Gravitational time dilation implies energy change?

[johne1618]

According to Einstein's Gravitational Time Dilation, if an oscillating physical system is elevated to a height H above the Earth then it oscillates at a higher frequency than the same system at ground level.

According to Planck's relation between energy and frequency this surely means that the oscillator at height H must have more energy than it does on the ground.

Therefore any photons emitted by the oscillator at height H must have more energy than those emitted by the same oscillator on the ground.

Contrary to a popular interpretation, if those blue-shifted photons are detected at ground level their extra energy is *not* due to their "fall" from height H. In reality they were emitted at that higher energy/frequency at height H in the first place.

Am I right or no? ;)

 

[PAllen]

According to Einstein's Gravitational Time Dilation, if an oscillating physical system is elevated to a height H above the Earth then it oscillates at a higher frequency than the same system at ground level.

According to Planck's relation between Energy and frequency this means that the oscillator at height H must have more energy than it does on the ground.

Any photons emitted by the oscillator at height H must have more energy than those emitted by the oscillator on the ground.

Contrary to a popular interpretation, if those blue-shifted photons are detected at ground level their extra energy is not due to their "fall" from height H. In fact they were emitted at that higher energy at height H in the first place.

You can look at this in a quasi-Newtonian way. First, note that to a ground observer, a physical process that emits green light will emit the same green light in deep space for a nearby observer. What is true is that a distant observer, receiving light from from the ground emission, will receive red light (for example). You can choose to look at this as the light needing to give up energy to escape the gravity well. Similarly, the green light emitted from the distant emitter will look blue when received on the ground - you can say potential energy was converted to 'kinetic energy' of the photon, thus they frequency went up and they got bluer. There are pifalls to such analogies, in that gravity in GR is not really representable as a conservative potential, but they work to a point.

It is also valid, and not necessarily contradictory, to say the photons emitted by the high emitter have more energy because they are 'green' at a higher potential. Then as they are received on the ground, with slower time, they are perceived with higher frequency or energy. Generally, I would agree the latter description is 'better', but the former is not invalid if used with care.

Many people have strong quasi-religious beliefs about these being mutually exclusive, right versus wrong interpretations. I don't have such a black and white view.

 

[atyy]

What does one mean by the frequency of the oscillator at height h above the ground? Frequency as measured by who? An observer at the same height, or an observer on the ground?

 

[Mentz114]

According to Einstein's Gravitational Time Dilation, if an oscillating physical system is elevated to a height H above the Earth then it oscillates at a higher frequency than the same system at ground level.

According to Planck's relation between energy and frequency this surely means that the oscillator at height H must have more energy than it does on the ground.

Therefore any photons emitted by the oscillator at height H must have more energy than those emitted by the same oscillator on the ground.

Contrary to a popular interpretation, if those blue-shifted photons are detected at ground level their extra energy is *not* due to their "fall" from height H. In reality they were emitted at that higher energy/frequency at height H in the first place.

Am I right or no? ;)

In quantum mechanical terms this is true. The energy of any wave function depends on $d\psi/dt$ and this always has a frequency term, so even a stationary brick has different energies at different heights. Of course this corresponds to the Newtonian case.

 

[johne1618]

What does one mean by the frequency of the oscillator at height h above the ground? Frequency as measured by who? An observer at the same height, or an observer on the ground?

The frequency as observed from the ground.

I think the "Newtonian" interpretation that the "falling" photon gains energy/frequency like a falling apple is untenable as it goes against the available physical evidence.

Rather the frequency of the photon from height H as measured on the ground is a valid remote measurement of the energy of the oscillating system at height H from a ground observer's point of view.

For instance let us start with two identical radio oscillators A and B at ground level.

We measure the frequency of radio waves that they both emit at ground level. They are both the same f_A = f_B.

Let us also assume that the oscillators have counters that count the number of oscillations. Assume that they are are both initially set to zero, N_A = N_B = 0.

Now assume that observer A stays at ground level with oscillator A while oscillator B is carried up to height H.

