Abstract
The Monster group, the biggest of the sporadic groups, is equipped with the highest known number of dimensions and symmetries. Taking into account variants of the Borsuk–Ulam theorem and a novel topological approach cast in a physical fashion that has the potential to be operationalized, the universe can be conceived as a lower-dimensional manifold encompassed in the Monster group. Our universe might arise from spontaneous dimension decrease and symmetry breaking that occur inside the very structure of the Monster Module. We elucidate how the energetic loss caused by projection from higher to lower dimensions and by the Monster group’s non-abelian features is correlated with the present-day asymmetry in the thermodynamic arrow. By linking the Monster Module to its theoretical physical counterparts, it is then possible to calculate its enthalpy and Lie group trajectories. Our approach also reveals how a symmetry break might lead to a universe based on multi-dimensional string theories and CFT/AdS (anti-de Sitter/conformal field theory) correspondence.
Highlights
The Fischer–Griess Monster group, the largest among the twenty-six sporadic groups, is equipped with 196,883 dimensions and an order of about 1054 elements [1]
We describe a generalized version of the Borsuk–Ulam theorem, in order to provide the topological machinery for further evaluations of the Monster in the context of theoretical physics
We propose a Borsuk–Ulam Theorem (BUT) model that describes our universe as located inside the Monster Module
Summary
The Fischer–Griess Monster group, the largest among the twenty-six sporadic groups, is equipped with 196,883 dimensions and an order of about 1054 elements [1]. It has been recently proposed that the symmetries, widespread invariances occurring at every level of organization in our universe, may be regarded as the most general feature of physical systems, perhaps more general than thermodynamic constraints [3,4]. Giving insights into the Monster symmetries would provide a very general approach to systems function, universe evolution and energetic dynamics. We describe a generalized version of the Borsuk–Ulam theorem, in order to provide the topological machinery for further evaluations of the Monster in the context of theoretical physics. Taking into account energetic arguments dictated by topological dimensions decrease, the section explains why and how our universe is equipped with the symmetry breaks, which give rise to the thermodynamic arrow. In the final sixth section, we raise a number of still open questions
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