Quantum Gravity and the Standard Model (Sundance + PI)

[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

 

[marcus]

... 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 immediate response that it was totally unfeasible).
...

I'd be happy if you would expand on that----as selfAdjoint also suggested. My understanding is that you are at Marseille and your group would be at the cpt there. If THEY say that it is "totally unfeasible" for Planckscale physics to replace higgs mechanism, that is really interesting to me. I would like to know anything you can give of the reasoning.

 

[Mike2]

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.

Thanks for asking this, marcus. I was going to ask this in a different form. I was going to ask if curved spacetime IS the "false vacuum". Previoiusly, the Higgs mechenism relied on a false vacuum discribed as a field precariously balanced at a high potential. And as the universe cooled, this field dropped in potential and gave up a Higgs boson which interacted with massless particles to give them the mass that we now see. But I wonder if a curvature of spacetime might also work as a false vacuum (or a vacuum of higher potential). Since we know that curved spacetime is accompanied with a mass/energy density, it might be that as spacetime becomes flat, this energy is given to bosons or otherwise results in particles.

I was inspired in this curiosity as I read in R.M Walds book on QFT is curved spacetime that there is no particle discription in transient curved spacetimes. And how N. D. Birrell book, Quantum Fields in Curved Space, is used to show how the first particles arise from the expansion of the universe. So if geometry also give rise to particles, there doesn't seem to be the need of an extra Higgs field to account for mass.

 

[marcus]

Thanks for asking this, marcus. I was going to ask this in a different form...

yes, I had better make extra clear that it is now definitely a QUESTION and not a statement! In fact f-h has contradicted what i said earlier---and I am waiting for him to say more about it.

If I understand f-h, it is accepted by (at least some, perhaps all) QG experts that there must be a higgs, and that inertia cannot be the result of how particles couple to the geometry-----and, if I understand him, it is definitely a FLAW in Sundance preon model that it does not predict a higgs.

If I am misinterpreting him I hope he corrects me on this, and also I hope he elaborates on this a little and explains the reasoning.

I hope we get some more comment on this.

 

[Mike2]

If I understand f-h, it is accepted by (at least some, perhaps all) QG experts that there must be a higgs, and that inertia cannot be the result of how particles couple to the geometry-----.

Wouldn't geometry have to be observer dependent? The faster objects move (with respect to you), the more mass and therefore the more curved space is perceived around that object? So if the laws of physics are velocity independent, then aren't they also background (geometry) independent?

 

[Kea]

Distlers statements are correct in so far that we can not expect Planck scale physics to replace the Higgs mechanism...

The only problem with this statement is that it sounds suspiciously like you mean Planck scale physics literally. This is not what Sundance et al. are talking about, though I agree their paper is very foggy on this point.

 

[f-h]

I'm at the CPT, so I'm not stringy and I'm only starting, certainly not deep in this as of yet, so take what I say with a grain of salt. That comment should not be overrated. I mostly meant that having a Higgs would not be "inconvenient or worse" for Quantum Gravity matter, it would cause the right masses to emerge, and these masses to curve spacetime just as it does if you couple the classical standard model+Higgs to classical GR.

We expect Quantum Gravity to provide lot's of effects for us. But the relevant scale should be the Planck scale. The Higgs mechanism provides an energy scale, too, in this sense it might seem like we could do with only the Quantum Gravity scale, without Higgs, but physically that scale is two dozens order of magnitude off. So how do you explain the emergence of mass scales as low as 0.5 MeV from 10^23 MeV Planck scale? If there is a mechanism for this it's "exotic" and not natural from the knowledge we have today. So while we can't rule it out (my totally unfeasible was probably to strong), we can't expect it to happen "naturally" either and nobody seems to have any idea how it could look.
I (wildly) guess if a mechanism for this exists naturally then you would be a good step closer to solving the hierarchy problem.

Distlers following statement basically seems to sum it up to me:

"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."

If this is wrong it's going to be wrong subtly. The point is that there must be some mechanism at the TeV scale, and this is likely to be explainable in terms of effective field theory. No effective field theory derived or conjectured to arise from LQG has such a mechanism so far.

On a lunch time group vote if we expect the Higgs to be found there was a slight majority for "no". The overall mood is that it'll be far more exciting if we find an alternative mechanism that tells us something structurally new about nature. But I don't think anybody expects that we'll see Quantum Gravity at the LHC instead of the Higgs.

