Fun fact: the Oklo reactor, a naturally occurring nuclear reactor that was active more than a billion years ago, was used to test if physical constants were the same in ancient times.
And we can split hairs and conclude that for "the last two billion years, on this planet, in this galaxy, the physics affecting nuclear decay have not changed"
It's great to know that say dating using carbon-14 decay is still useful over those time ranges on planet earth (I don't know if that is something we care about given that fossils don't tend to contain much carbon, but coal and oil deposits are around 400 million years old).
I don't want to imply that this is too small of a sample size, but I will imply that nuclear decay, and the movement of galaxies across the universe might be unrelated. Don't know. Not sure how we'd measure that. Supernova observations would tell us about nuclear fusion and it's limits. Does it tell us about nuclear fission? I don't know.
No, we measure the frequency of vibrations of _light_, not of a type of atom. Specifically, it is light emitted by cesium atoms that are transitioning from one specific energy state to another specific energy state. Although this is arbitrary, it is highly reproducible and would give precisely the same measured lengths of time at any point since the big bang.
That assumes that fundamental laws of physics did not change (will not change). This is what we believe and have no evidence otherwise. This is important since we rely on measuring atomic transitions of cesium atoms which itself were formed/forming billions of years after the big bang itself.
The laws of physics invariance under time is a core to our understanding. It would be very disrupting if we found otherwise.
Right, but most deviations one can think of (like, changes over time to physical "constants") would have an observable effect, so ancient galaxies would look much more different from modern galaxies and spectra wouldn't look the same other than a red shift, which moves all the lines in a uniform way.
We measure time in vibrations of a cesium isotope IIRC