The source of gravitational red shift

[Zman]

On the following website;

http://www.cfa.harvard.edu/Walsworth/Activities/Atomic%20clock/old_atomicclock.html

I read that;

The gravitational red-shift is a consequence of the local position invariance of the Einstein Equivalence Principle.

I know what gravitational red shift is and I understand the principle of Local Position Invariance but I don’t understand why gravitational red shift is a consequence of Local Position Invariance.

Can somebody enlighten me on this issue?

[Al68]

On the following website;

http://www.cfa.harvard.edu/Walsworth/Activities/Atomic%20clock/old_atomicclock.html

I read that;

The gravitational red-shift is a consequence of the local position invariance of the Einstein Equivalence Principle.

I know what gravitational red shift is and I understand the principle of Local Position Invariance but I don’t understand why gravitational red shift is a consequence of Local Position Invariance.

Can somebody enlighten me on this issue?

It just means that, in Einstein's elevator for example, a detector at the "top" will measure a redshift compared to a detector at the "bottom" from a source at the "bottom", if the elevator is accelerated "upward". And according to the Equivalence principle (local position invariance) it makes no difference whether the elevator is being accelerated in deep space or being accelerated in a gravitational field (at rest with the gravity source).

Gravitational redshift is a consequence of the proper acceleration, so if it's observed "at rest" in a gravitational field, then it's a consequence of local position invariance, since that's equivalent to accelerating in the absence of gravity.

[Bob S]

It just means that, in Einstein's elevator for example, a detector at the "top" will measure a redshift compared to a detector at the "bottom" from a source at the "bottom", if the elevator is accelerated "upward". And according to the Equivalence principle (local position invariance) it makes no difference whether the elevator is being accelerated in deep space or being accelerated in a gravitational field (at rest with the gravity source).
What you describe is exactly the Mossbauer Effect experiment (Pound and Rebka) that was carried out in 1959 at Harvard http://prola.aps.org/abstract/PRL/v3/i9/p439_1
The photons gained energy (blue-shifted) as they fell from the roof to the basement of the physics building, and the experimenters had to move the source away from the detector at a constant velocity to red-shift them back.

[Zman]

Al68, thank you very much for your explanation. It is now clear to me what that phrase means.