Quantum Gravity and the Standard Model (Sundance + PI)

[marcus]

http://arxiv.org/abs/hep-th/0603022
Quantum Gravity and the Standard Model
Sundance O. Bilson-Thompson, Fotini Markopoulou, Lee Smolin
12 pages, 21 figures

"We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic quantum dynamics. These are identified in terms of certain patterns of braiding of graphs, thus giving a quantum gravitational foundation for the topological preon model proposed by one of us.
These results apply to a large class of theories in which the Hilbert space has a basis of states given by ribbon graphs embedded in a three-dimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs, such as arise in the representation theory of quantum groups. For such models, matter appears to be already included in the microscopic kinematics and dynamics."Probably important.

=============================

also posted today:

http://arxiv.org/abs/gr-qc/0603008
Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks
Etera R. Livine, Daniel R. Terno
27 pages, 12 figures

"After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose to probe the structure of a surface through the analysis of the coarse-graining and renormalisation flow(s) of its area. We further introduce a procedure to coarse-grain spin network states and we quantitatively study the decrease in the number of degrees of freedom during this process. Finally, we use these coarse-graining tools to define the correlation and entanglement between parts of a spin network and discuss their potential interpretation as a natural measure of distance in such a state of quantum geometry."

 

[Kea]

http://arxiv.org/abs/hep-th/0603022
Quantum Gravity and the Standard Model
Sundance O. Bilson-Thompson, Fotini Markopoulou, Lee Smolin
12 pages, 21 figures

Cool!

 

[marcus]

Cool!

besides which Sundance is from Oz and amazingly attactive to women (even I can tell, it's not so difficult)

anyone who hasnt seen Sundance in action go here
http://streamer.perimeterinstitute....fa7-485f-8d5d-3b62fb7d3e4c&shouldResize=False
and flip to page 5
where he has a lecture called "Braid New World"
which you can view the streamer

the reason it is on page 5 is that it is dated 16 November 2005 and they list the most recent seminar talks first, so it is a pushdown stack and this talk keeps getting a larger page number as it recedes into the past

this is a great talk. I just watched some of it as a refresher. I recommend it without reservation.

 

[Kea]

besides which Sundance is from down under and amazingly attactive to women (even I can tell)

Marcus

Despite a long line of muscular beaus, I have never gone out with an Australian.

 

[arivero]

Note that one needs to get the previous papers (from Sundance, and the ones on preons quoted by Sundance) in order to get the feeling of the thread. Perhaps some chapters of Zee's book, on GUT theories and bits, could be of interest.

To me is a bit of surprise, I'd expect the standard model femions to be more a geometric object than a topological object.

 

[Kea]

To me is a bit of surprise, I'd expect the standard model femions to be more a geometric object than a topological object.

Categories make it geometric.

 

[marcus]

Note that one needs to get the previous papers (from Sundance, and the ones on preons quoted by Sundance)...

excellent suggestion
http://arxiv.org/abs/hep-ph/0503213
A topological model of composite preons
Sundance O.Bilson-Thompson
9 pages, 3 figures, submitted to Phys. Lett. B

"We present a modification of the preon model proposed independently by Shupe and Harari. A basic dynamics is developed by treating the binding of preons as topological in nature and identifying the substructure of quarks, leptons and gauge bosons with elements of the braid group B_3. Topological considerations and a straightforward set of assumptions lead directly to behaviour consistent with much of the known phenomenology of the Standard Model. The preons of this model may be viewed as composite in nature, and composed of sub-preons, representing exactly two levels of substructure within quarks and leptons."

we also had a PF thread called "Preons of Bilson-Thompson"
https://www.physicsforums.com/showthread.php?t=100183
that has some more links

 

[yanniru]

Lubos Motl makes fun of this paper on his blog today (i.e., QG & SM)
http://schwinger.harvard.edu/~motl/sf/frames.html

 

[arivero]

Lubos Motl makes fun of this paper on his blog today (i.e., QG & SM)
http://schwinger.harvard.edu/~motl/sf/frames.html

In this case I welcome Lubos' vents. The team of Smolin is doing here a risky bet and some moderation voice must be heard, even if it is Lubos. Knotting is an old art, legend tolds (I can not remember/quote the paper) that it was used even as an explanation of nuclear structure before the age of neutron and protons. And weaving the fermions into "Space-Time Code" is also a old dream nobody risks to touch (five dimensional and Connes-Lott theory have got a good step about weaving the bosons into).

