Stephen P. King (stephenk1@home.com)
Thu, 30 Sep 1999 08:29:40 -0400
Dear Hitoshi,
Hitoshi Kitada wrote:
>
> Dear Stephen,
>
> Stephen P. King <stephenk1@home.com> wrote:
>
> Subject: [time 835] Re: FW: [time 830] Re: Does a fundamental time exist in GR
> and QM? The thinking of others...
>
> > Dear Lance,
> >
> > I was trying to get some thinking focussed on the key issue: time and
> > how it is thought of. I too am interested in how Hitoshi contrasts his
> > notions with those of people like Baez.
>
> Your quotation of Baez did not suffice me to respond because I am not
> interested in his confined viewpoint. Lance's quotation of Paul Stewart
> Snyder's post was necessary for me to see your post.
Ok, I am just thinking that the ideas that Baez is working with might
be helpful, particularly those of n-category theory, viz:
Subject: Re: Does a fundamental time exist in GR and
QM?
Date: 1999/09/28
Author: baez <baez@galaxy.ucr.edu>
In article <37ED929E.1049@easyon.com>,
James Gibbons <gibbons@easyon.com> wrote:
>How does category theory play into Barbour's picture?
Barbour doesn't have much to say about this, nor about
the technical aspects of quantization, which tends to
be where category theory becomes important. His work
focuses on the classical phase space of general
relativity -
the "presymplectic manifold" we've been discussing in
this thread.
Personally I feel the true picture of quantum
gravity
will be rather different from what Barbour expects,
since
quantum field theories tend to have important
properties that
are not easy to guess just from a study of the
corresponding
classical phase space. For example, if you just study
the
classical Yang-Mills equations in 4d, you see a
conformally
invariant theory - you'd have to be very clever to
guess that
upon quantization, conformal invariance is broken, and
you'd
probably never dream of confinement. Similarly for
gravity:
the quantum theory of gravity at short distance scales
probably exhibits features that can't easily be seen
by
studying the classical Einstein equations.
Of course, there's not even any strong reason to
assume that
the ultimate laws of physics are obtained by
quantizing some
classical theory!
One of the reasons I like n-categories is that they
give an
approach to background-free quantum field theories
that
doesn't start by quantizing some pre-existing
classical
theory.
***
> > One problem that I see, is that
> > it is assumed that there exist only one space-time manifold in which all
> > observers are embedded. This is a very old notion and remains
> > unquestioned!
> > We need to consider the implications of LS theory with regards to this!
> > I believe that each LS would define its own space-time,
>
> Yes.
So would not each of the LS's space-times be "flat" given the LS's
clocking? This, I think, is important as it might be giving us a clue as
to how LS theory generalizes GR. Instead of a bunch of "patches" of flat
space-time that are used to tile a single Riemannian manifold, we have
the possibility of bounded space-time submanifolds (?) that can
'overlap'. Of course this would imply that the LS's fiber into a
non-Hausdorff structure, that is very different from the ordinary
Riemannian manifold that we have considered before... The lack of a
connection between the Euclidian spaces of the LSs relates to this.
> > both in terms of
> > the causal behavior of its observations and the group theoretical
> > behavior thereof. We can take a clue from the ideas were geometries were
> > defined by the algebraic properties of systems and not by some a priori
> > given.
> > We need to talk about clocking! We need to figure out a clear and
> > concise definition that is applicable at any level of complexity. I feel
> > that it will relate directly to what observation is in a
> > non-anthropocentric fashion. :-)
> > I cut and pasted your post [time 833]] below.
snip
> > ===================================
> >
> > From: "Paul Stewart Snyder" <ps@ws5.com>
> > Subject: Does a fundamental time exist in GR and QM?
> > Date: 06 Aug 1999 00:00:00 GMT
> > Message-ID: <rqe8crihq1tcq6@corp.supernews.com>
> > Approved: mmcirvin@world.std.com (sci.physics.research)
> > Sender: mmcirvin@world.std.com (Matthew J McIrvin)
> > Organization: Posted via Supernews, http://www.supernews.com
> > Newsgroups: sci.physics.research
> >
> > I have tried to digest the basic information in the recent threads about
> > spacetime in GR. To me the most interesting ideas follow from what Carlo
> > Rovelli suggested in 1991 (Physical Review D43, 442), that in GR time
> > should be treated as a derived and not a fundamental quantity. In
> > extending this
> > to the quantum world, he argues that "in the absence of a fundamental
> > time and
> > of an exact Schrodinger equation, there are gauge invariant observables,
> > that commute with the hamiltonian constraint, which describe evolution
> > with
> > respect to physical clocks. The observables are self-adjoint operators
> > on
> > the space of the solutions of the Wheeler-DeWitt equation.. Evolution
> > with
> > respect to physical clocks is described by self-adjoint operators
> > corresponding to the observables.. This extension is well-defined both
> > in
> > terms of the coherence of the formalism, and from the point of view of
> > the
> > viability of the standard probabilistic interpretation."
> >
> > It seems to me that rethinking the answers to the questions about what
> > is
> > "here and now" and what is "casuality", in terms of spatial contiguity
> > in
> > an atemporal universe, might resolve some of the apparent paradoxes of
> > GR/QM?
> > Indeed, the idea of hamiltonian mechanics in a presymplectic space seems
> > "elegant" and, if this actually models nature, might provide a useful
> > way
> > of viewing phenomena that seem to lack temporal constraints.
[HK]
> Symplectic structure appears when one considers a dynamical system with
> constraints, e.g., constraints to Minkowski manifold. Thus Snyder here refers
> to QM without any constraints. So I guess he is speaking about the usual QM in
> Euclidean space.
Are these constraints the light cone structures of the Minkowskian
manifolds?
> In this sense, his view looks quite close to mine. He should have developed
> his idea further enough to be appreciated by the people in the news group.
> Then he might have gotten other responses.
I could see that Snyder might be conservative as to not upset the
"ruling elite", we know what happens when we question "Dogma"! I will be
tracking Snyder as best I can...
snip
> > We think of a clocking as an act of observation within LS theory, as I
> > interprete it; so we distinguish observables from observers in the sense
> > of subject and object... We need to think about causality! What is
> > "presymplectic space"?
> >
> > Later,
> >
> > Stephen
> >
>
> Best wishes,
> Hitoshi
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