How the New Scale Relativity Theory resolves some quantum paradoxes

Abstract

It is explicitly shown that within the framework of the New Relativity Theory, some Quantum Mechanical Paradoxes like the Einstein–Rosen Podolsky and the Black Hole Information Loss, are easily resolved. Such New Relativity Theory requires the introduction of an infinite-dimensional quantum space-time as has been shown recently by one of us. This can be viewed as just another way of looking at Feynman's path integral formulation of Quantum Mechanics. Instead of having an infinite-dimensional functional integral over all paths, smooth, forwards and backwards in time, random and fractal, in a finite-dimensional space-time, one has a finite number of paths in an infinite-dimensional quantum space-time. We present a few-lines proof why there is no such thing as an EPR Paradox in this New Relativity theory. The reason is not due to a superluminal information speed but to a divergent information charge density. In the infinite-dimensional limit, due to the properties of gamma functions, the hypervolume enclosed by a D-dim hypersphere, of finite non-zero radius, shrinks to zero: to a hyperpoint, the infinite-dimensional analog to a point. For this reason, Information flows through the infinite-dimensional hypersurface of non-zero radius, but zero size, the hyperpoint, in an instant. In this fashion we imbue an abstract mathematical “point” with a true physical meaning: it is an entity in infinite dimensions that has zero hypervolume at non-zero radius. A plausible resolution of the Information Loss Paradox in Black Holes is proposed.