arXiv subjects

Murray Gell-Mann

Publications and source records attributed to Murray Gell-Mann.

23 records · Page 2Linked to original sources

arXiv2005

Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive

Phase space can be constructed for $N$ equal and distinguishable subsystems that could be (probabilistically) either {\it weakly} (or {\it "locally"}) correlated (e.g., independent, i.e., uncorrelated), or {\it strongly} (or {\it globally}) correlated. If they are locally correlated, we expect the Boltzmann-Gibbs entropy $S_{BG} \equiv -k \sum_i p_i \ln p_i$ to be {\it extensive}, i.e., $S_{BG}(N)\propto N $ for $N \to\infty$. In particular, if they are independent, $S_{BG}$ is {\it strictly additive}, i.e., $S_{BG}(N)=N S_{BG}(1), \forall N$. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy $S_q\equiv k [1- \sum_i p_i^q]/(q-1)$ (with $S_1=S_{BG}$) for some special value of $q\ne1$ to be the one which extensive (i.e., $S_q(N)\propto N $ for $N \to\infty$).

cond-mat.stat-mech↗

arXiv2005

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the approach to equilibrium, the electromagnetic system, and T-violation in the weak interactions in such universes. The decoherence of alternatives that is necessary for the prediction of probabilities in the quantum mechanics of closed systems is the origin of a fundamental limitation on quantum cosmologies with initial and final conditions. The initial and final density matrices cannot both be pure; if they are there is no decoherence and no prediction.

gr-qc↗

arXiv2002

Current Algebra: Quarks and What Else?

After receiving many requests for reprints of this article, describing the original ideas on the quark gluon gauge theory, which we later named QCD, we decided to place the article in the e-Print archive.

hep-ph↗

arXiv1996

Equivalent Sets of Histories and Multiple Quasiclassical Realms

We consider notions of physical equivalence of sets of histories in the quantum mechanics of a closed system. We show first how the same set of histories can be relabeled in various ways, including the use of the Heisenberg equations of motion and of passive transformations of field variables. In the the usual approximate quantum mechanics of a measured subsystem, two observables re- presented by different Hermitian operators are physically distinguished by the different apparatus used to measure them. In the quantum mechanics of a closed system, however, any apparatus is part of the system and the notion of physically distinct situations has a different character. We show that a triple consisting of an initial condition, a Hamiltonian, and a set of histories is physically equivalent to another triple if the operators representing these initial conditions, Hamiltonians, and histories are related by any fixed unitary transformation. We apply this result to the question of whether the universe might exhibit physically inequivalent quasiclassical realms (which we earlier called quasiclassical domains), not just the one that includes familiar experience. We describe how the probabilities of alternative forms, behaviors, and evolutionary histories of information gathering and utilizing systems (IGUSes) using the usual quasiclassical realm could in principle be calculated in quantum cosmology, although it is, of course, impractical to perform the computations. We discuss how, in principle, the probabilities of occurence of IGUSes could be calculated in realms distinct from the usual quasiclassical one. We discuss how IGUSes adapted mainly to two different realms could draw inferences about each other using a hybrid realm consisting of alternatives drawn from each.

gr-qc↗

arXiv1995

Strong Decoherence

We introduce a condition for the strong decoherence of a set of alternative histories of a closed quantum-mechanical system such as the universe. The condition applies, for a pure initial state, to sets of homogeneous histories that are chains of projections, generally branch-dependent. Strong decoherence implies the consistency of probability sum rules but not every set of consistent or even medium decoherent histories is strongly decoherent. Two conditions characterize a strongly decoherent set of histories: (1) At any time the operators that effectively commute with generalized records of history up to that moment provide the pool from which -- with suitable adjustment for elapsed time -- the chains of projections extending history to the future may be drawn. (2) Under the adjustment process, generalized record operators acting on the initial state of the universe are approximately unchanged. This expresses the permanence of generalized records. The strong decoherence conditions (1) and (2) guarantee what we call ``permanence of the past'' -- in particular the continued decoherence of past alternatives as the chains of projections are extended into the future. Strong decoherence is an idealization capturing in a general way this and other aspects of realistic physical mechanisms that destroy interference, as we illustrate in a simple model. We discuss the connection between the reduced density matrices that have often been used to characterize mechanisms of decoherence and the more general notion of strong decoherence. The relation between strong decoherence and a measure of classicality is briefly described.

gr-qc↗