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You are almost absolutely correct. To be pedantic, the photon is blue shifted "from", not "at" the top of the tower.The stuff you say you never read, is nonsense, which is why you never read it.
If two persons have contradictory opinions about something, one of them will think like the other need to study some more to understant the phenomenon. Obviously, the other will think the same way.
But the clock IS blue shifted 'at' elevation... (this has been the whole point of the thread)
Why does physics think that the gamma ray source will 'not' be blue shifted at top of tower?
(It may be that Relativity didn't predict that atoms are blue shifted in elevation, but it is most certainly not nonsense that they are because it is proven by the NIST experiment... And if a cesium atom is blue shifted at elevation, a gamma ray source will be as well.)
You are almost absolutely correct. To be pedantic, the photon is blue shifted "from", not "at" the top of the tower.
The stuff you say you never read, is nonsense, which is why you never read it.