Dimension Four Wins the Same Game as the Standard Model Group

TL;DR

This paper extends a theoretical game comparing gauge groups to different spacetime dimensions, revealing that four-dimensional spacetime uniquely wins, suggesting a deep connection between gauge symmetry and spacetime dimensionality.

Contribution

It introduces a novel game framework to compare potential spacetime dimensions based on gauge group properties, highlighting four dimensions as uniquely favored.

Findings

Four-dimensional spacetime wins in the game based on gauge group properties.

The same mathematical function singles out both the Standard Model gauge group and spacetime dimension.

Suggests a possible underlying physics linking gauge symmetry and spacetime dimensionality.

Abstract

In a previous article Don Bennett and I looked for,found and proposed a game in which the Standard Model group S(U(2)XU(3)) gets singled out as the "winner". Here I propose to extend this "game" to construct a corresponding game between different potential dimensions for space time. The idea is to formulate how the same competition as the one between the potential gauge groups would run out, if restricted to the potential Lorentz or Poincare groups achievable for different dimensions of space time d. The remarkable point is that it is the experimental dimension of space time 4 which wins. So the same function defined over Lie groups seems to single out both the gauge group and the space time dimension in nature. This seems a rather strange coincidence unless there is really some similar physics behind.