A Class of Elementary Particle Models Without Any Adjustable Real Parameters

Abstract

Conventional particle theories such as the Standard Model have a number of freely adjustable coupling constants and mass parameters, depending on the symmetry algebra of the local gauge group and the representations chosen for the spinor and scalar fields. There seems to be no physical principle to determine these parameters as long as they stay within certain domains dictated by the renormalization group. Here however, reasons are given to demand that, when gravity is coupled to the system, local conformal invariance should be a spontaneously broken exact symmetry. The argument has to do with the requirement that black holes obey a complementarity principle relating ingoing observers to outside observers, or equivalently, initial states to final states. This condition fixes all parameters, including masses and the cosmological constant. We suspect that only examples can be found where these are all of order one in Planck units, but the values depend on the algebra chosen. This paper combines findings reported in two previous preprints (G. 't Hooft in arXiv:1009.0669 [gr-qc], 2010; arXiv:1011.0061 [gr-qc], 2010) and puts these in a clearer perspective by shifting the emphasis towards the implications for particle models.

The Cellular Automaton Interpretation of Quantum Mechanics

“…The theory was originally conceived as an attempt to mitigate the black hole information paradox [111,112], then it was found that it could serve as a theory that determines the values of physical parameters that up to the present have been theoretically non calculable (this should follow from the requirement that all renormalization group functions β i should cancel out to be zero [112]). …”

“…The real problem is that space-time curvature runs out of control at the Planck scale. We will be forced to turn to a different book keeping system for Nature's physical degrees of freedom there.A promising approach was to employ local conformal symmetry [59,111,112] as a more fundamental principle than usually thought; this could be a way to make distance and time scales relative, so that what was dubbed as 'small distances' ceases to have an absolute meaning. The theory is recapitulated in Appendix B.…”

Conformal and non conformal dilaton gravity

“…This is non necessarily the case anymore when couplings to matter are considered, because we are going to assume that matter couples to g µν instead to G µν . Some interesting albeit speculative physical reasons as to why the metric g µν could be the only one physically observable have been advanced in [25,26]. The above considerations are taken as a motivation to study the non-minimally coupled system gravitational-scalar field in the following sense…”

Agravity

“…Claims in the literature are controversial [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73]. Sometimes in physics we have the right equations before having their right interpretation.…”