Marseille workshop on loops and spin foams

[marcus]

maybe we have enough mugshots for the moment

issues about the history of the "dynamical triangulations" line of research
(also Ambjorn calls it SQG simplicial quantum gravity, treating
that as a synonym for DT in one paper I saw) are bound to come up.

so the history of this (1985, 1992, 1998 are important years) is another thing to keep in mind
as a reminder here are some links I posted a while back

https://www.physicsforums.com/showthread.php?p=213245#post213245

for the notes on history, scroll down just past the end of the Larsson quote

 

[john baez]

area spectrum in the AJL model

Indeed beautiful.

[JB] said: I saw these sights, but I didn't take these photographs! I got them off the web, but now I can't find where I got them. If you know, please tell me so I can credit the photographer.

Check George Gollin's website: http://www.hep.uiuc.edu/home/g-gollin/graphics/france.html

Thanks! That's it! I'll credit him.

By the way, Marcus raised an interesting question about the spectrum of the area operator in the Ambjorn-Jurkiewicz-Loll model:

Will it come out the same as in Loop gravity, the same multiples of the Planck unit area, the same set of numbers for eigenvalues of the operator?

That seems very unlikely! The model is based on the assumption that all the tetrahedra of which space is built are regular tetrahedra, all with the same basic edge-length. So, every face of every tetrahedron is an equilateral triangle of the same size. This size is the "quantum of area" in this model - call it a. The model doesn't specify what this number a is, but the obvious area operator - I claim there's an obvious area operator on the Hilbert space of this theory - will have as its spectrum the numbers

0, a, 2a, 3a...

This is more like what Bekenstein and Mukhanov claim in their famous paper on black hole spectroscopy than anything one gets in loop quantum gravity.

How can the area operator in Simplicial Quantum Gravity be constructed?

There are lots of ways, and we could have a fun argument about which one is "right", just like people have had in loop quantum gravity, with the Ashtekar-Lewandowski area operator battling the Rovelli-Smolin area operator. The problem is that we can't tell which area operator is "right" until we find some calculations that only give nice answers with the "right" area operator. Or, do an experiment and measure areas at the Planck scale - not very practical, and this will only work if not only our area operator but also our whole theory is also right!

It seems pretty easy to cook up a nice area operator in the AJL model: there's a Hilbert space whose orthonormal basis consists of all ways of triangulating a given 3-manifold into tetrahedra. Picking a surface for each triangulation, with the surface made of triangles in that triangulation, we get an area operator such that each state in the above basis is an eigenstate with eigenvalue na, where n is the number of triangles in the surface for the given triangulation.

That was a bit terse, but it was a complete description of the "obvious" area operator. It even takes into account the fact that which surface we're talking about can only be specified after we say which state of the universe we've got! In other words, this is a physical observable, not a "kinematical" one.

Can computer (monte carlo) simulations be used to calculate areas?

I don't see the need for this, since the dynamics of the theory don't affect the area spectrum in any obvious way.

(This is what people hope in loop quantum gravity, which is why people dare talk about the area spectrum even before solving the Hamiltonian constraint. In other words, they're computing the spectrum of a kinematical observable and hoping that'll be the spectrum of a physical observable. But the AJL model is gauge-fixed, so there's no Hamiltonian constraint! - so it's much easier to construct physical observables.)

(Where of course "physical" is a technical term that doesn't imply any of this stuff is relevant to the real physical world!)

 

[sol2]

I have a question about topology.

If we accept the ideas of LQG as a basis of of these triangulations in quantum gravity, can we say that these are discrete.

As part of the http://superstringtheory.com/forum/extraboard/messages12/666.html of string theory based on Kaluza and Klein's ordering of geometries this would seem consistent to me, while LQG might be lacking in this discription and less pervasiveness?

Looking at the monte carlo for better comprehension of the energy bending plot, helped to define the structure for me in visualization.s If we can get better pictures then It goes a long way for me:)

I was looking for a consistent geometrical basis. Can this be done?

Also string frequencies can be http://www.superstringtheory.com/forum/stringboard/messages18/1.html why can LQG not?

 

[marcus]

getting back to the main topic of the thread (Simplicial Quantum Gravity---AJL model---Baez comments after the Marseille conference) here are exerpts from JB post from yesterday, 22 May:

... interesting question about the spectrum of the area operator in the Ambjorn-Jurkiewicz-Loll model:

"Will it come out the same as in Loop gravity, the same multiples of the Planck unit area, the same set of numbers for eigenvalues of the operator?"

That seems very unlikely! The model is based on the assumption
that all the tetrahedra of which space is built are regular tetrahedra, all
with the same basic edge-length. So, every face of every tetrahedron is an equilateral triangle of the same size. This size is the "quantum of area" in this model - call it a. The model doesn't specify what this number a is, but the obvious area operator - I claim there's an obvious area operator on the Hilbert space of this theory - will have as its spectrum the numbers

0, a, 2a, 3a...

This is more like what Bekenstein and Mukhanov claim in their famous paper on black hole spectroscopy than anything one gets in loop quantum gravity.

"How can the area operator in Simplicial Quantum Gravity be constructed?"

