A Possible Mathematical Structure for Physics

Abstract

The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings -the real, R, the complex, C, and the quaternion, H -known to meet the requirements of a mathematical description of our universe. The known forces and particle structure, in terms of families and color, can be associated with natural relationships within that structure. A "toy" scientific theory -based on the proposed mathematical structure -is presented to illustrate its applicability. It is shown how parity and time reversal invariance are broken. Two relevant predictions come from the formalism. First, there are no gravity waves and second, matter comes in three varieties, one of which is "dark" in the sense that it is oblivious to electromagnetic interactions. BackgroundThe relationship between mathematics and physics has been a matter of study since the time of the Pythagoreans. Notables such as Galilei, Hawking, Wheeler, and Wigner have pondered -to paraphrase each -"Why is mathematics so successful in describing the universe?" Recently Tegmark [1] has done an in depth study involving the tools of philosophy, mathematical descriptions, and physical systems to explore the relationship and to identify the requirements of a mathematical structure -such as computations and simulations -to represent physical reality and the reader is referred to his exhaustive set of references. Tegmark argues that "Our external physical reality is a mathematical universe" -the Mathematical Universe Hypothesis (MUH). Following his description Benioff [2] began the development of

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