Question about gravitational redshift

[Rolando]

If this thread has been moved to "Speculations", then good by.

Thanks to all of you for your contributions.

[Strange]

Alternative 1) tells you that you will see the flashes arriving in intervals of two seconds.

Alternative 2) tells you that you will see the flashes arriving in intervals of one second.

 

Alternative 2 says nothing about the rate of flashes. Actually, neither does 1. So this is doubly irrelevant.

[xyzt]

All electromagnetic radiations are affected EQUALLY. So, you can stop beating the strawman "light itself is not affected by this curvature". One of the tenents of logic is that , if you start with garbage assumptions, you can end up with any conclusions, in most cases garbage as well.

Here is the standard proof:

 

All periodical processes are affected equally by gravitation. Start with the Schwarzschild solution to the EFE's:

 

[math](cd\tau)^2=(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)-(rd\theta)^2[/math]

 

For two periodical processes located at Schwarzschild radial coordinates [math]r_1[/math] and [math]r_2[/math] one can write:

 

[math](cd\tau_1)^2=(1-r_s/r_1)(cdt)^2-dr^2/(1-r_s/r_1)-(r_1d\theta)^2[/math]

 

[math](cd\tau_2)^2=(1-r_s/r_2)(cdt)^2-dr^2/(1-r_s/r_2)-(r_2d\theta)^2[/math]

 

Dividing the two one gets, expressed in clock periods:

 

[math]\frac{d\tau_1}{d\tau_2}=\sqrt{\frac{1-r_s/r_1-(dr^2/(cdt)^2)/(1-r_s/r_1)-(r_1/cd\theta/dt)^2}{1-r_s/r_2-(dr^2/(cdt)^2)/(1-r_s/r_2)-(r_2/cd\theta/dt)^2}}[/math]

 

Most often, the above is expressed in terms of frequencies :

 

[math]\frac{f_2}{f_1}=\sqrt{\frac{1-r_s/r_1-(dr^2/(cdt)^2)/(1-r_s/r_1)-(r_1/cd\theta/dt)^2}{1-r_s/r_2-(dr^2/(cdt)^2)/(1-r_s/r_2)-(r_2/cd\theta/dt)^2}}[/math]

 

 

The above is the general equation that governs the functionality of GPS, so, its validity is confirmed on a daily basis, every second of it. The above also represents the most rigorous explanation of the Pound-Rebka experiment since it factors in not only the difference in altitude but also the difference in tangential speeds.

 

[math]\frac{f_2}{f_1}=\sqrt{\frac{1-r_s/r_1-(dr^2/(cdt)^2)/(1-r_s/r_1)-(v_1/c)^2}{1-r_s/r_2-(dr^2/(cdt)^2)/(1-r_s/r_2)-(v_2/c)^2}}[/math]

 

With a little effort, I can show you how the above explains the Hafele-Keating experiment (one needs to execute an integral wrt. coordinate time)..

Since this thread has degenerated into an incessant trolling on the same fringe claims, I would like to restore it to a semblamce of science. The above expressions for frequency change can be found in a slightly different form, a form that illustrates the differential influences. Indeed, if one uses a Taylor expansion, one gets:

 

[math]\frac{f_2}{f_1}=0.5((r_s/r_2-r_s/r_1)+(dr^2/(cdt)^2)/(1-r_s/r_2)-(dr^2/(cdt)^2)/(1-r_s/r_1)+((v_2/c)^2-(v_1/c)^2))[/math]

 

The above form applies only when [math]r_s/r[/math], [math]v[/math], etc are much smaller than 1 (which is often the case).