There are lots of ways, and we could have a fun argument about which one is "right", just like people have had in loop quantum gravity, with the Ashtekar-Lewandowski area operator battling the Rovelli-Smolin area operator. The problem is that we can't tell which area operator is "right" until we find some calculations that only give nice answers with the "right" area operator. Or, do an experiment and measure areas at the Planck scale - not very practical, and this will only work if not only our area operator but also our whole theory is also right!

It seems pretty easy to cook up a nice area operator in the AJL model: there's a Hilbert space whose orthonormal basis consists of all ways of triangulating a given 3-manifold into tetrahedra. Picking a surface for each triangulation, with the surface made of triangles in that triangulation, we get an area operator such that each state in the above basis is an eigenstate with eigenvalue na, where n is the number of triangles in the surface for the given triangulation.

That was a bit terse, but it was a complete description of the "obvious" area operator. It even takes into account the fact that which surface we're talking about can only be specified after we say which state of the universe we've got! In other words, this is a physical observable, not a "kinematical" one...

at first sight, at least, it strikes me as strange that there's been no mention of matter participating in defining the surface whose area is to be measured (maybe this would be grist for the "fun arguments" JB says could be possible)

but I am not looking for arguments! I just find it unintuitive that one should have an area operator that measures the area of a perfectly abstract immaterial surface apparently chosen arbitrarily---a different one for each quantum state. I would feel more comfortable if the surface was the surface of my desk or something tangible like that (or at least defined by the gravitational field like a BH horizon would be). Maybe this is qvetching.

 

[sol2]

Marcus I would like to remove my post to preserve continuity between you and JB, Should this be done? I like your questions about what is real as well, but tangibles are not always easy moving to hyperspace realizations and quantum gravity? We'll have to see what JB saids to your response.

 

[selfAdjoint]

getting back to the main topic of the thread (Simplicial Quantum Gravity---AJL model---Baez comments after the Marseille conference) here are exerpts from JB post from yesterday, 22 May:



at first sight, at least, it strikes me as strange that there's been no mention of matter participating in defining the surface whose area is to be measured (maybe this would be grist for the "fun arguments" JB says could be possible)

but I am not looking for arguments! I just find it unintuitive that one should have an area operator that measures the area of a perfectly abstract immaterial surface apparently chosen arbitrarily---a different one for each quantum state. I would feel more comfortable if the surface was the surface of my desk or something tangible like that (or at least defined by the gravitational field like a BH horizon would be). Maybe this is qvetching.

Note that in their work on two and three dimensional "toy models' they did fit them with a toy model of matter, specifically an Ising spin lattice. And they showed that in the continuum limit the parameters of the model which they could derive in their quantum gravity form matched the ones derived in flat Minkowski space. I would presume the next thing they are going to do with their four dimensional mosel is to repeat this calculation.

Note also that this is a "get our claim out there in print" kind of paper, which sets out to do no more than prove their claim to derive four dimensional space from their local quantization. And bells and whistles will come later.

 

[marcus]

Marcus I would like to remove my post.

Sol please don't feel you should remove your "I have a question about topology" post of yesterday. Everyone's (positive) expressions of interest adds to the welcome with which we honor a visiting expert.
It is considerate and sensitive of you to worry about on topic/off topic issues.

the fact is for me I have to focus (which is just my situation relative to this)
but that does not mean you have to do the same!
there is a place for intellectual leaping in these discussions
(and for starting new threads on related tangents too)

however i must say that SQG is still at a rudimentary stage and
dealing with the most basic nuts and bolts
or so it seems to me

and accordingly I think you will find more possibilities for tie-ins with
loop gravity foam and the rest later on when
SQG has been cooking a while longer

 

[john baez]

at first sight, at least, it strikes me as strange that there's been no mention of matter participating in defining the surface whose area is to be measured (maybe this would be grist for the "fun arguments" JB says could be possible).

Actually I don't find this particular type of argument very fun - it's based too much on philosophical taste and not enough on the details of the model being considered. The AJL model has no matter in it, so we can't use matter to locate a surface in spacetime in this model. We can include matter, but then we have a different model.

Some people have strong philosophical objections against models of quantum gravity that don't include matter, but I've never understood these, since classical gravity is a perfectly sensible theory without matter, and nobody ever explains why the philosophical objections are supposed to kick in only when you quantize this theory!

Of course our universe has matter and we're striving for a theory of that. Also of course, there may be technical reasons why a theory of quantum gravity without matter can't possibly work. Nobody knows: this is a big open question. But the vague philosophical argument that "you can't tell where anything is without matter" just seems wrong to me. In curved spacetime, different places are different, so you can tell where features are. The vacuum Einstein equations make perfect sense classically; they don't become ambiguous due to the lack of matter. So, we can try to quantize this theory and see what happens.

The "fun" arguments I was alluding to are those that start with the AJL model, accept the fact that this theory has no matter in it, write down some well-defined operators, and then argue about which one is "the right area operator". Here we are dealing with a tough problem that might actually have a solution.

but I am not looking for arguments!

Don't worry, I'm not really arguing - just explaining why certain arguments don't seem fun to me, while others do.