The frequency of the radio waves from oscillator B measured on the ground by A, f_B, is found to be greater than that emitted by his oscillator A by the following factor:

f_B = ( 1 + g H / c^2) f_A

Now after a period of time measured at A, the oscillator B is lowered back to ground level with A.

The counters A and B can now be compared by the ground-based observer A.

The number of oscillations of B, N_B, will be observed to be greater than the number of oscillations of A, N_A, by the same factor:

N_B = ( 1 + g H / c^2) N_A

(This effect has been measured directly by using a pair of identical atomic clocks - one left on the ground and the other sent around the Earth in an airplane.)

In order to take this evidence into account, the ground-based observer A must infer that the photons from oscillator B at height H were transmitted at the enhanced frequency f_B in the first place.

 

[bcrowell]

What does one mean by the frequency of the oscillator at height h above the ground? Frequency as measured by who? An observer at the same height, or an observer on the ground?

The frequency as observed from the ground.

An observer on the ground can't measure the frequency at the top, only the frequency at the ground.

There is a good, careful discussion of this in Feynman Lectures On Gravitation (which is a different book, not part of the well known undergraduate Feynman lectures).

 

[ZealScience]

But don't forget that frequency is oscillations divided by time. At higher place time is proceeding faster. How do you explain that?

The biggest problem in your theory is that when photon travels from higher place to lower place it is losing energy, but what does the energy become?

In your theory, if you observe the photons at higher level, then they have less energy, if you are observing it at lower level then , they have more energy? Though energy is relativistic, but it doesn't sound right in this case.

 

[PAllen]

The frequency as observed from the ground.

I think the "Newtonian" interpretation that the "falling" photon gains energy/frequency like a falling apple is untenable as it goes against the available physical evidence.

Rather the frequency of the photon from height H as measured on the ground is a valid remote measurement of the energy of the oscillating system at height H from a ground observer's point of view.

For instance let us start with two identical radio oscillators A and B at ground level.

We measure the frequency of radio waves that they both emit at ground level. They are both the same f_A = f_B.

Let us also assume that the oscillators have counters that count the number of oscillations. Assume that they are are both initially set to zero, N_A = N_B = 0.

Now assume that observer A stays at ground level with oscillator A while oscillator B is carried up to height H.

The frequency of the radio waves from oscillator B measured on the ground by A, f_B, is found to be greater than that emitted by his oscillator A by the following factor:

f_B = ( 1 + g H / c^2) f_A

Now after a period of time measured at A, the oscillator B is lowered back to ground level with A.

The counters A and B can now be compared by the ground-based observer A.

The number of oscillations of B, N_B, will be observed to be greater than the number of oscillations of A, N_A, by the same factor:

N_B = ( 1 + g H / c^2) N_A

(This effect has been measured directly by using a pair of identical atomic clocks - one left on the ground and the other sent around the Earth in an airplane.)

In order to take this evidence into account, the ground-based observer A must infer that the photons from oscillator B at height H were transmitted at the enhanced frequency f_B in the first place.

This is all valid, but it doesn't answer all mysteries. (I bet the reference Bcrowell gave is what you should look at for a best possible accessible explanation). Consider bringing atomic oscillator down deeper into gravity well: it gets slower as observed by a higher observer, and remains in sync with similar oscillators at each height. Classically, a pulse of light is oscillating EM field. How come this oscillation doesn't slow down as the light goes deeper into gravity field? So you need an independent explanation of this. One adhoc way to do this is, in fact, the Newtonian conversion of potential energy to kinetic energy. Just to be clear, I think the the gravitational time dilation model is the accurate one, but it is not as trivial as it seems, and the Newtonian explanation can be stretched to account for most observations, and can be a useful heuristic.

 

[Jonathan Scott]

According to Einstein's Gravitational Time Dilation, if an oscillating physical system is elevated to a height H above the Earth then it oscillates at a higher frequency than the same system at ground level.

According to Planck's relation between energy and frequency this surely means that the oscillator at height H must have more energy than it does on the ground.

Therefore any photons emitted by the oscillator at height H must have more energy than those emitted by the same oscillator on the ground.

