So, coming to the second postulate of Einstein's special relativity, it is basically two folded:PeterDonis said:It can be hard to see this because the most common convention that is adopted, namely, that the one-way speed of light is the same in all directions, is also the one most people's intuitions adopt anyway, so it doesn't seem like there's any convention that needs to be adopted, it just seems like "the way things are". But it isn't; it's a convention.
No, Einstein separately and explicitly assumes isotropy in his 1905 paper. He just doesn't call it a postulate.cianfa72 said:the second postulate of Einstein's special relativity, it is basically two folded:
Ah ok, so the SR's Einstein second postulate is just: the two-way speed of light (w.r.t. any inertial reference frame) is the invariant ##c##.Ibix said:No, Einstein separately and explicitly assumes isotropy in his 1905 paper. He just doesn't call it a postulate.
I think this boils down to details of where exactly you define what. Is an inertial frame necessarily orthogonal? Or does it merely require that inertial objects have constant coordinate velocity? If the former then you've already got isotropy; if the latter you need to specify it if you want to get it. Or arguably, Einstein not making a formal distinction between one- and two-way speeds means that he was assuming they were the same and hence assuming isotropy and didn't really need a separate assumption.cianfa72 said:Ah ok, so the SR's Einstein second postulate is just: the two-way speed of light (w.r.t. any inertial reference frame) is the invariant ##c##.
No. All we would need to get the speed of light to be different in different directions would be to change our simultaneity convention. But simultaneity conventions have no physical effects.Warp said:If the speed of light were different in different directions, couldn't this be observed in other ways, such as unexpected redshift/blueshift, or unexpected patterns in the cosmic microwave background radiation?
No. You get a different Doppler formula and a different emission frequency and the two cancel out.Warp said:If the speed of light were different in different directions, couldn't this be observed in other ways, such as unexpected redshift/blueshift, or unexpected patterns in the cosmic microwave background radiation?
Yes, and the coordinate-dependent thing in Romer's analysis is the simultaneity convention, or, equivalently, the assumption that the one-way speed of light is isotropic. But that has nothing to do with the "coordinate tick rate of Jupiter clocks".Ibix said:Something coordinate dependent has to enter your analysis if you are hoping to derive a coordinate dependent quantity like the one-way speed of light from invariant quantities like Rømer's observations (or indeed, any observations).
The coordinate time between ticks depends on the simultaneity convention for moving objects.PeterDonis said:Yes, and the coordinate-dependent thing in Romer's analysis is the simultaneity convention, or, equivalently, the assumption that the one-way speed of light is isotropic. But that has nothing to do with the "coordinate tick rate of Jupiter clocks".
Does not come into the analysis anywhere. The analysis uses the observed time between ticks (the "ticks", as I said before, being the observed orbits of Jupiter's satellites) as recorded by Earth clocks.Ibix said:The coordinate time between ticks
Are you saying that if the speed of light is different in different directions, that's completely unobservable?Ibix said:No. You get a different Doppler formula and a different emission frequency and the two cancel out.
It doesn't matter what question you ask. The difference between an isotropic one-way speed and an anisotropic one is how I personally choose to lay out my coordinate system. My personal choice cannot lead to any difference in measurements, only in how I describe how those measurements come to be.
That's exactly what I said, yes.Warp said:Are you saying that if the speed of light is different in different directions, that's completely unobservable?
That isn't consistent with relativity - you require the two-way speed to be ##c##, so the average of the two one-way speeds must be ##c## (in the sense that ##\frac 2c=\frac 1{c_\mathrm{fast}}+\frac 1{c_\mathrm{slow}}##). Note that electromagnetic theory depends on relativity, so you would need a completely different universe to describe your 1m/s vs c scenario.Warp said:Surely if light moved in one direction at c and in another direction at 1m per year, there would be some observable effect?
Yes. There is no experiment that depends on Anderson’s ##\kappa##Warp said:Are you saying that if the speed of light is different in different directions, that's completely unobservable?