Don't mess with the pass integral

[atyy]

@atyy: I don't think that there is a problem with the "causal restriction". This is true if you do ordinary QFT on a given background. But that's not the case; you try to construct the basic building blocks and there is no reason why you should use a building block X and not use a building block Y. Look at ordinary QFT: you just select a few fields (scalar, spinor, vector), write down the PI and check if it works. Of course you made a selection, but in the end nature will tell you if the selection was correct.

I wasn't thinking about a problem with the causal restriction per se, but in the context of CDT being an approximation to AS.

 

[Fra]

My idea was not to interfere with other approaches

Mmm given the first line in my previous post, I don't know if you refer to what I wrote? If so, my comment was not directed to you, I was more having S.Daedalus post in mind, commenting on how discrete infomation process influence "counting histories".

I just made the statement that My comment was not interfering with the LQG discussion here, since my thinking questions the LQG abstractions which has been discussed before it was better to state that my comments doesn't refer to LQG or CDT, it's more referring to the general construction of physical measures, rather than mathematical ones.

/Fredrik

 

[tom.stoer]

Fredrik, it's OK; we were both too polite :-)

 

[Micha]

Let me repeat my last sentence: Perturbative quantum gravity is nonsense.

Ok, so that is a pretty strong claim. Where is the reason?

 

[tom.stoer]

b/c all calculations in perturbative gravity over the years failed due to several reasons

1) gravity is (by power counting) not perturbative renormalizable
2) perturbative gravity violates background independence
2b) perturbative quantization uses a fixed causal structure which cannot be subjetc to dynamical changes by construction; this is unphysical
3) all approaches to QG use some additonal input (strings, SUGRA, LQG, ...) or method (AS, CDT)

Clearly the third point is a response the 1+2). Perturbative non-renormalizability is a hint that for UV completion some essential input is missing. So either you complete the theory by introducing new concepts (like in SUGRA - which has not been proven to be well-defined, but were one has at least strong hints for finiteness of certain SUGRAs in D=4), or you use non-perturbative techniques.

The difference becomes clear in AS where a non-gaussian fix point is assumed. This is a generalization of asymptotic freedom (all couplings tend to zero in the UV).

 

[marcus]

Just a footnote on what was just said. The grav field is unusual in that it determines the causal relations among events. (4d geometry determines lightcone structure.)

Suppose you fix a background, then you are committed to a web of causality. Now you perturb, by superimposing a ripple on the background. Previously assumed causal relations are now strictly invalidated.

Perturbative treatment of gravity is in a fundamental way unphysical compared to perturbative treatment of other fields.

 

[tom.stoer]

I'll add this to my list in post #40

 

[Micha]

b/c all calculations in perturbative gravity over the years failed due to several reasons.

You mean all calculations in QFT. In string theory pertubation theory for gravity works just fine.

 

[Fra]

There are a lot of things that one could discuss about these things, but I'm not sure what we're discussing beyond commenting on Lubos "analysis" but...

Not too unlike the notion of B/I, perturbative or non-perturbative ways can be discussed at two levels I think. I'm not sure if this is obvious but it may help to point it out.

The very simplest view is that perturbation theory is simply a mathematical method, to find the solution to a given well defined problem that's hard to solve, from "perturbing" a known solution, and then somehow expand the full solution in terms of the order of perturbation. Now if the perturbation can't be shown to converge, then the whole technique fails. To save the scheme one might try to renormalize the known solution, to a different one and the see if we get convergence.

So far this can be discussed in terms of a mathematical method; there is no "physics" in this picture!

But the more interesting perspective, which does contain the physics, is that if we take an inference perspective to physics (like I do) then we also try to predict the future, given the present. In a sense one can abstract that as picturing "perturbations" of the present, so that we can produce expectations of the future from the perturbation of information. This is a physical picture (if you take the inference view; which btw isn't just silly comp sci analogies, it can be seen as an extension and purification of the essens of measurement theory as interaction or communication theory).

In this latter view, the perturbation, and the prior (which is to be perturbed) are physical. So the PHYSICS is actually in the perturbation details - and it's actually the non-perturbative idea that is non-physical. The non-perturbative formulation simply doesn't exists, and the interaction properties between two systems is encoded in their abilities or INabilities for that matter, for two perturbative expansion to negotiate and find an equiliribum.

This latter thing, would mean that what's sometimes called "problems" actually could explain interaction phenomenology (if developed properly in the future).

Actually what I would call unphysical non-perturbative techniques in the second view, is really pretty much a form of structural realism, which a lot of people subscribe to (except me).

/Fredrik

 

[tom.stoer]

You mean all calculations in QFT. In string theory pertubation theory for gravity works just fine.

