Doppler shift and photons

[Danijel Gorupec]

I have some problems understanding the following scenario:

Suppose there is a source that emits a single high-energy photon. Suppose that this source is monochromatic and can only emit photons of single energy level, E=hf.

The photon travels some time through space and is then detected at some detector (suppose, for example, detectors are all around, and the photon will surely be detected).

My question is what if the detector (all of them) is receding farther away from the source at some constant speed? My understanding is that, due to Doppler shift, the detector should detect a photon of longer wavelength - of lower energy. What happened with the rest of the energy?

[beecee]

20 minutes ago, Danijel Gorupec said:

I have some problems understanding the following scenario:

Suppose there is a source that emits a single high-energy photon. Suppose that this source is monochromatic and can only emit photons of single energy level, E=hf.

The photon travels some time through space and is then detected at some detector (suppose, for example, detectors are all around, and the photon will surely be detected).

My question is what if the detector (all of them) is receding farther away from the source at some constant speed? My understanding is that, due to Doppler shift, the detector should detect a photon of longer wavelength - of lower energy. What happened with the rest of the energy?

OK, I'll have an attempt at this, and am open to possible correction....[1] The Doppler shift is dwarfed in comparison to the Cosmological redshift, due to spacetime expansion...[2] and light/photons, all follow geodesic paths in that spacetime...[3] All frames of references are as valid as each other, that is the frame with relation to the detectors, and the frame with relation to the photons. So in any selective frame, the conservation of energy is not broken.

But I would wait for a more professional answer.   

[Strange]

29 minutes ago, Danijel Gorupec said:

My question is what if the detector (all of them) is receding farther away from the source at some constant speed? My understanding is that, due to Doppler shift, the detector should detect a photon of longer wavelength - of lower energy. What happened with the rest of the energy?

The important point here is that energy, like velocity, is observer dependent. So, for example, if you fire a cannonball from a cannon it will have a massive amount of kinetic energy. But if you are flying next to the cannonball at the same speed, then you will say it has zero kinetic energy.

Similarly for a photon, the energy you measure depends on your state of motion relative to the source. (This is a bit different from the Doppler effect with classical objects because the speed of the photons doesn't change, but its frequency, momentum and energy do.)

[beecee]

And in the meantime I found this......

https://arxiv.org/ftp/physics/papers/0511/0511178.pdf

ABSTRACT:

Although the Universe is far from understood, we are fairly confident about some key features: Special Relativity (SR) describes the kinematics of inertial frames; General Relativity (GR) explains gravitation; the Universe had a beginning in time and has been expanding since. Nevertheless it is quite difficult to see the ‘big picture’, although the idea of applying GR to the entire Universe has been very successful with a model emerging that is consistent with observation. One unpleasant feature of the model is that cosmological photons appear not to conserve energy, and the only explanation forthcoming is the claim that GR is exempt from the principle of energy conservation. It is demonstrated here that cosmological observations may legitimately be projected onto flat spacetime and can then be treated Special Relativistically, whereupon energy conservation is restored. This is not to say that the concordance General Relativistic cosmological model is incorrect, just that in observational terms there is no energy conservation anomaly.

 

extract:

redshifts, by increasing wavelengths, must reduce the energy in the quanta. Any plausible interpretation of redshifts must account for the loss of energy.” It is important to recognise that, in contrast, the normal Doppler effect conserves energy. We can verify this by considering a spherical surface of static observers centred on a stationary isotropic radiating source with integrated luminosity L. If now the source is boosted to a velocity v in an arbitrary direction relative to the shell of observers, then observers in the general direction vˆ will measure the photons as blueshifted and observers in the general direction - vˆ will see the photons redshifted with the total integrated luminosity still L. This does not imply some sort of collusion between the blue- and red-shifted photons to ensure energy conservation – in fact all events individually conserve energy. This is easily demonstrated by a ‘before and after’ SR kinematic analysis [7]. The energy difference between the emitted energy and the absorbed energy in excess to the standard energy difference associated with the non-zero relative velocity is fully accounted for by momentum conservation (with an apparent recoil at the source as viewed from the observer).

