## Dark Energy

>> 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.

> (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

 >> 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/~...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
 In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" 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"?  In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" 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"?
 In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" 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"?  In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" 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"?
 In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" 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"?  In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" 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"?
 In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" 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"?  In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" 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"?
 In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" 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" wrote in message news:diqsgh$ppl$1@online.de... > In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" > 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" wrote in message news:diqsgh$ppl$1@online.de... > In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" > 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" wrote in message news:diqsgh$ppl$1@online.de... > In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" > 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" wrote in message news:diqsgh$ppl$1@online.de... > In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" > 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" wrote in message news:diqsgh$ppl$1@online.de... > In article <3%Q3f.1089$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" > 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" wrote in message news:diqsgh$ppl$1@online.de... > In article <3%Q3f.1089\$WI4.1078@newsfe4-gui.ntli.net>, "Michael C Price" > 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

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