What is the reason for the asymmetry between the twins in the twin paradox?

Gerrit Coddens (1)

1 LSI - Laboratoire des Solides Irradiés - Irradiated Solids Laboratory

The true difficulty of the twin paradox does not reside in the algebra that shows that the traveling twin ages less than the twin who stays at home. The truly startling part of the paradox resides in the much more difficult question why the argument cannot be reversed by symmetry, because there is no such thing as a preferred reference frame, and relative motion ought to be symmetrical. Can the traveling twin not claim with equal rights to have stayed at home while the other twin has made the journey? Most of the time text books invoke the accelerations intervening in the trip to explain the asymmetry. We will show that one can formulate and solve the paradox without making any reference to accelerations. There is actually something very simple that has been overlooked. In drafting the protocol which defines the journey, we unwittingly pick a preferred refrence frame, because we define the protocl with respect to a given frame, which thereby becomes special. It this selection of a special reference frame which introduces the asymmetry. Hence, it is the reference frame wherein we define the protocol that will act like an absolute frame and whose unavoidable introduction breaks the symmetry between the twins. There is an infinity of protocols that can be selected to define a trip and each of these trips leads to its own corresponding twin paradox, with its own outcome as to which twin will age less. Whereas the individual trips of the two twins with respect to this protocol are asymmetrical, the set of all possible trips is symmetrical, such that the symmetry of the Lorentz group is indeed respected.

Mots clés: twin paradox

Domaines: Physique mathématique [math-ph]

Gerrit Coddens. What is the reason for the asymmetry between the twins in the twin paradox?. 2019. ⟨hal-02263337v3⟩