Lubos asks how "the manifestly different octopi should transform as a representation of a group". Well, he asks "why", but I think that "how" it is already a good point to understand.

The other problem I see is how to put CKM matrix to play.

 

[marcus]

In this case I welcome Lubos' vents. The team of Smolin is doing here a risky bet and some moderation voice must be heard...

I enjoyed Lubos satire too---he is good at making fun. but I don't think his mockery is the kind of critical response that is needed

some "moderation voice must be heard" and I think there will inevitably be some thoughtful questioning responses (that go beyond Lubos mockery)

the critical evaluation was ALREADY INSUFFICIENT for Bilson-Thompson's paper of a year ago
http://arxiv.org/abs/hep-ph/0503213
A topological model of composite preons

this is possibly a very good idea and a way to generate the standard model particles with a small elegant set of components----it needs to be examined and either tried out in development or discarded---but it did not get enough examination

Smolin has given Bilson-Thompson preon model a lot of new visibility by making QG contact with it and connecting it to spin-network.

this involves risk, and that is part of the researcher's job I think
Since you, arivero, are skilled with humorous spanish proverbs I will challenge you with the obvious english proverb:
"Nothing ventured, nothing gained."

 

[arivero]

Hmm now I get the title of the thread. "Pi" got the "best director" award in Sundance festival in 1998. Darren Aronofsky was, the director.

 

[arivero]

Categories make it geometric.

Hmm I am not sure. We know that each fermion has a metrical quantity assigned, its mass. And we know that mass eigenstates do not coincide with charge eigenstates (thus cabibbo mixing). A preon model needs always to show how this kind of things, mass and CKM, are managed.

The electroweak group is very peculiar because it is doubly broken: the bosons are massive, and the particles in the same SU(2) multiplet have different mass.

 

[Kea]

And we know that mass eigenstates do not coincide with charge eigenstates (thus cabibbo mixing). A preon model needs always to show how this kind of things, mass and CKM, are managed.

The authors make it very clear in the paper that they are not answering these questions. When I mentioned categories, I didn't mean a simple re-interpretation of this paper, I meant a whole lot more stuff.

 

[Kea]

"Nothing ventured, nothing gained."

In this spirit:

Note that the reduced link of the electron (figure 17) is just the Hopf link, when the ends are connected up. Now taking Jones polynomials $J$ at 5th roots of unity for universal quantum computation, one finds that

$$J_{\textrm{Hopf}} = d = 1.618 \cdots$$

the golden ratio. Now let a deformation parameter be

$$q = e^{\frac{2 \pi}{2 + d}}$$

namely the $SU(2)_{q}$ conformal field theory expression. It is well known that the spin half rep quantum dimension is given by $[ 2 ]_{q} = q + q^{-1}$. Putting two of these electron graph invariants together one estimates

$$\alpha = 4 (q + q^{-1})^{2} = 137.08$$

This is of course an extremely coarse estimate, and hence not particularly accurate.

 

[marcus]

This is of course an extremely coarse estimate, and hence not particularly accurate.

Of course.
Had you performed the calculation more delicately it would doubtless have come out spot on 137.0359...

 

[marcus]

In the starter, a second paper was mentioned

http://arxiv.org/abs/gr-qc/0603008
Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks
Etera R. Livine, Daniel R. Terno
27 pages, 12 figures

"... to probe the structure of a surface through the analysis of the coarse-graining and renormalisation flow(s) of its area. We further introduce a procedure to coarse-grain spin network states and we quantitatively study the decrease in the number of degrees of freedom during this process..."

did anyone look at this paper? any reactions?
coarse-graining (which underlies the notion of entropy) has always been something of a mystery to me. so it sounds hopeful if one can define a regular "procedure" for coarsegraining----to me it would be like the philosopher's stone of the ancient alchemists, if you could actually say in generality what coarse-graining is then changing lead to gold would be mere childs-play.