But as I said, this was lunch conversation please don't overrate/quote/take serious. ;)

 

[f-h]

The only problem with this statement is that it sounds suspiciously like you mean Planck scale physics literally. This is not what Sundance et al. are talking about, though I agree their paper is very foggy on this point.

Could you expand on this?

 

[Kea]

We expect Quantum Gravity to provide lots of effects for us. But the relevant scale should be the Planck scale.

This statement is the problem. The Sundance+PI paper talks about pregeometry. One does not begin by invoking Planck scale geometry. Now, the Higgs mechanism is clearly very, very important for understanding the Standard Model. However, this does not necessarily mean that a Higgs particle is observable. If one takes geometric mass generation seriously, which some of us do, there is little insight available from the SM. Dare I mention again that the confinement of quarks, ie. their unobservability, has been understood in terms of (pre)monoidal structures, which are very closely related to the knotty type diagrams of the paper under discussion. But who knows what this means? Everyone would like to see a rigorous formulation of the SM. It is unfortunate that we will not have it before the LHC switches on. C'est la vie.

 

[Haelfix]

It doesn't make a difference if the Higgs is replaced by some weird geometrical mass generation (or whatever you want), the point is you have an electroweak symmetry breaking scale that we know has to be there for many reasons, and is some 15 orders of magnitude larger than anything the Planck scale can give.

In order for the particle content of their gravitational theory to match the standard model (a massive effective theory with anomalies as pointed out), they will essentially have a reverse hierarchy problem that is almost guarenteed to go horribly wrong in the IR b/c they have absolutely no residual gauges... This is a disaster, in fact its uncountably infinite times worse than working the other way around.

 

[Kea]

...they will essentially have a reverse hierarchy problem...

Yes.

This is a disaster, in fact its uncountably infinite times worse than working the other way around...

That remains to be seen.

 

[f-h]

Hmmm... I don't neccesarily see that statement as geometric. These ribbon graphs have an interpretation as particles, and they are also topological excitations of the quantized gravitational field (Rovelli always emphasizes that we should think of the gravitational field as a field rather then a geometry). If we write an effective field theory describing these excitations the natural physical scale to appear would be the Planck scale.

In other words, the point is, at what energy scale relative to the emergent classical world we see, do we expect what effects to show up? No matter what the structure of matter is if the mass maker is the interaction with the spinnetwork/the quantized gravitational field, the natural scale is the Planck scale...

That said, I don't understand half of your post so I'm not sure if we are at all talking about the same thing...

 

[Kea]

If we write an effective field theory describing these excitations the natural physical scale to appear would be the Planck scale...

If they were doing standard LQG - yes. But they are not. What they are doing is far from clear, but it's not that.

 

[f-h]

Lee Smolin said on CDs blog:

"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."

I don't think he sees this approach as outside the LQG framework.

On the point of pregeometry, I suspect it's highly feasible that the geometric meaning of LQG/Spinnetworks will emerge only once we understand how particles emerge first. In fact handwaving arguments suggest that you need (to identify) extra structure to define proper gauge invariant area and volume operators (to specify a certain region in a background independent, and hence relational theory you need something you can relate it too, like the value of a certain other physical field interacting with the spin network). That's how I understood their comment in the paper. But I don't see how that influences the scale argument...

 

[Kea]

From the bottom of page 9:

In summary, there are distinct ways for a spacetime geometry to emerge from a quantum theory. At one end of the spectrum lies the expectation that classical spacetime geometry will emerge as the classical/low energy limit of quantum general relativity (as in Loop Quantum Gravity) or a discrete and quantum version of Einstein's theory (as in Causal Dynamical Triangulations). Matter fields are to be added and coupled to the quantum geometry. At the other end, one may expect that the emergent spacetime is the collection of events that are the interactions of the excitations of an underlying pre-spacetime quantum theory, with matter being also emergent as these same excitations.

They then refer to Lloyd, the well-known Quantum Computation person. Of course, if Lee would say something here himself then I could shut up, but I think it's very clear that they are not talking about standard LQG, although the idea of networks may well be interpretable within that language.

 

[Kea]

...its uncountably infinite times worse...

Interesting concept!

 

[f-h]

I see, you are saying we should think of the process as more symmetric between geometry and particles, we are also mixing up several different questions here, I don't think your objection relates to marcus original point that particle/spinfoam interactions should naturally replace/explain the Higgs mechanism, does it?

I still don't understand how this avoids the scale argument. If spacetime should emerge the same way as particles as configurations of this pregeometry (the loop spaces), then you need to explain why particles emerge and drastically different Energy scale then geometry.

