[dekhn]

I took a stat thermo class and it was basically all about entropy, which was expresed as ln W- the log of the number of ways (permutations) that a system can be ordered, which gives a convenient denominator when calculating the probability of a specific permutation. Here's the professor's book, which was still only in latex form when we took the class: https://www.amazon.com/Molecular-Driving-Forces-Statistical-...

[javajosh]

yes, there are lots of quantitative details. I wanted to emphasize the key qualitative concept, from which the others can derive. In a similar way you can derive all of special relativity, and approach an intuition about the strangeness of spacetime, starting with only two ideas: the laws of physics are the same in all reference frames; the speed of light is constant. I prefer to start there and derive e.g. Lorentz factors than start with the mathy stuff.

[kergonath]

> starting with only two ideas: the laws of physics are the same in all reference frames; the speed of light is constant.

Isn’t this redundant, though? The constant velocity for light in a vacuum comes directly from the laws of (classical) electromagnetism in the form of Maxwell’s equations. So “the laws of Physics are the same in all reference frames” implies “Maxwell’s equations are valid in all reference frames”, which in turn implies “the velocity of light in vacuum is the same in all reference frames”. That’s what I understood reading Einstein himself.

I think it’s much stronger that way. Otherwise we get to why light should be a special case, which is difficult to defend. The constant velocity of light (in vacuum) being an unavoidable consequence of the laws of Physics makes it much stronger.

> I prefer to start there and derive e.g. Lorentz factors than start with the mathy stuff.

That’s how Einstein himself explained it (with trains and stuff, but still) and it makes a lot of sense to me. Much more than the professor who did start with the Lorentz transform and then lost everyone after 20 minutes of maths.

[staunton]

> So “the laws of Physics are the same in all reference frames” implies “Maxwell’s equations are valid in all reference frames”, which in turn implies “the velocity of light in vacuum is the same in all reference frames”

From the point of view of physicists before Einstein, this forces you to decide between Newtonian physics and Maxwell's theory, because the reference frames that are "equivalent" are irreconcilably different for those. The "irreconcilable" part is subtle and not obvious. Maxwell's theory "won", but it was the newer theory while Newton's was very well established. The contemporary physicists' efforts to reconcile the two using an "ether" were completely reasonable from their point of view. (And actually, you can't even completely exclude the existence of an ether, as some ether theories are consistent with the standard model to a reasonably high accuracy. What kills them is Occam's razor)

[kergonath]

I know. What I am saying is that the laws of physics being the same implies the velocity of light being the same. Of course it conflicts with Newton’s laws and Galilean transformations when changing reference frames. But what he demonstrated was that the apparent conflict could be solved in a logically consistent way, once you do away with the concept of universal time. From that point, Newton’s laws do not need to be invariant, because they were demonstrably incomplete, in contrast to Maxwell’s, which were verified as far as they could be with the experimental setups of the time.

Sure, postulating the existence of the ether was reasonable in a way at one point in time, I am not saying otherwise. But by 1905 it was on very shaky grounds, with no experimental result to support it. Saying that the theory can be tweaked to reproduce reality is not very useful: all theories can. What a theory needs to be verified is to predict things that the other established theories do not. And on that front, the ether theory is about as powerful as my pet theory that elementary particles are moved by tiny demons that we cannot see (I would make a joke about string theory but it’s way more serious than the ether one).

[javajosh]

>That’s how Einstein himself explained it

Yes, I think we're violently agreeing then. The original 1905 paper is extremely readable.