V. CONCLUSION
Since it was launched by P. Langevin in 1911 (and was indeed explicit in the Einstein’s
1905 famous article), the twin paradox proper framework was soon identified with general
relativity theory, because of accelerations to be considered along a twin worldline, at least.
This point of view was adopted by Einstein and supported by M. Planck. However, it has long
been recognized to be at fault, for both theoretical and experimental reasons (22). In particular,
accelerations can be consistently dealt with in flat spacetime manifolds, and should no way
be mistaken for gravitation (15). Moreover, the argument based on accelerations can also be
circumvented, so as to bring the paradox back to its original special relativity birthplace (23).
In this article, our intention has been to look for the principle at the origin of a so counterintuitive,
but established fact as “the non-trivial differential aging phenomenon”. And to this
end, it was certainly appropriate to look for such a principle in the simpler structure where
the phenomenon is manifest, that is, over the local scale of a Minkowski spacetime manifold.
If gravity, as described in general relativity, is responsible for another source of nontrivial
differential aging contributing on the same footing as special relativity effects in some
situations, a would be twin paradoxical case, in its conventional acceptation at least, is not a
natural issue of the general relativity framework (24). Two essential reasons may be proposed.
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of the hybrid nature of special relativity standard formalisms, where the paradox was first
conceived, discussed and confused with the (full reciprocity of) special relativity (non-invariant)
perspective effects. As such, it has no natural expression in the general relativity formalism.
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A flavour of this can be grasped out of the twin paradox resolution proposed, in this context,
by H. Reichenbach (25).
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possible twin paradox content gets translated into the pseudo-Riemannian theorems mentioned
in the introduction; that is, in terms of the geometrical properties of the spacetime manifoldM.
And indeed, the same explanation is proposed here for the twin paradox, at the more
local scale of a Minkowski spacetime manifold, M.
The twin paradox, in effect, has first been re-qualified into the path-functional dependence
of proper-time lapses, while preserving the name, so as to keep in touch with the historical
terminology. The paths are continuous timelike curves which, in virtue of a famous theorem,
completely “encodes” the geometrical, differential and topological structures of M (26). This
is why the “the non-trivial differential aging phenomenon” can, likewise, be thought of as a
property of the Minkowski spacetime geometry.
In the end, causality revealed to be the principle, and the only one, from which the (requalified)
twin paradox and the somewhat correlated Thomas-Wigner rotations come from.
Ten years ago, causality was advocated to provide a global constraint on the possible twins
histories, labelled, each, by some experimental/theoretical synchronization device (2).
Now, more than an overall constraint on the twin’s histories, one can see here, how the sole
principle of causality stands at the very source of the twin paradox. That is, how preservation
of causality along continuous timelike worldlines necessarily involves a functional dependence
of proper-time lapses on the paths themselves.
That space and time should be considered as melt into a one and single spacetime entity
is, definitely, a most salient feature of relativity theories. That this necessity comes from the
need of providing causality with a sound enough support is, we think, a remarkable fact. It
would seem to point to the requirement for History to be meaningful, in a physical and thus
restricted, still crucial sense.
Beyond the twin paradox itself, one may remark that it is possible to derive the whole
special relativity theory out of a single and intuitively clear principle of causality. In this
respect, the famous paradox may be looked upon in analogy with those situations encountered
in Mathematics, where unquestionable axioms are able to generate counter-intuitive .. if not
“paradoxical” consequences (27).