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Science Forum Index » Philosophy - Meta Forum » The problem of time in quantum cosmology
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| mariaodete.sm@gmail.com |
 Posted: Thu Mar 27, 2008 4:50 am |
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The Problem of Time in Quantum Cosmology and Non-chronometric
Temporality
Abstract:
"We review two lines of argument regarding the problem of time in
quantum cosmology and in quantum gravity, one that invokes the path
integral formalism for quantum gravity to state the absence of time
between two three-geometries, and another that defends the absence of
time, as a fundamental notion in physics, in terms of: (a) the
configuration space argument, put forward by Barbour, Smolin and
Kauffman, and (b) the Wheeler-DeWitt equation. We argue that although
being correct with respect to a space-time dependent physical
chronometrizable clock-time frame, both of these lines of argument
fail with respect to a general sense of temporality, expressed in
terms of the more elementary notions of a before and an after of a
quantum computation. With respect to the first line of argument, it is
shown that the early works on the subject address two kinds of
temporalities, one that is the space-time geometric dependent
temporality, which coincides with the usual definition of a space-time
dependent physical chronometrizable clock-time frame, the other is a
temporality associated to the notions of input and output of a general
quantum gravity computation, that is expressed, in the theoretical
discourse of quantum gravity, through the usage of the concepts of:
(1) propagation of a wave functional in superspace, as addressed by
Wheeler; (2) transition amplitudes of three-geometries and (3) the
path integral formalism, used to calculate such amplitudes, as
addressed by Hartle and Hawking. While the first temporality (space-
time dependent temporality) disappears from the theory, the second
plays a fundamental role, not only in the several aspects of the
theory's construction, but in the clock-time independence as well, as
Wheeler showed. Given this notion of time, different from a
chronometrizable, space-time geometry internal notion, we search for a
general mathematical and logical structure that is capable of
addressing it from a formal point of view. This is done through a
family of mathematical structures that is more general than the
mathematical category. These structures not only will allow us to
address the nature of the temporality present in the transition
amplitudes between two three-geometries, but they will also allow us
to refute the configuration space argument and to show how a static
clock-time-independent quantum state, can be put into a non-clock-time
processual expression in terms of fine-grained computational
histories, obtained from the relations between different observable's
bases."
Avaliable at:
http://www.ma.utexas.edu/mp_arc/c/08/08-62.pdf
http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=08-62
maria odete |
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