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Merab Gogberashvili 《Advances in Applied Clifford Algebras》2005,15(1):55-66
We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe
physical signals. The new geometrical interpretation of the products of octonionic basis units is presented. Eight real parameters
of octonions are interpreted as the space-time coordinates, momentum and energy. In our approach the two fundamental constants,
c and
have the geometrical meaning and appear from the condition of positive definiteness of the octonion norm. We connect the
property of non-associativity with the time irreversibility and fundamental probabilities in physics. 相似文献
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Merab Gogberashvili 《International Journal of Theoretical Physics》2011,50(8):2391-2402
We adopt a formulation of the Mach principle that the rest mass of a particle is a measure of it’s long-range collective interactions with all other particles inside the horizon. As a consequence, all particles in the universe form a ‘gravitationally entangled’ statistical ensemble and one can apply the approach of classical statistical mechanics to it. It is shown that both the Schrödinger equation and the Planck constant can be derived within this Machian model of the universe. The appearance of probabilities, complex wave functions, and quantization conditions is related to the discreetness and finiteness of the Machian ensemble. 相似文献