Twin Paradox from first order logic point of view
by
Gergely Székely
ELTE University
Coauthors: Judit X. Madarász

In this lecture, we study the Twin Paradox in the framework of first-order logic. First we recall a simple and streamlined first-order axiom-system for special relativity from the literature, which is complete with respect to questions about inertial motion. We will see that there is a mathematical principle coming from real analysis which needs to be added to this axiom-system in order to handle situations involving relativistic acceleration. We present an extended version of the axiom-system which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we will see that the Twin Paradox becomes provable from this extended version, but it is not without the mathematical principle from real analysis mentioned above even if we assume the whole first order theory of the real numbers.

Date received: May 13, 2005