this observable at time t, where H is the generator of
time translations that is identified with the observable of the
total energy of the system. Apparently

H(t) = exp(iHt)H exp(-iHt)
= H

which means that the total energy is exactly conserved.
The same is true in non-relativistic physics (the Poincare group
changes to the Galilei group). The same is true in classical physics,
i.e., in the limit hbar -> 0.

Eugene.

[Eugene Stefanovich]

Nick Maclaren wrote:

> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

In quantum physics, any system is described by a Hilbert space.
The principle of relativity demands that this Hilbert space carries
a unitary representation of the Poincare group. For example, if F
is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
is operator of this observable at time t, where H is the generator of
time translations that is identified with the observable of the
total energy of the system. Apparently

H(t) = exp(iHt)H exp(-iHt)
= H

which means that the total energy is exactly conserved.
The same is true in non-relativistic physics (the Poincare group
changes to the Galilei group). The same is true in classical physics,
i.e., in the limit hbar -> 0.

Eugene.

[Nick Maclaren]

In article <436820B3.2070905@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> writes:
|> Nick Maclaren wrote:
|>
|> > But back to the physics. Do you have any reason to say that
|> > energy must NECESSARILY be conserved? I.e. why is this a
|> > fundamental principle?
|>
|> In quantum physics, any system is described by a Hilbert space.
|> The principle of relativity demands that this Hilbert space carries
|> a unitary representation of the Poincare group. ....

That is really an answer to the question "Why is it conserved
in all current models?" rather than "Why it is necessarily
conserved?"

I agree that the principle shouldn't be abandoned lightly, but
to demand that all cosmological models must conserve energy is
effectively dogma. For example, it is very common for a
conservation rule to start off as 'perfect', to be found to be
imperfect, and then to be restored to perfection as part of a
more general conservation rule, which has previously been seen
only in part.

The rules about conservation of mass and energy (separately)
were exactly like that. It isn't impossible that mass-energy
might not be conserved on a cosmological scale but, say,
mass-energy-structure might be.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <436820B3.2070905@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> writes:
|> Nick Maclaren wrote:
|>
|> > But back to the physics. Do you have any reason to say that
|> > energy must NECESSARILY be conserved? I.e. why is this a
|> > fundamental principle?
|>
|> In quantum physics, any system is described by a Hilbert space.
|> The principle of relativity demands that this Hilbert space carries
|> a unitary representation of the Poincare group. ....

That is really an answer to the question "Why is it conserved
in all current models?" rather than "Why it is necessarily
conserved?"

I agree that the principle shouldn't be abandoned lightly, but
to demand that all cosmological models must conserve energy is
effectively dogma. For example, it is very common for a
conservation rule to start off as 'perfect', to be found to be
imperfect, and then to be restored to perfection as part of a
more general conservation rule, which has previously been seen
only in part.

The rules about conservation of mass and energy (separately)
were exactly like that. It isn't impossible that mass-energy
might not be conserved on a cosmological scale but, say,
mass-energy-structure might be.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <436820B3.2070905@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> writes:
|> Nick Maclaren wrote:
|>
|> > But back to the physics. Do you have any reason to say that
|> > energy must NECESSARILY be conserved? I.e. why is this a
|> > fundamental principle?
|>
|> In quantum physics, any system is described by a Hilbert space.
|> The principle of relativity demands that this Hilbert space carries
|> a unitary representation of the Poincare group. ....

That is really an answer to the question "Why is it conserved
in all current models?" rather than "Why it is necessarily
conserved?"

I agree that the principle shouldn't be abandoned lightly, but
to demand that all cosmological models must conserve energy is
effectively dogma. For example, it is very common for a
conservation rule to start off as 'perfect', to be found to be
imperfect, and then to be restored to perfection as part of a
more general conservation rule, which has previously been seen
only in part.

The rules about conservation of mass and energy (separately)
were exactly like that. It isn't impossible that mass-energy
might not be conserved on a cosmological scale but, say,
mass-energy-structure might be.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <436820B3.2070905@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> writes:
|> Nick Maclaren wrote:
|>
|> > But back to the physics. Do you have any reason to say that
|> > energy must NECESSARILY be conserved? I.e. why is this a
|> > fundamental principle?
|>
|> In quantum physics, any system is described by a Hilbert space.
|> The principle of relativity demands that this Hilbert space carries
|> a unitary representation of the Poincare group. ....

