# Where does the energy vanish to when light is red shifted

by SteveinLondon
Tags: energy conservation, expansion, red shift
 P: 9 When light is red shifted due to the expansion of the universe, it loses energy (E=hf). Doesn't the "conservation of energy rule" apply in this case? Where does all that energy vanish to?
 PF Patron P: 10,395 Conservation of energy does not apply at the cosmological scale, contrary to what you would expect. Guacamolewar, your description applies for standard redshift due to the doppler effect, but the problem is that light is redshifted to ALL frames of reference in the universe and is never blueshifted. The energy is disappearing. To my knowledge energy is not a well described feature in General Relativity.
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 Quote by SteveinLondon When light is red shifted due to the expansion of the universe, it loses energy (E=hf). Doesn't the "conservation of energy rule" apply in this case? Where does all that energy vanish to?
During a lecture by Leonard Susskind he responded to a similar question from a student by saying: "think of the energy as being stretched". This seemed slightly odd.

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P: 22,353

## Where does the energy vanish to when light is red shifted

 Quote by SteveinLondon When light is red shifted due to the expansion of the universe, it loses energy (E=hf). Doesn't the "conservation of energy rule" apply in this case?
No it does not apply. Sean Carroll a cosmologist has made this point. Once you move from Special Rel (non-expanding flat geometry) to General Rel, you lose conservation of momentum and conservation of energy.
By making special assumptions you can partially recover in certain cases but as a general rule "energy is not conserved in expanding geometry"

People try to cushion the shock by talking about "energy of the gravitational field" but this is not always globally defined. The simplest is just to face it. The CMB ancient light is redshifted by z=1100. Therefore it has lost some 99.9% of its energy and nobody can say where "it went".

There's probably something about this in the FAQ. There also is a bit in John Baez FAQ.

The flat nonexpanding geometry of Special Rel is only APPROXIMATELY right. Be grateful for that much. It is not perfectly realistic. General Rel is a little bit closer to nature, and some of the things you expect are only approximately correct.
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 Quote by marcus The CMB ancient light is redshifted by z=1100. Therefore it has lost some 99.9% of its energy and nobody can say where "it went".
Back into the vacuum tends to spring into my mind. The constant vaccum energy has to come from somewhere, plus it is the origin of the photon in the first place. It may be overly obvious to connect the two, but I'm assuming some relatively straight forward maths would reveal if one can account for the other. We have estimates for total energy, the photon contribution and the amount of expansion since last scattering.

Is the restoration of conservation of energy on the universal scale desired at all in current physics?
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 Quote by salvestrom Back into the vacuum tends to spring into my mind. The constant vaccum energy has to come from somewhere, plus it is the origin of the photon in the first place. It may be overly obvious to connect the two, but I'm assuming some relatively straight forward maths would reveal if one can account for the other. We have estimates for total energy, the photon contribution and the amount of expansion since last scattering...
I played around with that as a conjecture some back in 2004 or so. jokingly calling it the "marcus conjecture". the vanished CMB energy went into the "dark energy" of the new space.
It doesn't add up. No professional-grade math connects one to the other AFAIK. It is just an appealing idea that has not amounted to anything (AFAIK!)

the cosmologists Lambda seems very likely just a constant (a curvature not an energy) and does not necessarily have any simple relation to the QFT "vacuum energy". It is only the QFT people who insist on thinking of their "vacuum energy" as related to Lambda. Lambda can simply be a natural constant like newton G, not really anything that needs to be called "dark energy".

I suggest you try the idea out, if not already familiar to you. When you google
"bianchi prejudices against constant" you get http://arxiv.org/abs/1002.3966.
The article's title is "Why All These Prejudices Against a Constant?" Interesting reading.
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 Quote by marcus I played around with that as a conjecture some back in 2004 or so. jokingly calling it the "marcus conjecture". the vanished CMB energy went into the "dark energy" of the new space. It doesn't add up. No professional-grade math connects one to the other AFAIK. It is just an appealing idea that has not amounted to anything (AFAIK!)
This is the first time I've asked that sort of question and someone's actually said: "yeah, tried that. didn't work". <3 Marcus. I'm reading the paper at the moment.

