How Far Should the Principle of Relativity Go - Physics > General PhysicsReport as inadecuate

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Abstract: The Principle of Relativity has so far been understood as the {\itcovariance} of laws of Physics with respect to a general class of referenceframe transformations. That relativity, however, has only been expressed withthe help of {\it one single} type of mathematical entities, namely, the scalarsgiven by the usual continuum of the field $\mathbb{R}$ of real numbers, or bythe usual mathematical structures built upon $\mathbb{R}$, such as the scalarsgiven by the complex numbers $\mathbb{C}$, or the vectors in finite dimensionalEuclidean spaces $\mathbb{R}^n$, infinite dimensional Hilbert spaces, etc.This paper argues for {\it progressing deeper and wider} in furthering thePrinciple of Relativity, not by mere covariance with respect to referenceframes, but by studying the possible covariance with respect to a {\it largevariety} of algebras of scalars which extend significantly $\mathbb{R}$ or$\mathbb{C}$, variety of scalars in terms of which various theories of Physicscan equally well be formulated.First directions in this regard can be found naturally in the simpleMathematics of Special Relativity, the Bell Inequalities in Quantum Mechanics,or in the considerable amount of elementary Mathematics in finite dimensionalvector spaces which occurs in Quantum Computation.The large classes of algebras of scalars suggested, which contain$\mathbb{R}$ and $\mathbb{C}$ as particular cases, have the important featureof typically {\it no longer} being Archimedean, see Appendix, a feature whichcan prove to be valuable when dealing with the so called -infinities- inPhysics.The paper has a Comment on the so called -end of time-.

Author: Elemer E Rosinger


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