Contrary to a popular interpretation, if those blue-shifted photons are detected at ground level their extra energy is *not* due to their "fall" from height H. In reality they were emitted at that higher energy/frequency at height H in the first place.

Am I right or no? ;)

Yes, that's right. Gravitational red-shift or blue-shift is not something which "happens" to photons. A free-falling photon has constant frequency. Any perceived differences in frequency and energy are entirely due to differences in observer potential.

The same applies to any other timed activity, such as waving a flag and watching it from a distance. The image of the waved flag has the same frequency in all frames at rest relative to the flag, as seen by anyone observer, but the frequency appears to vary with observer potential because of time dilation.

 

[Jonathan Scott]

Consider bringing atomic oscillator down deeper into gravity well: it gets slower as observed by a higher observer, and remains in sync with similar oscillators at each height. Classically, a pulse of light is oscillating EM field. How come this oscillation doesn't slow down as the light goes deeper into gravity field?

Assuming you're not letting it fall freely (which could result in an expensive accident), you are extracting energy from the whole system, which is why everything slows down.

At the microscopic level, one effect of not letting it fall is to curve paths of horizontal light and to modify the path length of rising or falling photons between mirrors or similar, and this locally affects the energy.

Any pulse of light emitted outside the equipment and allowed to propagate freely will have a frequency determined by the potential at the location it is emitted.

 

[bcrowell]

Gravitational red-shift or blue-shift is not something which "happens" to photons. A free-falling photon has constant frequency. Any perceived differences in frequency and energy are entirely due to differences in observer potential.

I don't think you've made an empirically testable statement here. You can attribute the effect to a change in the photon's frequency, or you can attribute the effect to the observer's time dilation relative to the emitter. Neither description makes any testable prediction that the other doesn't make.

It's like asking whether Lorentz contraction "really" "happens" because the ruler is distorted or because the object being measured by the ruler is distorted.

 

[Jonathan Scott]

I don't think you've made an empirically testable statement here. You can attribute the effect to a change in the photon's frequency, or you can attribute the effect to the observer's time dilation relative to the emitter. Neither description makes any testable prediction that the other doesn't make.

It's like asking whether Lorentz contraction "really" "happens" because the ruler is distorted or because the object being measured by the ruler is distorted.

No, it's not like that. Any static observer will see the photon's frequency to be the same everywhere it moves in free fall, but different observers at different potentials will see different frequencies.

Consider the example of the image of a waving flag, which obeys exactly the same rules. You can observe the flag via telescopes stationed at different potentials which send their image signal back. Regardless of the potential, the received signal will show the flag waving at the same speed. Now attach a charge to the flag and you have an electromagnetic wave doing the same thing.

 

[bcrowell]

Any static observer will see the photon's frequency to be the same everywhere it moves in free fall, but different observers at different potentials will see different frequencies.

I'm having a hard time interpreting this statement. By "static" do you mean that the observer is at a constant height? Or did you mean "inertial" here rather than static? Does "in free fall" refer to the photon (which it sounds like), or to the observer (which would make more sense)?

Consider the example of the image of a waving flag, which obeys exactly the same rules. You can observe the flag via telescopes stationed at different potentials which send their image signal back. Regardless of the potential, the received signal will show the flag waving at the same speed. Now attach a charge to the flag and you have an electromagnetic wave doing the same thing.

This is all fine, but I don't see how it's relevant.

 

[Jonathan Scott]

I'm having a hard time interpreting this statement. By "static" do you mean that the observer is at a constant height? Or did you mean "inertial" here rather than static? Does "in free fall" refer to the photon (which it sounds like), or to the observer (which would make more sense)?


This is all fine, but I don't see how it's relevant.

By "static" I mean observer at rest relative to the source of the gravitational potential. And I mean that the photon is in free fall.

Instead of the photon or the flag, consider a vertical rod being rotated about its axis. It is clear that relative to any observer, all parts of the rod are rotating with the same frequency (for example, you can paint one side of the rod white to check that). However, the observer's clock will vary with time dilation, so the exact rate according to each observer will vary slightly as a result.

