**Stephen P. King** (*stephenk1@home.com*)

*Thu, 30 Sep 1999 08:29:40 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 838] Re: [Time 837]"**Previous message:**Hitoshi Kitada: "[time 836] Re: [time 835] Re: FW: [time 830] Re: Does a fundamental time exist in GR and QM? The thinking of others..."

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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