Since the gravitational potential is expressed as [math]\Phi=-\frac{k}{r}[/math], one can also see the form:

 

[math]\frac{f_2}{f_1}=0.5((\Phi_1-\Phi_2)+(dr^2/(cdt)^2)/(1-r_s/r_2)-(dr^2/(cdt)^2)/(1-r_s/r_1)+((v_2/c)^2-(v_1/c)^2))[/math]

 

or

 

[math]\frac{f_2}{f_1}=0.5((\Phi_1-\Phi_2)(1+(v_r/c)^2)+((v_2/c)^2-(v_1/c)^2))[/math]

 

frequency ratio

 

[math]\frac{d \tau_1}{d \tau_2}=0.5((\Phi_1-\Phi_2)(1+(v_r/c)^2)+((v_2/c)^2-(v_1/c)^2))[/math]

 

clock period ratio

 

 

where [math]v_r=\frac{dr}{dt}[/math],

[math]v_i=r_i\frac{d \theta}{dt}[/math]

are respectively the radial and the tangential speeds.

To fix the ideas, the term [math](\Phi_1-\Phi_2)(1+(v_r/c)^2)[/math] (called "gravitational term") has always the opposite sign from the term [math](v_2/c)^2-(v_1/c)^2[/math] (called "kinematic term"). There is a certain altitude where the two terms cancel each other. For example, if [math]r_2>r_1[/math] then [math](v_2/c)^2-(v_1/c)^2>0 [/math] and [math]\Phi_1-\Phi_2 <0[/math].

For example, the above is seen in the explanation of the Hafele-Keating experiment. Wiki used to host some not so bad, not so good equations on HK but they removed them, so I thought I'd post the correct equations.

Lastly, the above methodology (using the Schwarzschild metric) works equally well for the case when the experiment takes place within the Earth shell, like in a mineshaft. The only thing that need to be done is the replacement of the external Schwarzschild solution with the internal one. This is done trivially by replacing the exterior gravitational potential with the gravitational potential inside the Earth into the Schwarzschild solution. Actually, this approach is so general that it allows for the source and the observer to be situated on opposing sides of the Earth crust.

Edited April 15, 2015 by xyzt

[MigL]

Thank you xyzt ( I'm re-enforcing positive behavior ).

 

Rolando's consideration of the cause of the red shift presented two options...

1- The radiation is red-shifted because the atom emitting the light is time dilated, deeper in the gravity well.

2-The radiation is red-shifted as it loses energy climbing up the gravity well.

They are not mutually exclusive as he believes, nor are they additive.

 

Even without consideration of the math you presented, the atom emitting the radiation does not experience time dilation IN ITS OWN FRAME. The time dilation is only measured from the observer's frame, after the signal ( the radiation ) has climbed up the gravitational well. In other words, it is the exact same effect. The geometric explanation ( GR ) is the time dilation, but it can only ever be measured as the energy loss on the climb out ( as shown by the radial or potential dependence in xyzt's math )

Edited April 15, 2015 by MigL

[Rolando]

Thank you MigL. Your answer is to the point.

 

The time dilation is only measured from the observer's frame, after the signal ( the radiation ) has climbed up the gravitational well. In other words, it is the exact same effect. The geometric explanation ( GR ) is the time dilation, but it can only ever be measured as the energy loss on the climb out ( as shown by the radial or potential dependence in xyzt's math )

 

I had failed to not notice that also in alternative (2), the effects can be considered as due to time-dilation, which makes the two alternatives fully equivalent.

My mind had become locked on the other possible interpretation of alternative (2), in which the photons loose energy without there beeing any time dilation (as in Einstein’s model of 1911, which I mentioned).

Edited April 16, 2015 by Rolando

[Rolando]

Conclusions

 

The discussed alternative (1) is illustrated here. The caption says: ”In a gravitational filed, an atom emits light with a lower frequency and thus with larger wavelength.” This alternative is misleading since it evokes the question that I asked. Any attentive student at this level of knowledge might have asked it. I guess that this is the reason for why this alternative has lost popularity.

 

The discussed alternative (2) is illustrated here. This is misleading in a different way, since it can rather be seen as illustrative of how Einstein treated the problem before he came up with GR, i.e., before the idea of gravitational time dilation was born.

 

It is, of course, possible to illustrate GR in a way that is not misleading in any of these ways. Do it, if you are well acquainted with producing such figures, and when you think that it is not misleading in still another way, place it in the Wikipedia.