A photon is created by an electromagnetic oscillation, which is just like that physical oscillation. It then propagates that state at the speed of light, which may vary with coordinate system, but the delay to a given point which is at rest relative to the original source is fixed, so the oscillation of the wave as it passes that point is at the same frequency as it was created. It may be slower or faster than an oscillation produced by the same process locally, and we call that red-shift or blue-shift, but this isn't something which "happens" to a photon.

 

[PAllen]

Two cases to analyze and contrast (and compare to a light pulse, considered classically):

1) Light bouncing back and forth between two mirrors at the end of a 1 meter rigid (as possible) rod.

2) A marked cylinder spinning on a frictionless rod.

For each, examine what happens as it falls from a tower to the ground, then is gently caught by an observer on the ground (the frictionless rod allows the spinning cylinder to be caught without disturmbing the cylinder). For the process of falling and then being caught, consider as observed by the ground observer and the tower top observer.

I think a key difference in (2) is that conservation of angular momentum is significant, while no similar conservation law applies to (1).

 

[Jonathan Scott]

Two cases to analyze and contrast (and compare to a light pulse, considered classically):

1) Light bouncing back and forth between two mirrors at the end of a 1 meter rigid (as possible) rod.

2) A marked cylinder spinning on a frictionless rod.

For each, examine what happens as it falls from a tower to the ground, then is gently caught by an observer on the ground (the frictionless rod allows the spinning cylinder to be caught without disturmbing the cylinder). For the process of falling and then being caught, consider as observed by the ground observer and the tower top observer.

I think a key difference in (2) is that conservation of angular momentum is significant, while no similar conservation law applies to (1).

Why consider such complex cases? The time dilation rule gives the result in all cases.

If you try to analyze mirror cases, you find that relative to an isotropic coordinate system "parallel" mirrors reflecting light back and forth horizontally are actually closer together at the bottom (in the lower potential) than at the top because of the curvature of space, so locally light seems to accelerate downwards with the same acceleration as solid objects, but things shrink as they fall. You can see why the frequency has slowed down when you compare the result at two different potentials.

 

[PAllen]

Why consider such complex cases? The time dilation rule gives the result in all cases.

If you try to analyze mirror cases, you find that relative to an isotropic coordinate system "parallel" mirrors reflecting light back and forth horizontally are actually closer together at the bottom (in the lower potential) than at the top because of the curvature of space, so locally light seems to accelerate downwards with the same acceleration as solid objects, but things shrink as they fall. You can see why the frequency has slowed down when you compare the result at two different potentials.

I'm wondering whether the cylinder case is different, and more like light. That is, it will retain the rpm it had in the higher frame as observed by the higher frame, thus looking faster in the lower frame - modeling blueshift of light going down. Note that a similarly prepared spinning cylinder in the lower frame is not necessarily the same as one that was prepared in the higher frame.

[EDIT: Nah, this is nonsense. The cylinder will behave the same as any other clock, else you have a gyroscope speeding up in an inertial frame. Which raises the question: Why, actually, is light different from all other oscillators? If I have perfectly reflecting mirrors, and a beam bouncing between them, and fall with this apparatus from the tower, the light in the beam gets blue shifted? That can't be right either, then you can distinguish free fall from other inertial motion. So light directly received from higher source is blue shifted, but not if reflected back and forth between falling mirrors? I've gotten myself confused about this.]

 

[Jonathan Scott]

I'm wondering whether the cylinder case is different, and more like light. That is, it will retain the rpm it had in the higher frame as observed by the higher frame, thus looking faster in the lower frame - modeling blueshift of light going down. Note that a similarly prepared spinning cylinder in the lower frame is not necessarily the same as one that was prepared in the higher frame.

[EDIT: Nah, this is nonsense. The cylinder will behave the same as any other clock, else you have a gyroscope speeding up in an inertial frame. Which raises the question: Why, actually, is light different from all other oscillators? If I have perfectly reflecting mirrors, and a beam bouncing between them, and fall with this apparatus from the tower, the light in the beam gets blue shifted? That can't be right either, then you can distinguish free fall from other inertial motion. So light directly received from higher source is blue shifted, but not if reflected back and forth between falling mirrors? I've gotten myself confused about this.]

