Basic idea behind Quantum Gravity?
John Baez
Maynard Handley <hand...@ricochet.net> wrote:
>Within this scheme for what "quantizing" a theory means, the question
>arises of what's being done when people try to quantize gravity.
Lots of people try different things, of course. The biggest split
is between the string theorists and everyone else. In the "everyone
else" camp, there is a large group of people trying to combine
Einstein's equations with quantum mechanics in various different
ways, and a smaller group of people trying all sorts of ways to
"start from scratch" and cook up some theory not based on Einstein's
equations, which still somehow mimics Einstein's equations in the
classical limit. The former group of people includes people working
on "canonical quantum gravity" - roughly speaking, the Hamiltonian
approach - and "path-integral quantum gravity" - roughly speaking,
the Lagrangian approach. Among people working on canonical quantum
gravity, perhaps a majority are now working on ideas related to loop
quantum gravity (a particular approach initiated by Rovelli and Smolin).
In the path-integral camp one finds people like Hawking and his
collaborators, and also people working on spin foams (which however
are closely connected with loop quantum gravity).
>One possibility would be that "the points of spacetime" remain unchanged,
>but multiple metrics are superimposed, each with a complex factor.
>This fits easily with what was done for, eg, EM,
Yes, something like this is the basic idea in the more conservative
approaches to both canonical and path-integral quantum gravity.
The background-free nature of Einstein's equations introduces a
lot of subtleties that aren't present in EM, though.
>but it seems that at least Penrose doesn't like this given what
>he has said about how gravity causes "collapse of the wave function".
You should realize, just as a kind of cultural note, that very
few people working on quantum gravity agree with Penrose's ideas
about gravitationally induced wavefunction collapse. This does
not mean his ideas are wrong, of course: just that to the extent
you are trying to build a picture of the "conventional wisdom"
about quantum gravity, you should not count Penrose as representative.
One reason Penrose takes the viewpoint he does is that he finds
the idea of a superposition of two radically different spacetime
geometries distressing. It's certainly odd, but not really much
more odd than any other sort of superposition of macroscopically
different states (like Schrodinger's half-alive, half-dead cat).
Most people trying to quantize gravity are willing to accept
quantum mechanics in its current form, at least tentatively,
so they are willing to live with the notion of superpositions of
macroscopically different states.
>Another possibility would be to actually let the "points of space time
>move around" whatever that might mean---I guess now having the things that
>are superimposed be not metrics but actual spaces that differ by more than
>just metric---different dimensions, different connectednesses, whatever.
Right. The more radical you are, the more things you are willing to let
vary in your superpositions - this seems to be how the psychology of
physicists works.
Letting the *geometry* vary is pretty much a given when you are doing
quantum gravity, though string theory often keeps a fixed metric lurking
in the background to help with calculations. Letting the *smooth structure*
vary, or letting the *topology* vary, is getting more radical, but is in
fact quite popular. Hawking considers path integrals that allow different
topologies, and so does some work on "dynamical triangulations" and spin
foam models. In the latter two approaches, spacetime is often taken
to be a triangulated rather than smooth manifold - this is another form
of radicalism. When you go this far, it's but a small step to allowing
not only triangulated manifolds but more general "pseudomanifolds".
This is what I like to do, though I haven't gotten very good at it yet.
A still more radical step is to consider pseudomanifolds of variable
*dimension* - Lee Smolin does this, for example.
>Of course between these two extremes, there's scope for "quantizing" in
>the fashion I've described, each successive layer of structure one might
>add to a spacetime, which was where my question came from about the types
>of structures one might see in spacetime.
Right: once you name any structure, you can try to quantize it. Chris
Isham likes to joke about how in his youth he used to go around trying
to quantize everything in sight. Geometry, topology, causal structure -
whatever!
Personally I suspect that the "ultimate best approach" will not involve
quantizing some classical structure - it will be something thoroughly
quantum-mechanical from the very beginning. This is why I've been so
interested in spin networks, spin foams, and n-categories: these are
algebraic concepts that arise naturally when you think long and hard
about the math of quantum mechanics, and they seem in a sense more
primitive than the notion of smooth manifold with metric, even though
you *can* get to them via quantizing classical stuff if you want.
But that's just me - I was mainly trying to explain the "conventional
wisdom" in this post, not my own nutty ideas.
Maynard Handley
on a general relativity space and received a number of useful answers.
This question is part of two larger questions I am trying to resolve.
Right now I fear I may have terminology somewhat inexact to the irritation
of some people,
but John Baez suggested I go ahead with posting anyway.
So question 1 is what are people after when they discuss quantum gravity.
