6 research outputs found
Emergent Semiclassical Time in Quantum Gravity. Full Geometrodynamics and Minisuperspace Examples
I apply the preceding paper's semiclassical treatment to geometrodynamics.
The analogy between the two papers is quite useful at the level of the
quadratic constraints, while I document the differences between the two due to
the underlying differences in their linear constraints. I provide a specific
minisuperspace example for my emergent semiclassical time scheme and compare it
with the hidden York time scheme. Overall, interesting connections are shown
between Newtonian, Leibniz--Mach--Barbour, WKB and cosmic times, while the
Euler and York hidden dilational times are argued to be somewhat different from
these.Comment: References Update
Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
Strategies intended to resolve the problem of time in quantum gravity by
means of emergent or hidden timefunctions are considered in the arena of
relational particle toy models. In situations with `heavy' and `light' degrees
of freedom, two notions of emergent semiclassical WKB time emerge; these are
furthermore equivalent to two notions of emergent classical
`Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach,
in a geometric phase formalism, extended to include linear constraints, and
with particular care to make explicit those approximations and assumptions
used. I propose a new iterative scheme for this in the cosmologically-motivated
case with one heavy degree of freedom. I find that the usual semiclassical
quantum cosmology emergence of time comes hand in hand with the emergence of
other qualitatively significant terms, including back-reactions on the heavy
subsystem and second time derivatives. I illustrate my analysis by taking it
further for relational particle models with linearly-coupled harmonic
oscillator potentials. As these examples are exactly soluble by means outside
the semiclassical approach, they are additionally useful for testing the
justifiability of some of the approximations and assumptions habitually made in
the semiclassical approach to quantum cosmology. Finally, I contrast the
emergent semiclassical timefunction with its hidden dilational Euler time
counterpart.Comment: References Update
Foundations of Relational Particle Dynamics
Relational particle dynamics include the dynamics of pure shape and cases in
which absolute scale or absolute rotation are additionally meaningful. These
are interesting as regards the absolute versus relative motion debate as well
as discussion of conceptual issues connected with the problem of time in
quantum gravity. In spatial dimension 1 and 2 the relative configuration spaces
of shapes are n-spheres and complex projective spaces, from which knowledge I
construct natural mechanics on these spaces. I also show that these coincide
with Barbour's indirectly-constructed relational dynamics by performing a full
reduction on the latter. Then the identification of the configuration spaces as
n-spheres and complex projective spaces, for which spaces much mathematics is
available, significantly advances the understanding of Barbour's relational
theory in spatial dimensions 1 and 2. I also provide the parallel study of a
new theory for which positon and scale are purely relative but orientation is
absolute. The configuration space for this is an n-sphere regardless of the
spatial dimension, which renders this theory a more tractable arena for
investigation of implications of scale invariance than Barbour's theory itself.Comment: Minor typos corrected; references update
Relational Particle Models. II. Use as toy models for quantum geometrodynamics
Relational particle models are employed as toy models for the study of the
Problem of Time in quantum geometrodynamics. These models' analogue of the thin
sandwich is resolved. It is argued that the relative configuration space and
shape space of these models are close analogues from various perspectives of
superspace and conformal superspace respectively. The geometry of these spaces
and quantization thereupon is presented. A quantity that is frozen in the scale
invariant relational particle model is demonstrated to be an internal time in a
certain portion of the relational particle reformulation of Newtonian
mechanics. The semiclassical approach for these models is studied as an
emergent time resolution for these models, as are consistent records
approaches.Comment: Replaced with published version. Minor changes only; 1 reference
correcte