Axiomatic foundations of the kinematics common to classical physics and special relativity. (English) Zbl 0538.70001

Bressan, A.; Montanaro, A.

Rend. Sem. Mat. Univ. Padova 68, 163-182 (1982).

Starting from four primitive notions namely event point, particle, relation of being in the past and relation of being an event point occupied by a particle and certain suitable postulates, the authors present a system of purely kinematic axioms complying with both classical mechanics and special relativity. The main theorem proves that either the classical or the relativistic case holds. The work which makes a number of related interesting points is within the framework of modal logic as described in the first author’s book, A general interpreted modal calculus (1972; Zbl 0255.02015).

Reviewer: C.S.Sharma

MSC:

70A05	Axiomatics, foundations
03B45	Modal logic (including the logic of norms)
83A05	Special relativity
74Axx	Generalities, axiomatics, foundations of continuum mechanics of solids

Keywords:

axiomatic foundations of mechanics; event point occupied by particle; primitive notions; being in the past; purely kinematic axioms; classical mechanics and special relativity; modal logic

References:

[1]	A. Bressan , Metodo di assiomatizzazione in senso stretto della Meecanica classica. Applicazione di esso ad alcuni problemi di assiomatizzazione non ancora completamente risolti , Rend. Sem. Mat. Univ. di Padova , 32 ( 1962 ), pp. 55 - 212 . Numdam | MR 148437 | Zbl 0114.14902 · Zbl 0114.14902
[2]	A. Bressan , A General Interpreted Modal Calculus , New Haven , Yale University Press ( 1972 ). MR 401432 | Zbl 0255.02015 · Zbl 0255.02015
[3]	A. Bressan , On the usefulness of modal logic in axiomatizations of physics , in PSA 1972 (Boston Studies in the Philosophy of Science , Vol. 20 ), ed. by K. F. SCHAFFNER - R. S. COHEN, Dordrecht and Boston , Reidel ( 1974 ). Zbl 0322.02014 · Zbl 0322.02014
[4]	A. Bressan , On Physical Possibility, in Italian studies in the philosophy of science ( 1981 ), p. 197 . MR 604959
[5]	P.K. Feyerabend (a) Against method. Outline of an anarchistic theory of knowledge ( 1975 ). P.K. Feyerabend (b) Contro il metodo , Feltrinelli , Milano ( 1980 ).