# Quantum foam producing both particles and spacetime

1. May 20, 2006

### Mike2

So it seems some of these efforts suggest that spin networks, or the quantum foam, produce both virtual particles and even spacetime itself. Perhaps we can explore what the overall implication of this would be. I have a few questions along these lines that might be worth considering.

1) Would it be more correct to say that the spin network/ quantum foam produce both virtual particles and spacetime itself? Or would it be more correct to say that that the virtual particles of the quantum foam can be reinterpreted as spacetime - I think this is what J.C. Baez' work seems to suggest.

2) In either case, what does it mean to have a "vacuum energy" or zero point energy of a QFT or TQFT that produce both virtual particles and spacetime? Would there be only one value for any kind of spacetime and particle content? Or could we be facing a "Landscape" of vacuum energies even in these theories?

3) What does it mean that such a "vacuum" energy of the quantum foam may also produce spacetime? Does this mean quantum bits of spacetime also pop into and out of existence like virtual particles? If at each point in space, quantum space bits may also come into existence, is this responsible for the expansion of space and the Hubble law of cosmology?

4) Might a particular value of vacuum energy mean that whatever particles or virtual particles are not produced by the quantum foam must be compensated by quantum spacetime bits? If there is more quantum spacetime bits being produced more at one point than another, does that give rise to the curvature of spacetime? Might this also possibly explain the speed of light where in the FOR of the moving particle, quantum spacetime bits are changing more than at rest, etc?

5) Could there be some sort of entropy constraint that requires virtual spacetime and virtual particles to balance each other?

Perhaps considerations of this nature could rule out some theories in favor of another, for example, whether spacetime is an alternate interpretation of virtual particles or whether the quantum foam must produce both spacetime and particles?

2. May 22, 2006

### Mike2

Are these even the right questions?

3. May 22, 2006

### john baez

the question is, what's the right question?

That's the right question.

I'll tackle a few of them...

4. May 22, 2006

### john baez

The key point, which you seem to understand quite well, is that in some of these new spin foam models the difference between matter and spacetime becomes a bit blurry - in a very interesting and precise way.

On the one hand, we've guessed for a long time that this should happen. One of the lessons of general relativity is that the geometry of spacetime acts a lot like any other field. That is, any other form of matter! It's special just because it has the curious property of interacting with all other forms of matter based solely on their energy-momentum.

As Carlo Rovelli put it, suppose an intense bolt of gravitational radiation knocks down the Eiffel Tower. On what grounds is this radiation less deserving to be called matter than a correspondingly destructive lightning bolt made of electrons?

What's new is that in 3d spacetime, we can now get gravity to mimic particles of any spin and mass we like, simply by working on a spacetime that has some curves cut out of it.

We're trying to do something similar in spacetime. So far I can only get 4d topological gravity (a simplified theory, a form of BF theory) to mimic various kinds of strings. However, Laurent Freidel and Aristide Baratin have unearthed a spin foam model lurking behind the ordinary quantum field theory of particles in 4d spacetime. This suggests we can do particles too, if we get a bit smarter.

What excites me the most is that in lots of these theories, the underlying structure is a 2-category with:

objects corresponding to "matter"
morphisms corresponding to "space"
2-morphisms corresponding to "spacetime"

In n-dimensional spacetime, space is (n-1)-dimensional, and we now see that (n-2)-dimensional boundaries of space act like matter. If you make an algebraic gadget that keeps track of all the ways to glue together (n-1)-dimensional manifolds along their (n-2)-dimensional boundaries, and n-dimensional manifolds along their (n-1)-dimensional boundaries, you get a 2-category. This 2-category keeps track of everything.

This means that the analogy between space and state, spacetime and process get an extra layer that includes matter!

I'm sorry if these remarks seem cryptic. I've written two introductory papers on this stuff for philosophers, which explain the category theory but not the 2-category theory:

Higher-dimensional algebra and Planck-scale physics

Quantum quandaries: a category-theoretic perspective

And in a couple of weeks I'll be giving a talk about this at the Perimeter Institute, which should discuss the new 2-categorical stuff. Slides will be available here, as soon as I make them.

I'm also sorry that I didn't quite answer your questions. Instead, I took them as an excuse to say what I think is really going on.

5. May 22, 2006

Staff Emeritus
So the answer to quantumcarl's question "What is energy made of?" could be "cobordism"?:uhh:

And here I went and gave up on spectral sequences.

6. May 22, 2006

### marcus

:rofl:

that is memorable

You arent the only one, alas. I can't even rightly remember what they are, although it is etched in my memory being at the blackboard giving (or trying to give) a seminar talk on K-theory.

