Spatio-temporal Chaos and Vacuum Fluctuations of Quantized Fields

Abstract

We consider deterministic chaotic models of vacuum fluctuations on a small (quantum gravity) scale. As a suitable small-scale dynamics, nonlinear versions of strings, so-called `chaotic strings' are introduced. These can be used to provide the `noise' for second quantization of ordinary strings via the Parisi- Wu approach of stochastic quantization. Extensive numerical evidence is presented that the vacuum energy of chaotic strings is minimized for the numerical values of the observed standard model parameters, i.e. in this extended approach to second quantization concrete predictions for vacuum expectations of dilaton-like fields and hence on masses and coupling constants can be given. Low-energy fermion and boson masses are correctly obtained with a precision of 3-4 digits, the electroweak and strong coupling strengths with a precision of 4-5 digits. In particular, the minima of the vacuum energy yield high-precision predictions of the Higgs mass (154 GeV), of the neutrino masses (1.45E-5 eV, 2.57E-3 eV, 4.92E-2 eV) and of the GUT scale (1.73E16 GeV).