| Topic: |
Science > Physics |
| User: |
"Russell E. Rierson" |
| Date: |
25 Sep 2004 05:54:06 AM |
| Object: |
Euclidean Duality |
A theory of quantum gravity, will necessitate 21st century paradigm
shifting modifications to our physical-theoretic interpretations of
space-time. That is to say, it basically becomes a formalistic
canonical quantum gravity approach, that inevitably must be
understood to arise from the utmost compatibility of the statistical
geometry of distinguishable observations with the canonical structure
of Hamiltonian-Poisson dynamics. Consequently, the generally covariant
geometric perspective offers a background independent non-perturbative
formulation OF quantum gravity. It therefore becomes necessary to
invoke a quantum version of the equivalence principle, which requires
both the statistical and symplectic geometries of canonical quantum
theory to be fully dynamical entities. With the statistical-geometric
approach, the basic questions of quantum gravity regarding the nature
of observables, the problem of time, and the physics of the vacuum
become algebraic questions. Gravitons become quantum mechanical
operators.
Quantum mechanically, one defines "states" as objects that act upon
physical properties - with the association of a real number to each
property. But with the algebraic approach, one can treat the states
that arise in all unitarily inequivalent structures - on an equal
basis, thereby enabling one to define the theory without the need for
a preferred construction allowing for unification of GR and QM.
Symmetry forms the basis of unification.
Standard QM says that states are to be constructed as vectors in
hilbert space, or as density matrices on Hilbert space. Observables
are then defined as operators on Hilbert space acting upon the states.
The algebraic approach reverses the roles of states and observables
via the observables being constructed as elements of an abstract
algebra, with the association of a real number to each observable.
States become objects which "act" upon observables, which corresponds
to taking the expectation values, in the standard QM approach.
Construct physical properties of the hypothetical strings or branes,
as necessary elements in an algebraic language
Since there is no preferred construction, it naturally paves the way
for a union of GR and QM, using tensors. The quantization of
Einstein's field equation is not renormalizable but there is also the
"string" approach. The other avenue is taken by Wheeler and De Witt,
and gives the quantum cosmological analogue for the Schroedinger
equation. The solution of the Wheeler-DeWitt equation as a functional
in all locally defined spacetime metrics and is of infinite dimension.
The parameter space spanned by all quantum fields and geometrical
parameters, defines what is known as the "superspace". Generalize the
tunneling Hamiltonian - in which
tunneling between states are represented as wave functionals of the
scalar quantum field.
The Hamiltonian approach uses the Hamiltonian constraint, the Wheeler
DeWitt equation H*psi = 0 , representable by finite, diffeomorphism
covariant operators. An infinite dimensional space of solutions to the
Hamiltonian constraint can been constructed, allowing for commuting
physical operators to also be constructed. These include using path
integral methods to construct the projection operator onto physical
states, making use of matter fields as physical coordinates or
explicit operator constructions. Among those that can be so
represented are the area and volume operators, thus their spectra
represent genuine physical predictions of the theory. This
complementary path integral approach is then constructed with the
understanding of its relationship to the Hamiltonian theory. For the
Euclidean case, the path integral provides a projection operator onto
the space of solutions of the Hamiltonian constraints. Consequently,
it can be used to construct explicit expressions for the expectation
values -"commuting with all constraints"- of physical observables.
The expansion of the universe starting from an extremely curved
initial state i.e. the "big bang", must be described by the marriage
of GR and QFT ...of course. Split the full action of a physical
system into a harmonic action with unknown frequency - which is the
variational parameter, and the interaction, which is the difference
between the full potential and the harmonic potential. Expand the
interaction into a Taylor series, then calculate the elements as
harmonic meanvalues, approximating the euclidean path integrals to an
arbitrary degree.
In GR, the "superspace", of the geometrodynamics formulation, the
wavefunctions will be functional events that "define" space itself.