Well look at the bright side, we got some exposure (and you may have actually done something with it) and after all that

energy DID turn out to be made of cobordism!!!!!!!!! (hallelujah)
====================

BTW kudos to Mike2 starting this good thread. I will shut up so as not to risk distracting.

7. May 22, 2006

### marcus

Maybe instead of shutting up, and since I see John Baez is somewhere else at the moment, we should take a little post-room and PARAPHRASE what he said specializing to obvious cases.

So in 3D spacetime, space is 2D and 1D boundaries (like circles or the worldline of a moving point) act like MATTER....
And if you arrange to keep track of ways to glue 2D manifolds along their 1D boundaries....

the mental picture I'm getting stacking cobordisms, making a chain of them.

And what he just said about matter reminds me of Freidel Livine's several papers on the 3D case "ponzano-regge revisited"

Lets not linger but go to 4D and paraphrase what he said again:

In 4D spacetime, space is 3D and 2D boundaries (like black hole event horizons, or the tube-and-pants diagrams of Baez Wise Crans, or lots of other famous boundary surfaces, worldsheets and stuff) act like MATTER....
And if you arrange to keep track of ways to glue 3D manifolds along their 2D boundaries....

OK times up, go get lunch or do something useful.

but honestly, why not at lease PARAPHRASE what the guy says, even if one doesnt immediately "grasp the full implications" to put it mildly

It was funny what Rovelli said about a bolt of gravity knocking down the Eiffel Tower. For me the point was NOT that gravity is matter-----that I should picture gravity as a bunch of particles like matter particles---but that matter is gravity.

The point was that the bolt of gravity is a wrinkle working itself out---a ripple or tangle of geometry trying to get more comfortable---and that probably ELECTRONS are too. they also are probably some variety of crinkle in the geometry

so the Rovelli picture didnt say gravity is matter, it said matter is to think of as some extra features of the geometry

Mike2 already broached this idea so I am paraphrasing here as well.

Last edited: May 22, 2006
8. May 22, 2006

### Mike2

I do appreciate your efforts. Your Quantum Quandaries is what got me starting to think along these lines.

So to continue... we have spacetime produced by the same quantum foam as particles. If so, we have virtual and real spacetime bits just as much as virtual and real particles. But what is virtual spacetime? And what mechanism gives rise to the real from the virtual?

For particles, it seems virtual particles are made real due to the mechanism of acceleration (or otherwise an horizon). This is known as the Unruh effect or the Hawking effect, as you prefer. Is there a similar process for the creation of real spacetime out of virtual spacetime? Or how are they related? Is there a symmetry between particles and spacetime that mirrors for spacetime the acceleration production process of particles? Acceleration is obviously a changing of emount of space with time. So what would be the symmetrical process for spacetime, a change in the emount of particles? An increase in one corresponding to an increase in the other argues for spacetime being an alternate interpretation of particles.

However, cosmic inflation slowing down with the creation of matter argues for something fixed in the quantum foam that is divided between both particles and spacetime - more matter means less spacetime.

In order to get real/permanent particles you need pair production - particle/antiparticles to get separated by means of acceleration/horizons. So does that mean to get real/permanent space(time) that there has to be space and "anti"space that gets separated somehow to produce permanent space? And how could that be accomplished within the quantum foam models? What is the mathematical operation on particle/antiparticle in the quantum foam that causes permanent particles to be produced? And can we recognize a similar operation on space/antispace to produce permanent space?

It might also be that space is its own antispace just like photons are their own antiparticles.

Any thoughts, gentlemen?

Last edited: May 23, 2006
9. May 23, 2006

### francesca

if
why do you say
?

Maybe you are thinking of some kind of consevation law for the quantum foam, but I don't think we have it in this sense...
Well, we can postulate the conservation of information...
Some helps?

ps: sorry, i haven't read Bojowald or Ashtekar papers... what do they say about?

10. May 23, 2006

### marcus

Bo. and also most recently Asht. mainly concerned with LQG cosmology which is a symmetry-reduced simplified model of universe's overall geometry (like the Friedmann equation of usual cosmology---finite number of degrees of freedom----matter put in by hand in some simple form). I like their cosmology work very much indeed! It gets very interesting results about things like big bang and inflation and black holes. But it is, I would say, more effective and less risky. It does not address the issue of matter arising from details in the geometry. So it does not fit in so obviously with Mike's discussion.

Also technically, Mike is asking about spinfoam models and the Bojowald and Ashtekar work is mainly developing canonical LQG and the offshoot LQC (which are not spinfoam)

11. May 23, 2006

### Mike2

It seems to me that you discribed the last videos of Lee Smolin's Intro to Quantum Gravity as what... a Group Field Theory, where he, or his invited substitute, were showing how spin foams fix in with some of the operational or algebraic QFT's. Weren't you saying how spacetime "moves" on the "graphs" were how spacetime entered the QFT? My language might be a little off here, but I think you know what I mean, right?