 

Meanwhile, I have also learnt what is meant by trolling, and I understand that I have been the victim of a troll, who succeeded to some extent. I apologize if this has colored my responses to others as well.

 

I attach significance to the fact that I was urged to talk in mathematical language, although this would in no way have been helpful to answer my question, but just hide it under the carpet.

 

I also attach significance to the fact that the thread with my unspeculative pedagogical question has been moved to a box that is intended for pseudoscientific and speculative threads, which makes it most unlikely for the answer to this question to be noticed by those to whom it might be most relevant.

Edited April 16, 2015 by Rolando

[xyzt]

 

I also attach significance to the fact that the thread with my unspeculative pedagogical question has been moved to a box that is intended for pseudoscientific and speculative threads, which makes it most unlikely for the answer to this question to be noticed by those to whom it might be most relevant.

This is where your thread belongs, you did not ask a question, you pushed your fringe misconceptions, over and over despite being given quite clear answers. The responsibility for your thread being moved is all yours, you have been given mainstream answers, some containing a lot of detail that you persisted in ignoring.

Edited April 16, 2015 by xyzt

[Strange]

It is, of course, possible to illustrate GR in a way that is not misleading in any of these ways.

 

Yep. It is called mathematics.

 

The Wikipedia page you link to says:

 

While gravitational redshift refers to what is seen, gravitational time dilation refers to what is deduced to be "really" happening once observational effects are taken into account.

 

Which is pretty much what everyone has been trying to tell you.

[MigL]

I call attention to your first line...
”In a gravitational filed, an atom emits light with a lower frequency and thus with larger wavelength.”

 

No it doesn't.

An observer in that frame will not see any time dilation what-so-ever.

 

It is only when the observer is in a different frame, such as at a higher gravitational potential, that he/she will measure the emitted light to have a lower frequency/longer wavelength.

 

Almost all confusion usually associated with relativity is caused by mixing frames.

You're not the first to do so, and you won't be the last.

[Rolando]

I call attention to your first line...

”In a gravitational filed, an atom emits light with a lower frequency and thus with larger wavelength.”

 

No it doesn't.

An observer in that frame will not see any time dilation what-so-ever.

 

It is only when the observer is in a different frame, such as at a higher gravitational potential, that he/she will measure the emitted light to have a lower frequency/longer wavelength.

The caption of the figure in Atkin’s book (here) reads: ”In a gravitational filed, an atom emits light with a lower frequency and thus with larger wavelength.” The associated text suggests that the frame of a distant observer is adopted. No confusion so far. It would also be too odd an idea to think that it might hold in the frame of the source itself. (Time can hardly be dilated with respect to itself.)

 

Almost all confusion usually associated with relativity is caused by mixing frames.

You're not the first to do so, and you won't be the last.

I agree. But if you take a closer look at Atkin’s figure, you will see that frames have been mixed already there (which confirms that I am not the first). The context, as well as the difference between the waves emitted by the two sources, suggests that things are shown in the flat space of a distant observer. However, each wave itself is not shown as it would appear in that space. They are shown as they appear in the curved space in which they propagate. The wavelength remains constant only in this space. If projected onto a flat space, the wavelengths appear shorter close to the attracting body, as they do in the figure here, where the orientation agrees with that in Atkin’s figure. But even this figure is misleading, since it fails to show that the change in wavelength is due to the curvature of space. In order to be clear, it is necessary to show this. Otherwise it is simpler to think of it as Einstein did in 1911.

[xyzt]

The caption of the figure in Atkin’s book (here) reads: ”In a gravitational filed, an atom emits light with a lower frequency and thus with larger wavelength.” The associated text suggests that the frame of a distant observer is adopted. No confusion so far. It would also be too odd an idea to think that it might hold in the frame of the source itself. (Time can hardly be dilated with respect to itself.)

 

 

It's a bad book. Do yourself a favor and buy a better one. You've been told repeatedly that you are repeating errors, why not follow the advice?