I just find it unintuitive that one should have an area operator that measures the area of a perfectly abstract immaterial surface apparently chosen arbitrarily---a different one for each quantum state.

It may seem weird, but observables of this sort exist in the classical theory, so it should not really be shocking that they exist in the quantum theory. All we're saying here is that if you have a particular state of quantum gravity, you've got a particular "spacetime" of a quantum sort, and as in a classical spacetime you can talk about surfaces and their area.

I would feel more comfortable if the surface was the surface of my desk or something tangible like that (or at least defined by the gravitational field like a BH horizon would be).

I can see why these make you feel comfortable, but your comfort will turn to terror when you try to do calculations with an operator whose definition relies upon a mathematically precise definition of "the surface of my desk" - or even a "black hole horizon", which is much simpler to define, but still rather complicated. It's easier to first define the area of an arbitrary surface, and worry later about whether it's the surface of your desk. We do this in classical gravity, so I think we should do it in quantum gravity too.

 

[marcus]

very glad to have this lengthier discussion expanding on what you said earlier, which now seems quite reasonable or at least less strange.
so I should now imagine a hilbert space of (linear combinations of) all possible triangulations of a certain 3-manifold using a uniform set of tetrahedra

I have to stop and think if this is separable.

I think so.

for each N, all the possible ways of snapping together a set of N tetrahedra
the union of that has to be countable.

what is the inner product?

selfAdjoint might have an intelligent question (having proceeded ahead a ways), I am still getting my bearings.

 

[pelastration]

It's interesting to see what other people actually do on Elastic Interval Geometry.

Some movies showing dynamical triangulations in 3D: http://www.beautifulcode.nl/fluidiom/index.php?pagename=Main.FluidiomMovies The second mpg-movie (first image) (14Mb) is impressive.

http://www.beautifulcode.nl/gallery/

The server seems a little bit slow. Take your time.

 

[marcus]

what is the inner product?

Would it be nice if the inner product could somehow respect
dual triangulations.

Maybe it says in one of these papers we have links to how one
defines the inner product on a linear space consisting of linear combinations
of trglns of a 3-manifold---and I just missed it---or maybe it is a well-known proceedure I don't know about.

anyone other than JB have a page reference or link for this?

those "moves" that get you from one trgln to another turn into linear operators----possibly fun---any special properties?

 

[marcus]

I have a vague feeling of dejavu that the *star-category (from Q.Quandaries paper) idea could relate to this dynamical triangulations business. Was this spelled out somewhere and i just forgot about seeing it?
Maybe should just drink my coffee and not worry about this.

 

[marcus]

the big kahuna (selfAdjoint comment about AJL etc)

----from sA post on "Rovelli program" linkbasket thread----

...The two great historical exemplars of beauty first were Einstein and Dirac. In each case their approach achieved a great success early but then led them into unproductive wastelands. And it is at least arguable that both string physics and LQG research in the Ashtekar tradition are right now spinning their wheels. Maybe it's time for a younger generation, playing Feynman and Dyson to the Witten - Ashtekar version of Einstein-Dirac to have their say. Which is why I am very interseted in the AJL paper, a possibly rough hewed (remember Feyman's early rep?) but undoubtedly novel approach to the problem of background independent quantum mechanics (and THAT, not just quantum gravity is the big kahuna)...

------end exerpt----

some provocative idea(s) or seeds thereof here

AJL dynamical triangulations approach seems very close in spirit and practice to spinfoam
But also LQG and spinfoam are closely allied lines of research with people moving back and forth between them---even erecting theoretical bridges as in Livine' thesis.

we lack a good general classification-----all these research lines are aiming at a background independent quantum gravity----no official name but could call the goal a quantum general relativity
and there is a tailwagsdog effect that the background independence feature of GR is so massive that when you try to "quantize GR" it begins to look as if you are "bacgroundindependencing quantum mechanics".

two people on the ice, who is pulling whom, that kind of thing

well I didnt quite respond to your point about beauty and the historical parallels, but I want to see where it leads and also this big kahuna idea

BTW here's todays post on SPR by Thomas Larsson about the AJL paper:

https://www.physicsforums.com/showthread.php?p=221756#post221756

-----sample from Larsson----
Dear Zirkus,

Motl has of course completely missed the main point. Distler's
objection from 3 years ago was that he didn't believe in a good
continuum limit in 4D; a "miracle" as he puts it. This may have
been good point at that time; I thought so myself, although I
would have been much less pessimistic if I had known that
Ambjorn and Loll had already succeeded in 2 and 3D.

The new thing is that AJL have presented rather compelling
numerical evidence for a good continuum limit in 4D, thus making
Distler's objection obsolete. It is the fact that AJL have
apparently succeeded in quantizing gravity numerically that
people are so excited about...

------end quote-----

 

[marcus]

perspective on dynamical triangulation from a 1998 review by Rovelli

In his 1998 review Rovelli says that both spinfoam and dynamical triangulation simplicial QG can be seen as developing from Hawking's "Euclidean QG" which he discusses in the section called "Old Hopes turning into Approximate Theories".

