Question about gravitational redshift

[Rolando]

The gravitational redshift is described in the literature in two ways:

 

(1) the phenomenon is explained through the behaviour of atoms that emit radiation of lower frequency (or clocks that run more slowly) the deeper they are located in a potential well, while the frequency of the light (or photons) does not change with height.

 

(2) the phenomenon is alternatively discussed in terms of an energy loss of a photon as it overcomes the gravitational attraction of the massive body. In this case, the frequency of the light (or photons) decreases with increasing height.

 

Alternative (2) is rooted in Newtonian physics and it has often been repeated that it is inappropriate in the frame of GR, e.g., http://arxiv.org/pdf/physics/9907017, but it is, nevertheless, widely popularized, e.g., in http://en.wikipedia.org/wiki/Gravitational_redshift (see the colorful illustration there).

 

It is clear to me that alternative (2) is incompatible with GR. However, alternative (1) seems to me to be incompatible with the idea behind GR as well.

 

According to GR, time is dilated in gravitational wells, so that, e.g., the gamma rays emitted by ⁵⁷Fe in the Pound-Rebka experiment at the lower altitude will have a lower frequency than those emitted at the higher altitude. In GR, this is an effect of the curvature of space-time. However, if this is so, then why is the light itself not affected by this curvature? If it was affected to the same extent as the atoms, the gravitational frequency shift could not be detected experimentally, and if it is necessary to assume that light propagates through a different space-time, this is very much in need of a logical explanation.

 

[xyzt]

 

According to GR, time is dilated in gravitational wells, so that, e.g., the gamma rays emitted by ⁵⁷Fe in the Pound-Rebka experiment at the lower altitude will have a lower frequency than those emitted at the higher altitude. In GR, this is an effect of the curvature of space-time.

Correct.

 

 

 

However, if this is so, then why is the light itself not affected by this curvature?

 

What gives you this idea? Light is affected by spacetime curvature.

[swansont]

What gives you this idea? Light is affected by spacetime curvature.

So the resonance frequency of the Fe changes, and the light frequency changes?

[xyzt]

So the resonance frequency of the Fe changes, and the light frequency changes?

Yes, absolutely, the received frequency changes due to gravitational redshift. The resonance frequency cannot and does not change. This is precisely why the receiver is being moved in the Pound Rebka experiment, to cancel the gravitationally induced frequency change via a relativistic Doppler effect.

Edited April 11, 2015 by xyzt

[Rolando]

What gives you this idea? Light is affected by spacetime curvature.

 

In alternative (1), which is common in the literature, the frequency of the light does not change with height.

 

In alternative (2), it does change, but in a sense opposite to that of the Fe in alernative (1).

So the resonance frequency of the Fe changes, and the light frequency changes?

 

If the frequency of the Fe changes, and the light frequency changes by the same factor, there will be no observable change.

 

If the light frequency changes by the inverse factor, the observable change will be twice as large as the observed.

Edited April 10, 2015 by Rolando

[xyzt]

 

In alternative (1), which is common in the literature, the frequency of the light does not change with height.

 

What "literature"? There is no such citation , at least in mainstream literature. You must be looking at some crackpot site. Or, you are making things up.

 

[math]\frac{f'}{f}=\sqrt{\frac{1-r_s/r}{1-r_s/r'}}[/math]

 

 

 

If the frequency of the Fe changes, and the light frequency changes by the same factor, there will be no observable change.

 

Rubbish, there is no connection to light in the Pound-Rebka experiment. All electromagnetic radiation is affected the same way by the gravitational potential.

 

 

 

If the light frequency changes by the inverse factor, the observable change will be twice as large as the observed.

 

Rubbish, see above.

Edited April 10, 2015 by xyzt

[Rolando]

What "literature"? There is no such citation , at least in mainstream literature. You must be looking at some crackpot site. Or, you are making things up.

It suffices to mention the textbook ”Physics” by Kenneth R. Atkins, which was widely used during the last quarter of the past century.

 

Rubbish, there is no connection to light in the Pound-Rebka experiment. All electromagnetic radiation is affected the same way by the gravitational potential.

 

Rubbish, see above.

 

Sorry, I used ”light” as an abbreviation for ”electromagnetic radiation”.

 

If the resonance frequency of the Fe at the first level differs from that at the second level by a factor of

 

[math]\frac{f'}{f}=\sqrt{\frac{1-r_s/r}{1-r_s/r'}}[/math]

 

and the frequency of the radiation also changes by the same factor while it propagates from the first to the second level, there will be no observable change. The radiation will arrive at a frequency that agrees with the resonance frequency of the Fe at the second level.

