# Dark Energy

by nc
Tags: dark, energy
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 P: n/a In article <%ZD4f.3782$cA4.3019@newsfe3-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. > >>>> 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.)  P: n/a In article <%ZD4f.3782$cA4.3019@newsfe3-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. > >>>> 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.)
 P: n/a In article <%ZD4f.3782$cA4.3019@newsfe3-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. > >>>> 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.)  P: n/a In article <%ZD4f.3782$cA4.3019@newsfe3-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. > >>>> 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.)
 P: n/a In article <%ZD4f.3782$cA4.3019@newsfe3-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. > >>>> 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.)  P: n/a In article <%ZD4f.3782$cA4.3019@newsfe3-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. > >>>> 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.)
 P: n/a In article <%ZD4f.3782$cA4.3019@newsfe3-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. > >>>> 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.)  P: n/a In article <%ZD4f.3782$cA4.3019@newsfe3-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. > >>>> 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.)
 P: n/a Me: >> 8 pi G rho + gamma + -3H^2 = 0 >> >> ( gamma = cosmological constant, a form of dark energy. >> rho = average matter density >> G = Newton's constant >> H = Hubble's expansion factor. ) >> >> The question is: how do we interpret this equation? >> >> Since the first two terms are proportional to energy density then >> it is a reasonable inference that we have an expression of energy >> conservation if the last term is also proportional to energy density; >> in this case the energy of the dynamic geometry. >> [.......] Philip: > Let me rephrase my criticism. You say that there is a conservation > equation, and say that the energy of the cosmological constant "comes > from" the expansion and also that the equation is valid if there is no > cosmological constant. So, my question is, if there is no cosmological > constant, then, in the case of no cosmological constant, where does the > energy go which, in the case of a cosmological constant, is transformed > into the cosmological constant? Let me answer it this way: the cosmological constant currently dominates the expansion of the universe. The matter and photons are just being carried along for the ride. (This wasn't always the case. Earlier the matter dominated, and before that the photons.) The dominant flow of energy, today, is from the Hubble expansion to the cosmological constant, each one growing in magnitude although of opposite sign. Without a cosmological constant the presently insignificant flow from the photons (via the red shift) to the Hubble factor would dominate, as it did in the early universe. i.e. the direction of the energy flow would be reversed. > Imagine the Einstein static universe. There is no expansion. Yet there > is an energy density due to the cosmological constant. How does it > "come from" the (non-existent) expansion in this case? What about a > negative cosmological constant? Indeed, as you point out, in Einstein's original static universe the cosmological constant was negative and its now negative energy offset the energy in the matter and photons. With no expansion there was no energy transfer to/from the cosmological constant. > > I'll reply in more detail later. > > Perhaps we are merely using completely different terminology. However, > I think that what you are saying is misleading, or at least confusingly > phrased. You seem to be saying "no mystery where the dark energy comes > from, it comes from expansion". Of course if there is an equation which > holds while the universe expands, then something is conserved; the > question is how this relates to commonly used usages of the term. True. > I think Edward Harrison has explained rather well what is meant by > "energy is not conserved in the expanding universe". Do you disagree > with his analysis? Yes. If I understand Harrison's argument it is that pressure and pressure gradients mediate the transfer of energy in the thermodynamic dE = -P dV equation (which has a cosmological equivalent), which describes the expansion of, say, a pressurised gas against its environment. But in the universe there is no exterior system to push against and hence no transfer of energy. Instead he concludes the red-shift energy is lost and not transferred. I think he is being lead astray by the thermodynamic analogy with pressure. Pressure is the result of particles (including photons) with momenta, which have de Broglie wavelengths. It is the stretching of the wavelengths by the Hubble expansion which causes the loss of momenta and the red-shift. The loss of radiation pressure is a consequence of this stretching and not a mediating mechanism; no pressure gradient or exterior system is required. I agree with your point about definitions and the Doppler effect. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm
