Where does the energy vanish to when light is red shifted

[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?

 

[Drakkith]

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.

 

[salvestrom]

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.

 

[marcus]

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.

 

[salvestrom]

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 vacuum 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?

 

[marcus]

Back into the vacuum tends to spring into my mind. The constant vacuum 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!)

You might want to read this article (quite a lot is nontechnical):
Google "bianchi prejudices against constant".

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.

 

[salvestrom]

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"?

 

[Chronos]

Energy is not well defined in GR, hence the 'missing' energy enigma. It is obviously difficult to explain 'conservation' of anything that is undefined.

 

[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?

 

[juanrga]

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.

 

[marcus]

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?

 

[BillSaltLake]

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.

 

[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?

 

[Chronos]

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 balloon starts out as ... a dot, but, grows as the balloon is inflated. All the ink is still there, just spread out.

 

[anorlunda]

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 spaceship 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?

 

[surajt88]

I don't think so. If we were in a spaceship 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 traveling in a spaceship 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.

 

[adrianopolis]

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

 

[Chronos]

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.

 

[surajt88]

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.

So, the energy loss/gain of a photon by red/blue shifting is entirely frame dependant? If true, is the question of whether photon loses energy due to the accelerated expansion of the universe moot?

 

[bcrowell]

This thread is a year old. We have a FAQ about this: https://www.physicsforums.com/showthread.php?t=506985

 

[Naty1]

Chronos has the keypoint: Redshift is a frame dependent measurement.

This means that different observers will record different values. But certain interpretations of redshift are used and can offer insights. When distances are changing, as in cosmology, interpretations become less 'intuitive'.The issue of expansion and redshift continues...and is an interesting one.

My favorite discussion in these forums is here:
[I like this one in part because the originator is a cosmologist!]

Does Space expand? [2007]

https://www.physicsforums.com/showthread.php?t=162727&highlight=current+flow

Here are a couple of key viewpoints:

All forms of redshift have nothing to do with a change in the state of the photon. Instead it is related to the relative position and orientation [frames of reference] of the emitter and absorber in curved space-time.

The standard {cosmological} convention is that of the conservation of energy-momentum, (GR), which results in fundamental particles having constant mass. Therefore, atoms are defined to provide regular clocks and fixed rulers by which the universe can be measured. [wikipedia]

Photons are measured by those atoms, as the frequency of emission, determined in the laboratory, is compared to the frequency of absorption, the result is they are found to lose energy, i.e. red-shifted.

If another convention is chosen, such as the conservation of energy, it is the photon that remains constant in energy and hence frequency and the masses of atoms, and therefore atomic clocks and steel rulers that change over cosmological time. There are theories that take such an approach, such as

here.http://en.wikipedia.org/wiki/Self-creation_cosmology

"...
"Photon's being stretched by exanding space" is another one these absurd phrases. That an emitter and an absorber of a photon measures a different frequency is perfectly valid in relativity but it has nothing to do with a change in the state of the photon..."
“…we cannot prove that anything remains constant over cosmological space-time; All we can do is define a conservation principle and test it. At the heart of GR is the conservation of energy-momentum, which leads to the atom, atomic 'regular' clocks and 'rigid' steel rulers, being the standard by which to measure the universe..."
////////////

What all this means, I think, is [a] Our everyday intuition is about as useful in cosmology as in quantum mechanics {not very} and
even after we pick a model and it's underlying principles [FLRW Lambda-CDM, based on general relativity] we still have to interpret what the math means...and there is room for more than one interpretation.

 

[ConformalGrpOp]

Interesting discussion!

Some insight into the question of the conservation of energy of red shifted EM spectra may be found in extending Einstein's approach in considering a spherical "volume" containing a "light complex" which he discusses in his now famous 1905 paper "On the Electrodynamics of Moving Bodies".

If we consider a four dimensional volume in space-time which is defined as containing the energy of a single monochromatic EM wave cycle at the time/place of propagation, that same volume will contain the same energy of the same wave cycle at the point it is observed, (assuming the light path is otherwise field free, etc.). However, if the observer is moving with respect to the light source, the volume will appear to be compressed or expanded depending on the direction of the observer's relative motion.

For the astronomer, it comes down to counting photons. A monochromatic light wave which has its wavelength shifted to twice its original length will be understood to have one half the energy compared to original signal.

If it is understood that the metric of space-time in which light propagates is governed by a parameter that is isomorphic to Hubble's constant, there is no "lost energy". To compensate, the local observer would simply re-calibrate his instrument to account for the discrepancy between observations made in local Minkowskian space-time and the physical space-time in which the light is propagating. Doing so would permit an analysis of the existence of other sources of red shift associated with the object under observation, including a true doppler shift, a cosmological shift. etc. (One supposes that the contribution of these other sources of red (or blue) shift to the observed spectra might be challenging to resolve.)

