ANDRÉS RIVADULLA
THE NEWTONIAN LIMIT OF RELATIVITY THEORY AND THE
RATIONALITY OF THEORY CHANGE
ABSTRACT. The aim of this paper is to elucidate the question of whether Newtonian
mechanics can be derived from relativity theory. Physicists agree that classical mechanics
constitutes a limiting case of relativity theory. By contrast, philosophers of science like
Kuhn and Feyerabend affirm that classical mechanics cannot be deduced from relativity
theory because of the incommensurability between both theories; thus what we obtain
when we take the limit c →∞ in relativistic mechanics cannot be Newtonian mechanics
sensu stricto. In this paper I focus on the alleged change of reference of the term mass in
the transition from one theory to the other. Contradicting Kuhn and Feyerabend, special
relativity theory supports the view that the mass of an object is a characteristic property
of the object, that it has the same value in whatever frame of reference it is measured,
and that it does not depend on whether the object is in motion or at rest. Thus mass
preserves the reference through the change of theory, and the existence of a Newtonian
limit of relativity theory provides a good example of the rationality of theory change in
mathematical physics.
– Does mass really depend on velocity, Dad?
– No! Well, yes. Actually, no, but don’t tell your teacher.
Carl Adler, Am. J. Phys. 55, 1987
1. THE NEWTONIAN LIMIT OF RELATIVITY THEORY AND THE
RATIONALITY OF THEORY CHOICE
According to Albert Einstein (1917, §§22, 29), the most important aim of a
scientific theory is to point to the establishment of a more comprehensive
one, in which it survives as a limiting case. For instance, Newton’s gra-
vitational theory obtains as a first approximation by specializing general
relativity theory’s equations for the case of weak gravitation fields and low
velocities.
Einstein’s suggestion of the existence of a Newtonian limit is nowadays
a universally assumed idea in theoretical physics. Nobel prize winner Lev
Landau (1951, §1-1) claims for instance: “The limiting transition from re-
lativistic to classical mechanics can be produced formally by the transition
to the limit c →∞ in the formulas of relativistic mechanics.” Steven
Weinberg (1972, Ch.7) talks about the Newtonian limit of Einstein’s field
Synthese 141: 417–429, 2004.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.