Perhaps someone could list the current programme's that attempt to include spacetime in the QFT or spin foam models.

Last edited: May 23, 2006
12. May 23, 2006

### marcus

Hi Mike, if we get in a side discussion it may hurt your thread, you were having a really nice discussion. I stuck my nose in just now (after Francesca asked something) to say that Bojo and Ashtekar style stuff is not really on-topic as I see it. What they do is fine but it doesnt involve how matter could arise---how spacetime and matter could be the same thing. Didnt mean to sidetrack.

Four points and then I will shut up:
1. Smolin's Introduction to QG actually covers a lot of different approaches to QG, not just "his" approach or approaches (he has worked on several). One reason Smolin is good and unusual is that he can think generically about QG and get insights about all the field collectively----yet can also toil ahead along one particular path when he chooses to.

2. "moves" in that context is rather like moves in checkers or chess.
it is a local modification of the gameboard
according to some small codified list of legal operations that you can do.

"moves" with that meaning comes up in knot theory---there is a list of simple ways you can modify the knot so that it looks different----make this run over rather than under, whatever. It is a primitive idea and not mysterious.

a "graph" is also a pretty concrete idea, just a network, a web of lines meeting at vertices. Not mysterious, I think you would agree.

"moves" on a graph just means some list of legal ways to make small local modifications----insert a vertex here, remove a vertex there. reconnect a handful of adjacent vertices differently (like half a dozen that are near each other: redraw the connections in some way specified by the rules)

3. It would be something of a coup if it turned out that one can adequately represent a quantum state of spacetime and matter by something as primitive and unmysterious as a graph, and then could represent the natural evolution of spacetime and matter by an invisible hand performing countless local moves on that graph (according to some set of probabilities listed for each of the legal moves). That would be neat and the possibility is seen as worth exploring, but so far NOBODY SAYS YOU CAN get an adequate representation of nature that way. It just has not yet been shown that you cannot.

the idea is beautiful because it represents a mysterious and complex process by a very simple gameboard and unmysterious set of rules.

4. furthermore we shouldnt focus on this in a onetrackmind obsessive way because John Baez you were just talking to has AN ENTIRELY DIFFERENT IDEA OF HOW TO PROCEDE. With him you base it on Beef, and beef is different from graphs. It is also a very beautiful idea of how to procede. this is why the field is intriguing to watch. progress is subtle, multipronged and unpredictable, the story resists simplification.

Last edited: May 23, 2006
13. May 23, 2006

### Mike2

I may have been a little terse in my response. Please don't take my remarks as a challenge or as criticism. It just seemed as though you might know from what I've read from your posts who might be working in similar areas that are similar to JC. Baez' work.

It might be instructive to note the differences in these similar approaches. Perhaps we could categorize them as to whose makes space(time) out to be somehow equal to QFT, and whose makes space(time) come out of a QFT in addition to virtual/real particles.

For example, I wonder how Torsten's efforts might fit together with Baez' effort. Both seem to make spacetime to somehow be equal to QFT. Torstem derives the algebra of QFT, but using differential structure equates this to curvature IIRC. This seems pretty close to the 4D cobordism of Baez. That's all I got for now. I must get back to work before they catch me

Last edited: May 23, 2006
14. Jun 13, 2006

### Mike2

The Standard Model is derived based on symmetries of continuous spacetime. But quantum gravity is expected to make spacetime have quantum properties that destroy that continuity. So are the particles of QFT a feature of a scale many orders of magnitude larger than the Planck scale of quantum gravity, where the discontinuities have been averaged out and are virtually undetectable at that scale? If so, then what does that mean for string theory whose particles are the size of the Planck scale?

I have to wonder about those efforts that have developed a quantum foam or spin network for quantum spacetime but have not been able to produce particles. I just read an 1995 article:

http://www.arxiv.org/multi?archive=...asses&subj_physics=->+physics+subject+classes

In it the author describes how the mass of the quarks (or was it a mass ratio?) can be derived from a Planck size Lattice version QFT. Isn't this exactly what Dynamical Triangulation and Spin Networks is all about which have not produced matter in their models? So why isn't this paper taken more seriously? Is it because no quantum numbers are used to describe the spacetime of the Planck scale lattice? Is it because this lattice is achieved ad hoc and not derived by any quantization of field equations?

Last edited: Jun 13, 2006
15. Jun 14, 2006

### francesca

Preparata isn't mainstream since QCD days...

