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Conformally Compactified Minkowski Space, Quantum & Classical, & Quaternon Mass

Conformally Compactified Minkowski Space: Myths and Facts (by Arkadiusz Jadczyk): Maxwell's equations are invariant not only under the Lorentz group but also under the conformal group. Irving E. Segal has shown that while the Galilei group is a limiting case of the Poincare group, and the Poincare group comes from a contraction of the conformal group, the conformal group ends the road, it is rigid. There are thus compelling mathematical and physical reasons for promoting the conformal group to the role of the fundamental symmetry of space-time, more important than the Poincare group that formed the group-theoretical basis of special and general theories of relativity. While the action of the conformal group on Minkowski space is singular, it naturally extends to a nonsingular action on the compactified Minkowski space, often referred to in the literature as “Minkowski space plus light-cone at infinity". Unfortunately in some textbooks the true structure of the compactified Minkowski space is sometimes misrepresented, including false proofs and statements that are simply wrong.

In this paper we present in, a simple way, two different constructions of the compactified Minkowski space, both stemming from the original idea of Roger Penrose, but putting stress on the mathematically subtle points and relating the constructions to the Clifford algebra tools. In particular the little-known antilinear Hodge star operator is introduced in order to connect real and complex structures of the algebra. A possible relation to Waldyr Rodrigues' idea of gravity as a plastic deformation of Minkowski's vacuum is also indicated.

Considerations: Classical and Quantum (by B. G. Sidharth): In this paper we consider certain Classical, Semi Classical and Quantum situations with interesting consequences. Starting with Entanglement we go on to deviations from Special Relativity, leading to the possibility of super luminal neutrinos, if they exist escaping from Black Holes. We also consider extra energy that is generated due to Quantum effects, the decay of fast moving Bosons, as for example in the case of Kaons, and finally the magnetism generated by non commutative effects.

The Quaternionic Particle Mass (by Lukasz A. Glinka, Andrew W. Beckwith): In this article we derive the formula for a particle mass arising from the quaternionic particle physics model recently offered by Hans van Leunen.

Administrator · Sep 23 '12 · Tags: quantum, conformally compactified, minkowski space, classical, quaternon mass

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