 P: n/a Me: >> 8 pi G rho + gamma + -3H^2 = 0 >> >> ( gamma = cosmological constant, a form of dark energy. >> rho = average matter density >> G = Newton's constant >> H = Hubble's expansion factor. ) >> >> The question is: how do we interpret this equation? >> >> Since the first two terms are proportional to energy density then >> it is a reasonable inference that we have an expression of energy >> conservation if the last term is also proportional to energy density; >> in this case the energy of the dynamic geometry. >> [.......] Philip: > Let me rephrase my criticism. You say that there is a conservation > equation, and say that the energy of the cosmological constant "comes > from" the expansion and also that the equation is valid if there is no > cosmological constant. So, my question is, if there is no cosmological > constant, then, in the case of no cosmological constant, where does the > energy go which, in the case of a cosmological constant, is transformed > into the cosmological constant? Let me answer it this way: the cosmological constant currently dominates the expansion of the universe. The matter and photons are just being carried along for the ride. (This wasn't always the case. Earlier the matter dominated, and before that the photons.) The dominant flow of energy, today, is from the Hubble expansion to the cosmological constant, each one growing in magnitude although of opposite sign. Without a cosmological constant the presently insignificant flow from the photons (via the red shift) to the Hubble factor would dominate, as it did in the early universe. i.e. the direction of the energy flow would be reversed. > Imagine the Einstein static universe. There is no expansion. Yet there > is an energy density due to the cosmological constant. How does it > "come from" the (non-existent) expansion in this case? What about a > negative cosmological constant? Indeed, as you point out, in Einstein's original static universe the cosmological constant was negative and its now negative energy offset the energy in the matter and photons. With no expansion there was no energy transfer to/from the cosmological constant. > > I'll reply in more detail later. > > Perhaps we are merely using completely different terminology. However, > I think that what you are saying is misleading, or at least confusingly > phrased. You seem to be saying "no mystery where the dark energy comes > from, it comes from expansion". Of course if there is an equation which > holds while the universe expands, then something is conserved; the > question is how this relates to commonly used usages of the term. True. > I think Edward Harrison has explained rather well what is meant by > "energy is not conserved in the expanding universe". Do you disagree > with his analysis? Yes. If I understand Harrison's argument it is that pressure and pressure gradients mediate the transfer of energy in the thermodynamic dE = -P dV equation (which has a cosmological equivalent), which describes the expansion of, say, a pressurised gas against its environment. But in the universe there is no exterior system to push against and hence no transfer of energy. Instead he concludes the red-shift energy is lost and not transferred. I think he is being lead astray by the thermodynamic analogy with pressure. Pressure is the result of particles (including photons) with momenta, which have de Broglie wavelengths. It is the stretching of the wavelengths by the Hubble expansion which causes the loss of momenta and the red-shift. The loss of radiation pressure is a consequence of this stretching and not a mediating mechanism; no pressure gradient or exterior system is required. I agree with your point about definitions and the Doppler effect. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm
 P: n/a Me: >> 8 pi G rho + gamma + -3H^2 = 0 >> >> ( gamma = cosmological constant, a form of dark energy. >> rho = average matter density >> G = Newton's constant >> H = Hubble's expansion factor. ) >> >> The question is: how do we interpret this equation? >> >> Since the first two terms are proportional to energy density then >> it is a reasonable inference that we have an expression of energy >> conservation if the last term is also proportional to energy density; >> in this case the energy of the dynamic geometry. >> [.......] Philip: > Let me rephrase my criticism. You say that there is a conservation > equation, and say that the energy of the cosmological constant "comes > from" the expansion and also that the equation is valid if there is no > cosmological constant. So, my question is, if there is no cosmological > constant, then, in the case of no cosmological constant, where does the > energy go which, in the case of a cosmological constant, is transformed > into the cosmological constant? Let me answer it this way: the cosmological constant currently dominates the expansion of the universe. The matter and photons are just being carried along for the ride. (This wasn't always the case. Earlier the matter dominated, and before that the photons.) The dominant flow of energy, today, is from the Hubble expansion to the cosmological constant, each one growing in magnitude although of opposite sign. Without a cosmological constant the presently insignificant flow from the photons (via the red shift) to the Hubble factor would dominate, as it did in the early universe. i.e. the direction of the energy flow would be reversed. > Imagine the Einstein static universe. There is no expansion. Yet there > is an energy density due to the cosmological constant. How does it > "come from" the (non-existent) expansion in this case? What about a > negative cosmological constant? Indeed, as you point out, in Einstein's original static universe the cosmological constant was negative and its now negative energy offset the energy in the matter and photons. With no expansion there was no energy transfer to/from the cosmological constant. > > I'll reply in more detail