-------quote from Rovelli gr-qc/9803024--------

B. Old hopes --> approximate theories

1. Euclidean quantum gravity
Euclidean quantum gravity is the approach based on a formal sum over Euclidean geometries (6):

$$Z = N \int D[g] e^{-\int d^4x \sqrt {g} R[g]}$$

As far as I understand, Hawking and his close collaborators do not anymore view this approach as an attempt to directly define a fundamental theory. The integral is badly ill defined, and does not lead to any known viable perturbation expansion. However, the main ideas of this approach are still alive in several ways.

First, Hawking’s picture of quantum gravity as a sum over spacetimes continues to provide a powerful intuitive reference point for most of the research related to quantum gravity. Indeed, many approaches can be sees as attempts to replace the ill defined and non-renormalizable formal integral (6) with a well defined expression. The dynamical triangulation approach (Section IV-A) and the spin foam approach (Section V-C2) are examples of attempts to realize Hawking’s intuition. Influence of Euclidean quantum gravity can also be found in the Atiyah axioms for TQFT (Section V-C1).

Second, this approach can be used as an approximate method for describing certain regimes of nonperturbative spacetime physics...

------end exerpt----

 

[Mike2]

I hate to be late to the discussion, but I just got through reading Three roads to Quantum Gravity and it amazes me that I still have basic questions such as: how is the discrete spacetime connected in a topologal sense. I mean, does each "cell" of spacetime share a side with adjacent cells? Or are there infinitesimal edges that connect regions together? What are the loops in quantum gravity? And how does this differ from the AJL picture of a spacetime?

Thanks.

 

[marcus]

how is the discrete spacetime connected in a topological sense.

I don't think a discrete spacetime model needs to be topologically connected.

At least I never heard it said that one needed a space to be connected before one could define fields and waves and stuff on it.

A lattice of points isn't connected but you can define stuff on it
that looks and acts like waves.

Computers do that all the time, like waves in computer animations are defined on a finite array of points.

Mike2 maybe you are asking the wrong question. Instead of how is the underlying space connected
maybe you should be asking whether and whether there is any reason it needs to be.

I just took a bath in a deep tub of hot water. it looked continuous to me, the water. It acted continuous and connected. It conducts heat and sound and water-waves and is transparent to lightwaves. It would conduct electricity if I was unlucky enough to be struck by lightning while in the bathtub
But it wasnt topologically connected or anythinglike a differentiable manifold.

It was actually a finite set of molecules, behaving like a continuum.

[edit: clarification, I infer from your next post that you thought I was making a reference to LQG, but without mentioning LQG, when i was mentioned lattices! As far as i know LQG is not a lattice theory and does not model space by discrete points. It has an underlying manifold, just no pre-specified geometry. We really need a general classifier word for
the various background indep. approaches to quantizing General Relativity.
they have a lot of resemblances but differ in details. What shall we call them, maybe "Loop etc. gravity" so that it is clear we are including the spin foam and simplicial models?]

 

[Mike2]

I don't think a discrete spacetime model needs to be topologically connected.

At least I never heard it said that one needed a space to be connected before one could define fields and waves and stuff on it.

A lattice of points isn't connected but you can define stuff on it
that looks and acts like waves.

Computers do that all the time, like waves in computer animations are defined on a finite array of points.

Mike2 maybe you are asking the wrong question. Instead of how is the underlying space connected
maybe you should be asking whether and whether there is any reason it needs to be.

I just took a bath in a deep tub of hot water. it looked continuous to me, the water. It acted continuous and connected. It conducts heat and sound and water-waves and is transparent to lightwaves. It would conduct electricity if I was unlucky enough to be struck by lightning while in the bathtub
But it wasnt topologically connected or anythinglike a differentiable manifold.

It was actually a finite set of molecules, behaving like a continuum.

It seems necessary to me that there be some sort of connected space or connected items in order to transmit any kind of signal through a medium. Otherwise, how does information travel from one point to the next if there is absolutely no medium of any kind between the points? So I wonder how the lattice of LQG is connected. Perhaps information travels through the edges. But then can information travel through an infinitesimally thin line? Is LQG creating point particles of space-time, with action at a distance through no medium at all? What?

 

[marcus]

... So I wonder how the lattice of LQG is connected...

Mike2, as selfAdjoint has explained to you in another thread, LQG is based on a continuum, on a differentiable manifold, not on a lattice. You don't have to worry about it being connected.
As sA also remarked the simplicial AJL model, which is really more the topic of this thread, is also a continuum. Think of it as a diff. manif that has been "triangulated" ----built up out of simplices----fused glued welded together from simplices----partitioned into simplices without actually splitting them (they touch).
We need to get on with following developments around the SQG (simplicial quantum gravity) or "dynamical triangulations" model of Ambjorn Jurkiewicz Loll

 

[marcus]

the AJL paper and Simplicial Gravity is a fast moving story so I think we should try to keep up on it
Yesterday Baez posted on SPR---some strong statements about AJL approach in response to Charlie Stromeyer

--------Baez post Sunday, quote----
In article <61773ed7.0405240822.1c7108de@posting.google.com>,
Charlie Stromeyer Jr. <cstromey@hotmail.com> wrote:

>Here are three other reasons to be skeptical of discretized approaches
>to gravity:
>
>1) How are such approaches to be made compatible with vector
>supersymmetry (or vsusy) which is a topological type of symmetry that
>appears in both gravity and topological gauge theories [1].

