Einstein’s Ultrareferential Space-time and Alain Connes’ Noncommutative Geometry

Ludwik Kostro
Department for Logic Methodology and Philosophy of Science
University of Gdansk
ul. Biela?ska 5
Gda?sk, Poland, Pl 80-851
email: fizlk@univ.gda.pl

In 1905 A. Einstein banished the ether from physics in connection with the formulation of his Special Relativity Theory. This fact is very well known but less known is the fact that in in 1916 he reintroduced the ether in connection with his General Relativity. He denominated it „new ether” because, in oppposition to the old one, the new one did not violate his Special and General Principle of Relativity. It did’nt violate it because the new ether is not an privilleged reference frame but it constitutes an ultrarefernetial primordial reality which is not composed of points (or particles) and divisible in parts and to which therefore the notions of motion and rest are not applicable. In his Leiden speech Einstein expressed it as follows: Extended physical objects can be imagined to which the idea of motion cannot be applied. They are not to be thought of as consisting of particles whose course can be followed out separately through time. In Minkowski’s idiom this is expressed as follows: Not every extended entity in the four-dimensional world can be regarded as composed of world-lines. (A. Einstein, Aether und Relativitatstheory, Berlin: Verlag von J. Spriger, 1920, p. 10) According to A. Einstein, already in the Special Relativity Theory, we are dealing with one and unique ultrareferencial physical space-time as such which enables the existence of an infinite number of reference space-times The reference space-times are composed of world-lines and momentary spaces. In the contrary the unique physical space-time as such is not composed of world-lines and momentary spaces. The ultrareferential space-time is something more fundamental and basic and makes possible the existence of all reference space-times. It constitutes an fundamental material field. The purpose of this paper is to present a short outline of the history of Einstein’s concepts on ether and to show which elements of the mathematical formalism of General Relativity were considered by Einstein as mathematical tools describing the relativistic ether i.e. the ultrareferential space-time It will be also indicated in which sens the Einstein’s ideas can be expressed in the framework of Alain Connes noncommutative geometry In Poland Micha? Heller and his collegues try to create an unification of General Relatoivity and Quantum Mechanics with the help of Connes’ geometry.