 

[arivero]

In the starter, a second paper was mentioned

did anyone look at this paper? any reactions?
coarse-graining (which underlies the notion of entropy) has always been something of a mystery to me. so it sounds hopeful if one can define a regular "procedure" for coarsegraining----to me it would be like the philosopher's stone of the ancient alchemists, if you could actually say in generality what coarse-graining is then changing lead to gold would be mere childs-play.

Quicksilver to Gold is actually childs-play, as a look to the table of isotopic weights reveals On the contrary, lead to gold requires energy.

As for the paper, it also requires energy to get something out of it, it seems mostly a technical one, interested on how to recover classical distance from quantum gravity. I guess that via some decimation procedure, but I have not read it, only glanced over very very fast.

 

[Careful]

The Smolin octopussy leaves different impressions:
(a) it is an old an cute idea, especially the fact that you can get out the first generation of SM - particles from simple knotted configurations carrying only one type of U(1) charge is what I would like it to be. Actually, this resembles *very* much an old idea of Lorentz who postulated all matter to be electromagnetic in origin.
(b) I would at least expect the paper to contain the inclusion of the second and third generations of particles as well as a verification that all known *scattering* processes can be recovered diagramatically. It gave me the creeps when I noticed their toy model was about a noiseless dynamics...
(c) So, this is as LQG itself (not LQC) - all just kinematics, where is the (classical) dynamics which is supposed to:
(i) be invariant under some representation of the strong and electroweak groups
(ii) allows for the different effective dynamical (distributional) moves, including the ones which should account for interactions.
(iii) why do the fermions satisfy the pauli exclusion principle (under conditions where the spin statistics theorem is valid anyway) - I am not insisting that they should be spinors
(d) In principle, the theory could remain entirely topological : one could try to define the measure stick by counting the number of particles in chains containing particles of the same species. However, causal set practice learns that this is an almost impossible task to do and I would not bet my money on it.

Now is the time for hard work.

Cheers,

Careful

 

[Kea]

In the starter, a second paper was mentioned ... did anyone look at this paper?

Marcus

I glanced at it. It doesn't really belong in the same thread as the Sundance+PI paper. In the latter they emphasise a quite different view on classical limits when they talk about micro vs macro locality.

 

[f-h]

Smolin talked about this a bit at Loops05, John Baez says about this talk in week 208:

"Now that I've thrown around enough buzzwords to scare off the kids, I can tell you about Lee Smolin's talk, which was definitely X-rated: for adults only, people who can listen to speculations with just the right mixture of disbelief and open-mindedness."

It's an old idea indeed, Riemann, Einstein, Wheeler. Relativists have always thought about reducing matter to ripples in geometry. But matter is Quantum Mechanical so it's worth a shot now that we have at least a framework for a decent theory of Quantum Gravity/Geometry.

In this sense these ideas are extremely significant. If they pan out LQG predicts matter.

Just ponder that for a moment. Take a Lorentzian Manifold with geometry, quantize it, and you find matter degrees of freedom.

The next question then is if it predicts the right kind of matter.

 

[Kea]

Smolin talked about this a bit at Loops05...

Yes, f-h. Here is the link:

http://loops05.aei.mpg.de/index_files/abstract_smolin.html

Presumably the 18th root-of-unity rule was too speculative for the new paper.

 

[Mike2]

Just ponder that for a moment. Take a Lorentzian Manifold with geometry, quantize it, and you find matter degrees of freedom.

Wouldn't this mean that the geometry of emtpy space is determined by the virtual particles of the vacuum energy? And wouldn't this mean that the more curved space is, the more the ZPE is in that region? Thanks.