Light isn't different. If you create an oscillation, mechanic or electromagnetic, anywhere, and then propagate information about it to somewhere else which is a fixed distance, the received information will still have the same frequency as when it was emitted.

If you have a mechanism which produces a local oscillation, including a mechanism involving reflecting light, then the frequency of that local oscillation will depend on the gravitational potential. If you look at that oscillation equipment from a different potential using some sort of flat background coordinate system for comparison, then relative to that coordinate system you will see light traveling at a different speed or rulers changing size or some combination of both, but the net effect will simply be that the oscillation rate follows the time dilation factor.

 

[PAllen]

I have to admit something still seems pretty mysterious here. See below.

Light isn't different. If you create an oscillation, mechanic or electromagnetic, anywhere, and then propagate information about it to somewhere else which is a fixed distance, the received information will still have the same frequency as when it was emitted.

Can you propose an example of this other than light? What exactly is meant by propagating information? Any actual mechanical oscillator moving from higher to lower potential seems to change to match local time rate.

If you have a mechanism which produces a local oscillation, including a mechanism involving reflecting light, then the frequency of that local oscillation will depend on the gravitational potential. If you look at that oscillation equipment from a different potential using some sort of flat background coordinate system for comparison, then relative to that coordinate system you will see light traveling at a different speed or rulers changing size or some combination of both, but the net effect will simply be that the oscillation rate follows the time dilation factor.

Consider a tower emitting pulses of green light received on the ground as blue. If one of these pulses is captured by mirrors on the ground and reflected back and forth, it remains blue. If one of them is captured at tower height and slowly brought down, it is green. This conclusion seems necessary, but it is pretty strange to me - the path of light between mirrors affects its frequency.

 

[harrylin]

No, it's not like that. Any static observer will see the photon's frequency to be the same everywhere it moves in free fall, but different observers at different potentials will see different frequencies. [...]

That is correct in two ways:

- It's according to the theory (Einstein's GR conserves the emitted number of cycles)
- It's according to experiment plus common sense. Radio waves from satellite clocks that are observed to run at the same rate as Earth clocks (because their proper rate has been reduced) would have to magically add cycles "in flight" in order for the right number of cycles to arrive per 24 h period on Earth.

This does not imply an energy change but a different reference energy standard at a different height.

Cheers,
Harald

 

[PAllen]

That is correct in two ways:

- It's according to the theory (Einstein's GR conserves the emitted number of cycles)
- It's according to experiment plus common sense. Radio waves from satellite clocks that are observed to run at the same rate as Earth clocks (because their proper rate has been reduced) would have to magically add cycles "in flight" in order for the right number of cycles to arrive per 24 h period on Earth.

This does not imply an energy change but a different reference energy standard at a different height.

Cheers,
Harald

FYI: there has been no disagreement on this thread about what happens, and about the validity of the interpretation you give. There has been discussion about whether another interpretation is defensible. Part of motivating that is examining what is going on with light compared to other oscillators. In examining that, I've gotten myself a bit mystified.

 

[Jonathan Scott]

I have to admit something still seems pretty mysterious here. See below.


Can you propose an example of this other than light? What exactly is meant by propagating information? Any actual mechanical oscillator moving from higher to lower potential seems to change to match local time rate.


Consider a tower emitting pulses of green light received on the ground as blue. If one of these pulses is captured by mirrors on the ground and reflected back and forth, it remains blue. If one of them is captured at tower height and slowly brought down, it is green. This conclusion seems necessary, but it is pretty strange to me - the path of light between mirrors affects its frequency.

Ah - this depends on what you mean by "capturing" the light.

If you are talking about a device which creates light at a certain frequency, for example using a laser, and you move the device, then it will obviously simply change the frequency of the generated light at different heights by time dilation.

If you have a hypothetical 100% reflective mirror box and you shine a light into it briefly then have the light rattling around inside it, then that loses energy when you lower it slowly. This is because the box on average has to apply some upwards force to the light to keep it from falling, but if you let the box move downwards that force does work and the light loses energy.

 

[PAllen]

Ah - this depends on what you mean by "capturing" the light.

