Poincaré

We do not realize the immense flash of genius brought to humanity by Poincaré.
His transformations are as brilliant as they are magnificent. Lorentz had searched for them for years, without ever succeeding.
But Poincaré was an immense mathematician, the greatest of his time.
Coupled with philosophical reflections and very advanced physical knowledge.
It is very regrettable that out of hatred, out of self-loathing (the French people are in the entire history of peoples the ones who are the most self-loathing), we have come to adulate instead a 27-year-old cretin copyist whose closest friends said that he was incapable of dividing by 2.
It was his friend Grossmann who had to do his calculations.
But that's life.
We will return to the transformations given by Poincaré in June 1905 (copied in September 1905 by Einstein).
They are magnificent, and open to a lot of conclusions, such as, for example, the elasticity of lengths
by change of reference frame. I wrote: elasticity, not contraction.
We have a bar of length l in R, what will be its length in R'?
What does Poincaré tell us?
x'=(x-Vo.To)/sqrt(1-Vo²/c²)
y'=y
z'=z
To'=(To-x.Vo/c²)/sqrt(1-Vo²/c²)
Well understood, these transformations give us the length of the rod, and we have directly in R':
l'=l.sqrt(1-Vo²/c²)/(1+cosµ.Vo/c)
This is simply a mathematical deduction (in case the angle of sight towards A and towards B is small enough to be considered almost zero, µ being on the other hand the angle between the projected sight and the direction of the mobile studied).
You can do the calculation by yourself, it is at the level of a good middle school student.
We can therefore see that setting l'=l.sqrt(1-Vo²/c²) is totally inappropriate, and that it only works if the rod passes into an orthogonal position relative to the observer in R'.
This is enough for physicists, but the concept still seems quite different to me.
Poincaré, if we understand him well, indicates, by his transformations, that the length depends on the relative speed (gamma factor) but ALSO on the position of the observer, and that is incredibly hard to swallow. Yet that is what Poincaré says in his transformations.
Do some numerical tests. For example, set a rod A(12.9)-B(24.18) in R.
Length?
l=15.
Let's change the frame of reference. Will we have a smaller rod by contraction of x (y invariant)?
That's what physicists say.
That's not what the TLs say.
No, we'll have a much longer stem in R'.
A(40,9)-B(80,18)
l'=41.
You can check for yourself.
R.H.