Using Logical Interpretation and Definitional Equivalence to Compare Classical Kinematics and Special Relativity Theory

Abstract

This dissertation is a study in philosophy of science on using methods from mathematical logic to compare different, non-equivalent scientific theories, applied to two important theories in physics.
The aim is to present a new logic based understanding of the connection be-
tween special relativity and classical kinematics.
We show that the axioms of special relativity can be interpreted in the language of classical kinematics. This means that there is a logical translation function from the language of special relativity to the language of classical kinematics which translates the axioms of special relativity into consequences of classical kinematics.
This is not in contradiction with physics, as some key concepts such as simultaneity, time difference or distance are changed by this translation.
We will also show that if we distinguish a class of observers which are stationary relative to each other (representing the observers stationary with respect to the “Ether”) in special relativity and exclude the non-slower-than light observers from classical kinematics by an extra axiom, then the two theories become definitionally equivalent (i.e., they become equivalent theories in the sense as the theory of lattices as algebraic structures is the same as the theory of lattices as partially ordered sets).
Furthermore, we show that classical kinematics is definitionally equivalent to
classical kinematics with only slower-than-light inertial observers, and hence by transitivity of definitional equivalence that special relativity theory extended with “Ether” is definitional equivalent to classical kinematics.
So within an axiomatic framework of mathematical logic, we explicitly show
that the transition from classical kinematics to special relativity is the knowledge acquisition of that there is no “Ether”.

Date of Award	26 May 2017
Original language	English
Awarding Institution	Vrije Universiteit Brussel
Supervisor	Jean Paul Van Bendegem (Promotor) & Gergely Szekely (Promotor)