Selecting Fundamental Transformations in Spacetime

Details Selecting Fundamental Transformations in Spacetime Selecting Fundamental Transformations in Spacetime

2011-03-08

arxiv.org/abs/1103.1863v1

Physics

Mathematical Physics

20 pages

Scientific paper

The problem is to deduce the fundamental transformations of spacetime without using invariance of a quadratic form or covariance of a set of equations, e.g. Maxwell's. Rulers and clocks are made of molecules, atoms, electrons, protons, neutrons and quarks. Thus it seems possible, at least, that the fundamental spacetime transformations, often described with rulers and clocks, can also be deduced from the groups like SU(2) which describe the quantum behavior of the constituent particles. Here we generalize to the group U(N), with N at least 2, and a `spacetime' with N-squared dimensions one of them being time. We use algebraic constraints and build on the algebra of NxN hermitian matrices, i.e. the generators of U(N). We find rotations, boosts, translations, and scale transformations, together making the `Poincar\'{e}-Weyl group in N-squared dimensional spacetime'.

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