### Could the Fundamental Laws of Nature be Inferred Logically (Mathematically) from Only a Very Few Axioms?

*ZAHEDI, Ramin*

Permalink : http://hdl.handle.net/2115/75453

#### Abstract

This article is a summary of an expanded version : R. Zahedi, "On the Logical Origin of the Laws Governing the Fundamental Forces of Nature : A New Axiomatic Matrix Approach", Archive for Studies in Logic (AFSIL), Hokkaido University Publs., 16 (2): 1-97，2015. In this expanded version, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Sec. 2), "it is shown that certain mathematical forms of fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms" : where in agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energymomentum can only take rational values. Based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented by the corresponding quantum matrix operators) of the fundamentally derived field equations, it is concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional spacetimes. On the basis of these discrete symmetries of the derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents.

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