That is really an answer to the question "Why is it conserved
in all current models?" rather than "Why it is necessarily
conserved?"

I agree that the principle shouldn't be abandoned lightly, but
to demand that all cosmological models must conserve energy is
effectively dogma. For example, it is very common for a
conservation rule to start off as 'perfect', to be found to be
imperfect, and then to be restored to perfection as part of a
more general conservation rule, which has previously been seen
only in part.

The rules about conservation of mass and energy (separately)
were exactly like that. It isn't impossible that mass-energy
might not be conserved on a cosmological scale but, say,
mass-energy-structure might be.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <436820B3.2070905@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> writes:
|> Nick Maclaren wrote:
|>
|> > But back to the physics. Do you have any reason to say that
|> > energy must NECESSARILY be conserved? I.e. why is this a
|> > fundamental principle?
|>
|> In quantum physics, any system is described by a Hilbert space.
|> The principle of relativity demands that this Hilbert space carries
|> a unitary representation of the Poincare group. ....

That is really an answer to the question "Why is it conserved
in all current models?" rather than "Why it is necessarily
conserved?"

I agree that the principle shouldn't be abandoned lightly, but
to demand that all cosmological models must conserve energy is
effectively dogma. For example, it is very common for a
conservation rule to start off as 'perfect', to be found to be
imperfect, and then to be restored to perfection as part of a
more general conservation rule, which has previously been seen
only in part.

The rules about conservation of mass and energy (separately)
were exactly like that. It isn't impossible that mass-energy
might not be conserved on a cosmological scale but, say,
mass-energy-structure might be.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <436820B3.2070905@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> writes:
|> Nick Maclaren wrote:
|>
|> > But back to the physics. Do you have any reason to say that
|> > energy must NECESSARILY be conserved? I.e. why is this a
|> > fundamental principle?
|>
|> In quantum physics, any system is described by a Hilbert space.
|> The principle of relativity demands that this Hilbert space carries
|> a unitary representation of the Poincare group. ....

That is really an answer to the question "Why is it conserved
in all current models?" rather than "Why it is necessarily
conserved?"

I agree that the principle shouldn't be abandoned lightly, but
to demand that all cosmological models must conserve energy is
effectively dogma. For example, it is very common for a
conservation rule to start off as 'perfect', to be found to be
imperfect, and then to be restored to perfection as part of a
more general conservation rule, which has previously been seen
only in part.

The rules about conservation of mass and energy (separately)
were exactly like that. It isn't impossible that mass-energy
might not be conserved on a cosmological scale but, say,
mass-energy-structure might be.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <436820B3.2070905@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> writes:
|> Nick Maclaren wrote:
|>
|> > But back to the physics. Do you have any reason to say that
|> > energy must NECESSARILY be conserved? I.e. why is this a
|> > fundamental principle?
|>
|> In quantum physics, any system is described by a Hilbert space.
|> The principle of relativity demands that this Hilbert space carries
|> a unitary representation of the Poincare group. ....

That is really an answer to the question "Why is it conserved
in all current models?" rather than "Why it is necessarily
conserved?"

I agree that the principle shouldn't be abandoned lightly, but
to demand that all cosmological models must conserve energy is
effectively dogma. For example, it is very common for a
conservation rule to start off as 'perfect', to be found to be
imperfect, and then to be restored to perfection as part of a
more general conservation rule, which has previously been seen
only in part.

The rules about conservation of mass and energy (separately)
were exactly like that. It isn't impossible that mass-energy
might not be conserved on a cosmological scale but, say,
mass-energy-structure might be.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <436820B3.2070905@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> writes:
|> Nick Maclaren wrote:
|>
|> > But back to the physics. Do you have any reason to say that
|> > energy must NECESSARILY be conserved? I.e. why is this a
|> > fundamental principle?
|>
|> In quantum physics, any system is described by a Hilbert space.
|> The principle of relativity demands that this Hilbert space carries
|> a unitary representation of the Poincare group. ....

That is really an answer to the question "Why is it conserved
in all current models?" rather than "Why it is necessarily
conserved?"