If you are talking about a device which creates light at a certain frequency, for example using a laser, and you move the device, then it will obviously simply change the frequency of the generated light at different heights by time dilation.

If you have a hypothetical 100% reflective mirror box and you shine a light into it briefly then have the light rattling around inside it, then that loses energy when you lower it slowly. This is because the box on average has to apply some upwards force to the light to keep it from falling, but if you let the box move downwards that force does work and the light loses energy.

Ok, and to create an extreme version of the phenomenon, imagine two tall mirrors (mythical 100% reflecting), and a tower near them. It beams green light at one of the mirrors angled so it very slowly makes its way down the mirrors to the ground. Also, imagine the tower beams green light at the same 'near horizontal angle' at one a pair of parallel mirrors that are lowered as the light path slowly goes down. Assume the slow moving mirrors and the static tall mirrors trace a pulse of light down to the ground at the same rate, similar number of total reflections. At the bottom, the slowly descending mirrors have green light between them, while blue light emerges from the base of the static mirrors. You got to admit that though this infeasible in so many ways, it is a really peculiar effect of GR.

 

[Jonathan Scott]

Ok, and to create an extreme version of the phenomenon, imagine two tall mirrors (mythical 100% reflecting), and a tower near them. It beams green light at one of the mirrors angled so it very slowly makes its way down the mirrors to the ground. Also, imagine the tower beams green light at the same 'near horizontal angle' at one a pair of parallel mirrors that are lowered as the light path slowly goes down. Assume the slow moving mirrors and the static tall mirrors trace a pulse of light down to the ground at the same rate, similar number of total reflections. At the bottom, the slowly descending mirrors have green light between them, while blue light emerges from the base of the static mirrors. You got to admit that though this infeasible in so many ways, it is a really peculiar effect of GR.

In a gravitational field, light curves downwards, with the same acceleration relative to local coordinates as static objects, so the mirrors would have to be in a very slight v-shape to hold the light up and prevent it simply accelerating away at g. If that v-shape is moving downwards, then it is slightly receding from the light compared with the static case, which takes away energy.

 

[harrylin]

FYI: there has been no disagreement on this thread about what happens, and about the validity of the interpretation you give. There has been discussion about whether another interpretation is defensible. Part of motivating that is examining what is going on with light compared to other oscillators. In examining that, I've gotten myself a bit mystified.

Also FYI :
There appeared not to be full agreement on what happens (in contrast to what is observed), so it seemed good to clarify it. But I now wonder what it is that mystifies you... ah I see what you mean with a "light oscillator". Yes that's an interesting puzzle

 

[bcrowell]

Any static observer will see the photon's frequency to be the same everywhere it moves in free fall, but different observers at different potentials will see different frequencies.

I'm having a hard time interpreting this statement. By "static" do you mean that the observer is at a constant height? Or did you mean "inertial" here rather than static? Does "in free fall" refer to the photon (which it sounds like), or to the observer (which would make more sense)?

By "static" I mean observer at rest relative to the source of the gravitational potential. And I mean that the photon is in free fall.

Hmm...then in that case I still don't know what to make of your original statement. Your statement consists of two parts: (1) "Any static observer will see the photon's frequency to be the same everywhere it moves in free fall,[...]" (2) "[...]but different observers at different potentials will see different frequencies."

#1 predicts that the Pound-Rebka experiment would give a null result. #2 predicts that the Pound-Rebka experiment would give a non-null result. In reality, it gave a non-null result.

Light isn't different. If you create an oscillation, mechanic or electromagnetic, anywhere, and then propagate information about it to somewhere else which is a fixed distance, the received information will still have the same frequency as when it was emitted.

This is one of the two interpretations I referred to in #11. You haven't given any argument that the other interpretation is invalid. Both are valid.

BTW, when you say things like "rest relative to the source of the gravitational potential" and "propagate information about it to somewhere else which is a fixed distance," you're using words that do not have any well-defined meaning for a general spacetime. This discussion has been in the context of the Earth's field, which is static to an excellent approximation, but you should be aware that these statements that you're making, which sound like very general claims, don't mean anything in a non-static spacetime. For example, in a cosmological spacetime, there is no well-defined notion of benig at rest relative to a distant object.