 

[Careful]

**
It's an old idea indeed, Riemann, Einstein, Wheeler. Relativists have always thought about reducing matter to ripples in geometry. But matter is Quantum Mechanical so it's worth a shot now that we have at least a framework for a decent theory of Quantum Gravity/Geometry.
**

I disagree in three ways:

(a) first at all: QM does not say *anything* about matter itself, only about its ``dynamics´´, remember the parameters in the standard model (particle masses, electron charge, the disputed mass of the Higgs and so on)! QM does not explain the appearantly ``discrete´´ (at least within some bounds of measurement) nature of elementary particles, it uses it. So, these are complementary ideas; therefore there is no a priori reason to wait for development in QG (whatever that may be) before one gives a unified matter model a shot. On the contrary, I think that the construction of a suitable matter model is indispensable for a good theory of microscopic phenomena.

(b) LQG is still being far form a THEORY of quantum gravity (they would better solve the Hamiltonian constraint first).

(c) I repeat that this paper does not really add much to already existing ideas and that the real problems in this framework are as wide open as they were before. One would expect more in depth results to be presented in such paper...

Cheers,

Careful

 

[marcus]

Discussion of the Sundance + PI paper at Christine's

http://christinedantas.blogspot.com/2006/03/quantum-gravity-and-standard-model.html

Jacques Distler and Lee Smolin converse about it.

follow the link and scroll down around 10 or 11 comments

 

[marcus]

I will copy exerpts of the discussion at Christine's to look at a bit more closely
=====quote from Christine's blog "QG and SM" thread=====

AARON
Gravatar Worse, and I'm trying to be as kind as possible here, Smolin and his collaborators seem to be confused about what anomaly matching means. It is a condition on the global anomalies of the theory. If it had something to do with gauge anomalies (which render a theory inconsistent), they wouldn't be of much use.

It's also a good thing. At least in the old preon models based on QFT, it was matching the anomalies that ensured that you got the 'massless' bound states to match up with the standard model spectrum.
Aaron Bergman | 03.09.06 - 5:34 pm | #
---------------------

LEE

3/09/2006 09:37:19 PM
Lee Smolin said...
Dear Johan,

In Sundance's original model there are vector bosons and rules that govern interactions. A consequence of the rules that govern the vector bosons is that electrons cannot turn into quarks. Whether or how those rules are realized in the quantum gravity embedding is still under study.

Dear Aaron, Thanks, but even if we expressed it in a way that confused you, the point is that the condition cannot be applied to this kind of theory. Do you have an argument that this is wrong? Beyond expressing your dislike, do you have an actual objection to any of the actual results of the paper? (the comment on amomalies being just a side comment and not a result.) By the way were it not for Christine's rule against personal comments I would protest your tone which as usual is a bit unpleasant. Rather than nitpicking on a side comment, do you actually have an objection against the main results of the paper?

Dear Christine, thanks very much for all the support. Its nice to be commented on in a blog where someone actually spends more than 38 minutes reading the paper and making fun of it.


Thanks,

Lee

-----------------
AARON

3/10/2006 12:57:38 AM
Aaron Bergman said...
Lee,

What am I supposed to make of the statement "we already know there is none, as it is the standard model."? The standard model has anomalies. Anomaly matching is a constraint on matching any effective field theory with some UV theory. If your UV theory doesn't have anomalies and if you claim that it really is a QFT, you have a problem. This is hardly nitpicking.

I chose to comment on this particular aspect of the paper because this is a well-known physical constraint on preon models and because it's fairly concrete. I don't have anything helpful to say about the rest.

-------------
JACQUES

3/10/2006 02:06:03 AM
Jacques Distler said...
Lee,

Since the Bilson-Thompson model does not have a Higgs, and you wish to take the compositeness scale to be the Planck scales, what is it that unitarizes W-W scattering at energy scales above a few 10s of TeV?

Of course, my vain attempt to pierce the fog of Bilson-Thompson's earlier paper did not reveal the vertices (which we know must be there) which lead to W-W scattering in the first place
------------
LEE

3/10/2006 11:30:46 AM
Lee Smolin said...
Dear Jacques,

These of course are very fair comments. We don't claim to have now more than we claim in the paper and, as I hope is clear, we are well aware of how much else has to go right before this is physics. At the same time, it is important to know that local excitations naturally arise in a large classs of quantum gravity models that might be elementary particles. Whether there are any such models that get elementary particle physics exactly right is of course an open question which we are only at the beginning of investigating. But it is a question that could not be asked before we had Fotini and Sundance's work.