I agree that the principle shouldn't be abandoned lightly, but
to demand that all cosmological models must conserve energy is
effectively dogma. For example, it is very common for a
conservation rule to start off as 'perfect', to be found to be
imperfect, and then to be restored to perfection as part of a
more general conservation rule, which has previously been seen
only in part.

The rules about conservation of mass and energy (separately)
were exactly like that. It isn't impossible that mass-energy
might not be conserved on a cosmological scale but, say,
mass-energy-structure might be.


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <436820B3.2070905@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> writes:
|> Nick Maclaren wrote:
|>
|> > But back to the physics. Do you have any reason to say that
|> > energy must NECESSARILY be conserved? I.e. why is this a
|> > fundamental principle?
|>
|> In quantum physics, any system is described by a Hilbert space.
|> The principle of relativity demands that this Hilbert space carries
|> a unitary representation of the Poincare group. ....

That is really an answer to the question "Why is it conserved
in all current models?" rather than "Why it is necessarily
conserved?"

I agree that the principle shouldn't be abandoned lightly, but
to demand that all cosmological models must conserve energy is
effectively dogma. For example, it is very common for a
conservation rule to start off as 'perfect', to be found to be
imperfect, and then to be restored to perfection as part of a
more general conservation rule, which has previously been seen
only in part.

The rules about conservation of mass and energy (separately)
were exactly like that. It isn't impossible that mass-energy
might not be conserved on a cosmological scale but, say,
mass-energy-structure might be.


Regards,
Nick Maclaren.

[Igor Khavkine]

Eugene Stefanovich wrote:
> Nick Maclaren wrote:
>
> > But back to the physics. Do you have any reason to say that
> > energy must NECESSARILY be conserved? I.e. why is this a
> > fundamental principle?
>
> In quantum physics, any system is described by a Hilbert space.
> The principle of relativity demands that this Hilbert space carries
> a unitary representation of the Poincare group. For example, if F
> is operator of an observable at time t=0 then F(t)=exp(iHt)Fexp(-iHt)
> is operator of this observable at time t, where H is the generator of
> time translations that is identified with the observable of the
> total energy of the system. Apparently
>
> H(t) = exp(iHt)H exp(-iHt)
> = H
>
> which means that the total energy is exactly conserved.
> The same is true in non-relativistic physics (the Poincare group
> changes to the Galilei group). The same is true in classical physics,
> i.e., in the limit hbar -> 0.

This is true, but there is no need to bring in quantum mechanics
because the exact same argument can be used in the Hamiltonian
formulation of classical mechanics. Moreover, the reason energy
conservation holds in this way is precisely because the space-time on
which the theory is formulated posesses Poincare or Galilei symmetry.
In general, only time translation symmetry is required, that is a
consequence of Noether's theorem.

However, when the underlying space-time is neither Minkowski, or
Galilean, but some non-static solution of Einstein's equations, like
the one of the Friedman-Robertson-Walker space-times, a time
translation symmetry cannot be found. That is why global energy
conservation does not hold. However, locally, energy conservation still
holds as long as we can neglect the rate of cosmological expansion.

Igor

[Michael C Price]

Nick:
>
> But back to the physics. Do you have any reason to say that
> energy must NECESSARILY be conserved? I.e. why is this a
> fundamental principle?

1) Because energy is what we choose to define it as,
and we have come to choose to define it so that it is
conserved.
Those people who claim that energy isn't conserved
simply aren't trying hard enough or have an unjustified
aversion to pseudotensors.
2) Noether's theorem says we necessarily have conserved
energy(ies) on a flat space time with fields; gravity can be
regarded as a field theory in a flat space time; ergo energy
can be conserved in GR and hence cosmology. This is
not to detract from tensors and the genometrical
approach to GR, but we shouldn't let one approach
cloud truths that are more apparent in other approaches.

> My point is that it is a derivative principle, just as the law
> that entropy increases is, and there is no obvious reason why
> exact conservation should be required on a cosmological scale.

I agree that it started out as a derivative principle, but I think
it has moved beyond that. In the example you give later of
subsuming the energy-matter conservation law into an
energy-matter-structure conservation law we would simply
*redefine* "new energy" = "old energy + f(structure)",
which is what we did with matter around 1905.

> Equally, there is no reason why it shouldn't be, and I agree
> that most evidence is that it probably is conserved :-)

Thanks!

