Dark Energy


by nc
Tags: dark, energy
Phillip Helbig---remove CLOTHES to reply
#55
Oct12-06, 05:06 AM
P: n/a
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/~...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
#56
Oct12-06, 05:06 AM
P: n/a
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/~...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
#57
Oct12-06, 05:06 AM
P: n/a
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/~...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
#58
Oct12-06, 05:06 AM
P: n/a
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/~...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
#59
Oct12-06, 05:06 AM
P: n/a
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/~...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
#60
Oct12-06, 05:06 AM
P: n/a
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/~...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
#61
Oct12-06, 05:07 AM
P: n/a
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/~...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
#62
Oct12-06, 05:07 AM
P: n/a
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/~...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
#63
Oct12-06, 05:07 AM
P: n/a
"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/~...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
#64
Oct12-06, 05:07 AM
P: n/a
"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/~...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
#65
Oct12-06, 05:07 AM
P: n/a
"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/~...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
#66
Oct12-06, 05:07 AM
P: n/a
"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/~...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
#67
Oct12-06, 05:07 AM
P: n/a
"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/~...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
#68
Oct12-06, 05:07 AM
P: n/a
"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/~...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
#69
Oct12-06, 05:07 AM
P: n/a
"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/~...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
#70
Oct12-06, 05:07 AM
P: n/a
"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/~...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
#71
Oct12-06, 05:07 AM
P: n/a
"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/~...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
#72
Oct12-06, 05:08 AM
P: n/a
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.)



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