TY - JOUR

T1 - Comparing Classical And Relativistic Kinematics In First-Order Logic

AU - Lefever, Koen

AU - Székely, Gergely

PY - 2018/3

Y1 - 2018/3

N2 - The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic 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. We will also show that if we distinguish a class of observers (representing 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 definitionally equivalent to classical kinematics. So within an axiomatic framework of mathematical logic, we explicitly show that the transition from classical kinematics to relativistic kinematics is the knowledge acquisition that there is no "Ether", accompanied by a redefinition of the concepts of time and space.

AB - The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic 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. We will also show that if we distinguish a class of observers (representing 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 definitionally equivalent to classical kinematics. So within an axiomatic framework of mathematical logic, we explicitly show that the transition from classical kinematics to relativistic kinematics is the knowledge acquisition that there is no "Ether", accompanied by a redefinition of the concepts of time and space.

KW - Axiomatization

KW - Classical kinematics

KW - Definitional equivalence

KW - First-order logic

KW - Logical interpretation

KW - Special relativity

UR - https://arxiv.org/abs/1707.05371

UR - http://philsci-archive.pitt.edu/13200/

UR - http://www.scopus.com/inward/record.url?scp=85044995598&partnerID=8YFLogxK

U2 - 10.2143/LEA.241.0.3275105

DO - 10.2143/LEA.241.0.3275105

M3 - Article

VL - 61

SP - 57

EP - 117

JO - Logique et Analyse

JF - Logique et Analyse

SN - 0024-5836

IS - 241

ER -