The structure of the world from pure numbers
Abstract
I investigate the relationship between physics and mathematics. I argue that physics can shed light on the proper foundations of mathematics, and that the nature of number can constrain the nature of physical reality. I show that requiring the joint mathematical consistency of the Standard Model of particle physics and the DeWittFeynmanWeinberg theory of quantum gravity can resolve the horizon, flatness and isotropy problems of cosmology. Joint mathematical consistency naturally yields a scalefree, Gaussian, adiabatic perturbation spectrum, and more matter than antimatter. I show that consistency requires the universe to begin at an initial singularity with a pure SU(2)_{L} gauge field. I show that quantum mechanics requires this field to have a Planckian spectrum whatever its temperature. If this field has managed to survive thermalization to the present day, then it would be the cosmic microwave background radiation (CMBR). If so, then we would have a natural explanation for the dark matter and the dark energy. I show that isotropic ultrahigh energy cosmic rays are explained if the CMBR is a pure SU(2)_{L} gauge field. The SU(2)_{L} nature of the CMBR may have been seen in the SunyaevZel'dovich effect. I propose several simple experiments to test the hypothesis.
 Publication:

Reports on Progress in Physics
 Pub Date:
 April 2005
 DOI:
 10.1088/00344885/68/4/R04
 arXiv:
 arXiv:0704.3276
 Bibcode:
 2005RPPh...68..897T
 Keywords:

 Axiom of Choice Axiom of Constructibility Power Set Axiom Large Cardinal Axioms Continuum Hypothesis Generalized Continuum Hypothesis dark matter dark energy cosmological constant flatness problem isotropy problem horizon problem HarrisonZel'dovich spectrum quantum cosmology UHE cosmic rays varying constants curvature singularities singularity hypostases finite quantum gravity gauge hierarchy problem strong CP problem triviality black hole information problem event horizons holography SunyaevZel'dovich effect CMBR Penning Traps;
 High Energy Physics  Theory
 EPrint:
 Rept.Prog.PHys.68:897964,2005