Oh, how far short were you? Or was the lost photon energy actually too much to be accounting for the "dark energy"?
 PF Patron Sci Advisor P: 8,899 Energy is not well defined in GR, hence the 'missing' energy enigma. It is obviously difficult to explain 'conservation' of anything that is undefined.
 PF Patron P: 183 Is energy also non-conserved in GR due to local curvature? For example, If a system consists of a hollow spherical reflector with lots of photons bouncing around inside, and it collapses to a BH, does the equivalent gravitational mass of the system change as measured by a distant observer?
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 Quote by SteveinLondon When light is red shifted due to the expansion of the universe, it loses energy (E=hf). Doesn't the "conservation of energy rule" apply in this case? Where does all that energy vanish to?
One of the well-known problems of GR is that lacks conservation laws. Energy cannot be conserved in GR and you cannot ask to it where that energy goes.
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 Quote by BillSaltLake Is energy also non-conserved in GR due to local curvature? For example, If a system consists of a hollow spherical reflector with lots of photons bouncing around inside, and it collapses to a BH, does the equivalent gravitational mass of the system change as measured by a distant observer?
That's a beautiful question. My impression is that you know this subject very well and I would like to know what you think about this example.

I also have the impression that one ought to be able to treat this example in a space that is asymptotically flat (ordinary non-expanding space out at the limit far away from the collapse). My intuition is not reliable but my hunch is that one should expect ordinary energy conservation in this case. What is your hunch?

If we go with my naive suspicion that conservation holds with this being asymptotically flat (out where your observer is) then it seems to me that it leads to a paradox. Is there some relevant literature?
 PF Patron P: 183 If a spherically-symmetric collapse of this system changed its equivalent mass, the collapse would sent out gravity waves. I am under the impression that a closed system which undergoes spherically-symmetric oscillations cannot send out gravity waves. This includes any kinetic energy that a massive shell acquires as it collapses. I would guess then that the equivalent mass of the reflector-photon system is unchanged by the collapse. In expansion, any motion of massive particles with respect to the comoving frame is reduced over time, and this effect (in addition to photon wavelength increase) contributes to the global non-conservation of energy. If spherical oscillations do not send out gravity waves and if this statement is true even if the massive particles start with some relative motions, then the reflector-photon system will conserve energy.
 P: 1 Can this question be usefully reversed? Could some of the observed red shift be the result of photons shedding energy in some way that is difficult measure on human timescales? Could this hypothesis help to explain the observed increase in the rate of expansion of space-time?
 PF Patron Sci Advisor P: 8,899 Obviously spacetime is not conserved in an expanding universe. I've always been attracted to the idea that expansion dilutes energy. An ink dot on a ballon starts out as ... a dot, but, grows as the balloon is inflated. All the ink is still there, just spread out.
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 Quote by Wood_Pecker Can this question be usefully reversed? Could some of the observed red shift be the result of photons shedding energy in some way that is difficult measure on human timescales? Could this hypothesis help to explain the observed increase in the rate of expansion of space-time?
I don't think so. If we were in a space ship moving at a substantial fraction of c, then even distant light from far galaxies dead ahead of us would be blue shifted. From that I conclude that the photon doesn't shed energy along the way, but that the Doppler shift is proportional to the speed difference of the light emitter and the light receiver.

I too have trouble with the idea of non-conservation of energy in general relativity. As the universe expands, of course the energy density will decease, but the integral of the energy density (i.e. the total energy) of the universe should be constant. At least I would imagine it so.

So do cosmologists say that in an open universe as we approach heat death, that both the energy density and the energy approach zero?
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 Quote by anorlunda I don't think so. If we were in a space ship moving at a substantial fraction of c, then even distant light from far galaxies dead ahead of us would be blue shifted. From that I conclude that the photon doesn't shed energy along the way, but that the Doppler shift is proportional to the speed difference of the light emitter and the light receiver.
Interesting thought. If a distant galaxy is accelerating away at a current speed of 0.9c and if I am travelling in a space ship towards the galaxy at 0.9c, what I would see is the "normal" light without any shifts right? Is the photon assumed to "not lose energy at all" or "gain energy" in this case? In either case, the relative velocity has something to do with the perceived energy loss/gain of energy of the photon.
 P: 10 Aren't the photons stretched in length so that the redshifted photons are longer to make up for their decreased frequency. I'm sure this is a dumb question
 PF Patron Sci Advisor P: 8,899 Redshift is a frame dependent measurement. If you were approaching a distant galaxy at the same speed as it is receeding, you would see no redshift. The problem arises when you try to compare photon energy in different reference frames. It is sort of like a baseball player chasing a line drive. If you run toward the ball it hits your glove with more force than it does if you catch it running toward the fence. A stationary observer, however, would perceive no difference in the kinetic energy of the baseball.

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