This "vector supersymmetry" is a mathematical feature of certain
field theories - not something that anyone has observed experimentally.

Nobody has yet constructed a background-free quantum theory that has
general relativity as its limit at large distance scales. The Ambjorn-
Jurkiewicz-Loll model is the closest anyone has come. If they succeed,
this will be of interest regardless of whether their model displays
mathematical features that appear in certain other theories!

>2) How are such approaches to be made compatible with Bell-like
>correlations, non-locality and non-causality which are each present in
>the experiment described in this brief four page paper [2].

As a quantum theory, the Ambjorn-Jurkiewicz-Loll model automatically
has Bell-like "entanglement" and all that jazz.

>3) To paraphrase a sentence that Stephen Hawking once wrote, to not
>believe in the beauty and unity of the dualities of M-theory is like
>believing that evolution did not occur because instead God placed by
>hand all the fossils in the Earth just to play a joke on the
>paleontologists :-)

We resort to theological arguments in physics only when better arguments
are lacking. If a scintilla of experimental evidence for M-theory is
ever found, people will instantly stop making arguments of the sort
you mention here.

Please understand what I'm saying:

I'm not saying that M-theory is "wrong" or that the Ambjorn-Jurkiewicz-Loll
model is "right". M-theory makes too few definite predictions to be wrong.
The AJL model does not include matter, so it cannot be right. But the
AJL model is *interesting*, because it represents the best attempt so far
to find a background-free quantum theory that reduces to general relativity
in the large-scale limit!

---------end quote-------

for me the key point in this post is a mathematician's or mathematical physicist's judgement call:

Nobody has yet constructed a background-free quantum theory that has
general relativity as its limit at large distance scales. The Ambjorn-
Jurkiewicz-Loll model is the closest anyone has come.

 

[marcus]

Another recent Baez post on the AJL paper, this time in response to Thomas Larsson:
-------quote from Sunday 6 June SPR post----

In article <24a23f36.0405170344.69e74067@posting.google.com>,
Thomas Larsson <thomas_larsson_01@hotmail.com> wrote:

>1. Is the AJL model really quantum?

Yes! It has a Hilbert space of states, observables described
as noncommuting self-adjoint operators on this Hilbert space,
and discrete time evolution described by unitary operators on
this Hilbert space.

>Some time ago, Urs
>Schreiber argued that LQG, or at least the LQG string,
>fails to be a true quantum theory, and I tend to agree.

I disagree, but it's not really relevant here: we're not
talking about those other theories.

>However, the AJL model can be viewed as a statistical
>lattice model, and if such a model has a good continuum
>limit, it is AFAIK always described by some kind of QFT.
>What else could it be?

Right!

>2. Is the AJL model really gravity. The action is a rather
>straightforward discretization of the Einstein action with
>a cosmological term:
>
> sum over (d-2)-simplices
>
> det g = volume => sum over d-simplices.
>
>What is perhaps somewhat unusual is that all edges have
>the same length, which is different from Regge calculus.
>Nevertheless, I don't think that this really matters, but
>one could check if the results look different if you
>allow for variable edge lengths.

Right! But, the test of whether the model "is really
gravity" is to carefully examine its behavior in the limit
of large distance scales (i.e. lots of 4-simplices). One
can't easily guess this from looking at the action.
Nonperturbative effects are too important! So, in the
absence of good analytical techniques, one really needs
to run computer simulations - as AJL are doing.

>3. Is the measure right? Here is the place where AJL differ
>significantly from previous simulations. AFAIU, the crux is
>that AJL insist on a strict form of causality: they exclude
>spacetimes where the metric is singular, even at isolated
>points. This may seem like an innoscent restriction, but it
>rules out things like topology change and baby universes,
>which require that the metric be singular somewhere.
>
>It is not obvious to me whether one should insist on such a
>strong form of causality or not, but this assumption leads
>at least to better results, e.g. a reasonably smooth 4D
>spacetime. Thus, I believe that it is a fair chance that
>AJL have indeed succeeded in quantizing gravity.

The issue of the "right measure" is very tricky, so tricky
in fact that I again think the most efficient way to begin
tackling it is to run computer simulations and see if the
AJL model acts like general relativity at large length scales.

>They do so not by assuming a lot of experimentally unconfirmed
>new physics, but rather by strictly implementing the
>time-honored principles of old physics, especially
>causality. That is cool.

Yes! Very cool!

----end quote----

For me, there are two key statements here:

---exerpts---

>1. Is the AJL model really quantum?

Yes! It has a Hilbert space of states, observables described
as noncommuting self-adjoint operators on this Hilbert space,
and discrete time evolution described by unitary operators on
this Hilbert space.

...

>They do so not by assuming a lot of experimentally unconfirmed
>new physics, but rather by strictly implementing the
>time-honored principles of old physics, especially
>causality. That is cool.

Yes! Very cool!