The spaces are generally covariant and "coordinate patches" are just a
convienient modeling tool. There is an independence of coordinate
systems; the classical geometrodynamics constitutes an
wavefunction/algorithm for constructing a leaf history of foliations
through superspace in an interlocking of three geometries.
Since space is only definable by the events that "relate" within it,
it becomes abundantly and self-evidently clear, that matter[events]
generates[defines] space. this is our first step in the realization of
the fundamental 21st century paradigm shift. Spacetime cannot exist
without matter-energy[events] that define it.
The thermodynamic arrow of time is defined as a geometric stacking of
space like foliations. The continual stacking is a universal self
inclusion, where the universe becomes a self referential iteration
function. Space is relativistically contracted as time is
relativistically dilated. Matter shrinks relative to previous
iterations, as overlapping Lorentz invariant circular light cone cross
sections - act as refractive density filters. As the time evolution
proceeds in the thermodynamic direction of t, the space like sheets
continually increase in density. The information storage of space time
= Shannon entropy.
(<-(->(<-(U)->)<-)->)
This increasing refractive spacetime density must be background
independent. The increasing density functions are, a dualistic
interpretation, being exactly equivalent to the non-Euclidean geometry
of Riemann and Einstein.
.
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| User: "Uncle Al" |
|
| Title: Re: Euclidean Duality |
25 Sep 2004 10:29:37 AM |
|
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"Russell E. Rierson" wrote:
A theory of quantum gravity, will necessitate 21st century paradigm
shifting modifications to our physical-theoretic interpretations of
space-time.
My ***** meter just pegged - and it is still in its packing crate.
Use once, disinfect, discard.
[snip]
The expansion of the universe starting from an extremely curved
initial state i.e. the "big bang", must be described by the marriage
of GR and QFT ...of course.
What does "curvature" mean across *all* spacetime at any time after
the Big Bang? What does curvature mean during inflation when the
boundary is moving way above internal lighspeed? All one can say is
that nether GR or QM is sufficient. Better theory woud have GR and QM
as limiting cases but need not look like either one. It had better
not look like either one - they are violently incompatible.
Split the full action of a physical
system into a harmonic action with unknown frequency - which is the
variational parameter, and the interaction, which is the difference
between the full potential and the harmonic potential. Expand the
interaction into a Taylor series, then calculate the elements as
harmonic meanvalues, approximating the euclidean path integrals to an
arbitrary degree.
Given N points on your graph and (N-1) parameters, I bet you can get a
pretty good interpolative model. So? The (N+1)th point will screw
you. Economics calls this "heteroskedasticity" - the stubborn refusal
of plebeian observation to obey elegant complex theory.
[snip]
The thermodynamic arrow of time is defined as a geometric stacking of
space like foliations. The continual stacking is a universal self
inclusion, where the universe becomes a self referential iteration
function. Space is relativistically contracted as time is
relativistically dilated. Matter shrinks relative to previous
iterations, as overlapping Lorentz invariant circular light cone cross
sections - act as refractive density filters. As the time evolution
proceeds in the thermodynamic direction of t, the space like sheets
continually increase in density. The information storage of space time
= Shannon entropy.
(<-(->(<-(U)->)<-)->)
This increasing refractive spacetime density must be background
independent. The increasing density functions are, a dualistic
interpretation, being exactly equivalent to the non-Euclidean geometry
of Riemann and Einstein.
If it is exactly equivalent then it is uninteresting, as matrix
mechanics and wave mechanics did not both persist. The overlap of
metric and affine gravitation theories - which is almost perfect - is
boring. The shared predictions of observables are qualitatively and
quantitatively utterly identical to the last decimal place. One can
safely study any of it and be assured of a least publishable bit
exactly PERT-charted in the grant funding proposal years before
execution. The sexy part is where the two theories are disjoint.
Almost nobody goes there because it would involve discovery. No
competent MBA would fund risk.
If you don't have anything new you don't have anything at all except
bottle washing and button sortting. We hire Mexicans for the former
and Malaysians for the latter. Record keeping is outsourced to East
Indians.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
.
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