Thanks,

Lee

-------------------
JACQUES

3/10/2006 11:44:20 AM
Jacques Distler said...
One more question, which is the issue that Aaron raised.

Normally, in a preon model, one expects all of the bound states to have masses on the order of the compositeness scale. (Think QCD, where the proton and neutron have masses of order the QCD scale, even in the limit of massless quarks.)

The 't Hooft anomaly-matching conditions are what guarantee, in preon models, that there are fermions with masses much much lower than the compositeness scale.

(If you want the gauge bosons to also be composites, then you have a much tougher row to hoe, as you need to find a mechanism by which the gauge-invariance, that ensures their masslessness, arises in the IR. But let's stick to the fermions.)

I found your response to Aaron a little unsatisfactory. There certainly are some conditions which would follow by attempting to impose the 't Hooft anomaly matching conditions on your UV theory. Do the quarks and leptons of the Standard Model saturate the 't Hooft anomaly matching conditions of your theory, or don't they?

======endquote=======

 

[marcus]

continuation:
======quote from Christine's blog======

LEE

Lee Smolin said...
Dear Jacques,

Thanks very much for clarifying the issue. Here is my understanding. There are three regimes in which you might compute currents and check for anomalies, 1) the fundamental Planck scale, which is a pure quantum gravity theory, 2) at a lower scale in which one includes the emergent conserved quantities, but still at a background independent level and 3) a low energy effective field theory.

The first is background independent (BI) and the only degrees of freedom are gravitational. There are no fermionic currents, so I don’t see what anomaly to compute. The second is the level where you identify the topological excitations. There are conserved quantities and they are chiral, so it might be interesting to study currents. But this is still at a completely BI level, so one cannot use our experience and intuition coming from background dependent quantum field theory. This raises interesting questions, deserving of study. Then, given two assumptions, there will be an effective field theory at scales much below Planck energies. These assumptions are that there is a low energy limit in terms of local fields on flat spacetime and the at the chiral braid excitations become chiral fermions in this approximation. Both assumptions are under study but neither have been demonstrated. But our point is that if this effective field theory exists it will have the particle content of the standard model.

Does this help? I can repeat that there is much to do before this can be claimed to be physics. At the same time I don’t see any argument involving anomalies pointing to an inconsistency of our results.

Thanks,

Lee
3/11/2006 02:36:59 AM
-------------------

JACQUES

Jacques Distler said...
First of all, stop assuming that every time someone uses the term "anomaly", they are trying to point to an inconsistency of your theory.

There are many uses of the term "anomaly" in high energy physics, and only some of them lead to inconsistencies of the theory.

In the case of the 't Hooft anomaly-matching conditions, the "anomalies" in question are actually your friends ...

As I said, in any preon model, all excitations will typically have masses of the order of the compositeness scale, unless something intervenes to make them light.

In QCD, I mentioned that the fermionic bound states (the proton and the neutron) have QCD-scale masses. So do the vector bosons bound states (the rho, ...). Only the pions are much lighter than the compositeness scale. And they are light because they are pseudo-goldstone bosons.

Some of your chiral braid excitations (you think) become fermions. Some (you think) become vector bosons. In both cases, you would expect them to have masses of order the compositeness scale (the Planck scale) unless something enforces that they are light.

I've already discussed the fermions.

Let's turn to the vector bosons. In QCD, the rho is heavy. But you could have light composite vector bosons in your model if, by some mechanism, a gauge symmetry emerges which forbids a mass for them.

So ... how does gauge symmetry emerge in your model?

In Bilson-Thomas's version, this is quite unclear. He doesn't have the various gluon self-interactions (nor, crucially, the relations between them) required for the emergence of SU(3) gauge symmetry.

He doesn't have a Higgs, so the SU(2)xU(1) gauge symmetry is *explicitly* broken in his model. Which is even more bizarre, as I don't see why the Ward-Takahashi identities satisfied by the couplings of a spontaneously-broken gauge theory should be satisfied by his explicitly-broken one (indeed, many of the couplings which should be there ... aren't).