----end exerpts---

the last is again a professional mathematician's judgement call. It may be time to quantize the theory of gravity we all use and to do that in a way
that does not "assume a lot of experimentally unconfirmed new physics".
It looks cool to these guys to get GR quantized by conservatively implementing the tried-and-true established principles. In other words spare us the fairy tales about extra dimensions and just get the job done.

You pay mathematicians in part to make educated guesses about what is cool and not cool, what is interesting and not interesting, and what might work. Part aesthetic and part a kind of laboriously enhanced common sense. I'm listening to both these guy's judgement.

https://www.physicsforums.com/showthread.php?p=227813#post227813

 

[Mike2]

Mike2, as selfAdjoint has explained to you in another thread, LQG is based on a continuum, on a differentiable manifold, not on a lattice. You don't have to worry about it being connected.
As sA also remarked the simplicial AJL model, which is really more the topic of this thread, is also a continuum. Think of it as a diff. manif that has been "triangulated" ----built up out of simplices----fused glued welded together from simplices----partitioned into simplices without actually splitting them (they touch).

You seem to be missing the fundamental delemma. Or perhaps I'm hard of hearing. To quantize gravity IS to quantize the spacetime metric. But quantizing spacetime would of necessity make spacetime discrete and makes impossible any propagation of signals. This is too fundamental of a delemma. What could possibly fix it? So at the moment is seems impossible that you will ever quantize gravity.

 

[selfAdjoint]

Suppose we did have a complete quantization of spacetime. Then we would have interacting spaceons, no doubt exchanging gravitons, and communicating thus across distances. Where's the problem?

 

[Olias]

You seem to be missing the fundamental delemma. Or perhaps I'm hard of hearing. To quantize gravity IS to quantize the spacetime metric. But quantizing spacetime would of necessity make spacetime discrete and makes impossible any propagation of signals. This is too fundamental of a delemma. What could possibly fix it? So at the moment is seems impossible that you will ever quantize gravity.

Spacetime is relevant to 3+1 Dimensionsn and has a metric which gives constant results.

Space-Field, where 'TIME' is detached(exchanged) from the above metric follows certain values in GR, the major factor it is a 2 dimensional arena, and not 3+1, as one 'lose's' the time component in Einsteins field equations, this compactifies and restrains all measures into a non-time dependant arena.

The simplistic overview is that there are only Directional values of motion, all directions are based on 'back-to-back' interactions, like with all Field Equations the action, re-action are similtainious, for every Positive Action there is a corresponding Negative reaction.

 

[sol2]

Spacetime is relevant to 3+1 Dimensionsn and has a metric which gives constant results.

Space-Field, where 'TIME' is detached(exchanged) from the above metric follows certain values in GR, the major factor it is a 2 dimensional arena, and not 3+1, as one 'lose's' the time component in Einsteins field equations, this compactifies and restrains all measures into a non-time dependant arena.

The simplistic overview is that there are only Directional values of motion, all directions are based on 'back-to-back' interactions, like with all Field Equations the action, re-action are similtainious, for every Positive Action there is a corresponding Negative reaction.

When you get to one dimension(string) what happens then

Gr had to be consistently expressed, but it is surrounded, before and after ?

Gravity and electromagnetism are now one( you can't see it but the one is white )?

 

[marcus]

You seem to be missing the fundamental delemma. Or perhaps I'm hard of hearing. To quantize gravity IS to quantize the spacetime metric. But quantizing spacetime would of necessity make spacetime discrete and makes impossible any propagation of signals. This is too fundamental of a delemma. What could possibly fix it? So at the moment is seems impossible that you will ever quantize gravity.

Suppose we did have a complete quantization of spacetime. Then we would have interacting spaceons, no doubt exchanging gravitons, and communicating thus across distances. Where's the problem?

want to try to respond
no time now since i have to go out briefly

will bring in this quote
-------quote from JB post on SPR Sunday 6 June------
Please understand what I'm saying:

I'm not saying that M-theory is "wrong" or that the Ambjorn-Jurkiewicz-Loll
model is "right". M-theory makes too few definite predictions to be wrong.
The AJL model does not include matter, so it cannot be right. But the
AJL model is *interesting*, because it represents the best attempt so far
to find a background-free quantum theory that reduces to general relativity
in the large-scale limit!

---------end quote-------

It is important to realize that quantizing the geometry of a continuum (a manifold) does not necessarily mean to chop up the manifold into little bits.
the manifold can stay continuous and smooth and connected while its
geometry-observables----areas, volumes, angles---become operators on a hilbertspace.

quantization is a way of representing observables, measurements.
it does not necessarily divide everything in sight into discrete quanta.

Mike2 is right in saying that to quantize gravity means to quantize the metric----in that the metric is one common mathematical representation of the geometry. It does not necessarily mean to divide the metric into little bits or force it to have discretized values. Above all it does not mean one necessarily pulverizes space into little bits! I guess that is one possibility (as selfAdjoint suggests) but it is not the necessary outcome.

