Everyone knows the Poincaré-Lorentz transformations relating to reference
frames in Galilean motion.
I don't see any transformations involving rotating frames of reference.
Many have thrown in the towel saying that the problem is too difficult,
and we have proposed stupid things like "The circumference contracts but
not the radius, and you have to use a saddle geometry".
LOL.
Proof that they understood nothing of the very basis of the theory, and,
among them, the world's greatest physicists.
Okay, the good transformers, I'll give them away.
It's not insurmountably difficult, and a high school student could do
it.
You just need to master the concepts and clearly understand in your mind
what you are talking about.
R.H.

On Monday, January 1, 2024 at 4:03:47 AM UTC-8, Richard Hachel wrote:
> Everyone knows the Poincaré-Lorentz transformations relating to reference
> frames in Galilean motion.

You use undefined secret terms ("Galilean motion") but I think I know what
you are saying here. OK.

> I don't see any transformations involving rotating frames of reference.

Then look them up, if you cannot derive them. One of them is a simple rotation
preserving the time coordinate:

X = x cos(wt) - y sin(wt)
Y = x sin(wt) + y cos(wt)
Z = z
T = t

....where w is the angular speed of the disc (w < c/radius).

> Many have thrown in the towel saying that the problem is too difficult,

It's not particularly difficult but it's more tricky than originally (1905) thought.
First of all, the above transformed T (time) coordinate does not need to
represent the proper (elapsed) time anymore (for the observer sitting on the
rotating disc). When one calculates that, it turns out that it's not possible to
assign a time coordinate using this method. This is known as the Sagnac effect:
two clocks transported (arbitrarily) slowly from one point back to that point
along different paths end up with different readings in some cases.

> and we have proposed stupid things like "The circumference contracts but
> not the radius, and you have to use a saddle geometry".

This is neither "stupid" not relevant. Again, a closer analysis reveals that the
question is more subtle than appeared at first glance. When one considers
the geometry on the rotating platform, say by using strings pulled taut between
various points, one necessarily is looking at the space made of infinitesimal
patches each of which is Lorentz-orthogonal to the worldline of the disc point
the patch represents. The resulting space is not a natural submanifold of the Minkowski
spacetime (as people used to assume, falsely) but it's by definition a quotient space
(this is a technical term from general topology, its meaning is very precise) and
its geometry turns out to be hyperbolic.

> Proof that they understood nothing of the very basis of the theory, and,
> among them, the world's greatest physicists.

Nonsense. You keep projecting your own lack of understanding. All this stuff
is *extremely well known*.

> It's not insurmountably difficult, and a high school student could do
> it.
>
> You just need to master the concepts and clearly understand in your mind
> what you are talking about.

Oh stop it. Grow up already. You just don't understand this theory, you refuse
to learn it, and all you do all day is cough up mental fur balls.

--
Jan