Edited April 10, 2015 by Rolando

[swansont]

Yes, absolutely. This is precisely why the receiver is being moved in the Pound Rebka experiment, to cancel the gravitationally induced frequency change via a relativistic Doppler effect.

 

But they measured a fractional frequency shift of 4.92 x 10^-15 as the difference between the upward shift and downward shift, which is what you expect from 2x gh/c² . If both the photon and the nucleus felt a shift (which would be in opposite directions), you should get twice that amount.

 

Rubbish, see above.

 

Light moving up is red-shifted, and clocks at higher potentials run at a faster rate. One frequency is low, the other is high. So relatively speaking, that's consistent. The Pound-Rebka results are only consistent with it being one or the other, not both.

[xyzt]

 

 

 

Light moving up is red-shifted, and clocks at higher potentials run at a faster rate. One frequency is low, the other is high. So relatively speaking, that's consistent. The Pound-Rebka results are only consistent with it being one or the other, not both.

The ratio of clock frequencies is equal to the ratio of light frequencies. Gravitational redshift affects all types of electromagnetic radiation identically.

 

 

 

But they measured a fractional frequency shift of 4.92 x 10^-15 as the difference between the upward shift and downward shift, which is what you expect from 2x gh/c² . If both the photon and the nucleus felt a shift (which would be in opposite directions), you should get twice that amount.

 

I think you misunderstood what I said. There is no "light" in the Pound Rebka experiment. What I was explaining is that, in order to measure the shift in the frequency of the [math]Fe^{57}[/math] isotope Pound came up with the clever idea of achieving the resonance at the receiver end by canceling the shift in frequency due to the gravitational effect by moving the receiver: if the gravitational shift is towards red, Pound created a blue Doppler effect by moving the receiver towards the source. If the gravitational shift is blue, Pound generated the cancellation via a red Doppler effect.

It suffices to mention the textbook ”Physics” by Kenneth R. Atkins, which was widely used during the last quarter of the past century.

 

 

Sorry, I used ”light” as an abbreviation for ”electromagnetic radiation”.

 

If the resonance frequency of the Fe at the first level differs from that at the second level by a factor of

 

[math]\frac{f'}{f}=\sqrt{\frac{1-r_s/r}{1-r_s/r'}}[/math]

 

and the frequency of the radiation also changes by the same factor while it propagates from the first to the second level, there will be no observable change. The radiation will arrive at a frequency that agrees with the resonance frequency of the Fe at the second level.

I don't think you understand the experiment, nor the effect. The frequency as measured at the receiver, relates to the frequency at the emitter via:

 

 

[math]\frac{f'_r}{f_e}=\sqrt{\frac{1-r_s/r_e}{1-r_s/r'_r}}[/math]

 

Since the frequency is shifted (up or down, depending on the relative positions of the receiver and emitter), one CANNOT achieve resonance anymore UNLESS, the frequency shift is cancelled somehow. This is done via moving the emitter wrt the receiver (see my answer to swansont , above) by generating a relativistic Doppler effect.

 

 

 

It suffices to mention the textbook ”Physics” by Kenneth R. Atkins, which was widely used during the last quarter of the past century.

 

You obviously do not understand what you are reading. Can you copy and paste the exact citation?

Edited April 11, 2015 by xyzt

[swansont]

 

I think you misunderstood what I said. There is no "light" in the Pound Rebka experiment.

 

 

So what were the Fe nuclei emitting and absorbing? Marbles? Why did they call it "The Apparent Weight of Photons" if there are no photons? Why do they mention gammas and electromagnetic radiation?

 

I don't think you understand the experiment, nor the effect. The frequency as measured at the receiver, relates to the frequency at the emitter via:

 

 

[math]\frac{f'_r}{f_e}=\sqrt{\frac{1-r_s/r_e}{1-r_s/r'_r}}[/math]

 

Since the frequency is shifted (up or down, depending on the relative positions of the receiver and emitter), one CANNOT achieve resonance anymore UNLESS, the frequency shift is cancelled somehow. This is done via moving the emitter wrt the receiver (see my answer to swansont , above) by generating a relativistic Doppler effect.

 

Perhaps you misunderstood the question: Is it the resonance frequency of the Fe that changes, or the frequency of the gamma, or do they both shift? You've given conflicting answers.

[xyzt]

 

So what were the Fe nuclei emitting and absorbing? Marbles? Why did they call it "The Apparent Weight of Photons" if there are no photons? Why do they mention gammas and electromagnetic radiation?

Perhaps you misunderstood the question: Is it the resonance frequency of the Fe that changes, or the frequency of the gamma, or do they both shift? You've given conflicting answers.