Going back to the Seventies (and probably earlier) I think what seemed to a lot of people to be an obvious approach to quantizing GR was to have a smooth manifold and take the space of all (smooth) metrics on that manifold and make a hilbertspace which was
L2 functions on that space of geometries. And then you define operators on that hilbert space.
that is, don't think you have to discretize space and don't think you have to discretize the metric. what you want is to have the measurement of geometric properties like areas correspond to operators on a hilbertspace.
and they might turn out to have discrete spectra.

this approach did not work in the Seventies, although later Rovelli and Smolin did get area and volume operators with discrete spectra. by then (the Nineties) they were using the connection, instead of the metric, to represent the geometry.

None of these approaches recognizes a necessity to divide space up into isolated bits.

And the AJL approach which is the focus of this thread does not either.
differential geometers have been triangulating manifolds for ages (over a hundred years I guess) it is a standard thing
and AJL take a manifold---called S³ in their paper---and
triangulate it in a "dynamical" changing way

So Mike2 you are mistaken when you say:
"But quantizing spacetime would of necessity make spacetime discrete and makes impossible any propagation of signals."

It simply isn't true that quantizing spacetime (or more precisely the geometry of spacetime) would make spacetime discrete.

 

[Mike2]

-------quote from JB post on SPR Sunday 6 June------
Please understand what I'm saying:

I'm not saying that M-theory is "wrong" or that the Ambjorn-Jurkiewicz-Loll
model is "right". M-theory makes too few definite predictions to be wrong.
The AJL model does not include matter, so it cannot be right. But the
AJL model is *interesting*, because it represents the best attempt so far
to find a background-free quantum theory that reduces to general relativity
in the large-scale limit!

---------end quote-------

So it sounds like they are saying that GR does not hold up at very, very small distances. Then quantizing gravity is not equivalent to quantizing (discretizing) spacetime itself. Nevertheless,... discrete causality? That is a contradiction of terms. If a change at a point does not even have a start to an effect on a neighbor, then there is no "immediate" reason why it should have any effect at all.

 

[selfAdjoint]

Mike, you continue to equate quantizing to discretizing. You really need to study more about what quantizing really is. States, operators, and uncertainty, superposition and entanglement. Not "separate chunks".

 

[Mike2]

Mike, you continue to equate quantizing to discretizing. You really need to study more about what quantizing really is. States, operators, and uncertainty, superposition and entanglement. Not "separate chunks".

Admittedly, I am not as informed as many in this field. I am trying to develop a better intuition about all this. And I know that QM does not lend itself to any kind of intuition. That said, I have studied sum higher math and physics. And I don't know of any variables/observables that are quantized that do not take on discrete values. What I am trying to understand is how gravity/spacetime can be "quantized" without being made discrete. And if it is discrete, what does that mean. Your response, of course, is no answer to that. Thank you.

 

[setAI]

What I am trying to understand is how gravity/spacetime can be "quantized" without being made discrete.

hint: fractal structures are in a way both discrete and continous- they represent hierarchies of quantized structures which can seem discrete but are really fundamentally continuous- and vice versa!

interestingly enough fractal structures are what always emerge from chaos- and any truly fundamental view of the ontology of Existence itself suggests that the spacetime/forces/energy/matter of a universe must emerge and crystalize out of an "initially" chaotic state-

ultimately you can either have Existence or Non-existence- if you have existence it must be absolute Chaos because if it existed and wasn't random it must have resulted from some more fundamntal ordered process which excluded an infinity of possible forms- you have to "start" with Chaos-

so the ultimate ontology of existence is Chaos> annihilation of equal-opposite interacting structures > remaining structures seeking entropic equilibration [the fundamental origin of Motion itself] crystalizing into a fractal hierarchy > emergence of seemingly discrete matrices/foams/graphs/lattices that emerge as spacetime vacua/branes > particles/forces

um- but don't listen to me- I think I went off topic- sorry for the crazytalk
___________________________

/:set\AI transmedia laboratories

http://setai-transmedia.com

 

[selfAdjoint]

Admittedly, I am not as informed as many in this field. I am trying to develop a better intuition about all this. And I know that QM does not lend itself to any kind of intuition. That said, I have studied sum higher math and physics. And I don't know of any variables/observables that are quantized that do not take on discrete values. What I am trying to understand is how gravity/spacetime can be "quantized" without being made discrete. And if it is discrete, what does that mean. Your response, of course, is no answer to that. Thank you.

Consider a quantized field. The field is continuous, although discrete packets can be exchanged. Remember that a photon is not just a particle; it also manifests as a continuous wave. In basic quantum mechanics the discreteness comes in the measurement or observation. There can be a discrete set of outcomes (eigenvalues) when the Hermitian operator acts on the continuous state function.

 

[Mike2]

Consider a quantized field. The field is continuous, although discrete packets can be exchanged. Remember that a photon is not just a particle; it also manifests as a continuous wave. In basic quantum mechanics the discreteness comes in the measurement or observation. There can be a discrete set of outcomes (eigenvalues) when the Hermitian operator acts on the continuous state function.