later. > > Perhaps we are merely using completely different terminology. However, > I think that what you are saying is misleading, or at least confusingly > phrased. You seem to be saying "no mystery where the dark energy comes > from, it comes from expansion". Of course if there is an equation which > holds while the universe expands, then something is conserved; the > question is how this relates to commonly used usages of the term. True. > I think Edward Harrison has explained rather well what is meant by > "energy is not conserved in the expanding universe". Do you disagree > with his analysis? Yes. If I understand Harrison's argument it is that pressure and pressure gradients mediate the transfer of energy in the thermodynamic dE = -P dV equation (which has a cosmological equivalent), which describes the expansion of, say, a pressurised gas against its environment. But in the universe there is no exterior system to push against and hence no transfer of energy. Instead he concludes the red-shift energy is lost and not transferred. I think he is being lead astray by the thermodynamic analogy with pressure. Pressure is the result of particles (including photons) with momenta, which have de Broglie wavelengths. It is the stretching of the wavelengths by the Hubble expansion which causes the loss of momenta and the red-shift. The loss of radiation pressure is a consequence of this stretching and not a mediating mechanism; no pressure gradient or exterior system is required. I agree with your point about definitions and the Doppler effect. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm
 P: n/a Me: >> 8 pi G rho + gamma + -3H^2 = 0 >> >> ( gamma = cosmological constant, a form of dark energy. >> rho = average matter density >> G = Newton's constant >> H = Hubble's expansion factor. ) >> >> The question is: how do we interpret this equation? >> >> Since the first two terms are proportional to energy density then >> it is a reasonable inference that we have an expression of energy >> conservation if the last term is also proportional to energy density; >> in this case the energy of the dynamic geometry. >> [.......] Philip: > Let me rephrase my criticism. You say that there is a conservation > equation, and say that the energy of the cosmological constant "comes > from" the expansion and also that the equation is valid if there is no > cosmological constant. So, my question is, if there is no cosmological > constant, then, in the case of no cosmological constant, where does the > energy go which, in the case of a cosmological constant, is transformed > into the cosmological constant? Let me answer it this way: the cosmological constant currently dominates the expansion of the universe. The matter and photons are just being carried along for the ride. (This wasn't always the case. Earlier the matter dominated, and before that the photons.) The dominant flow of energy, today, is from the Hubble expansion to the cosmological constant, each one growing in magnitude although of opposite sign. Without a cosmological constant the presently insignificant flow from the photons (via the red shift) to the Hubble factor would dominate, as it did in the early universe. i.e. the direction of the energy flow would be reversed. > Imagine the Einstein static universe. There is no expansion. Yet there > is an energy density due to the cosmological constant. How does it > "come from" the (non-existent) expansion in this case? What about a > negative cosmological constant? Indeed, as you point out, in Einstein's original static universe the cosmological constant was negative and its now negative energy offset the energy in the matter and photons. With no expansion there was no energy transfer to/from the cosmological constant. > > I'll reply in more detail later. > > Perhaps we are merely using completely different terminology. However, > I think that what you are saying is misleading, or at least confusingly > phrased. You seem to be saying "no mystery where the dark energy comes > from, it comes from expansion". Of course if there is an equation which > holds while the universe expands, then something is conserved; the > question is how this relates to commonly used usages of the term. True. > I think Edward Harrison has explained rather well what is meant by > "energy is not conserved in the expanding universe". Do you disagree > with his analysis? Yes. If I understand Harrison's argument it is that pressure and pressure gradients mediate the transfer of energy in the thermodynamic dE = -P dV equation (which has a cosmological equivalent), which describes the expansion of, say, a pressurised gas against its environment. But in the universe there is no exterior system to push against and hence no transfer of energy. Instead he concludes the red-shift energy is lost and not transferred. I think he is being lead astray by the thermodynamic analogy with pressure. Pressure is the result of particles (including photons) with momenta, which have de Broglie wavelengths. It is the stretching of the wavelengths by the Hubble expansion which causes the loss of momenta and the red-shift. The loss of radiation pressure is a consequence of this stretching and not a mediating mechanism; no pressure gradient or exterior system is required. I agree with your point about definitions and the Doppler effect. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm
 P: n/a Me: >> 8 pi G rho + gamma + -3H^2 = 0 >> >> ( gamma = cosmological constant, a form of dark energy. >> rho = average matter density >> G = Newton's constant >> H = Hubble's expansion factor. ) >> >> The question is: how do we interpret this equation? >> >> Since the first two terms are proportional to energy density then >> it is a reasonable inference that we have an expression of energy >> conservation if the last term is also proportional to energy density; >> in this case the energy of the dynamic geometry. >> [.......] Philip: > Let me rephrase my criticism. You say that there is a conservation > equation, and say that the energy of the cosmological constant "comes > from" the expansion and also that the equation is valid if there is no > cosmological constant. So, my question is, if there is no cosmological > constant, then, in the case of no cosmological constant, where does the > energy go which, in the case of a cosmological constant, is transformed > into the cosmological constant? Let me answer it this way: the cosmological constant currently dominates the expansion of the universe. The matter and photons are just being carried along for the ride. (This wasn't always the case. Earlier the matter dominated, and before that the photons.) The dominant flow of energy, today, is from the Hubble expansion to the cosmological constant, each one growing in magnitude although of opposite sign. Without a cosmological constant the presently insignificant flow from the photons (via the red shift) to the Hubble factor would dominate, as it did in the early universe. i.e. the direction of the energy flow would be reversed. > Imagine the Einstein static universe. There is no expansion. Yet there > is an energy density due to the cosmological constant. How does it > "come from" the (non-existent) expansion in this case? What about a > negative cosmological constant? Indeed, as you point out, in Einstein's original static universe the cosmological constant was negative and its now negative energy offset the energy in the matter and photons. With no expansion there was no energy transfer to/from the cosmological constant. > > I'll reply in more detail later. > > Perhaps we are merely using completely different terminology. However, > I think that what you are saying is misleading, or at least confusingly > phrased. You seem to be saying "no mystery where the dark energy comes > from, it comes from expansion". Of course if there is an equation which > holds while the universe expands, then something is conserved; the > question is how this relates to commonly used usages of the term. True. > I think Edward Harrison has explained rather well what is meant by > "energy is not conserved in the expanding universe". Do you disagree > with his analysis? Yes. If I understand Harrison's argument it is that pressure and pressure gradients mediate the transfer of energy in the thermodynamic dE = -P dV equation (which has a cosmological equivalent), which describes the expansion of, say, a pressurised gas against its environment. But in the universe there is no exterior system to push against and hence no transfer of energy. Instead he concludes the red-shift energy is lost and not transferred. I think he is being lead astray by the thermodynamic analogy with pressure. Pressure is the result of particles (including photons) with momenta, which have de Broglie wavelengths. It is the stretching of the wavelengths by the Hubble expansion which causes the loss of momenta and the red-shift. The loss of radiation pressure is a consequence of this stretching and not a mediating mechanism; no pressure gradient or exterior system is required. I agree with your point about definitions and the Doppler effect. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm
 P: n/a Me: >> 8 pi G rho + gamma + -3H^2 = 0 >> >> ( gamma = cosmological constant, a form of dark energy. >> rho = average matter density >> G = Newton's constant >> H = Hubble's expansion factor. ) >> >> The question is: how do we interpret this equation? >> >> Since the first two terms are proportional to energy density then >> it is a reasonable inference that we have an expression of energy >> conservation if the last term is also proportional to energy density; >> in this case the energy of the dynamic geometry. >> [.......] Philip: > Let me rephrase my criticism. You say that there is a conservation > equation, and say that the energy of the cosmological constant "comes > from" the expansion and also that the equation is valid if there is no > cosmological constant. So, my question is, if there is no cosmological > constant, then, in the case of no cosmological constant, where does the > energy go which, in the case of a cosmological constant, is transformed > into the cosmological constant? Let me answer it this way: the cosmological constant currently dominates the expansion of the universe. The matter and photons are just being carried along for the ride. (This wasn't always the case. Earlier the matter dominated, and before that the photons.) The dominant flow of energy, today, is from the Hubble expansion to the cosmological constant, each one growing in magnitude although of opposite sign. Without a cosmological constant the presently insignificant flow from the photons (via the red shift) to the Hubble factor would dominate, as it did in the early universe. i.e. the direction of the energy flow would be reversed. > Imagine the Einstein static universe. There is no expansion. Yet there > is an energy density due to the cosmological constant. How does it > "come from" the (non-existent) expansion in this case? What about a > negative cosmological constant? Indeed, as you point out, in Einstein's original static universe the cosmological constant was negative and