You don't need to get rude. The resonance frequency cannot change, it is a a local value, like proper time, What changes is the frequency of the received em radiation (as per the formula I posted). As such, in order to "recapture" the resonance at the receiver end, the receiver must be moved. This makes the frequency received from the emitter equal again to the resonance frequency.

Edited April 11, 2015 by xyzt

[Strange]

So it sounds like (1) and (2) are just different ways of describing the same effect?

[xyzt]

So it sounds like (1) and (2) are just different ways of describing the same effect?

Yes but Okun seems to make a very big deal about (2) not being correct. Opportunity for him to publish yet another paper.

[Rolando]

So it sounds like (1) and (2) are just different ways of describing the same effect?

 

While this is true, their theoretical background is different, and only one of them can be appropriate within a given theoretical frame.

 

Given the frame of Newtonian mechanics, photons will lose energy when they move out of a gravtiational field. Their frequency will therefore shift to the red. This is in agreement with alternative (2), and also Einstein treated the question in this way before he presented GR. It is clear that alternative (1) is inappropriate within this frame.

 

In GR, gravitation is basically not a force, but just geometry. If photons on their way out of a gravitational field are not affected by a force, they will not lose any energy. Therefore, alternative (2) is inappropriate within this frame. The observable redshift is, instead, ascribed to gravitational time dilation, which is effective at the source, although it can only be seen by an observer that is higher up in the potential well. This is the background to alternative (1).

 

I am not comfortable with alternative (1) either, since I do not understand how it can be that geometry (space-time curvature) can affect atoms when it fails to affect photons.

 

I noticed a third alternative in a link added by Mordred, 22 January 2015 in the related threed: Gravitational Red Shift Confusion:

http://cosmology101.wikidot.com/redshift-and-expansion

There, the gravitational redshift is interpreted as a Doppler shift in a curved space-time. I find this reasonable, it might solve my problem, but the account is too short and superficial to be fully intelligible.

Edited April 12, 2015 by Rolando

[xyzt]

 

I do not understand how it can be that geometry (space-time curvature) can affect atoms when it fails to affect photons.

 

You do not understand it because your claim is false (contradicted by experiment).

[Mordred]

 

While this is true, their theoretical background is different, and only one of them can be appropriate within a given theoretical frame.

 

Given the frame of Newtonian mechanics, photons will lose energy when they move out of a gravtiational field. Their frequency will therefore shift to the red. This is in agreement with alternative (2), and also Einstein treated the question in this way before he presented GR. It is clear that alternative (1) is inappropriate within this frame.

 

In GR, gravitation is basically not a force, but just geometry. If photons on their way out of a gravitational field are not affected by a force, they will not lose any energy. Therefore, alternative (2) is inappropriate within this frame. The observable redshift is, instead, ascribed to gravitational time dilation, which is effective at the source, although it can only be seen by an observer that is higher up in the potential well. This is the background to alternative (1).

 

I am not comfortable with alternative (1) either, since I do not understand how it can be that geometry (space-time curvature) can affect atoms when it fails to affect photons.

 

I noticed a third alternative in a link added by Mordred, 22 January 2015 in the related threed: Gravitational Red Shift Confusion:

http://cosmology101.wikidot.com/redshift-and-expansion

There, the gravitational redshift is interpreted as a Doppler shift in a curved space-time. I find this reasonable, it might solve my problem, but the account is too short and superficial to be fully intelligible.

A large body of that paper is based upon Bunn and Hoggs paper. These ones discusses the cosmological redshift and a series of smaller Doppler shifts.

 

http://arxiv.org/abs/0808.1081

 

http://arxiv.org/abs/0911.3536

 

There is several key factors to study.

 

One is relatistic Doppler effect

http://en.m.wikipedia.org/wiki/Relativistic_Doppler_effect

 

 

http://en.m.wikipedia.org/wiki/Redshift

 

Gravitational redshift utilyzes the relativistic Doppler redshift, The cosmological redshift can also be interpreted as a series of relatistic Doppler shifts.

 

To understand those details you have to look at how each form is derived from Doppler redshift to relativistic Doppler. Then look at how relativistic Doppler derives into the gravitational redshift. The above papers also show the correlation in terms of Cosmological redshift.

 

http://www.iucaa.ernet.in:8080/jspui/bitstream/11007/1135/1/211A_1994.pdf

 

The above is a paper covering the equivelence principle in regards to Doppler. Et ala Synche.

 

 

http://astronomy.case.edu/heather/151/davis.pdf

 

These are the reference papers I used to write the above article with the help of PAllen and the other contributors.

