# Pound Rebka experiment

exmarine
I read on Wikipedia that their experiment was accurate to within 10%. (Later experiments improved that.) My question is exactly what does that mean? All their experimental data points were within plus or minus 10% of the theoretical value? Or 1-sigma, 3-sigma, 6-sigma...? Are their experimental data points in a report somewhere available to the public? Maybe in their original paper?

Staff Emeritus
2021 Award
It means, exactly (I got this from Googling the original paper), "The error assigned is the rms statistical deviation including that of independent sensitivity calibrations taken as representative of their respected periods of operation." They saw a 5% deviation from the predicted value with a +/- 10% absolute uncertainty - so entirely consistent.

exmarine
Thanks. And wow - experimentalists are impressive. Back to the Wikipedia entry for this experiment: Can that discussion of the theory involved be correct? The part where the SRT and GRT effects are "superimposed"? Someone on here (Dale Spam?) showed me in a previous thread that there are no separate SRT and GRT parts for time dilation. Both effects are included in the rearrangement of the (Schwarzschild) metric, and that does not look like what is on Wikipedia. I must be missing something...

Gold Member
In most simple cases involving the weak field approximation you can add the separate parts for GR and SR time dilation. You just need to be very careful whose point of view you are using.

Mentor
In most simple cases involving the weak field approximation you can add the separate parts for GR and SR time dilation.

The actual conditions are broader, in one sense, but narrower in another, than the weak field approximation. For any stationary spacetime, you can define a "gravitational potential" and a notion of "being at rest" in that potential. Once you do that, you can separate out the time dilation due to differences in potential and the time dilation due to being in motion (relative to the notion of "being at rest" in the potential). These are what you and exmarine are calling the "GR" and "SR" parts of time dilation.

Stationary spacetimes include strong fields, so, for example, you could make this work even for observers close to the horizon of a black hole, provided it could be idealized as not gaining any mass--or angular momentum, if it's rotating--during the experiment. But you could not, for example, make it work in a system like a binary star, even if the field is "weak" everywhere, because such a system is not stationary. (You might be able to make it work as an approximation over a short enough time period in the region far enough from the two stars that the non-stationary nature of the system was negligible.) You also can't make it work in a case like the universe as a whole; for example, there is no invariant way to separate the "GR" and "SR" contributions to the observed redshift of a distant galaxy, even though the average density of mass-energy is low enough in the universe that the field is arguably "weak" everywhere.

In a sense, Pound Rebka should be viewed as a test of the principle of equivalence. The scale and precision of the experiment is not sensitive tidal effects, and the prediction for what is observed could be made viewing Jefferson Tower as uniformly accelerating in empty space. The scale and precision of the experiment is in every way within the required 'local' qualifier of the POE. Also, equivalently, the effect is completely indistinguishable from a pure SR Doppler analysis in a free fall frame.

This speaks to the issue of separating GR and SR effects. For this experiment, on accepting that it is valid to treat static objects in free fall frame as accelerating objects in a pure SR inertial frame, the balancing act they did was to make two pure SR Doppler effects cancel. Consider emitter on the ground and receiver on the top. In a free fall frame, receiver at time of detection is moving (away) relative to emitter at time of emission by (gΔt). Then, to compensate, receiver should be made to move down relative to tower top by this speed. Note, this exactly corresponds to the formula actually used.

I do not know for sure, but would assume that solar system tests redshift at high precision do distinguish the tidal predictions of GR.

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Staff Emeritus