 

[PAllen]

Hmm...then in that case I still don't know what to make of your original statement. Your statement consists of two parts: (1) "Any static observer will see the photon's frequency to be the same everywhere it moves in free fall,[...]" (2) "[...]but different observers at different potentials will see different frequencies."

#1 predicts that the Pound-Rebka experiment would give a null result. #2 predicts that the Pound-Rebka experiment would give a non-null result. In reality, it gave a non-null result.

I think I understand what Jonathan Scott is trying to say here. Let's see if I can remove ambiguity.

1) A given static observer would 'consider' a given light signal to have unchanging frequency no matter where it is in a gravitational field. I think this is sort of true, but vacuous - how do you see or measure a distant light signal? The best you can do is have it go up or down and be reflected back to you and see it is the same frequency, which is really telling you nothing related to the claim.

2) A given light signal will be perceived to have different frequency by different static observers at different 'potentials' in a gravitiational field. This obvoulsy makes a measurable prediction, that was confirmed.

 

[Jonathan Scott]

#1 predicts that the Pound-Rebka experiment would give a null result. #2 predicts that the Pound-Rebka experiment would give a non-null result. In reality, it gave a non-null result.

The Pound-Rebka experiment was effectively comparing clocks at two different potentials by sending a wave at the frequency of one clock to the other (then cancelling that out by Doppler shift to determine the difference). It would have worked either way.

There is no problem with comparing frequencies at different locations provided that the distance remains constant. If a repeating signal of any form is emitted from one location and observed at another and the time between emission and reception is constant then the signal arrives at the same frequency as it was sent. For this purpose, a light wave (or any other electromagnetic field) is simply signalling the state of an oscillating electromagnetic field.

 

[bcrowell]

The Pound-Rebka experiment was effectively comparing clocks at two different potentials by sending a wave at the frequency of one clock to the other (then cancelling that out by Doppler shift to determine the difference). It would have worked either way.

There is no problem with comparing frequencies at different locations provided that the distance remains constant. If a repeating signal of any form is emitted from one location and observed at another and the time between emission and reception is constant then the signal arrives at the same frequency as it was sent. For this purpose, a light wave (or any other electromagnetic field) is simply signalling the state of an oscillating electromagnetic field.

This doesn't demonstrate anything about whether one of the two interpretations I referred to in #11 is more valid than the other.

Note again that as I pointed out in #26, phrases like "provided that the distance remains constant" generally do not have any well-defined meaning in GR. GR does not have a well-defined notion of whether distant objects are at rest relative to one another.

 

[Jonathan Scott]

This doesn't demonstrate anything about whether one of the two interpretations I referred to in #11 is more valid than the other.

Note again that as I pointed out in #26, phrases like "provided that the distance remains constant" generally do not have any well-defined meaning in GR. GR does not have a well-defined notion of whether distant objects are at rest relative to one another.

For Pound-Rebka purposes, by "distant" we mean "upstairs", not in another galaxy! There's a perfectly usable definition of constant distance between an observer and another object in that the round-trip light time remains constant.

A signal traveling at a speed which is only a function of location and does not vary at a given location with time cannot change frequency between two locations a fixed distance apart as seen by any given observer, because the received signal is just a delayed version of the original.

 

[bcrowell]

For Pound-Rebka purposes, by "distant" we mean "upstairs", not in another galaxy! There's a perfectly usable definition of constant distance between an observer and another object in that the round-trip light time remains constant.

Sure, I agree that there's no ambiguity in the Pound-Rebka case. However, I'm trying to point out to you that there's a logical flaw in the rule that you're proposing as being self-evident -- the rule doesn't make sense in a general context in GR.

A signal traveling at a speed which is only a function of location and does not vary at a given location with time cannot change frequency between two locations a fixed distance apart as seen by any given observer, because the received signal is just a delayed version of the original.

