[SR] relativistic elasticities

I am absolutely certain that if I pose a problem to physicists, they will be absolutely incapable of approaching the solution correctly.
The problem is however well known and if we had listened to Richard Hachel, it would not have posed any difficulties for a long time.
The problem is simple.
We propose to pass a rod 50 cm long through an opaque cylinder, also 50 cm long.
We will pass the rod from left to right, and at a speed of 240,000 km/s.
It's very fast. This is equivalent to 0.8c.
An observer placed transversely quite far from the cylinder, say thirty meters, observes the cylinder which therefore measures 50 cms.
When the rod reaches the cylinder, it becomes completely invisible, since it only measures 30 centimeters (which is true) and it is momentarily inside the opaque cylinder.
So far, everyone has understood.
If we could take a high-speed photo, we would only see the cylinder.
But now, we are going to place ourselves at the level of an observer who is in the frame of reference of the rod, and who crosses the first observer at the same place, and this one too, will take a photo
at the same time, and while they are married.
Breathe, breathe.
What does the great, the immense, the celestial light Richard Hachel say?
Nah, I say that to piss off Python.
Though...
The great, the immense, the brilliant Richard Hachel, he says that when two observers cross paths, they see exactly the same universe (but very spatially distorted).
N.B. The opposite would be quite absurd, it would mean that if a rocket passed close to the earth and photographed the universe, it would not collect the same photons as those captured by the terrestrial photograph.
The two observers therefore see the same thing, that is to say an invisible rod placed in an opaque cylinder.
We will ask ourselves the question: but in the frame of reference of the rod, how much does the rod measure?
The answer is obvious: 50 cm of proper length, not 30.
This is where an error in reasoning can occur, we will say that in fact the stem is 50 cm,
but the cylinder is only 30 and therefore we will see the rod in the other photo and not in the first (but we have just said that this is absurd).
No, no, we will not see the rod, and the error in reasoning comes from the fact that we believe that the observer placed in the frame of reference of the rod, sees at this moment, a rod placed transversely,
and a transverse cylinder measuring only 30 cms.
There is an alpha angle which will bring the cylinder and the rod to the left (Lorentz transformation) by an alpha angle such that sin alpha=Vo/c and if the rod measures 50 cms, the cylinder measures much more than 50 cms (and not less).
And the rod is well inside the cylinder.
The two photos will be concordant (taken at the same place) and identical (but with spatial deformations well known to physicists who correctly use Lorentz transformations).
There is therefore neither paradox nor possible misunderstanding.
R.H.