12,046 research outputs found
Quasiclassical Coarse Graining and Thermodynamic Entropy
Our everyday descriptions of the universe are highly coarse-grained,
following only a tiny fraction of the variables necessary for a perfectly
fine-grained description. Coarse graining in classical physics is made natural
by our limited powers of observation and computation. But in the modern quantum
mechanics of closed systems, some measure of coarse graining is inescapable
because there are no non-trivial, probabilistic, fine-grained descriptions.
This essay explores the consequences of that fact. Quantum theory allows for
various coarse-grained descriptions some of which are mutually incompatible.
For most purposes, however, we are interested in the small subset of
``quasiclassical descriptions'' defined by ranges of values of averages over
small volumes of densities of conserved quantities such as energy and momentum
and approximately conserved quantities such as baryon number. The
near-conservation of these quasiclassical quantities results in approximate
decoherence, predictability, and local equilibrium, leading to closed sets of
equations of motion. In any description, information is sacrificed through the
coarse graining that yields decoherence and gives rise to probabilities for
histories. In quasiclassical descriptions, further information is sacrificed in
exhibiting the emergent regularities summarized by classical equations of
motion. An appropriate entropy measures the loss of information. For a
``quasiclassical realm'' this is connected with the usual thermodynamic entropy
as obtained from statistical mechanics. It was low for the initial state of our
universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th
birthday, minor correction
Quantum Pasts and the Utility of History
From data in the present we can predict the future and retrodict the past.
These predictions and retrodictions are for histories -- most simply time
sequences of events. Quantum mechanics gives probabilities for individual
histories in a decoherent set of alternative histories. This paper discusses
several issues connected with the distinction between prediction and
retrodiction in quantum cosmology: the difference between classical and quantum
retrodiction, the permanence of the past, why we predict the future but
remember the past, the nature and utility of reconstructing the past(s), and
information theoretic measures of the utility of history. (Talk presented at
the Nobel Symposium: Modern Studies of Basic Quantum Concepts and Phenomena,
Gimo, Sweden, June 13-17, 1997)Comment: 22pages, uses REVTEX 3.
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