CONCLUSION:

We have described a model-free description of the expansion based solely on consistency. This is in many ways a complementary description to GR cosmology and in no way invalidates the established explanation – we are merely claiming GR cosmology is not the only explanation for observational data. SR already deals nicely with concepts like the stretching of supernovae light curves and apparent superluminal motion, but there are certain problems in supernovae data that need to be investigated, but it must be remembered that the SR description can be adapted in various ways to deal with this. Of course, by reverting to SR, we have in some ways taken a retrograde step as the Universe becomes even more mysterious to us. This is a heavy price to pay for the restoration of the principle of energy conservation. At least with the GR model, there was something that could be visualised: SR is a descriptive framework of rules, not a model. SR explains how the Universe is, but not why it is. We have no idea even about the basics - why must the speed of light be constant in each inertial frame in the absence of gravitation? Now we are claiming as an additional rule that the Universe will not permit space-time discontinuities. Why not? Any answer would merely be philosophical speculation, but it is hard to get away from the notion that the Universe is a unified structure in space and time and our problems in comprehension arise because the photon exchange mechanism grants us limited access to the Whole, much less that is necessary to understand the dynamics of the Universe. Our theories and equations are then simply an expression of our limited vision 8 .

Edited November 5, 2018 by beecee

[Strange]

1 hour ago, Strange said:

The important point here is that energy, like velocity, is observer dependent. So, for example, if you fire a cannonball from a cannon it will have a massive amount of kinetic energy. But if you are flying next to the cannonball at the same speed, then you will say it has zero kinetic energy.

Similarly for a photon, the energy you measure depends on your state of motion relative to the source. (This is a bit different from the Doppler effect with classical objects because the speed of the photons doesn't change, but its frequency, momentum and energy do.)

As beecee has introduced cosmological redshift (and the associated loss of energy) it is worth noting that a similar argument applies in this case. 

But in the case of cosmological redshift, it is not the difference in speed that is the cause of the redshift, it is the difference in "scale factor" (ie how much the universe has expanded). Basic thermodynamics tell us that as the universe expands, it cools. And so the photons we receive from the distant (early) universe are "cooler" (lower energy) than when they were emitted. The energy hasn't "gone" anywhere; it just has a different value in different frames of reference.

[Danijel Gorupec]

10 hours ago, Strange said:

The important point here is that energy, like velocity, is observer dependent. So, for example, if you fire a cannonball from a cannon it will have a massive amount of kinetic energy. But if you are flying next to the cannonball at the same speed, then you will say it has zero kinetic energy.

Similarly for a photon, the energy you measure depends on your state of motion relative to the source. (This is a bit different from the Doppler effect with classical objects because the speed of the photons doesn't change, but its frequency, momentum and energy do.)

Clear. The two observer don't have to agree about photon energy.

I was, however, more interested about single observer in a lab. He makes the experiment and notes that the source gives off energy quanta E1, and the detector receives energy quanta E2 (E2<E1). Where he should look for the energy difference - from your answer I infer that he should look into change of kinetic energy (recoil) of detector (and possibly source), right?

[swansont]

2 hours ago, Danijel Gorupec said:

Clear. The two observer don't have to agree about photon energy.

I was, however, more interested about single observer in a lab. He makes the experiment and notes that the source gives off energy quanta E1, and the detector receives energy quanta E2 (E2<E1). Where he should look for the energy difference - from your answer I infer that he should look into change of kinetic energy (recoil) of detector (and possibly source), right?

The lab observer sees the energy as E1. No energy is "lost". If one looks at the recoil of the detector, it will be consistent with an energy E1 and a momentum E1/c.

To predict what energy the detector sees, the observer has to transform into the detector's frame. The energy is different, with no expectation that it will be the same. If one analyzes the interaction in the detector's frame, it will be a photon of energy E2, and momentum E2/c.

This is no different than analyzing any collision, even in Newtonian physics. The energy and momentum of the objects is frame dependent. There is no energy "lost" in going from one frame to another.