Different Universes?

The present limited understanding of our universe allows for much speculation with regard to whether we live in but one of many universes, possibly with connections among them. These wild conjectures are permitted simply because we do not know enough about the origins of the fundamental constants such as Planck’s constant, the gravitational constant, or the lepton and quark masses, for example. Indeed, the other possible universes could have different values for these constants. Suppose that the lepton and quark mass values are discovered to be determined by some fundamental properties in mathematics such as the invariants of elliptic functions. How might this discovery end speculation about many universes?

Answer

If the lepton and quark masses are dictated by fundamental mathematical quantities, we are behooved to consider that all fundamental quantities in nature have an origin in fundamental mathematics. There can be no alternative universes, each supposedly having different fundamental constants, for they must have the same mathematics dictating the same physical constants.

In 1994 F. Potter, within the confines of the Standard Model of Leptons and Quarks, related the lepton and quark mass ratios to a mathematical invariant called the elliptic modular invariant J, which is invariant under all linear transformations. The critical prediction is a fourth quark family with a b′ quark mass of about 80 GeV/c² and a t′ quark mass of about 2,600 GeV/c². Although searches for a b′ quark have been under way at the Fermilab collider for several years, its existence cannot be ruled out yet because the decay reactions have very low probability and will be overwhelmed by many other particle decays into the same final products. Perhaps when the Large Hadron Collider is turned on in a few years, with its very high rate of production of quarks, the statistics will be so much better that the b′ quark should be easy to find.

If the b′ quark is found, then we expect that all other fundamental physical constants should also be derivable from mathematical invariants. If the proposed scheme is correct, then our universe is the only universe possible. Even exotic speculations such as time travel could be eliminated if the direction of time is one of the innate properties of the particle state definition. However, we must remember always that Nature is more clever than we can hope to be, so we must continue to test every reasonable proposal for the truth.