>
> Regards,
> Nick Maclaren.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Aaron Denney]

On 2005-11-04, Michael C Price <michaelEXCISESPAMprice917@tesco.net> wrote:
> gravity can be regarded as a field theory in a flat space time;

In the weak-field limit, sure. Is there any reason to believe this true
for more exotic regimes? Non-trivial topologies?

--
Aaron Denney
-><-

[Michael C Price]

*****************************
Note to moderators: I first sent the below
message over a week ago and it hasn't appeared
yet. If there's a problem let me know.
*****************************

Me:
>> gravity can be regarded as a field theory in a flat space
>> time;
>
Aaron:
> In the weak-field limit, sure. Is there any reason to believe
> this true for more exotic regimes? Non-trivial topologies?

True for strong field regimes as well, AFAIK.
I suspect non-trivial topologies can be handled. Puncture and
project ("flatten") a sphere onto a disk and the resulting "metric"
(now regarded as just another field) prevents any straying beyond
the edge of the circle (or 3-D vol' in our case).

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

*****************************
Note to moderators: I first sent the below
message over a week ago and it hasn't appeared
yet. If there's a problem let me know.
*****************************
Phillip Helbig:
> Within the context of general relativity, if a static universe contains
> matter and a cosmological constant, then it cannot be spatially flat.

Why cannot we set the cosmological constant to -rho/(8 pi G),
which balances the equation for static flatness? (Like Einstein's
original static closed universe, probably unstable.)

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Phillip Helbig:
> Within the context of general relativity, if a static universe contains
> matter and a cosmological constant, then it cannot be spatially flat.

Why cannot we set the cosmological constant to -rho/(8 pi G),
which balances the equation for static flatness? (Like Einstein's
original static closed universe, probably unstable.)

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

Me:
>> gravity can be regarded as a field theory in a flat space
>> time;
>
Aaron:
> In the weak-field limit, sure. Is there any reason to believe
> this true for more exotic regimes? Non-trivial topologies?

True for strong field regimes as well, AFAIK.
I suspect non-trivial topologies can be handled. Puncture and
project ("flatten") a sphere onto a disk and the resulting "metric"
(now regarded as just another field) prevents any straying beyond
the edge of the circle (or 3-D vol' in our case).

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Michael C Price]

****************
Note to moderators: I am resending this (for the 2nd time) since
it hasn't appeared on s.p.r. (nor have I been notified of its rejection),
whilst the thread has continued through several iterations.
Was it lost in the ether?
***************
Me:
>>To add a new point about energy conservation in this thread;
>>Noether's theorem. Energy, as we know, is the conserved
>>Noether charge implied by the invariance of physical law with
>>time. Ergo the universe obeys energy conservation or
>>physical law is a function of time..... and who would be happy
>>with the latter?
>
Ted:
> Noether's theorem gives you a way to construct a local conservation
> law from a local symmetry. It does indeed apply in this case, and
> energy is locally conserved in general relativity. The problem comes
> when you try to integrate that up to get a global conservation law.
> That can't be done for energy in general relativity.
>
> Compare the situation with that of charge conservation. You
> can express charge conservation locally this way:
>
> d rho / dt = -div j
>
> (rate of change of charge density at a given point is related to
> the current flow into or out of that point). If you like, you
> can integrate that over some volume to get
>
> (d/dt)(Charge enclosed in a volume) = (Current flow across the boundary)
>
> In a situation where there is no boundary, or where you know
> there's no current flow across the boundary, you get global
> conservation of charge.
>
> The first version is the version that pops out of Noether's theorem,
> and it has an analogue for energy conservation in general relatitivity
> (the 4-dimensional divergence of the stress-energy tensor equals zero).
> But the step where you integrate that up to get a global
> law doesn't work in a nice way, so there's no nice law of
> global energy conservation.
>
> (To see what "nice" means in this context, see the FAQ.)
>
> -Ted
>
Thank you for the explanation of where the difficulties lie. I presume
that "nice" refers to not resorting to the use of pseudo-tensors?
I don't have a problem with them, although not tensors their integrals
across suitable space-like hypersurfaces are constants, as we require.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

[Phillip Helbig---remove CLOTHES to reply]

In article <dlb3or$dfi$1@fiasco.xenopsyche.net>, "Michael C Price"
<michael.price917@tesco.net> writes:

> Phillip Helbig:
> > Within the context of general relativity, if a static universe contains
> > matter and a cosmological constant, then it cannot be spatially flat.
>
> Why cannot we set the cosmological constant to -rho/(8 pi G),
> which balances the equation for static flatness? (Like Einstein's
> original static closed universe, probably unstable.)