This argument works fine in flat spacetime, but not in a curved spacetime. Conditions like "speed...does not vary at a given location with time" and "a fixed distance apart as seen by any given observer" are not unambiguously well defined in a general curved spacetime. You can do something like this in the special case of a stationary spacetime. In a stationary spacetime, it is possible to globally rate-match clocks in a certain natural way. If you do that, then you assign the entire gravitational Doppler shift to some silly people's use of non-matched clocks, and none of it to the photon. However, GR has no preferred set of coordinates, so there is no fundamental reason that you have to do this. If you prefer to use identical clocks rather than rate-matched ones, then you assign the entire Doppler shift to the photon, and none of it to the clocks. Both interpretations are valid.

 

[Jonathan Scott]

If you prefer to use identical clocks rather than rate-matched ones, then you assign the entire Doppler shift to the photon, and none of it to the clocks. Both interpretations are valid.

That would be a very odd thing to do, and I don't think it could really work.

If an observer has established a coordinate system which assigns a global time coordinate over a region, equal locally to the observer's own clock time, then if they want a coordinate which has the usual properties of "time" it is expected to elapse at an equal rate at different locations. If instead they allow it to vary with potential to match local time, so as to see photon frequencies as being red-shifted or blue-shifted relative to the local clocks at different locations, then they can't keep going very long, as planes of local time get increasingly curved and out of sync with conventional time, which is after all what curved space-time is about.

I think that the only sensible viewpoint is that a freefalling test particle (regardless of whether it's a photon or a whale) in a static gravitational field has constant energy, and that "red-shift" or "blue-shift" is not something that happens to the object but rather is how it is seen from different potentials when compared with local clocks.

I do however agree that cosmological red-shift can be viewed in various different valid ways (and an infinite number of invalid ones, as frequently demonstrated on these forums).

 

[bcrowell]

If an observer has established a coordinate system which assigns a global time coordinate over a region, equal locally to the observer's own clock time, then if they want a coordinate which has the usual properties of "time" it is expected to elapse at an equal rate at different locations.

This sounds like a statement that you feel that general covariance is aesthetically unappealing. General covariance says that we're absolutely entitled to do a transformation like $t\rightarrow f(t,x,y,z)$, and as long as f is smooth and one-to-one, everything is OK, the laws of physics still have the same form, and all measurements are predicted to have the same results. Moreover, your preference for times that "elapse at an equal rate at different locations" isn't a preference that has any well-defined meaning in non-stationary spacetimes.

That would be a very odd thing to do, and I don't think it could really work.

This sounds like a statement that general covariance is not logically self-consistent. If so, then I think it would come as a pretty big surprise to every relativist since Einstein.

 

[Jonathan Scott]

This sounds like a statement that you feel that general covariance is aesthetically unappealing. General covariance says that we're absolutely entitled to do a transformation like $t\rightarrow f(t,x,y,z)$, and as long as f is smooth and one-to-one, everything is OK, the laws of physics still have the same form, and all measurements are predicted to have the same results. Moreover, your preference for times that "elapse at an equal rate at different locations" isn't a preference that has any well-defined meaning in non-stationary spacetimes.


This sounds like a statement that general covariance is not logically self-consistent. If so, then I think it would come as a pretty big surprise to every relativist since Einstein.

We were not talking about total generality; we are talking about essentially static gravitational configurations.

You seem to be asserting that you can choose a coordinate system in which the time coordinate can match local clocks in different potentials in such a configuration. You can indeed, but it won't be very practical for describing anything non-local, as the space and time coordinates defined in that way cannot be static and must in fact be accelerating relative to conventional coordinates such as isotropic ones.

 

[harrylin]

We were not talking about total generality; we are talking about essentially static gravitational configurations.

You seem to be asserting that you can choose a coordinate system in which the time coordinate can match local clocks in different potentials in such a configuration. You can indeed, but it won't be very practical for describing anything non-local, as the space and time coordinates defined in that way cannot be static and must in fact be accelerating relative to conventional coordinates such as isotropic ones.

Indeed - we cannot reasonably assume an enormous undetectable black hole, right? And would the assumption of such an acceleration not also lead to self contradiction for clocks at the opposite side of the earth? I don't think that the Earth is blowing up.