[Rolando]

I thought for a while that I had understood. However, let me quote from Okun, Selivanov & Telegdi (page 7):

 

”Now we are in a position to explain the redshift in the laboratory frame. According to Eq. (8) or Eq. (10) the energy difference ε_lab of atomic or nuclear levels in that frame depends on the location of the atom. The deeper atom sits in the gravitational potential the smaller is ε_lab. For an absorber atom which is located at height h above an identical atom which emits the photon, the relative change in the energy difference is gh/c²,

 

Delta ε_lab /ε_lab = gh/c². (11)”

 

...”One can say that the energy levels of the absorber atoms are shifted towards the blue in the laboratory frame. Eq. (11) is, of course, nothing but a way to describe the difference in the rates of atomic clocks located at a height h one above the other. On the other hand, the energy (frequency) of the photon is conserved as it propagates in a static gravitational field. This can, for example, be seen from the wave equation of electromagnetic field in the presence of a static gravitational potential or from the equations of motion of a massless (or massive) particle in a static metric. Clearly, in the laboratory system there is no room for the interpretation in which the photon loses its energy when working against the gravitational field.” [This interpretation is alternative (2) in the present discussion.]

 

While the quoted explanation is not made explicit in Atkins’ book, the illustration there is fully in accord with it.

Edited April 18, 2015 by Rolando

[xyzt]

I thought for a while that I had understood. However, let me quote from Okun, Selivanov & Telegdi (page 7):

 

”Now we are in a position to explain the redshift in the laboratory frame. According to Eq. (8) or Eq. (10) the energy difference ε_lab of atomic or nuclear levels in that frame depends on the location of the atom. The deeper atom sits in the gravitational potential the smaller is ε_lab. For an absorber atom which is located at height h above an identical atom which emits the photon, the relative change in the energy difference is gh/c²,

 

Delta ε_lab /ε_lab = gh/c². (11)”

 

...”One can say that the energy levels of the absorber atoms are shifted towards the blue in the laboratory frame. Eq. (11) is, of course, nothing but a way to describe the difference in the rates of atomic clocks located at a height h one above the other. On the other hand, the energy (frequency) of the photon is conserved as it propagates in a static gravitational field. This can, for example, be seen from the wave equation of electromagnetic field in the presence of a static gravitational potential or from the equations of motion of a massless (or massive) particle in a static metric. Clearly, in the laboratory system there is no room for the interpretation in which the photon loses its energy when working against the gravitational field.” [This interpretation is alternative (2) in the present discussion.]

 

While the quoted explanation is not made explicit in Atkins’ book, the illustration there is fully in accord with it.

Err, you still don't get it, do you? From the page that you are citing:

 

 

”One can say that the energy levels of the absorber atoms are shifted towards the blue IN THE LABORATORY FRAME".

 

Better phrased: "The em radiation emitted from the top of the tower is received blue shifted at the bottom, in the laboratory frame".

[Rolando]

I thought for a while that I had understood. However, let me quote from Okun, Selivanov & Telegdi (page 7):

 

”Now we are in a position to explain the redshift in the laboratory frame. According to Eq. (8) or Eq. (10) the energy difference ε_lab of atomic or nuclear levels in that frame depends on the location of the atom. The deeper atom sits in the gravitational potential the smaller is ε_lab. For an absorber atom which is located at height h above an identical atom which emits the photon, the relative change in the energy difference is gh/c²,

 

Delta ε_lab /ε_lab = gh/c². (11)”

 

...”One can say that the energy levels of the absorber atoms are shifted towards the blue in the laboratory frame. Eq. (11) is, of course, nothing but a way to describe the difference in the rates of atomic clocks located at a height h one above the other. On the other hand, the energy (frequency) of the photon is conserved as it propagates in a static gravitational field. This can, for example, be seen from the wave equation of electromagnetic field in the presence of a static gravitational potential or from the equations of motion of a massless (or massive) particle in a static metric. Clearly, in the laboratory system there is no room for the interpretation in which the photon loses its energy when working against the gravitational field.” [This interpretation is alternative (2) in the present discussion.]

 

While the quoted explanation is not made explicit in Atkins’ book, the illustration there is fully in accord with it.

