Search

Abstract: Using a pair of linear invariant operators satisfying the Liouville–von Neumann equation, we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum. [Copyright &y& Elsevier]

Abstract: It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an observer. Then the probability of an observation cannot be deduced simply from the quantum state (say as the expectation value of the projection operator for the observation, as in traditional quantum theory). One needs additional rules to get the probabilities. What these rules are is not logically deducible from the quantum state, so the quantum state itself is insufficient for deducing observational probabilities. This is the measure problem of cosmology. [Copyright &y& Elsevier]

Abstract: By combining a renormalization group argument relating the charge e and mass of the proton by (in Planck units) with the Carter–Carr–Rees anthropic argument that gives an independent approximate relation between these two constants, both can be crudely estimated. These equations have the factor of 0.1π and the exponent of 20 which depend upon known discrete parameters (e.g., the number of generations of quarks and leptons, and the number of spatial dimensions), but they contain no continuous observed parameters. Their solution gives the charge of the proton correct to within about 8%, though the mass estimate is off by a factor of about 1000 (16% error on a logarithmic scale). When one adds a fudge factor of 10 previously given by Carr and Rees, the agreement for the charge is within about 2%, and the mass is off by a factor of about 3 (2.4% error on a logarithmic scale). If this 10 were replaced by 15, the charge agrees within 1.1% and the mass itself agrees within 0.7%. [Copyright &y& Elsevier]

Abstract: Unless our universe is decaying at an astronomical rate (i.e., on the present cosmological timescale of Gigayears, rather than on the quantum recurrence timescale of googolplexes), it would apparently produce an infinite number of observers per comoving volume by thermal or vacuum fluctuations (Boltzmann brains). If the number of ordinary observers per comoving volume is finite, this scenario seems to imply zero likelihood for us to be ordinary observers and minuscule likelihoods for our actual observations. Hence, our observations suggest that this scenario is incorrect and that perhaps our universe is decaying at an astronomical rate. [Copyright &y& Elsevier]

We construct new complete, compact, inhomogeneous Einstein metrics on Sm+2 sphere bundles over 2n-dimensional Einstein–Kähler spaces K2n, for all n⩾1 and all m⩾1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of Sm with S2 bundles over K2n, for m>1. Additionally, we construct new complete, non-compact Ricci-flat metrics with topologies Sm times R2 bundles over K2n that generalise the higher-dimensional Taub-BOLT metrics, and with topologies Sm×R2n+2 that generalise the higher-dimensional Taub-NUT metrics, again for m>1. [Copyright &y& Elsevier]

Abstract: If the initial quantum state of the universe is a multiverse superposition over many different sets of values of the effective coupling ‘constants’ of physics, and if this quantum state collapses to an eigenstate of the set of coupling ‘constants’ with a probability purely proportional to the absolute square of the amplitude (with no additional factor for something like life or consciousness), then one should not expect that the coupling ‘constants’ would be so biophilic as they are observed to be. Therefore, the observed biophilic values (apparent fine tuning) of the coupling ‘constants’ is statistical evidence against such simple forms of wavefunction collapse. [Copyright &y& Elsevier]

Abstract: Using a novel numerical spectral method, we have constructed an – solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. This method is independent of the Ricci–DeTurck-flow method used by Figueras, Lucietti, and Wiseman. We have perturbed the solution to get large static black hole solutions to the Randall–Sundrum II (RSII) braneworld model. Our solution agrees closely with that of Figueras et al. and also allows us to deduce the new results that to first order in , the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about . [Copyright &y& Elsevier]