For the purposes of this thread, the governing principle is a somewhat elementary consequence, (if not a trivial restatement) of Einstein's analysis in Section 8 "Transformation of the Energy of Light Rays...", of his 1905 paper. There he makes the intriguing observation that "it is remarkable that both the energy and the frequency of a light complex vary with the motion of the observer in accordance with the same law."

@surajt: That is to say, a local observer in relative motion to the source will detect a frequency shift (and a change in the energy of the photon), which is a function of the observer's relative velocity to the source. It is probably worthwhile to note here that in concluding his analysis of the "theory of Doppler's principle" in Section 7 of the same paper, Einstein makes the observation that it follows that "to an observer approaching a source of light with the velocity c, the source of light must appear of infinite intensity." [Maybe that's where the term "blinding speed" came from!]

Einstein's approach with respect to the application of Maxwell's equations to moving bodies is straight forward (for his purposes). However, the implications that can be drawn from it are not, and no further mention of it appears in the paper. Treating the energy of a "light complex" as contained in a volume informs the interpretation of observed spectra from plane waves in Minkowski space, as well as in space-times defined by other metrics, the relevance of which has been all but overlooked. [But see Francis, et als., Expanding Space: the Root of all Evil? arXiv:0707.0380v1 at p.7].

In this later case, if the value of the metric parameter is equivalent to the value of Hubble's constant, red shifts in spectra observed locally would be interpreted to be velocity dependent, when the phenomena would be better understood as reflecting a time/distance dependency (to the second order), allowed by Maxwell's equations. This is important and is not well understood primarily because few astrophysicists and cosmologists are familiar with relevance of the Bateman-Cunningham conformal group to the physical behavior of light. No matter how many books, treatises, monographs and papers one reads on modern cosmology, it appears that there is completely absent from the literature any fundamental treatment which examines Maxwell's equations to determine whether they exclude the possibility that, to use Humason/Hubble and Milne's terms, the observed red shift is an intrinsic characteristic of EM radiation.

Nevertheless, astronomy, astrophysics and cosmology would be well served if the a priori assumption that Minkowski's metric is the metric of physical gravitation-free space-time received experimental verification on a scale of, say 80 AU(+/-). In absence of such an experiment, (to the extent of my understanding of the subject), the issue of the cosmological red shift will remain unsettled, and stand on nothing more than an assumption based on what our model's tell us, informed only by what we know about the behavior of light on, in cosmological terms, a nano scale.

 

[adrianopolis]

Where does the energy come from in a blue shift?

 

[Naty1]

adrianopolis:

redshift:
You posted this question in cosmology..so I'll offer another cosmological perspective:

When the cosmic microwave background radiation [CMBR] was emitted it was almost to 3000 Kelvin...down from billions of degrees a few moments earlier...and at such temperatures everyday particles could not exist, galaxies would not coalesce, stars would not form...nor would we.

Today that same CMBR has been stretched by expanding distances via our cosmological model mathematics...and we now observe it at about 2.73 degrees K. 3000/2.73 [rounded] is the amount of increased distance during transit...of z = 1090. As the CMBR cooled, all around condensed from the early radiation and subsequent particle production.

blue shift: Consider radiation [such as light] approaching a large mass...or a black hole...it is entering a more negative gravitational potential as it approaches closer and closer...so it loses PE as it approaches a center of mass. Unlike a mass that would increase it's speed, light speed is constant...so it gains offsetting energy via blueshift,,,an increase in frequency...E = hf.

 

[ConformalGrpOp]

Adrian- A blue shift generally implies a relative motion of the observer in the direction of the source of the light wave. The observed blue shift is due to the fact that as the observer moves toward the source, the source appears to be emitting photons at a faster rate, or probably more correctly, the observer is running into the photons emitted by the source at a faster rate than they were emitted. So, to the observer, it appears that the light from the source has a higher energy (frequency), than would be observed if the observer was not moving toward the source.

A rather feeble analogy is to imagine yourself driving a vehicle in a rain shower. The faster the vehicle travels, the harder it seems to be raining, and the faster you need to set your windshield wipers. It is not that the rain is gaining energy when you drive into it at high speed, its that your velocity makes it seem like its raining harder (that the rain has more energy), than it does if you were simply walking in the rain.

There are several problems with this particular analogy, in that, to be traveling "toward" the source of the rain, you'd need to be in a rocket heading up toward the cloud that was dropping the rain, and of course, the velocity of the falling rain is due to Earth's gravity, and not to the emission of protons.

I hope this helps.

 

[Drakkith]

Adrian- A blue shift generally implies a relative motion of the observer in the direction of the source of the light wave. The observed blue shift is due to the fact that as the observer moves toward the source, the source appears to be emitting photons at a faster rate, or probably more correctly, the observer is running into photons emitted by the source at a faster rate than the photon were emitted. So, to the observer, it appears that the light from the source has a higher energy (frequency), than would be observed if the observer was not moving toward the source.

