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On a Physical and Mathematical Discontinuity in Relativity Theory

Franco Selleri
Year: 1997
Keywords: discontinuity, relativity theory, isotropic reference frame, circular disk, radius, velocity of light
An isotropic inertial reference frame ("stationary") is considererd, in which a circular disk of radius R rotates uniformly. The velocity of light [] relative to the rim of the disk is calculated under very general assumptions and found to satisfy []. This [] remains the same if R is increased but the peripheral velocity of the disk is kept constant. Since by so doing any small part of the circumference can be considered (for a short time) better and better at rest in a ("moving") inertial system, there is a discontinuity between accelerated reference frames with arbitrarily small acceleration and inertial frames, if the velocity of light is assumed to be c in the latter. Elimination of the discontinuity is shown to imply fos inertial systems a velocity of light [], necessarily equal to that obtained from recently published "inertial transformations."