FATHER FAYNMAN

"You are old, Father Feynmann", Preparata declared,
"And yur hair has turned visibly gray;
And yet you keep tossing ideas around
At our age, a disgreceful display!"

"In my youth", said the master, as he shook his long locks,
"I took a great fancy to sketching;
I drew many diagrams, which most thought profound
While others thought just merely fetching".

"Yes, I know", said the youth, interrupting the sage,
"That you once were so awfully clever;
But now is the time for quark sausage with chrome.
Do you think you can last on forever?"

"In your words, my young fellow", the crone did retort,
As his face turned perceptibly redder;
"In your words I detect an impatience, I'm sure,

"You are old", quoth the youth, in his accented speech,
While eyeing the throne of the Master;
Or would yuo prefer that mach faster?"

"No, thanks, Giuliano", the sage did rebuff,
"Enough of your own brand of sass;
Do you think I can listen all day to such stuff?
Be off. Or I'll kick-in your ass!"

Tomek Ferbelski - Kaysersberg Conference, 1976​

Last edited: Jun 14, 2006
16. Jun 15, 2006

### Mike2

It would be nice if I could get a better answer. The author seems to get around the "no go" theorm which suggests that it is not possible to use a lattice approximation with QFT based on continuum spacetime. Since there are other efforts to use what appears to be a lattice, "Spin Networks", "Graphs of LQG", Dynamical Triangulation, and Causal Sets, if I'm not mistaken (Please feel free to correct me if I'm wrong), it would seem such an effort would naturally be of instantaneous use. I don't understand why it is not. Can anyone shed light on the subject? Thanks.

Again the paper is at:

http://www.arxiv.org/multi?archive=...asses&subj_physics=->+physics+subject+classes

17. Jun 24, 2006

### Mike2

Or is there some other reason why the continuous Lie groups might be used in the operator algebra or group theory that would also give rise to discontinuous quantum spacetime?

18. Jun 24, 2006

### Mike2

If quantum spacetime is bits and pieces of spacetime fluctuating at the Planck scale, then it is hard to see how Lie groups based on continuous spacetime can be relevant to particles unless particles emerge at a much larger scale where a continuum can be assumed. However, if quantum spacetime is a superposition of continuous sections of spacetime much larger than the Planck scale, then for each section (state?) the continuous Lie groups would be relevant, right?

19. Jun 25, 2006

### Farsight

This looks interesting. Was that a crease I saw back there?

20. Jun 25, 2006

### CarlB

Well I read it and thought it was a cool article, but I'm not a lattice type. The "quadrilinear" terms added in equation (13) seems to have a resonance with the Koide mass formula for leptons, which suggests that the mass term should be bilinear. That is, instead of

$$m \bar{\psi}_L\;\psi_R$$

the "m" should be expanded as if it, too, were as bilinear as the fermion. Something like:

$$\bar{m}_{L}\; m_R\; \bar{\psi}_L\;\psi_R$$

which is quadrilinear. Now the above has two different fields going on, but I suspect that you can transform it to equation (13) of your reference:
http://www.arxiv.org/abs/hep-th/9503102

The upshot of the above is the bilinear lepton mass term is that the masses turn out to be simpler in form when their square roots are examined instead of the masses directly: That is, translating from QFT back down to QM, the mass term becomes:

$$|m\rangle\langle m| |\psi\rangle \langle \psi|$$

and the natural coupling is

$$\langle m|\psi\rangle$$

which has units of square root of mass. As in the reference you gave, this avoids the Higgs mechanism. My paper on it is here:
http://www.brannenworks.com/MASSES2.pdf

and Yoshio Koide has a Higgs type VeV explanation for the same mass relations here:
http://www.arxiv.org/abs/hep-ph/0605074

Now the other lattice equation, that of (14), is too complicated for me to understand. It looks like a spatial derivative, sort of, but has way too many multiplicative products. I guess I will take the word of the author that it is a correction term for SU(3) stuff.

But here's a question: Why are you having to put SU(3) stuff into a mass term for the leptons? Or did I miss something here? The authors are using "f" for fermion, rather than "q" for quark in equation (14), so that is why I think that this is what they mean. This is also evocative of the Koide formula because it can be thought of as relying on an assumption that the leptons are composites of colored preons that are bound in an SU(3) singlet state. So it's not surprising to see SU(3) stuff going into their mass.

I have to suspect that it is possible to walk this backwards and get a Lagrangian that works on continuous space time. Or is there some sort of problem doing this? Perhaps you can't get it to be Lorentz symmetric?

By the way, the paper should have the names of both authors listed on the title page.

Carl

Last edited: Jun 25, 2006