On the other hand wrt your point, our best idea about how geometry emerges from Spinfoams is LQG in particular the Area/Volume operators, that particles emerge at all is surprising but it seems for the moment that there is nothing on the table that could explain why they should emerge at such different energy scales either, right?

 

[Careful]

** At the other end, one may expect that the emergent spacetime is the collection of events that are the interactions of the excitations of an underlying pre-spacetime quantum theory, with matter being also emergent as these same excitations.[/i] **


I am glad you underline this point yourself; since I remember you or Hossi being sceptic when I told that it is meaningless to study vacuum ``quantum gravity´´. Option (a) is simply bogus.

**
They then refer to Lloyd, the well-known Quantum Computation person. **

I see you still did not detect the mistakes in his ``fundamental´´ paper; probably you did not read that one either.


Careful

 

[rtharbaugh1]

Consider an infinitesimal dust evenly distributed in an open, infinite universe...(Mach space?) Is there any gravity? In other words, can we think of gravity except in

the local, perturbative sense?

Consider the scale in such a universe at which perturbations just begin. That scale must expand as the effect of the perturbations reaches longer and longer lengths.

So the scale at which perturbations just begin must be an expanding scale. Below this scale, the infinitesimal dust loses its continuity and begins to become

discrete...that is, local effects begin to predominate. Particulate matter then would be a sort of clumping or curdling of the infinitesimal dust.

Now as the perturbations expand and as the dust clumps, we observe that there are some consistant parameters. The clumps tend to settle into certain classes of sizes.

There are preferred scales. They may be expanding scales, but they have a consistant particulate horizon as they expand. The neutrino, the electron, and the proton

are examples of these horizons. The preferred scales also occur at much lower energies, as planets, stars, galaxies, but at some scale the number of possible states

becomes essentially infinite, and the appearence of continuity is restored. So we have all sorts of masses and sizes of rocks. At a slightly higher energy the clumps

have much more limited possible states, and we have the table of elements.

We have to ask ourselves then why some states are preferred, and why the number of preferred states seems to vary with scale. Is there some fundamental geometric

relationship in the infinitesimal dust which results in preferred states? Might the infinitesimal dust mites have some definite shape that causes them to prefer to pack

in certain groupings, such that certain numbers of them tend to be stable, while a few more or less tend to be unstable?

How can we make sense of the standard model, at which scale there seems to be a perfect uniformity, with every clump of matter as far as the eye can see existing in

one or another of only a few possible states?

Just wondering.

R.

 

[Kea]

...since I remember you or Hossi being sceptic when I told that it is meaningless to study vacuum ``quantum gravity´´.

Careful, I have always thought it was meaningless to study vacuum QG. I'm sorry if I somehow gave you another impression at some point.

 

[Kea]

...then you need to explain why particles emerge and drastically different Energy scale then geometry.

f-h

No one is claiming to have solved the (reverse) heirarchy problem. Also, remember that energy scales themselves are part of the geometric question.

 

[Kea]

I see you still did not detect the mistakes in his ``fundamental´´ paper; probably you did not read that one either.

I'm quite happy to admit that I have no interest whatsoever in reading Lloyd's papers. This thread is about what Sundance+PI are thinking.

 

[f-h]

f-h

No one is claiming to have solved the (reverse) heirarchy problem.

Ok, so I guess we are in agreement after all and I just misunderstood what you were saying.

My original statement was that:
"We can not expect Planck scale physics to replace the Higgs mechanism." where I meant gravitational spin networks with "Planck scale physics" and I erronously read your statements as a response to that.

Back on topic, do you have references to ideas how to get geometry from this kind of ribbon graph quantum theories in a non LQG way? I would be highly interested in that...

 

[Kea]

Back on topic, do you have references to ideas how to get geometry from this kind of ribbon graph quantum theories in a non LQG way? I would be highly interested in that...

Dear me, f-h, this is just what category theoretic M-theory is all about. Yes, I mean String theory. I'm afraid a lot of people would consider that very off-topic.

 

[Careful]

Careful, I have always thought it was meaningless to study vacuum QG. I'm sorry if I somehow gave you another impression at some point.

Ah, then it was die schone Hossi. But don't misunderstand me, I find some points of the Sundance paper(s) interesting, but they do not serve for LQG purposes...

Cheers,

Careful

 

[Kea]

But don't misunderstand me, I find some points of the Sundance paper(s) interesting, but they do not serve for LQG purposes...

I completely agree.