(Lol I should note it took a considerable effort and rewrites to consider those references as well as textbook examples the biggest trick was keeping it short in length lol)

 

 

Also keep in mind none of the formulas cover the transverse Doppler in my article. We kept the numerous redshift formulas to the basic three.

Forgot a reference papers

 

http://arxiv.org/abs/1111.6704

Edited April 12, 2015 by Mordred

[Strange]

 

While this is true, their theoretical background is different, and only one of them can be appropriate within a given theoretical frame.

 

I don't see why. They are just different descriptions of the same effect. That one effect is described by GR.

[swansont]

 

I don't see why. They are just different descriptions of the same effect. That one effect is described by GR.

Right. There will be a frequency shift of a signal relative to an oscillator if the signal originated at a different gravitational potential. We adopt the explanation that the clock runs fast or the photon is red-shifted (when going up) but that's short-hand for "clock runs fast relative to the signal" or "the photon is red-shifted relative to the clock". Two different ways of saying the same thing.

[Rolando]

They are just different descriptions of the same effect.

 

Right.

 

 

I am sorry for havig been too narrow-minded, which may have narrowed your minds as well.

 

The two alternatives are equivalent explanations of frequency shifts (and shifts in power these imply) such as observed by Pound & Rebka.

As for cumulative effects, they lead to different predictions.

Only alternative (1) predicts a general time dilation. Alternative (2) does not predict clocks further down in a gravitational well to appear to be slow. Instead, it predicts periods of the radiation to be lost on its way up.

Edited April 12, 2015 by Rolando

[swansont]

 

Alternative (2) does not predict clocks further down in a gravitational well to appear to be slow. Instead, it predicts periods of the radiation to be lost on its way up.

 

How would you measure such an effect? All clock measurements are comparisons of two oscillator signals. All you can measure is the relative frequency and phase.

[Rolando]

How would you measure such an effect?

 

It requires counting the periods emitted and received. I do not know whether this is practically feasible. However, there is another, much simpler way to test the alternatives against each other.

 

When I read the paper by Pound & Rebka about their experimental verification of the existence of a gravitational frequency shift, I was somewhat disappointed (I think this was in the past century). These people just went to the close-by tower in their institute without considering that in this stetting Newtonian theory predicts practically the same frequency shift as GR.

In Newtonian theory the frequency shift is due to the difference in the gravitational acceleration g between the two levels. In GR, it is instead due to the difference in the gravitational potential φ. Above the surface of the Earth, g is nearly proportional to -φ. This is not so below the surface of the Earth, where φ becomes still more negative as we go down, while g decreases (it has its maximum value close to the surface of the Earth).

 

If these researchers had not been so lazy, they could have done their experiment within a sufficently deep mine instead and so come up with a conclusive test of the theories, i.e., with a falsification of one of them. Has the experiment ever been repeated in such a setting?

Edited April 12, 2015 by Rolando

[xyzt]

 

There is quite a simple way to test the alternatives against each other.

 

When I read the paper by Pound & Rebka about their experimental verification of the existence of a gravitational frequency shift, I was somewhat disappointed (I think this was in the past century). These people just went to the close-by tower in their institute without considering that in this stetting Newtonian theory predicts practically the same frequency shift as GR.

In Newtonian theory the frequency shift is due to the difference in the gravitational acceleration g between the two levels. In GR, it is instead due to the difference in the gravitational potential φ. Above the surface of the Earth, g is nearly proportional to -φ. This is not so below the surface of the Earth, where φ becomes still more negative as we go down, while g decreases (it has its maximum value close to the surface of the Earth).

Can you prove your claim. I.e. produce the math that shows that the Newtonian theory predicts the same answer as GR?

 

 

 

If these researchers had not been so lazy, they could have done their experiment within a sufficently deep mine instead and so come up with a conclusive test of the theories, i.e., with a falsification of one of them. Has the experiment ever been repeated in such a setting?

 

Yes, it has been done, see here

[swansont]

 

There is quite a simple way to test the alternatives against each other.

 

When I read the paper by Pound & Rebka about their experimental verification of the existence of a gravitational frequency shift, I was somewhat disappointed (I think this was in the past century). These people just went to the close-by tower in their institute without considering that in this stetting Newtonian theory predicts practically the same frequency shift as GR.

In Newtonian theory the frequency shift is due to the difference in the gravitational acceleration g between the two levels. In GR, it is instead due to the difference in the gravitational potential φ. Above the surface of the Earth, g is nearly proportional to -φ. This is not so below the surface of the Earth, where φ becomes still more negative as we go down, while g decreases (it has its maximum value close to the surface of the Earth).

