Red Shift Q: Where Does Lost Energy Go?

[Gary Boothe]

I understand that because galaxies are receding from us due to the expanding universe, that we see a red shift in the light from these galaxies. If there is a red shift, the light loses energy, but where does this lost energy go? Is it that in the photon's reference frame there is no change in frequency, or is there some sort of radiation that is created, like cerenkov radiation. An answer would be appreciated.

 

[Dale]

In curved spacetime, like the expanding universe, there is not generally a globally conserved energy. Unfortunately, that means that there is not an answer to your question. Energy is only locally conserved.

 

[phinds]

Gary, this is a common question and certainly an obvious one that I think causes many of us some confusion when we first read it. Where DOES it go? As Dale said, we don't have an answer for that ... it just isn't there any more, and as Dale also noted, this does not violate any laws since conservation of energy does not apply on cosmological scales.

 

[harrylin]

I understand that because galaxies are receding from us due to the expanding universe, that we see a red shift in the light from these galaxies. If there is a red shift, the light loses energy, but where does this lost energy go? Is it that in the photon's reference frame there is no change in frequency, or is there some sort of radiation that is created, like cerenkov radiation. An answer would be appreciated.

It will not be necessary to invoke cosmological mysteries in order to answer your question in a qualitatively satisfying way: for we would expect receding galaxies to show redshift already in special relativity's static space. And as you guessed, according to wave theory the frequency of light in vacuum does not change.
For simplicity, let's assume ourselves to be in rest. Then SR predicts a so-called "relativistic Doppler" shift which consists of two factors:
1. classical Doppler shift is expected due to the increasing distance - and with that there is a continuous accumulation of radiation energy on its way to us; it simply gets spread out.
2. time dilation shift, that is: the emission frequency of the stars is reduced, so that part of the "missing" energy already wasn't there from the start.

With that fundamental understanding, you will be better equipped to read about cosmological models.

 

[PeterDonis]

we would expect receding galaxies to show redshift already in special relativity's static space

But the relationship between redshift and distance (or, more precisely, between redshift and other observables that are proxies for distance) will not be the same in SR's flat spacetime as it is in our actual universe, which is modeled by an expanding FRW spacetime.

 

[ConformalGrpOp]

SR predicts a so-called "relativistic Doppler" shift which consists of two factors:
1. classical Doppler shift is expected due to the increasing distance - and with that there is a continuous accumulation of radiation energy on its way to us; it simply gets spread out.
2. time dilation shift, that is: the emission frequency of the stars is reduced, so that part of the "missing" energy already wasn't there from the start.

harrylin: Is there a reference you can provide that directly explains the last statement, "the emission frequency of stars is reduced so that part of the "missing" energy already wasnt there"? I guess I am unclear by what you mean by "already" wasnt there...

Question: Suppose we have a spectrometer and a photometer which are situated to provide data with respect to light propagating from a distant point source, S, where the frequency (ν) and wavelength (λ) of the light at the time of emission from S are known.

According to the spectrometer, the apparent redshift of the spectra of the radiation received from S equals 2λ, i.e., the wavelength is doubled from what we know it was at the time it was emitted from S.

Now, if t_n is the time it takes for n number of wave cycles (λ_n) (representing P_tn number of discrete photons), to transit across a discrete point "x" situated proximate to and in the same inertial frame of reference as S, and we allow our photometer to detect photons propagating from S for a period of 2t_n, so that exactly λ_n wave cycles, and thus, exactly P_tn discrete photons will be received and recorded by the photometer, will the energy reported by the photometer be equal to the energy carried by λ_n wave cycles at the time of emission at the source? Nothwithstanding the fact that we are dealing with background conditions of a GR based model of the Universe?

Isn't this implicit in Einstein's discussion in Section 8. Transformation of the Energy of Light Rays. Theory of the Pressure of Radiation Exerted on Perfect Reflectors, of his 1905 paper, On the Electrodynamics of Moving Bodies?

It is interesting that Einstein wrote that it was "remarkable" that "the energy and the frequency of a light complex vary with the state of motion of the observer in accordance with the same law." ( Einstein, 1905, Sect. 8).

 

[harrylin]

But the relationship between redshift and distance (or, more precisely, between redshift and other observables that are proxies for distance) will not be the same in SR's flat spacetime as it is in our actual universe, which is modeled by an expanding FRW spacetime.

Exactly- except for your "but" which I don't understand: I stressed "qualitatively". Based on the wrong assertion "If there is a red shift, the light loses energy", Gary apparently thought that redshift as a phenomenon is somehow weird and mysterious; and several others even fueled that misunderstanding.

 

[harrylin]

harrylin: Is there a reference you can provide that directly explains the last statement, "the emission frequency of stars is reduced so that part of the "missing" energy already wasnt there"? I guess I am unclear by what you mean by "already" wasnt there...

That quote is incomplete, but for the right context there are several references, likely also cited in the archives of this forum; regretfully in the coming days I'll only have minutes time to search for them; and I'll look at your next question later. However I also had in mind the following:

[..] Isn't this implicit in Einstein's discussion in Section 8. Transformation of the Energy of Light Rays. Theory of the Pressure of Radiation Exerted on Perfect Reflectors, of his 1905 paper, On the Electrodynamics of Moving Bodies?
It is interesting that Einstein wrote that it was "remarkable" that "the energy and the frequency of a light complex vary with the state of motion of the observer in accordance with the same law." ( Einstein, 1905, Sect. 8).

Yes, my comment merely splits his result there* into pure classical Doppler and time dilation, but for the interpretation of a receiver in rest in static space.
* http://fourmilab.ch/etexts/einstein/specrel/www/

 

[harrylin]

In addition, here's an old post with a link that explains in detail how "relativistic Doppler" relates to "classical Doppler":
https://www.physicsforums.com/threa...ffect-and-doppler-effect.612582/#post-3949209

harrylin: Is there a reference you can provide that directly explains the last statement, "the emission frequency of stars is reduced so that part of the "missing" energy already wasnt there"? I guess I am unclear by what you mean by "already" wasnt there...

Light that is emitted at lower frequency has less energy (c.p.).

Question: Suppose we have a spectrometer and a photometer which are situated to provide data with respect to light propagating from a distant point source, S, where the frequency (ν) and wavelength (λ) of the light at the time of emission from S are known.

According to the spectrometer, the apparent redshift of the spectra of the radiation received from S equals 2λ, i.e., the wavelength is doubled from what we know it was at the time it was emitted from S.

Now, if t_n is the time it takes for n number of wave cycles (λ_n) (representing P_tn number of discrete photons), to transit across a discrete point "x" situated proximate to and in the same inertial frame of reference as S, and we allow our photometer to detect photons propagating from S for a period of 2t_n, so that exactly λ_n wave cycles, and thus, exactly P_tn discrete photons will be received and recorded by the photometer, will the energy reported by the photometer be equal to the energy carried by λ_n wave cycles at the time of emission at the source? Nothwithstanding the fact that we are dealing with background conditions of a GR based model of the Universe? [..].

I'm unsure about the tricky relationship with wave theory; Einstein discussed waves (but I think that a discussion about Einstein's derivation and photons is also somewhere in the archives - just search!).
About waves: Yes, it appears to me that that is correct for SR. However, for your calculation the stars must move away at constant speed. And for GR you have to think of gravitational time dilation as well, although that only affects the emission frequency compared with your reference frequency.