Comment on Anton Petrov video on astrophysical measurement of fine structure constant variations
Your link goes to “pay per view”. Here is an open version
A limit on variations in the fine-structure constant from spectra of nearby Sun-like stars
https://arxiv.org/abs/2211.05150
Mysterious Fine Structure Constant (1/137) Measured In Nearby Stars
https://www.youtube.com/watch?v=z5IF7WNmnS0
The exact term, “fine structure constant” has 1.1 Million entry points (Google search, 26 Nov 2022). And you have talked about 1 paper. If you are going to be the world’s leading scientific spokesperson, you might need to review topics, not just summarize what others seem to be doing. I first learned (1967) about the fine structure constant as the ratio of the speed of an electron in the first Bohr orbit to the speed of light. You can see a bit of that in the Wikipedia article on the Bohr model where they talk about Rydberg energy. https://en.wikipedia.org/wiki/Bohr_model#Rydberg_formula These are great for remembering the scale of things. The importance of an astronomical survey is somewhat lost because they are not correcting for the changes in gravitational field at the detector, and at the source.
The relativistic effect of that velocity (v = alpha*c) can be calculated on Google
=1/sqrt(1-(0.0072973525693)^2) = 1.00002662674
To get that in simpler terms, convert to part per million time dilation
=1E6*(1-(1/sqrt(1-(0.0072973525693)^2) )) = -26.6267407 parts per million time contraction. That is because the electron will be in a higher potential region so time runs slower there. “Potential, like gravitational potential, magnetic potential, velocity potential is always Joules/Kilogram in Internet standard units. That is the same as (meters/second)^2.
These kinds of corrections are routine for all gravitational imaging arrays, orbital communications, precise time coordination and precise gravitational surveys. Then it is parts per 10^12 (pico) or parts per 10^15 (femto).
https://en.wikipedia.org/wiki/Time_dilation
(Wikipedia curators are in-numerate and in-mathematic, so they do not label equations, nor standardize them, nor remove the massive duplication.) Otherwise I could point you to ONE definition of time dilation, with a universal selection of units, applications and implications. Talking about stuff won’t cut it. You also have to do it.
