Gravitational redshift and time dilation

Question

I understand as light moves away from gravity/curvature, let's use earth as an example, it is redshifted. Then it is usually said imagine a light clock that ticks according to the frequency of the light, and an observer at a location higher above earth will see earth clock ticking slower because the light received from earth is now shifted to a lower frequency.

Does this imply then, time only appears to be slower to the observer at a higher location? If the far away observer's local clock indicates 2 hours have passed, the observer would "think/observer" that earth clock only shows say 1 hour because the light it received is shifted, but the earth clock itself actually ticked 2 hours too. If this is the case, when you bring the earth clock up to the same height as the observer, wouldn't this "illusion" of delay go away, and the two clocks should show the same time? But clearly that's the wrong conclusion. The correct one is the earth clock would be slower when brought to the same height of the observer.

Edit: I'm making edit here in response to multiple answers since they seem to point to the same key: clock ticking slower is not an observational "illusion". Then it seems the way that the gravitational time dilation is introduced and calculated in typical textbook (such as Caroll and Ostlie) is confusing. It uses the shifted light frequency observed by a faraway observer to argue that earth clock ticks slower, which implies it's an "observational" effect.

Answer 1

If this is the case, when you bring the Earth clock up to the same height as the observer, wouldn't this "illusion" of delay go away and the two clocks should show the same time?

It is not an illusion. The lower clock actually ticks slower than the higher clock and registers less elapsed time than the upper clock when the lower clock is brought slowly back again and put next to the upper clock that did not move. I think the control group and I are basically in agreement here.

This was demonstrated in the Hafele-Keating experiment, where atomic clocks were placed on aircraft and flown around the world in different directions and then brought back together again. When they accounted for the time dilation due to relative motion, the remaining difference in elapsed times was accounted for by differences in the height of the flights.

There is a gravitational equivalent to the regular twin's paradox, where the twin that travels down to the surface of the gravitational body and remains there for several years will be younger than the twin that remained higher up when he eventually travels down to join the lower twin.

If we have two concentric rings around a black hole and we measure the circumference of the rings, we can calculate the coordinate distance between the rings. If we send a light signal from the outer ring to the inner ring and back again, the round trip time for the light signal will be longer than would be expected in the absence of gravity because the light actually moves slower lower down in the gravitational field. This has also been demonstrated in actual experiments that test an effect called Shapiro time delay. Everything moves slower and ages slower lower in a gravitational field relative to higher up.

In another question/answer, I demonstrated that a vertical cylinder that is spinning around its vertical axis would experience stresses when lowered deep into a gravitational field and would eventually break because the lower part is trying to spin slower than the upper part. Gravitational time dilation has real physical consequences.

Answer 2

You can watch a clock continuously as you drop it to a lower altitude, wait a while, and then raise it up again. While it's at the lower altitude it will appear redshifted. While you're lowering it, it will appear somewhat more redshifted. You can raise it slowly enough that it will be redshifted on the way up also, with perhaps a brief slight blueshift near the end. At the end of the experiment, it must have ticked fewer times in total than a higher-altitude clock, simply because it had no opportunity to catch up.

You shouldn't dismiss redshift as mere appearance. Light is a real thing, and the fact that it must fit in a certain way in the spacetime region between the clocks in this experiment tells you something about the rate of the clocks.

Answer 3

Time does actually flow slower in the presence of gravitational fields. This has been observed at the quantum scale, when atomic clocks (relying on a quantum oscillator that has a very precisely-known frequency) are placed on the ground vs. on mountains high up vs. on airplanes moving fast and also high up vs. in orbit very far away.

If I'm at a Lagrange point (at rest to the Earth and very far from the gravity well) and I have an atomic clock, as well as a telescope through which I can observe another atomic clock on Earth sending signals to me via light, I will actually see the Earth clock tick slower than mine because of time dilation. The frequency of light that it emits will be redshifted, but redshift and time dilation, although both confirmed relativistic effects, aren't directly related in the direction you propose. That is, I don't observe that the Earth clock is slower because the light coming from it is redshifted, I observe that the light coming from it is redshifted because it (and photons it emits) are experiencing time dilation.

Answer 4

Put one Joule of light in a box, then, using a rope, manually lower it into a gravity well. The light is doing work on your hands. Then open the lid of the box, and absorb all the light into your eyes.

If the work that was done on your hands by the light was 0.9 J, then the work that will be done on your eyes by the light will be 0.1 J.

My point is that you put blue light in a box, your eyes absorbed red light, because something happened to the light at some time during the experiment.

Answer 5

I can see why you ask that because I questioned the same thing.

The most logical explanation I could come up with was that the redshift in the light is due to the gravitational time dilation at the point of emission, which doesn't change as the light travels.

What changes as the light moves away from the surface is the time dilation affecting locally emitted waves, which is reducing, which increases their frequencies away from the surface relative to the travelling light.

So it's not that the light travelling away from the surface is reducing further in frequency as it travels, but that locally emitted light is increasing in frequency relative to it due to reduced time dilation.