Gravitational redshift and time dilation

[Zman]

Gravitational redshift seems to be measured as if gravitational time dilation has no effect upon it.
What effect if any does gravitational time dilation have on the measurement of gravitational redshift?

 

[Dale]

I don't understand your comment. They are pretty much the same thing, or maybe you could slightly separate them by saying that gravitational time dilation causes gravitational redshift.

 

[Zman]

If light was replaced with sound wouldn’t there still be a gravitational redshift, assuming a uniform medium for the sound.
But in this case there would be negligible time dilation.
I am working on the assumption that redshift can be explained by acceleration alone.

 

[Dale]

If light was replaced with sound wouldn’t there still be a gravitational redshift, assuming a uniform medium for the sound.
But in this case there would be negligible time dilation.
I am working on the assumption that redshift can be explained by acceleration alone.

Yes, there is still gravitational redshift for sound, but there is also still time dilation for sound. Otherwise the first postulate would be violated. And what does acceleration have to do with anything?

 

[Zman]

And what does acceleration have to do with anything?

With the equivalence principle an accelerating body outside of a gravitational field emitting a beam of light will cause that beam of light to be ‘gravitationally redshifted’.
This is the Einstein elevator scenario. One elevator accelerating, the other stationary in a gravity field.

Without acceleration (or gravity) you do not get gravitational redshift.

With sound there will still be time dilation, but its effect will be insignificant compared to the stretching/compression of the sound wave wavelength.
With light this is not the case.

 

[Dale]

With sound there will still be time dilation, but its effect will be insignificant compared to the stretching/compression of the sound wave wavelength.
With light this is not the case.

I thought you specified a uniform medium, in which case there will be no stretching/compression of the sound wavelength wrt the medium.

 

[Zman]

My original question was never about sound but now the issue of how sound compares to light has led to new questions.
Sound wave energy is proportional to the amplitude squared and not the frequency.
But if a fixed frequency sound source emits sound and the observer absorbs that sound then;

If an observer travels towards that sound source at a constant velocity (no gravity) the frequency of the sound will be Doppler blueshifted.
If the observer measures the amplitude of that sound wave it won’t have changed.
If the observer measures the frequency of that sound it will have increased.

Is it valid to say;
The faster the observer travels the more sound energy is absorbed per second.
If sound energy is proportional to the amplitude squared then the above is not valid and the energy transferred to the observer in independent of the relative velocity of the observer.

Does it then follow that a sound wave that travels vertically downward in a uniform medium would not gain gravitational energy?

 

[Jonathan Scott]

If any signal, whether visual, sound, mechanical or whatever, is sent from a higher gravitational potential to a lower one, then to an observer at the lower potential it will appear to have a higher frequency (blue-shifted) compared with the frequency observed by an observer at the higher potential, simply because of the different observer clock rates.

Gravitational red shift or blue shift is not something that happens to a signal; from the point of view of an external observer the signal has the same frequency from the time it is emitted to the time it is received. It is rather an observation effect caused by different clock rates at different gravitational potentials.

 

[cfrogue]

Gravitational redshift seems to be measured as if gravitational time dilation has no effect upon it.
What effect if any does gravitational time dilation have on the measurement of gravitational redshift?

Here are the exact calculations performed for GPS satellites and the effects of gravity. The equations for all relativistic effects are listed in this page of the link below and in particular, the gravitation effect.

This correction must be made by the receiver; it is a correction to the coordinate time as transmitted by the satellite. For a satellite of eccentricity , the maximum size of this term is about 23 ns. The correction is needed because of a combination of effects on the satellite clock due to gravitational frequency shift and second-order Doppler shift, which vary due to orbit eccentricity

http://relativity.livingreviews.org/Articles/lrr-2003-1/
See Section 5.

 

[atyy]

Gravitational red shift is gravitational time dilation.

The definition is different from the special relativity case where Doppler shifts and time dilation are not the same.

 

[Dale]

My original question was never about sound but now the issue of how sound compares to light has led to new questions.
Sound wave energy is proportional to the amplitude squared and not the frequency...

Same with light classically. It is only with the introduction of quantum mechanics that you find the relationship between energy and frequency. Although I don't know much about the QM description of phonons I assume that they exhibit the same frequency dependence as photons.