I do not mean QFT, but exactly what I wrote - perturbative gravity - w/o any new formalisms, ingredients etc.

Regarding perturbative string theory: it is well-known in string theory that perturbative calculations are not sufficient; look at all the dualities, M-theory stuff, AdS/CFT, lack of a background independent formulation, ... all these ideas have been discussed in the literature (and here in this forum :-); they clearly indicate that even in string theory perturbation theory alone is not sufficient. I think that applies to maximal 4-dim SUGRA as well; even if finiteness can be proven order by order it is by no means clear that the whole series does converge.

Btw.: afaik it has not been proven that string theory is finite to all orders in perturbation theory; it has not been proven that the perturbation series as a whole does converge. That means that in string theory - as in any other QFT - perturbation theory is valid only in a very restricted regime.

 

[Fra]

I'm not disagreeing with what Tom wrote but I thought I'd just expand on this to illustrate further the subtle point I tried to make. I don't know if anyone appreciates the distiction though:

perturbation theory is valid only in a very restricted regime.

Seen as a mathematical method to solve a mathematical problem, this then of course means the method fails and simply isn't working. Just forget it, and try to find another solution method.

But, in the second perspective above, this isn't necessarily bad. Since it's not possible to have detailed expectations infinitely far into the future. The expectations are still bounded by the observers ability to formulate and encode possible future information states. So this "unability" to produce an expectation of an infinite future, is not a flawed technical method, it is (in the second view) how nature works(*). In particular this would suggest that the action of the observer (think PI) simply doesn't sum over all these unformulable possibilities, it is formed only over the physicall distinguishable and encodable. So this indeed makes the actions different.

I'm not suggesting here that this means that perturbative ST is OK, although no one has prooved convergence to all orders. This is because string theory does not IMO quite fully implement the second perspective properly.

But in other approaches, it could be that the "perturbation scheme" does not in fact correspond to physics, and not ONLY mathematical methods.

This is what I see a third way except sticking with perturbation theory in despite of it's possible non-convergence, or insisting on non-perturbative solutions. The third way could be to try to understand how even in the physical picture (future beeing a perturbation of the present; and the expected action sums over POSSIBLE expected futures only) what can be seen as perturbations. This latter unifies I think even more than renormalization as we konw today, interactions and observer-observer transformation and it should hold falsifiable predictions as this schemes puts constraints on possible interactions.

(*) IMO it's even the seed to understand causality and event order in nature as it imples action upon information at hand only.

/Fredrik

 

[Demystifier]

What about lattice QCD? It is a discrete path-integral theory, and yet it is in excellent agreement with observations. Would Motl say that lattice QCD is wrong?

 

[tom.stoer]

What about lattice QCD? It is a discrete path-integral theory, and yet it is in excellent agreement with observations. Would Motl say that lattice QCD is wrong?

Good question.

The point is that lattice QCD breaks certain symmetries (translational, rotational and Lorentz invariance) which should be (approximately) recovered in the continuum limit. So the issue could be that
a) in lattice QCD small violations of these invariances do not matter as they are small in the constinuum limit
b) lattice QCD is not a definiton of QCD but a calculational tool in a certain regime
c) breaking of the above mentioned theories is not as severe as the breaking of symmetries of QG (diff.-inv.?)
d) strictly speaking there is no continumm limit in the ordinary sense in QG as there is no artificial scale applied from the outside; the theory itself defines the scale and therefore sending something to zero is not possible

But in order to be sure one should ask Lubos

 

[Demystifier]

b) lattice QCD is not a definiton of QCD but a calculational tool in a certain regime

I think some lattice people would say lattice QCD *is* the definition of QCD, because QCD without a cutoff cannot be properly defined at all.

And LQG people have a similar reasoning about quantum gravity - that only discretization (in terms of networks or something alike) makes quantum gravity properly defined.

 

[tom.stoer]

Yes and no.

The lattice in lattice QCD is somehow artificial as the lattice people will eventually send the lattice spacing to zero which means they do not believe in a discretized spacetime. In that sense it's a calculational tool only. And it certainly does apply in all cases; e.g. scattering like DIS cannot be calculated using lattice QCD.

But I agree that regardign to the Wilsonian renormalization group approach requires some UV cutoff; lattice QCD is just one method to do that.

Lattice QCD is rather different from LQG. In lattice QCD the lattice is introduced as a calculational tool, whereas in lattice QCD the discretization is derived using loop space + diff. invariance. There is no parameter which can be controlled and send to zero at will (but I agree that in different approaches like triangulation / spin foams the discrete structure is introduced by hand - and that we are currently not sure about the final result of all these theories :-)