For that matter, I don't even see why the photon is massless in his model.

Moreover, as I said above, if, by some miracle, it were true that his theory corresponded to a (Higg-less) Standard Model, it is quite impossible for a theory with (just) those degrees of freedom to exist above a few 10s of TeV. Certainly, it could not exist all the way up to the Planck scale.

Something else that you said to Aaron above greatly puzzled me. You said that lepton- and baryon-number violating processes are explicitly forbidden in your model.

Do you mean that as a perturbative statement, or as a statement about the exact quantum theory?

3/11/2006 04:38:21 AM
--------------------------------
[edited to focus on Smolin Distler dialog]
--------------------------------

JACQUES

Jacques Distler said...
Well, Christine, I would have said that the fact that W-W scattering violates unitarity at energies above a few 10s of TeV (unless some new degrees of freedom, like the Higgs, appear in the theory at that scale to restore unitarity), is enough to kill the Bilson-Thompson theory, and anything built upon it.

This is a low-energy statement -- 15 orders of magnitude below the Planck scale -- and so cannot be saved by any magic happening at the Planck scale.

There are many, many other things that are rather unclear. Perhaps they can be explained by saying words like "background independent quantum field theory" and "Planck scale physics".

But physics at the scale of a few TeV is described by conventional quantum field theory (with gravity decoupled) and none of those magic words are relevant. In fact, in just a couple of years, the LHC will directly probe that regime, and will discover the Higgs (or whatever replaces it).

I jumped in here because it looked to me as if Aaron's questions were not being adequately addressed. Having gotten something of a response, perhaps it would be best if I faded away, again, and returned the discussion to its regular participants...

3/11/2006 10:51:32 AM
--------------------------------

LEE

Lee Smolin said...
Dear Jacques,

Thanks for your comments. I do not want to overclaim-one feature of the quantum gravity world is that we are careful and don't hype and overclaim- Fotini and I had an argument several years ago which showed that elementary particle states emerge from background idnependent quantum gravity theories but we sat on it until we had precise results. The importance of these results is that now we know that theories related to LQG are unified theories--they contain elementary particles. So the question is now, are there theories that have the right elementary particles and forces? This new paper is an indication that the answer is not obviously no. You know as well as I that a lot of handwaving can and has been done about gauge interactions emerging, both by condensed matter and high energy physicists. I hope note is taken that we are not engaging in such hand waveing. At the same time, the possibility is there and we are working on this, among several other open questions.

Now, if I understand your comments, you basically dismiss the whole effort because we have not yet shown that all elementary particle physics comes out exactly right. I agree the problem of how light states emerge is key, but I would ask for a reasonable amount of time and tolerance.

This is a completely new idea and approach and there is a lot to do. String theory has had more than 3 decades from the time it was realized it was a potential unified theory, and despite work of on the order of a thousand people over these decades there are still no clear predictions. So is it really wise to throw out a new discovery that may lead to a unified theory of elementary particles, the week it is posted, because three people were not in a few months able to solve all the open problems of elementary particle theory? Wouldn't it be wiser to give it some time?

Indeed, why not get involved yourself? The problem of anomalies in a background independent theory needs to be studied. Perhaps you could lend your considerable expertise to this?

Thanks,

Lee

3/11/2006 01:53:29 PM
====endquote=====

 

[Kea]

Well, interesting. It seems to me that Lee isn't really listening to Jacques, who was actually being very polite, and also that Jacques isn't really listening to Lee, because the background independence argument really does mean that Jacques' foibles about Planck scale masses need to be addressed from outside ones QFT intuition.

 

[marcus]

...Jacques' foibles about Planck scale masses need to be addressed from outside ones QFT intuition.
...

I think so too. Tell me if you agree or understand what I say next.

It would actually be INCONVENIENT (or worse) if Sundance preon scheme predicted a Higgs.

Because mass is how matter curves space----the mass-maker should be interaction with the spin-network state of space itself.

