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PLAN OF DB SPECIAL RELATIVITY
dba axioms of special relativity
dbb lorentz transformations
dbc length contraction and time dilation
dbd speed cumulation
dbe E=MC^2
dbf paradox of langevins traveller
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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.
