arXiv subjects

Tony Rothman

Publications and source records attributed to Tony Rothman.

22 records · Page 2Linked to original sources

arXiv2001

Hidden Variables or Positive Probabilities?

Despite claims that Bell's inequalities are based on the Einstein locality condition, or equivalent, all derivations make an identical mathematical assumption: that local hidden-variable theories produce a set of positive-definite probabilities for detecting a particle with a given spin orientation. The standard argument is that because quantum mechanics assumes that particles are emitted in a superposition of states the theory cannot produce such a set of probabilities. We examine a paper by Eberhard, and several similar papers, which claim to show that a generalized Bell inequality, the CHSH inequality, can be derived solely on the basis of the locality condition, without recourse to hidden variables. We point out that these authors nonetheless assumes a set of positive-definite probabilities, which supports the claim that hidden variables or "locality" is not at issue here, positive-definite probabilities are. We demonstrate that quantum mechanics does predict a set of probabilities that violate the CHSH inequality; however these probabilities are not positive-definite. Nevertheless, they are physically meaningful in that they give the usual quantum-mechanical predictions in physical situations. We discuss in what sense our results are related to the Wigner distribution.

quant-ph↗

arXiv2000

Extremal Black holes and the limits of the third law

Recent results of quantum field theory on a curved spacetime suggest that extremal black holes are not thermal objects and that the notion of zero temperature is ill-defined for them. If this is correct, one may have to go to a full semiclassical theory of gravity, including backreaction, in order to make sense of the third law of black hole thermodynamics. Alternatively, it is possible that we shall have to drastically revise the status of extremality in black hole thermodynamics.

gr-qc↗

arXiv1999

A Phase Space Approach to Gravitational Enropy

We examine the definition S = ln Omega as a candidate "gravitational entropy" function. We calculate its behavior for gravitationl and density perturbations in closed, open and flat cosmologies and find that in all cases it increases monotonically. Using the formalism to calculate the gravitational entropy produced during inflation gives the canonical answer. We compare the behavior of S with the behavior of the square of the Weyl tensor. Applying the formalism to black holes has proven more problematical.

gr-qc↗

arXiv1996

A Phase Space Approach to the Gravitational Arrow of Time

We attempt to find a function that characterizes gravitational clumping and that increases monotonically as inhomogeneity increases. We choose $S = lnΩ$ as the candidate ``gravitational entropy'' function, where $Ω$ is the phase-space volume below the Hamiltonian H of the system under consideration. We compute $Ω$ for transverse electromagnetic waves and for gravitational wave, radiation and density perturbations in an expanding FLRW universe. These calculations are carried out in the linear regime under the assumption that the phases of the oscillators comprising the system are random. Entropy is thus attributed to the lack of knowledge of the exact field configuration. We find that $Ω$, and hence $lnΩ$ behaves as required. We also carry out calculations for Bianchi IX cosmological models and find that, even in this homogeneous case, the function can be interpreted sensibly. We compare our results with Penrose's C^2 hypothesis. Because S is defined to resemble the fundamental statistical mechanics definition of entropy, we are able to recover the entropy in a variety of familiar circumstances including, evidently, black-hole entropy. The results point to the utility of the relativistic ADM Hamiltonian formalism in establishing a connection between general relativity and statistical mechanics, although fully nonlinear calculations will need to be performed to remove any doubt.

gr-qc↗