A positive cosmological constant acts like matter with respect to
curvature, but opposite to matter with respect to expansion. Vice versa
for a negative cosmological constant. If you select a negative
cosmological constant so that it balances matter with respect to
curvature, both terms will have the same sign with respect to expansion,
thus such a universe can't be static.

Note that it is not unstable in the sense of Einstein's original static
universe (or, with respect to the cosmological parameters if not the
expansion itself, in the sense of the Einstein-de Sitter universe);
here, UNPERTURBED the universe can exist forever. Rather, even in the
unperturbed state such a universe as you describe above will be
decelerating. (There is the trivial case at the turnaround point where
maximum expansion is reached before recollapse (this happens in all
universes with a negative cosmological constant): here, the universe is
instantaneously static in that dR/dt is 0, but of course d²R/dt² is not
0.)

[Aaron Denney]

On 2005-11-14, Michael C Price <michaelEXCISESPAM.price917@tesco.net> wrote:
> Me:
>>> gravity can be regarded as a field theory in a flat space
>>> time;
>>
> Aaron:
>> In the weak-field limit, sure. Is there any reason to believe
>> this true for more exotic regimes? Non-trivial topologies?
>
> True for strong field regimes as well, AFAIK.
> I suspect non-trivial topologies can be handled. Puncture and
> project ("flatten") a sphere onto a disk and the resulting "metric"
> (now regarded as just another field) prevents any straying beyond
> the edge of the circle (or 3-D vol' in our case).

I was thinking more of something more extreme like toroids, or spaces
that allow embedding of CTCs, such as Goedel's rotating solution.
Now, you may say that excluding these sorts of things is a feature...

--
Aaron Denney
-><-

[Ilja Schmelzer]

"Aaron Denney" <wnoise@ofb.net> schrieb
> Michael C Price <michaelEXCISESPAM.price917@tesco.net> wrote:
> > Me:
> >>> gravity can be regarded as a field theory in a flat space
> >>> time;
> >>
> > Aaron:
> >> In the weak-field limit, sure. Is there any reason to believe
> >> this true for more exotic regimes? Non-trivial topologies?
> >
> > True for strong field regimes as well, AFAIK.
> > I suspect non-trivial topologies can be handled. Puncture and
> > project ("flatten") a sphere onto a disk and the resulting "metric"
> > (now regarded as just another field) prevents any straying beyond
> > the edge of the circle (or 3-D vol' in our case).
>
> I was thinking more of something more extreme like toroids, or spaces
> that allow embedding of CTCs, such as Goedel's rotating solution.
> Now, you may say that excluding these sorts of things is a feature...

In gr-qc/0205035 I propose a modification of GR on a flat background,
with condensed matter interpretation. (The EEP holds, and the Einstein
equations appear in a natural limit. Essentially, it is GR in harmonic
gauge.)

I think indeed that excluding nontrivial topologies is a feature. It
simplifies quantization. The fixed background may be used for canonical
quantization. And the condensed matter interpretation may be used to
follow the standard procedure to quantize condensed matter for the
quantization of gravity. (The harmonic gauge becomes the continuity and
Euler equations. In a discretization where the "density" g^00 sqrt(-g)
becomes the density of nodes the continuity equation disappears and the
Euler equation becomes second order. Thus, the first order constraints
make no problems.)

It is interesting to look how nontrivial topologies and causal loops are
handled. First, the additional terms which enforce the harmonic gauge
prevent some singularities (big bang, black hole). Then, the metric is
only effective, thus, there is no argument that enforces that the metric
has to be complete. The solution is complete if defined on the whole
background, not if the metric is complete. Last not least, in solutions
with closed causal loops the condensed matter interpretation fails,
somewhere we obtain rho = g^00 sqrt(-g) = 0. Nothing we would wonder
about, if we have a very large disc and rotate him, somewhere we will
obtain rho=0, and after this the continuous condensed matter description
is inappropriate.

Ilja