One could say, figuratively, that the quantum state of geometry----the spin network----IS the Higgs. Or how matter couples with geometry is the Higgs.

So if one is going to incorporate a preon model of matter into spin network or spinfoam gravity, then it is better if the model should NOT have a higgs. The mass-making will arise from the way the preon model is COUPLED INTO the QG model.

==================

but I think that Smolin WAS listening carefully to Distler and he knew just how much he could say to Distler (who I suspect was uncomfortable and wanted out as soon as he could) without evoking total incomprehension and consternation on Distler's part.

He knew that Distler was focused on the expectation that the next collider will bring us all Higgs for christmas. It is the devout wish from the conventional QFT view. He realized, or so i think, that he simply could not say to Distler, look my approach may well be wrong and we need to develop and test it, but in my approach we DO NOT NEED the kind of Higgs you have in mind. We do not want that sort of thing to come out of Sundance topological preons---it would just get in the way!
===============

does this make sense to you Kea? or even is it a fair elaboration on what you said?

 

[Kea]

It would actually be INCONVENIENT (or worse) if Sundance preon scheme predicted a Higgs.

Yes, of course, I agree. The SM does not explain masses. Period.

You need Gray category cohomology for that!

 

[Mike2]

Yes, of course, I agree. The SM does not explain masses. Period.

You need Gray category cohomology for that!

Does category theory and topos theory try to define sets independent of any underlying point set topology? Is this why it is useful in background independent efforts? Is topos theory the underlying mathematics of Algebraic QFT which define an algebra of operators (and not states) in order to get away from the background dependence of states?

If so, where can I get a good introduction to topos and category theory? Thanks.

 

[Kea]

If so, where can I get a good introduction to topos and category theory? Thanks.

Hi Mike

The answer to all your questions is yes. There are lots of references on the Third Road thread. We shouldn't go OT.

 

[f-h]

I think so too. Tell me if you agree or understand what I say next.

It would actually be INCONVENIENT (or worse) if Sundance preon scheme predicted a Higgs.

I don't know if this is correct. Energy curves spacetime, in the Higgs mechanism there is a universal energy scale arising from the vacuum that appears as mass effectivly through interacting with the particles.

If you put matter on a Spinfoam by hand (as Freidel and a slew of others are doing at the moment) it will alter the vertex (and possibly edge?) amplitudes, and this induces the matter curving spacetime. It's not at all clear that mass should have gravitational origins, and Distlers statements are correct in so far that we can not expect Planck scale physics to replace the Higgs mechanism (incidentally I jokingly suggested just that in my group a while ago and got the immidiate response that it was totally unfeasible).

However, we are very far from understanding what kind of particle like excitations exist in LQG and how they behave (especially dynamically). LQG pqrticle physics is still infintesimal at the moment, in so far Distler is right that these successes of standard particle physics are not mirrored in the new approach, and Smolin is right that it's to early to say that they can't be.

 

[selfAdjoint]

Distlers statements are correct in so far that we can not expect Planck scale physics to replace the Higgs mechanism (incidentally I jokingly suggested just that in my group a while ago and got the immidiate response that it was totally unfeasible).

So this is apparently a no-brainer for the physicists who are deep in stringy analysis. Can you expand the reasoning for those of us can follow it but not generate it?

 

[Mike2]

Does category theory and topos theory try to define sets independent of any underlying point set topology? Is this why it is useful in background independent efforts? Is topos theory the underlying mathematics of Algebraic QFT which define an algebra of operators (and not states) in order to get away from the background dependence of states?

Hi Mike

The answer to all your questions is yes. There are lots of references on the Third Road thread. We shouldn't go OT.

Delightful! So could it be that we have a new paradigm on which to construct a TOE: that the universe can be derived on pure logic (of sets) as long as those set operations are true independent of what those sets contain or how big they are or how they change? Is this what Topos theory of Catagory theory offer?

 

[marcus]

... in so far Distler is right that these successes of standard particle physics are not mirrored in the new approach, and Smolin is right that it's to early to say that they can't be.

I can go with that
thanks for putting it succinctly
sounds like a fair summary to me