Summary of quantum aspects of gravitation workshop

This is a summary of the presentations at the parallel session on ‘Quantum Aspects of Gravitation’ (QAG) of the ICGC-2004.     

Radial Quantization in Rotating Space–Times

We examine the time discontinuity in rotating space–times for which the topology of time is S¹. A kinematic restriction is enforced that requires the discontinuity to be an integral number of the periodicity of time. Quantized radii emerge for which the associated tangential velocities are less than the speed of light. Using the de Broglie relationship, we show that quantum theory may determine the periodicity of time. A rotating Kerr–Newman black hole and a rigidly rotating disk of dust are also considered; we find that the quantized radii do not lie in the regions that possess CTCs.     

Beyond the standard model: Working group report

This report summarises the activities of the working group on ‘Physics beyond the Standard Model’. The results of investigations in incorporatingR-parity in grand unification, the possibility of a light charged Higgs boson in extension of MSSM and radiative generation of neutral vector boson self-couplings within the MSSM are described. Also given is an account of activities in neutrino physics, namely a proposal for a study of the atmospheric muon anomaly in deep underground mines, a field theoretic study of neutrino oscillations and a mechanism to generate appropriate masses of three active plus one sterile neutrino species.     

Projective Invariance in Cosmological Models and Dark Energy

We study theories of gravitation that are based on the Einstein – Hilbert action that are not projectively invariant and can therefore completely determine their connections. We are thus lead to the conclusion that the geometry is necessarily Riemann – Cartan and at least the trace part of a torsion field must be present. We examine the consequence of including these torsion fields in cosmological models. Our results differ from those obtained earlier in the Einstein – Cartan – Sciama – Kibble theory. We also consider a model that includes a series of quadratic torsion terms. This series leads to a potential function that has the effect of “turning on” the cosmological constant. This potential function then acts like dark energy. This model also shows that the torsion field can produce an inflationary period. PACS: 04.02 Cv, 95.30 Sf, 98.80-k     

The simplest black holes

A relativistic gravitational theory in (1 + 1) dimensions is presented which exhibits many of the qualitative features of (3 + 1)-dimensional general relativity. The field equations are simple enough for undergraduates to solve yet rich enough in structure to form a useful pedagogical example for exploring the qualitative features of relativistic gravitation. Black hole solutions to the field equations of the theory are derived and its relationship to Newtonian gravity is discussed in detail.     

The Fundamental Equations of Change in Statistical Ensembles and Biological Populations

A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline.     

Possible Alterations of Local Gravitational Field Inside a Superconductor

We calculate the possible interaction between a superconductor and the static Earth’s gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg–Landau theory. We try to estimate which are the most favorable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behavior of high–Tc and classical low–Tc superconductors with respect to the gravity/superfluid interplay.