Carlos Pedro dos Santos Gonçalves
UNIDE - ISCTE Business School - Lisbon University Institute
Massacritica, Lda.July 23, 2009
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 pathintegral 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.
Keywords: quantum cosmology, time, relational structures, relational nexus
Working Paper Series
2 comments:
That's thought provoking, the central features scanning picometric spacetime with path integral gravity. One solution for utramicro volume modeling is just as you suggest, the GT integral atomic topological function based on a series differential expansion of nuclear radiation rates of force emission, by [ e = m(c^2) ] physics, confined by the boundaries of time and space. This relative quantum model sees space as bonded to the atom by gravity, creating [ Gravity<->Time ] integral limits for the atom's pulsations at the quantum frequency [ Nhu = e/h ]. When the atomic internal momentum function is written, rearranged to give the photon gain rule and integrated for the GT boundaries a series of 26 energy intermedon particle topological functions results. Their energy values intersect those of the fundamental physical constants: h, h-bar, delta, nuclear magneton, beta magneton. Each of the atom's 5/2 kT J internal heat capacity energy particles is displayed as an animated picoyoctometric 3D video image.
The image of the h-bar magnetic energy particle of ~175 picoyoctometers is available online at http://www.symmecon.com along with essays, discussions, graphics, and the atomic video modeling manual The Crystalon Door.
(C) 2009, Dale Ritter, B.A.
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