It's easy to visualize these things for quantized fields with respect to spacetime variables, the wave function squared tells you the probability of finding the particle at a certain location and time, etc. But I have difficulty imagining what it would even mean to quantize spaetime itself. Is it like the metric is tells you the probability of finding a particle of spacetime? And what happens to the validity of QED and QCD in a world of quantized gravity/spacetime? Wouldn't QED and QCD have to be reformulated with respect to something other than spacetime so that all quantization procedures are with respect to the same variables? If photons, gluons, and gravitons all must interact, then you'd expect their quantization procedure to be based on some commonality; evidently, spacetime/gravity is NOT that commonality. What then is?

 

[marcus]

It's easy to visualize these things for quantized fields with respect to spacetime variables, the wave function squared tells you the probability of finding the particle at a certain location and time, etc.

Mike2, do you mind if I answer----you asked this of selfAdjoint and he can also answer, anyway I only refer to a part of your question (and don't mean to horn in)


an important analogy. think of a very simple space of locations, like the unit interval or the real axis. you say:
"...the wave function squared tells you the probability of finding the particle at a certain location..."

now think of the set of all metrics on some manifold
that is analogous to the unit interval
the set of all possible geometries on this manifold
can be imagined as itself a mathematical space
and wave functions can be defined on it

"...the wave function squared tells you the probability of finding the geometry of the universe in a certain configuration..."

In practice things may be done differently but this gives you
a rough idea of what quantizing the geometry can mean
the wavefunctions are a hilbert space and
then one has operators on that hilbertspace corresponding to
measuring particular observable facts about the quantum state or wavefunction of the geomtry.

but one never totally nails down the geometry, just as one never nails down the position of a particle on the unit interval or the real axis.
does this make it more understandable?

 

[Mike2]

Mike2, do you mind if I answer----you asked this of selfAdjoint and he can also answer, anyway I only refer to a part of your question (and don't mean to horn in)

You should never appologize for contributing to an open forum. That's what it's here for. Just put your 2 cents in, please.

an important analogy. think of a very simple space of locations, like the unit interval or the real axis. you say:
"...the wave function squared tells you the probability of finding the particle at a certain location..."

now think of the set of all metrics on some manifold
that is analogous to the unit interval
the set of all possible geometries on this manifold
can be imagined as itself a mathematical space
and wave functions can be defined on it

"...the wave function squared tells you the probability of finding the geometry of the universe in a certain configuration..."

In practice things may be done differently but this gives you
a rough idea of what quantizing the geometry can mean
the wavefunctions are a hilbert space and
then one has operators on that hilbertspace corresponding to
measuring particular observable facts about the quantum state or wavefunction of the geomtry.

but one never totally nails down the geometry, just as one never nails down the position of a particle on the unit interval or the real axis.
does this make it more understandable?

That's beginning to make sense, thank you. So would our universe then be a particular one of the geometries (a collapsed wave function), or is it always a superposition, and what we see is a classical limit of a type of "geodesic" average?

This all sounds like a 3rd level of quantization. And just as the 2nd level of quantization cannot be used to describe the 1st level (or can it?), the 3 level cannot be considered on par with the results of the 2nd level? Paths cannot be considered the same as particles, and particles cannot be considered the same as geometries, right? How then can the geometries (gravitons?) interact with particles?

 

[Olias]

You should never appologize for contributing to an open forum. That's what it's here for. Just put your 2 cents in, please.




That's beginning to make sense, thank you. So would our universe then be a particular one of the geometries (a collapsed wave function), or is it always a superposition, and what we see is a classical limit of a type of "geodesic" average?

This all sounds like a 3rd level of quantization. And just as the 2nd level of quantization cannot be used to describe the 1st level (or can it?), the 3 level cannot be considered on par with the results of the 2nd level? Paths cannot be considered the same as particles, and particles cannot be considered the same as geometries, right? How then can the geometries (gravitons?) interact with particles?

Mike you want to review this recent paper, it has an interesting angle of relevence:

http://uk.arxiv.org/abs/quant-ph/0406028
http://uk.arxiv.org/abs/quant-ph/0406029


A previous paper: http://uk.arxiv.org/abs/quant-ph/0308101

 

[Mike2]

This all sounds like a 3rd level of quantization. And just as the 2nd level of quantization cannot be used to describe the 1st level (or can it?), the 3 level cannot be considered on par with the results of the 2nd level? Paths cannot be considered the same as particles, and particles cannot be considered the same as geometries, right? How then can the geometries (gravitons?) interact with particles?

What confuses me is that you are treating a graviton as a particle within some background geometry. But it is suppose to represent a quanta of geometry itself. It seems a particle assumes a backgound geometry used to describe its feature such as where and when it is and how big it is and how fast it is vibrating, etc. So how can one possibly describe a particle of "backgound", what non-background measures can be used to describe it? If the graviton is just another mode of vibration of a string, and strings assume a background, then a graviton cannot be a description of that background geometry, and so it does not describe gravity. I need a better picture because this sound like a contradiction. If quantum gravity means quantum spacetime, how do I visualize this? So all of space is a superposition of various quantum geometries? What does that mean? Does that mean that our particular spacetime is just one of the possible states of quantum geometry/spacetime/gravity? Or if there are other observations of a different quanta of spacetime, then how are the boundaries manifest between the different quanta of spacetimes? Thanks.