Not quite. While you do "run into photons" at an increased rate, this is not the cause of blueshift. The blueshift is caused because light is an EM wave and as you move towards the emitting source the wavelength of the EM wave is shorter, leading to a higher energy per photon. If you were to measure the energy of the received radiation (of the whole wave, not per photon) you would see an increase due to both effects, but the blueshift is only a result of the change in the wavelength, not because you run into photons at an increased rate.

 

[ConformalGrpOp]

Drakkith, Indeed, I miswrote. The observed blue shift is, of course, the result of the shorter wavelength of the EM in the frame moving towards the source. Adrian was concerned with where the energy came from. Clearly, I was a bit hasty in articulating the explanation and wasnt careful to properly explain the basis of the observation of blue shift in the moving frame, and I can be faulted for not adequately (specifically), articulating why the observer in this frame would observe the photons to have a higher energy than would be observed in the same inertial frame as the source. (Its all because the rain drops were falling on my head!) :) Thank you.

 

[Drakkith]

Drakkith, Indeed, I miswrote. The observed blue shift is, of course, the result of the shorter wavelength of the EM in the frame moving towards the source. Adrian was concerned with where the energy came from. Clearly, I was a bit hasty in articulating the explanation and wasnt careful to properly explain the basis of the observation of blue shift in the moving frame, and I can be faulted for not adequately (specifically), articulating why the observer in this frame would observe the photons to have a higher energy than would be observed in the same inertial frame as the source. (Its all because the rain drops were falling on my head!) :) Thank you.

No problem. We all get rain drops on the head every once in a while.

 

[Naty1]

So back the the OP question to try to summarize:

The first few posts answered the question noting energy is not conserved either in GR nor in our main cosmological model. So there is no single answer to 'where the energy goes in redshift'.

One view is that a photon does not change it's characteristics as it moves through space-time anymore than an electron changes it charge as it does so. A photon [or light wave] is emitted at a color [that is, an energy,frequency] and stays that way.

The alternative view is the one Chronos posted "...expansion dilutes energy". That also seems to be a realistic answer since the universe has cooled via CMBR observations from when it was emitted [close to 3000 K] to that which we observe today [about 2.73K].

 

[timmdeeg]

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 balloon starts out as ... a dot, but, grows as the balloon is inflated. All the ink is still there, just spread out.

An attractive idea. I would expect that once a spherical universe starts to contract, the photon's energy would be "gained back" (it't wavelength would shrink) and thus never was lost. To me it makes sense to think of it as being some kind of a potential energy, which varies with the scale factor.

 

[ConformalGrpOp]

Referring to Chronos' comment, I'm not sure that the concept of dilution he is using is inconsistent with the concept that a photon's energy is unchanged by the expansion.

I don't suppose he is suggesting that the expansion of the universe in the FWR model causes photons to expand like dots on the surface of an inflating balloon such that the energy they carry can be thought of as being somehow diluted in local space. Regardless of the macro state of the expanding universe, it is unclear how such an expansion would have any localizable effect on the energy of photons propagating along an unobstructed path in a field free space.

 

[Drakkith]

Hmm. I had this thought after a conversation with Sophiecentaur yesterday in another post. It seems to me that if you stop thinking about light as just photons, and start thinking about light as an EM wave where photons can only be talked about during the interaction of the wave with matter, there is not really a problem. Expansion stretches out the wave as it travels, and every doubling in size of the universe causes the wavelength to double. Where has the energy gone? Nowhere. The wavefront contains the same amount of energy as it always did, but the wavefront now encompasses a much larger volume of space, spreading the energy out. That seems to match up with what Chronos was saying about the ink dot on a balloon. Chronos does what I said match up with actual physics?

 

[Tanelorn]

The energy and momentum of a photon depend only on its frequency (ν) or inversely, to its wavelength (λ)

Therefore, since the wavelength is 1090 times longer in our current frame of reference, we measure 1090 times less energy.
As an analogy isn't it as simple as the energy released due to the relative velocities of two colliding masses?

If we were able to match the relative velocity of the orignal emitting atoms then we would measure the same photon frequency and energy.
However, to do this in our current frame of reference we would have to greatly exceed the speed of light.

 

[Drakkith]

If we were able to match the relative velocity of the orignal emitting atoms then we would measure the same photon frequency and energy.
However, to do this in our current frame of reference we would have to greatly exceed the speed of light.

We would not have to exceed c to measure the original energy, but we would have to get to a very high fraction of c. Probably greater than 0.99c.

 

[Tanelorn]

Drakkith, thanks I was getting my frames of reference mixed up. That light today is in our own frame.