 

If these researchers had not been so lazy, they could have done their experiment within a sufficently deep mine instead and so come up with a conclusive test of the theories, i.e., with a falsification of one of them. Has the experiment ever been repeated in such a setting?

 

You're going to hang the tag of "lazy" on people doing a cutting-edge experiment. Seriously?

 

And allow me to clarify my question: how are you going to distinguish between a photon frequency change and a clock frequency change, when you are comparing one against the other?

 

And can you quantify the difference between the "Newtonian" shift and the GR shift? What do you think the equation is?

[Rolando]

A large body of that paper is based upon Bunn and Hoggs paper. These ones discusses the cosmological redshift and a series of smaller Doppler shifts.

http://arxiv.org/abs/0808.1081

http://arxiv.org/abs/0911.3536

There is several key factors to study.

One is relatistic Doppler effect

http://en.m.wikipedia.org/wiki/Relativistic_Doppler_effect

http://en.m.wikipedia.org/wiki/Redshift

Gravitational redshift utilyzes the relativistic Doppler redshift, The cosmological redshift can also be interpreted as a series of relatistic Doppler shifts.

To understand those details you have to look at how each form is derived from Doppler redshift to relativistic Doppler. Then look at how relativistic Doppler derives into the gravitational redshift. The above papers also show the correlation in terms of Cosmological redshift.

http://www.iucaa.ernet.in:8080/jspui/bitstream/11007/1135/1/211A_1994.pdf

The above is a paper covering the equivelence principle in regards to Doppler. Et ala Synche.

 

To judge from the abstracts, in http://arxiv.org/abs/0808.1081, it is the cosmological redshift, not the gravitational redshift, that is interpreted in terms of a Doppler shift, and http://arxiv.org/abs/0911.3536 disagrees. (I have run across similar discussions previously.)

The relativistic modification of the Doppler effect, http://en.m.wikipedi..._Doppler_effect, needs to be considered at high velocities, while the problem under discussion in the present thread arises at very low velocities as well (e.g., the velocity at at which Powel & Rebka needed to move one of their radiation sources to compensate for the gravitational frequency shift).

In http://en.m.wikipedia.org/wiki/Redshift, one can read: ”This gravitational redshift result can be derived from the assumptions of special relativity and the equivalence principle; the full theory of general relativity is not required.” While this is correct, it does not hold for cumulative effects, as I said above.

The paper by Narlikar http://www.iucaa.ern...1/211A_1994.pdf is most to the point, but it requires some effort to read. Thanks for having drawn my attention to it.

Can you prove your claim. I.e. produce the math that shows that the Newtonian theory predicts the same answer as GR?

 

Yes, it has been done, see here

 

This paper by A. Sfarti describes a proposal – not an actually performed experiment, and it is written by an author who shows no awareness of the difference between GR and Newtonian physics. This is clear already in the first clause of the Abstract, which reads ”Einstein predicted a change in the energy of photons in the proximity of a gravitational field, the change being directly proportional to the distance from the gravitational source.” This is true of Einstein (1911), but nowadays everybody associates Einstein in this context with GR (1916), and in GR, it is not true! [in GR, there is a difference in energy but no change.] Actually, Pound and Rebka reasoned similarly. They were not concerned with GR either. They referred only to Einstein (1911).

 

Although Sfarti proposes a mineshaft experiment of the kind I asked for, he does not consider its potential of falsifying one of the theories. [Edited: I am not sure that the predictions differ.]

 

You're going to hang the tag of "lazy" on people doing a cutting-edge experiment. Seriously?

 

I wanted to be a little funny, but having had a quick look at several papers by Pound & Rebka again, I am left with the impression that they were just disinterested in GR.

 

And allow me to clarify my question: how are you going to distinguish between a photon frequency change and a clock frequency change, when you are comparing one against the other?

 

There is no difference between these, but in Newtonian theory the photon frequency change is not matched by a corresponding difference in elapsed time at the two places.

And can you quantify the difference between the "Newtonian" shift and the GR shift? What do you think the equation is?

 

Let me try it:

[Edited: I should rather simply say that I cannot.]

Edited April 13, 2015 by Rolando

[imatfaal]

...

I wanted to be a little funny, but having had a quick look at several papers by Pound & Rebka again, I am left with the impression that they were just disinterested in GR.

...

 

Certainly - like all reputable scientists they had no bias and were certainly disinterested; but again like all good scientists they were very keen to learn about the world. and were certainly interested in GR. Interested enough to set up an experiment that seems to most to be the last of the classical tests of GR proposed by Einstein