Without fussing too much about details, having read various things John
Baez and others have posted, at least some of us on this group are willing
to buy in to the claim that the essential difference between QM and
classical mech is that QM allows one to bundle together a large number of
classical entities (fields, positions, whatever) each with an associated
complex number (probability plus phase) into a state, that the "components,
appropriately resolved" of the state all propagate independently until
something triggers collapse of the wave function.
I'm not really interested in hearing about why this is a completely wrong
interpretation of QM relative to some other theory---if any reader doesn't
know what I mean by the above, then we probably don't have much to discuss
with each other right now as I try to work my way through QM along this
path.
Within this scheme for what "quantizing" a theory means, the question
arises of what's being done when people try to quantize gravity.
One possibility would be that "the points of spacetime" remain unchanged,
but multiple metrics are superimposed, each with a complex factor. This
fits easily with what was done for, eg, EM, but it seems that at least
Penrose doesn't like this given what he has said about how gravity causes
"collapse of the wave function".
Another possibility would be to actually let the "points of space time
move around" whatever that might mean---I guess now having the things that
are superimposed be not metrics but actual spaces that differ by more than
just metric---different dimensions, different connectednesses, whatever.
This sounds like what the quantum foam people are on about, but is a
somewhat more drastic step.
Of course between these two extremes, there's scope for "quantizing" in
the fashion I've described, each successive layer of structure one might
add to a spacetime, which was where my question came from about the types
of structures one might see in spacetime.
Maynard
Tom Potter
news:83faib$n...@charity.ucr.edu...
> In article <handleym-161...@handma3.apple.com>,
> Maynard Handley <hand...@ricochet.net> wrote:
>
> >Within this scheme for what "quantizing" a theory means, the
question
> >arises of what's being done when people try to quantize gravity.
>
> Lots of people try different things, of course. The biggest split
> is between the string theorists and everyone else. In the "everyone
> else" camp, there is a large group of people trying to combine
> Einstein's equations with quantum mechanics in various different
> ways, and a smaller group of people trying all sorts of ways to
> "start from scratch" and cook up some theory not based on Einstein's
> equations, which still somehow mimics Einstein's equations in the
> classical limit
It seems to me that it would make more sense
to use measured "reality" and "Ockham's Razor"
as the criteria for developing a theory of "reality",
rather than Einstein' equations,
or the solutions to thereof.
--
Tom Potter http://jump.to/tp
Sean Case
<t...@earthlink.net> wrote:
> It seems to me that it would make more sense
> to use measured "reality" and "Ockham's Razor"
> as the criteria for developing a theory of "reality",
> rather than Einstein' equations,
> or the solutions to thereof.
Since Einstein's equations fit so beautifully with measured reality,
there is very little to choose between these approaches.
Sean Case
--
Sean Case g...@zipworld.com.au
Code is an illusion. Only assertions are real.
Borcis
>
> You should realize, just as a kind of cultural note, that very
> few people working on quantum gravity agree with Penrose's ideas
> about gravitationally induced wavefunction collapse.
Are there any people believing the converse, e.g., gravity
as the averaged effect of wavefunction collapses ?
john baez
Borcis <zo...@zipzap.ch> wrote:
>John Baez wrote:
>> You should realize, just as a kind of cultural note, that very
>> few people working on quantum gravity agree with Penrose's ideas
>> about gravitationally induced wavefunction collapse.
>Are there any people believing the converse, e.g., gravity
>as the averaged effect of wavefunction collapses ?
Not that I know of! But Penrose suggests there's a different
kind of "converse" to gravitationally induced wavefunction
collapse - namely, entropy production by the evaporation of
black holes. In this scenario, the mystery of quantum mechanics
and the mystery of the "information loss puzzle" are somehow
supposed to be two sides of the same coin: wavefunction collapse
decreases entropy, while evaporating black holes create it,
so maybe it all balances out.... Unfortunately, Penrose has
never shaped these ideas into a precise theory, where you can
see how it's all supposed to work, so very few physicists are
pursuing this line of thought.
etar...@my-deja.com
Borcis <zo...@zipzap.ch> wrote:
> John Baez wrote:
> >
> > few people working on quantum gravity agree with Penrose's ideas
> > about gravitationally induced wavefunction collapse.
>
> as the averaged effect of wavefunction collapses ?
>
>
to the quantity of information about the position of an object. If you
take the wave function collapse as a measurement of the position of an
object, then I would probably fall into that camp. My position in some
ways contains, both Penrose's conjecture and the converse that you have
stated.
Of course, my conjecture is highly speculative and I am not a
professional physicist so this may be of little consequence. It however
does appear to resolve a number of problematic issues if you are
willing to accept the conjecture. I am still very far from a
quantifiable formulation of the thesis at this point.
Cheers,
Elliot
--
"If you don't go to other folks funerals, they
won't come to yours."
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