[Physics] Gravitational Time Dilation and Gravitational Redshift - two separate things?

[Doug Marett]

Hi All,

    This just came up in a question I had to my website - it has to do with
the Pound-Rebka experiment and whether gravitational time dilation of
clocks and gravitational redshift of EM are two different things or the
same thing. The problem is set out by L.B. Okun is plain language in an
article here: https://arxiv.org/pdf/hep-ph/0010256.pdf
   The essence of it is that if you take a clock and move it from the
ground to the top of a tower, the clock should speed up in it's rate at the
higher altitude. If you then send an EM signal from this clock back to the
ground, Einstein says that the EM should be blue-shifted. However, this
would mean that the signal sent to the ground has now been blue-shifted
TWICE, once due to the clock speeding up,  and once due to the fall of the
EM through the gravitational gradient.
However, the Pound-Rebka experiment finds that it is blue-shifted only
once. So which effect is redundant, gravitational time dilation of clocks
or gravitational red-shift of light? They can't be the same thing, since
the latter is an operation performed on the EM during transit, and is
supposed to make it bend. And the former is something which happens to
clocks independent of EM signals sent between them.
Interestingly, the experiment proposed by Okun to answer the question was
performed in a slightly different form by Tom Van Baak as described here:

http://leapsecond.com/great2005/

Another link that is useful is the paper here which examines the math used
in the Pound-Rebka experiment and finds it is full of errors!

http://milesmathis.com/pound.html

Just wondering if anyone else is aware of this apparent contradiction in
the relativistic thinking : )

Doug
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