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PARADOX OF LANGEVIN'S TRAVELER 

Problem


Interpreting the time dilation of the Special Relativity (SR) 
Langevin imagined his famous Traveler who after having moved 
during 2 years along a straight line, with the constant 
speed v=(799/800)/c would find Earthians older by 40 years.

That takes us a bit in deep waters. In SR movement is 
strictly relative. If observer O1 of inertial referential R1 
observes some speed effect in another inertial R2, then O2 
of R2 will observe an equivalent effect in R1.

To somebody flying fast with respect to us earth will look 
like a flat ellipsoid. But, then, to us, this flying fellow 
will look just as flat.

So, in spite of the recognized authority of Langevin, we see 
that something must be wrong: 
if Earthian gets 40 years older for the Traveler during the
latter's 2 years, then Traveler gets symmetrically 40 years 
older for Earthians during their 2 years. Each gets 
relatively younger and older than the other, while both age
2 years following their own clocks.

To make it easier, the Traveler could never have quitted us, 
nor can he return to the Earth to enjoy his splendid youth: 
both start and landing mean acceleration and in SR there is 
no such phenomenon; inertial Referentials move with respect 
to one another with constant speed along Euclidean straight 
lines.

Within General Relativity (GR) we could easily transfer the  
Traveler to the "Twins Paradox", which, BTW, is no paradox 
at all (see Appendix). Yet, textbooks consider him as part 
and illustration of the SR, so we must comment it within 
SR's context.


COMMENTS


The Traveler is no clearly no example, nor an illustration 
of SR, but a warning against silly textbooks.

But what about Langevin himself? Was he as silly, as the 
textbooks quoting him? 

Certainly not. Langevin was a great scientist and when he 
talked about his Traveler, he addressed the club: Einstein, 
Lorentz, Bohr, etc. These people could read between the 
lines. 

He was not addressing poor science fiction writers who jumped 
on the opportunity to depict supermen coming back from the 
space young and fit, just in time to prevent their former  
contemporaries, gotten senile and stupid, to blow up the 
planet.

We cannot say for sure what he really meant, but a good 
guess would be that he predicted such Travelers as the meson. 

Now, meson's relative lifetime T increases with its relative 
energy E (Eo being its rest energy):

T = To(E/Eo) = To * sqrt(1-v^2/c^2)

It's whole "life" is spent on inertial progression and it 
appears to us "younger" than to itself, in the manner of an
exact Langevin's Traveller, entirely within the frame of SR.

That would mean that even assertions of best scientists 
should be carefully interpreted before being dumped on 
innocent students.


Appendix. The Twins Paradox.


Given two twins, one "sedentary", (ST) and the other 
"travelling" (TT). ST stays on the Earth, while TT makes
a space trip. When he comes back, he states that his clock
advanced less than that of ST and, that he aged biologically
less than ST.
Here there is no paradox. During his trip, TT was exposed
to acceleration, thus to the Inertial Field resulting in
his time advancing slower than the time of ST.