its now negative energy offset the energy in the matter and photons. With no expansion there was no energy transfer to/from the cosmological constant. > > I'll reply in more detail later. > > Perhaps we are merely using completely different terminology. However, > I think that what you are saying is misleading, or at least confusingly > phrased. You seem to be saying "no mystery where the dark energy comes > from, it comes from expansion". Of course if there is an equation which > holds while the universe expands, then something is conserved; the > question is how this relates to commonly used usages of the term. True. > I think Edward Harrison has explained rather well what is meant by > "energy is not conserved in the expanding universe". Do you disagree > with his analysis? Yes. If I understand Harrison's argument it is that pressure and pressure gradients mediate the transfer of energy in the thermodynamic dE = -P dV equation (which has a cosmological equivalent), which describes the expansion of, say, a pressurised gas against its environment. But in the universe there is no exterior system to push against and hence no transfer of energy. Instead he concludes the red-shift energy is lost and not transferred. I think he is being lead astray by the thermodynamic analogy with pressure. Pressure is the result of particles (including photons) with momenta, which have de Broglie wavelengths. It is the stretching of the wavelengths by the Hubble expansion which causes the loss of momenta and the red-shift. The loss of radiation pressure is a consequence of this stretching and not a mediating mechanism; no pressure gradient or exterior system is required. I agree with your point about definitions and the Doppler effect. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm
 P: n/a Me: >> 8 pi G rho + gamma + -3H^2 = 0 >> >> ( gamma = cosmological constant, a form of dark energy. >> rho = average matter density >> G = Newton's constant >> H = Hubble's expansion factor. ) >> >> The question is: how do we interpret this equation? >> >> Since the first two terms are proportional to energy density then >> it is a reasonable inference that we have an expression of energy >> conservation if the last term is also proportional to energy density; >> in this case the energy of the dynamic geometry. >> [.......] Philip: > Let me rephrase my criticism. You say that there is a conservation > equation, and say that the energy of the cosmological constant "comes > from" the expansion and also that the equation is valid if there is no > cosmological constant. So, my question is, if there is no cosmological > constant, then, in the case of no cosmological constant, where does the > energy go which, in the case of a cosmological constant, is transformed > into the cosmological constant? Let me answer it this way: the cosmological constant currently dominates the expansion of the universe. The matter and photons are just being carried along for the ride. (This wasn't always the case. Earlier the matter dominated, and before that the photons.) The dominant flow of energy, today, is from the Hubble expansion to the cosmological constant, each one growing in magnitude although of opposite sign. Without a cosmological constant the presently insignificant flow from the photons (via the red shift) to the Hubble factor would dominate, as it did in the early universe. i.e. the direction of the energy flow would be reversed. > Imagine the Einstein static universe. There is no expansion. Yet there > is an energy density due to the cosmological constant. How does it > "come from" the (non-existent) expansion in this case? What about a > negative cosmological constant? Indeed, as you point out, in Einstein's original static universe the cosmological constant was negative and its now negative energy offset the energy in the matter and photons. With no expansion there was no energy transfer to/from the cosmological constant. > > I'll reply in more detail later. > > Perhaps we are merely using completely different terminology. However, > I think that what you are saying is misleading, or at least confusingly > phrased. You seem to be saying "no mystery where the dark energy comes > from, it comes from expansion". Of course if there is an equation which > holds while the universe expands, then something is conserved; the > question is how this relates to commonly used usages of the term. True. > I think Edward Harrison has explained rather well what is meant by > "energy is not conserved in the expanding universe". Do you disagree > with his analysis? Yes. If I understand Harrison's argument it is that pressure and pressure gradients mediate the transfer of energy in the thermodynamic dE = -P dV equation (which has a cosmological equivalent), which describes the expansion of, say, a pressurised gas against its environment. But in the universe there is no exterior system to push against and hence no transfer of energy. Instead he concludes the red-shift energy is lost and not transferred. I think he is being lead astray by the thermodynamic analogy with pressure. Pressure is the result of particles (including photons) with momenta, which have de Broglie wavelengths. It is the stretching of the wavelengths by the Hubble expansion which causes the loss of momenta and the red-shift. The loss of radiation pressure is a consequence of this stretching and not a mediating mechanism; no pressure gradient or exterior system is required. I agree with your point about definitions and the Doppler effect. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm
