Volume 21: Pages 16-25, 2008

Covariance versus invariance: Remarks on Arunasalam’s papers

T. E. Phipps Jr. ¹

¹908 S. Busey Avenue, Urbana, Illinois 61801, USA

Two papers by Arunasalam in this issue are considered. These treat his views on the twin paradox and on the subject of covariance versus invariance. He proposes to resolve the twin paradox in terms of asymmetrical acceleration. An alternative not involving acceleration is provided in Taylor and Wheeler, Spacetime Physics (Freeman, San Francisco, CA, 1966) p. 94. I agree that an alternative resolution is desirable, but feel that those offered by special relativity theory leave much to be desired. Instead, it may prove necessary to acknowledge clock running-rate asymmetries as physically real. More significant is Arunasalam’s championing of covariance. He provides definitions of Lorentz covariance and Lorentz invariance that are helpful in clarifying discussion, but gives no definition of the general concept of “invariance” as I should like to see it understood. I offer my own definitions and on that basis sketch a variety of physics [developed in Old Physics for New (Apeiron, Montreal, 2006)] that employs an invariant covering theory of Maxwell’s equations due to Hertz, as well as a “collective time” patterned upon the clock running-rate correction methods of the global positioning system. In this alternative physics, invariance plays the same central role that covariance plays in Einstein’s physics.

Keywords: Covariance, Invariance, Lorentz covariance, Lorentz invariance, Twin paradox, Relativity theory, Collective time, Global Positioning System

Received: April 2, 2007; Accepted: June 16, 2007; Published Online: December 15, 2008