[swansont]

Your latest is all quote and no added text. However, in anticipation, I'll note that "the relative change in the energy difference is gh/c²" is the physics.

 

 

All else is interpretation.

[Rolando]

Your latest is all quote and no added text. However, in anticipation, I'll note that "the relative change in the energy difference is gh/c²" is the physics.

 

 

All else is interpretation.

 

I can agree with this. But if there is such a change and this change is due to geometry, this raises the question of why the photons are not affected by this geometry (in the interpretation advocated by Okun et al. and apparently also by Atkins). In the alternative interpretation, the photons are affected on their way and the atoms cannot be assumed to be affected as well.

 

I am looking for a tenable interpretation.

Edited April 23, 2015 by Rolando

[swansont]

 

I am looking for a tenable interpretation.

 

Pick one. But be consistent with the choice.

[Rolando]

 

Pick one. But be consistent with the choice.

The first one leaves my question without an answer.

The second one denies your claim of what the physics is.

[xyzt]

The first one leaves my question without an answer.

The second one denies your claim of what the physics is.

...and the trolling has restarted. Instead of wasting your time carping about things you do not understand why not invest in a book like "Gravitation" by Misner, Thorne, Wheeler? Then you too could learn the modern explanation of gravitational redshift (and more than that).

Edited April 23, 2015 by xyzt

[swansont]

The first one leaves my question without an answer.

The second one denies your claim of what the physics is.

 

No, I don't think that's true. (If I understand what you're saying by "my question"). Okun picked an interpretation by choosing a frame from which to do the observation. The equation remains the same. You could just as easily choose the other interpretation but what you can't do is choose both, or switch in the middle of the analysis.

[Rolando]

In Schwarzschild geometry, it holds that the deeper an atom sits in a gravitational potential well the smaller is the energy difference of atomic levels. This is an effect of space-time geometry and reflected in the frequency of photons observed in a frame of reference in which source and receiver are stationary. This is all that is captured by the usual equations.

 

The problem arises when one tries to locate (ascribe) the effect either to the atoms or to the photons, which needs to be decided in order to illustrate and understand what is going on.

 

Ascribing the effect to the atoms gives rise to the question of why the photons on their way are not affected by the geometry if it is the geometry that gives rise to the effect on atoms.

 

Ascribing the effect to the photons fails to account for observable clock rate differences. Okun et al. reject this alternative with a different motivation.

 

One might also consider Painlevé-Gullstrand coordinates, in which the frequency shifts and clock rate differences under discussion here reflect the same Doppler effect. This may be more transparent.

[Strange]

Ascribing the effect to the atoms gives rise to the question of why the photons on their way are not affected by the geometry if it is the geometry that gives rise to the effect on atoms.

 

Ascribing the effect to the photons fails to account for observable clock rate differences.

 

Of course. Obviously. These two descriptions are mutually exclusive. Therefore, if you choose one the other is not applicable.

 

Which part of "choose one or the other" do you not understand?

• You can choose one.
• Or you can choose the other.
• You cannot choose both.

Really, how hard is that?

 

One hundred and twenty posts and you still can't understand that one simple fact.

 

Let's try again. Slowly:

• You can choose one description.

 

• Or you can choose the other description.

 

• You cannot choose both descriptions.

 

• Because they are mutually exclusive.

 

Maybe if you carry on for another 7 pages, you will begin to understand what you are being told.

[Rolando]

 

Of course. Obviously. These two descriptions are mutually exclusive. Therefore, if you choose one the other is not applicable.

 

How could you fail to see that these descriptions are just the mutually exclusive alternatives under discussion?

Each one has to be considered on its own, and the problem is that none of them appears to be acceptable.

[Strange]

How could you fail to see that these descriptions are just the mutually exclusive alternatives under discussion?

 

Exactly. That is what I said.

 

Each one has to be considered on its own, and the problem is that none of them appears to be acceptable.

 

The fact you don;t find them acceptable is your problem. The solution is to ignore them both.

 

Focus on the science instead.

[Rolando]

This was a waste of time.