 P: n/a Me: >> 8 pi G rho + gamma + -3H^2 = 0 >> >> ( gamma = cosmological constant, a form of dark energy. >> rho = average matter density >> G = Newton's constant >> H = Hubble's expansion factor. ) >> >> The question is: how do we interpret this equation? >> >> Since the first two terms are proportional to energy density then >> it is a reasonable inference that we have an expression of energy >> conservation if the last term is also proportional to energy density; >> in this case the energy of the dynamic geometry. >> [.......] Philip: > Let me rephrase my criticism. You say that there is a conservation > equation, and say that the energy of the cosmological constant "comes > from" the expansion and also that the equation is valid if there is no > cosmological constant. So, my question is, if there is no cosmological > constant, then, in the case of no cosmological constant, where does the > energy go which, in the case of a cosmological constant, is transformed > into the cosmological constant? Let me answer it this way: the cosmological constant currently dominates the expansion of the universe. The matter and photons are just being carried along for the ride. (This wasn't always the case. Earlier the matter dominated, and before that the photons.) The dominant flow of energy, today, is from the Hubble expansion to the cosmological constant, each one growing in magnitude although of opposite sign. Without a cosmological constant the presently insignificant flow from the photons (via the red shift) to the Hubble factor would dominate, as it did in the early universe. i.e. the direction of the energy flow would be reversed. > Imagine the Einstein static universe. There is no expansion. Yet there > is an energy density due to the cosmological constant. How does it > "come from" the (non-existent) expansion in this case? What about a > negative cosmological constant? Indeed, as you point out, in Einstein's original static universe the cosmological constant was negative and its now negative energy offset the energy in the matter and photons. With no expansion there was no energy transfer to/from the cosmological constant. > > I'll reply in more detail later. > > Perhaps we are merely using completely different terminology. However, > I think that what you are saying is misleading, or at least confusingly > phrased. You seem to be saying "no mystery where the dark energy comes > from, it comes from expansion". Of course if there is an equation which > holds while the universe expands, then something is conserved; the > question is how this relates to commonly used usages of the term. True. > I think Edward Harrison has explained rather well what is meant by > "energy is not conserved in the expanding universe". Do you disagree > with his analysis? Yes. If I understand Harrison's argument it is that pressure and pressure gradients mediate the transfer of energy in the thermodynamic dE = -P dV equation (which has a cosmological equivalent), which describes the expansion of, say, a pressurised gas against its environment. But in the universe there is no exterior system to push against and hence no transfer of energy. Instead he concludes the red-shift energy is lost and not transferred. I think he is being lead astray by the thermodynamic analogy with pressure. Pressure is the result of particles (including photons) with momenta, which have de Broglie wavelengths. It is the stretching of the wavelengths by the Hubble expansion which causes the loss of momenta and the red-shift. The loss of radiation pressure is a consequence of this stretching and not a mediating mechanism; no pressure gradient or exterior system is required. I agree with your point about definitions and the Doppler effect. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm
 P: n/a Me: >> 8 pi G rho + gamma + -3H^2 = 0 >> >> ( gamma = cosmological constant, a form of dark energy. >> rho = average matter density >> G = Newton's constant >> H = Hubble's expansion factor. ) >> >> The question is: how do we interpret this equation? >> >> Since the first two terms are proportional to energy density then >> it is a reasonable inference that we have an expression of energy >> conservation if the last term is also proportional to energy density; >> in this case the energy of the dynamic geometry. >> [.......] Philip: > Let me rephrase my criticism. You say that there is a conservation > equation, and say that the energy of the cosmological constant "comes > from" the expansion and also that the equation is valid if there is no > cosmological constant. So, my question is, if there is no cosmological > constant, then, in the case of no cosmological constant, where does the > energy go which, in the case of a cosmological constant, is transformed > into the cosmological constant? Let me answer it this way: the cosmological constant currently dominates the expansion of the universe. The matter and photons are just being carried along for the ride. (This wasn't always the case. Earlier the matter dominated, and before that the photons.) The dominant flow of energy, today, is from the Hubble expansion to the cosmological constant, each one growing in magnitude although of opposite sign. Without a cosmological constant the presently insignificant flow from the photons (via the red shift) to the Hubble factor would dominate, as it did in the early universe. i.e. the direction of the energy flow would be reversed. > Imagine the Einstein static universe. There is no expansion. Yet there > is an energy density due to the cosmological constant. How does it > "come from" the (non-existent) expansion in this case? What about a > negative cosmological constant? Indeed, as you point out, in Einstein's original static universe the cosmological constant was negative and its now negative energy offset the energy in the matter and photons. With no expansion there was no energy transfer to/from the cosmological constant. > > I'll reply in more detail later. > > Perhaps we are merely using completely different terminology. However, > I think that what you are saying is misleading, or at least confusingly > phrased. You seem to be saying "no mystery where the dark energy comes > from, it comes from expansion". Of course if there is an equation which > holds while the universe expands, then something is conserved; the > question is how this relates to commonly used usages of the term. True. > I think Edward Harrison has explained rather well what is meant by > "energy is not conserved in the expanding universe". Do you disagree > with his analysis? Yes. If I understand Harrison's argument it is that pressure and pressure gradients mediate the transfer of energy in the thermodynamic dE = -P dV equation (which has a cosmological equivalent), which describes the expansion of, say, a pressurised gas against its environment. But in the universe there is no exterior system to push against and hence no transfer of energy. Instead he concludes the red-shift energy is lost and not transferred. I think he is being lead astray by the thermodynamic analogy with pressure. Pressure is the result of particles (including photons) with momenta, which have de Broglie wavelengths. It is the stretching of the wavelengths by the Hubble expansion which causes the loss of momenta and the red-shift. The loss of radiation pressure is a consequence of this stretching and not a mediating mechanism; no pressure gradient or exterior system is required. I agree with your point about definitions and the Doppler effect. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm
 P: n/a In article , "Michael C Price" writes: > Let me answer it this way: the cosmological constant currently dominates > the expansion of the universe. The matter and photons are just being > carried along for the ride. (This wasn't always the case. Earlier the > matter dominated, and before that the photons.) The dominant flow of > energy, today, is from the Hubble expansion to the cosmological constant, > each one growing in magnitude although of opposite sign. Without a > cosmological constant the presently insignificant flow from the photons > (via the red shift) to the Hubble factor would dominate, as it did in the > early universe. i.e. the direction of the energy flow would be reversed. You seem to think that this "flow" is some sort of physical transformation. Can you explain this in more detail? > > Imagine the Einstein static universe. There is no expansion. Yet there > > is an energy density due to the cosmological constant. How does it > > "come from" the (non-existent) expansion in this case? What about a > > negative cosmological constant? > > Indeed, as you point out, in Einstein's original static universe the > cosmological constant was negative The cosmological constant in the Einstein static universe is positive. I was providing two examples: one in which there can be no "flow" since there is no expansion, and in addition mentioning that the cosmological constant can, theoretically, be negative while the expansion has the same sign as it has today. I don't see how you can say that there is a "flow" in all three cases (static, negative cosmological constant, positive cosmological constant) or, if you don't claim this (which seems to be the case), how you can say that in some cases (like the one which corresponds to our universe), there IS a flow. Let me EXAGGERATE. Fewer children are born where fewer storks nest. Does this prove that storks bring children? No. It is due to a common cause (fewer children are born in industrialised societies, and storks are less common here as well). Historically, global warming is also negatively correlated with the number of pirates sailing the seven seas, but that doesn't mean that pirates prevent global warming. You seem to be saying a) there is expansion and b) there is a cosmological constant and then claiming that one "causes" the other in some sense. > > I think Edward Harrison has explained rather well what is meant by > > "energy is not conserved in the expanding universe". Do you disagree > > with his analysis? > > Yes. If I understand Harrison's argument it is that pressure and pressure > gradients mediate the transfer of energy in the thermodynamic dE = -P dV > equation (which has a cosmological equivalent), which describes the > expansion of, say, a pressurised gas against its environment. But in the > universe there is no exterior system to push against and hence no transfer > of energy. Instead he concludes the red-shift energy is lost and not > transferred. I think he is being lead astray by the thermodynamic > analogy with pressure. Pressure is the result of particles (including > photons) with momenta, which have de Broglie wavelengths. It is the > stretching of the wavelengths by the Hubble expansion which causes the > loss of momenta and the red-shift. The loss of radiation pressure is a > consequence of this stretching and not a mediating mechanism; no > pressure gradient or exterior system is required. Harrison (in his textbook) explicitly states that the universe is not like a steam engine, so I think the disagreement has another cause.

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