A critical look at strings - Carlo Rovelli

[suprised]

Well whenever you have a cutoff scale things will be finite. The question is whether the quantities you compute depend on this cutoff in a bad way or not; conventional QG is non-renormalizable, so even if you put a cutoff, the theory depends on it in a bad way, ie. you need to specify an infinite amount of data in order to make sense of scattering amplitudes. I am not sure how LQG deals with this problem; in ordinary QFT, putting a non-renormalizable theory on a discrete lattice and thereby regularizing divergences by brute force, does not really solve this problem. Perhaps someone else can explain whether/how in LQG higher order quantum corrections are rendered harmless, in this sense.

 

[haushofer]

But how does one concretely calculate for instance interactions in LQG if spacetime is discrete? How are e.g. integrals defined in the first place (without worrying about cutoffs)?

To which extend is one able to do real calculations in LQG and check this statement explicitly for explicit cases?

 

[atyy]

UV usually requires a metric to be defined. Since there is no metric, there are no UV divergences (if I understand Rovelli's use of language). There are nonetheless potential divergences analogous to UV divergences https://www.physicsforums.com/showthread.php?t=517464

 

[suprised]

I guess LQG is in the "wrong phase" for doing such calculations. Because such calculations need a background around which one perturbs, one would first need to develop an appropriate framework to even formulate the problem. It seems strings can provide the appropriate framework for this kind of problems. It is hard to see how one could avoid the geometry of riemann surfaces (ie their moduli spaces) if one wants to have unitary scattering amplitudes. This is an extra ingredient that goes beyond usual QFT.

If in such a "broken" phase LQG would just reproduce gravity with a cutoff, then most likely it would not be consistent. Or perhaps it would be equivalent to strings (which however would imply extra degrees of freedom, so it is not standard gravity).

Again, the issue is not just finiteness. It is also about consistent, unitary scattering amplitudes.

 

[marcus]

I guess LQG is in the "wrong phase" for doing such calculations. Because such calculations need a background around which one perturbs, one would first need to develop an appropriate framework to even formulate the problem...
... scattering amplitudes.

But one can introduce a specific background as a context for calculating scattering amplitudes.
Nothing says that in a background independent theory one cannot specify a given background for some particular purpose.

In Lqg this is done by fixing the quantum state of the boundary geometry, and then some n-point function calculations have been made. This has some references:
http://arxiv.org/abs/1105.0566

 

[mitchell porter]

http://golem.ph.utexas.edu/~distler/blog/archives/000855.html#c003962", Jacques Distler managed to establish that he and Lee Smolin meant different things by "UV-finite".

One interesting thing about the recent LQG developments (also see https://www.physicsforums.com/showthread.php?t=520125") is that the continuum may be reappearing, as an infinite refinement of a spin foam, produced when the Immirzi parameter flows to zero. This does look promising as a framework in which the particle physics perspective can be embedded.

 

[atyy]

One interesting thing about the recent LQG developments (also see https://www.physicsforums.com/showthread.php?t=520125") is that the continuum may be reappearing, as an infinite refinement of a spin foam, produced when the Immirzi parameter flows to zero. This does look promising as a framework in which the particle physics perspective can be embedded.

http://arxiv.org/abs/1108.2258 "We have disregarded other possible contributions to the amplitude (symmetry related spacetimes, vector geometries, degenerate geometries etc.) that could spoil the correct semiclassical behaviour."

They then mention a specific term - but there is no consensus on what to do with it.
http://arxiv.org/abs/0808.1107
http://arxiv.org/abs/1107.0709

 

[marcus]

UV usually requires a metric to be defined. Since there is no metric, there are no UV divergences (if I understand Rovelli's use of language). There are nonetheless potential divergences analogous to UV divergences https://www.physicsforums.com/showthread.php?t=517464

I can't think of any connection between what you say and anything I've ever seen from Rovelli or anyone else writing about loop gravity, Atyy.

It bears no resemblance to any loop researcher's discussion of UV finiteness as far as I know.

Rovelli is certainly clear enough about UV finite, already on page 2 of the current standard source describing the theory.

UV-finiteness is based on the discrete spectra of the geometric operators. There is a minimum area and a minimum volume. So at small scale no place for infinities to develop.

==quote http://arxiv.org/abs/1102.3660 page 2==
Its most remarkable feature is the discreteness of the geometry at the Planck scale, which appears in this context as a rather conventional quantization effect: In GR, the gravitational field determines lengths, areas and volumes. Since the gravitational field is a quantum operator, these quantities are given by quantum operators. Planck scale discreteness follows from the spectral analysis of such operators.

To avoid a common misunderstanding, I emphasize that the discreteness is not given by the fact that the grains of space in Figure 1 are discrete objects. Rather, it is given by the fact that the size of each grain is quantized in discrete steps³, with minimum non-vanishing size at the Planck scale. This is the key result of the theory, which becomes later responsible for the UV finiteness of the transition amplitudes.
==endquote==

Is this actually what you are saying in your post, but in a different language? You don't refer to geometric operators having discrete spectra, a remarkable feature (on which the UV finiteness is based) and one of the principal results of the theory.

 

[atyy]

Look at the figure on p21 of http://arxiv.org/abs/1102.3660. That is a "continuous limit" - yet it is apparently, not a "UV limit". That is where the divergence in his model occurs. His model has a potential continuum limit divergence, but not a UV divergence. So the lack of UV divergence is essentially defined away.

 

[Fra]

Isn't this related/rooted back in the different views of what is observable in a measurement theory?

At least how I see it, divergences and UV blow ups is all about overcounting to the point where it can't be fixed by renormalization.

This in turn has to do with WHAT we are counting, and WHO is counting. This is another of questioning what's obsevable and measureable.

IMHO, the one counting is an observer. No observers - no counters and no measurements. A measurement can be thought of as a "counting" of distinguishable events.

And since Rovelli seems to want to "quantize" the observer invariants of GR, rather than "relativize" the observations, the strage situation appears as to what the states in LQG really connects to a real observation by a real observer, which for example comes with a choice of spacetime frame. The point would be that what rovelli "counts" does not correspond to what an inside observer would count, it rather somehow corresponds to counting equivalence classes. But it's questionable how one is about to INFER this equivalence classes. Beucase at leat IMHO, even this inference is a measurement (a generalized indirect one) carried out by an observing system.

I think there are obvious problems with this picture of counting, beause where is the observing and thus counting and encoding system? I can't see the soundness here.

ST OTOH, seems to also have an issue. I hope someone will correct me if I'm way wrong, but as far as I understand the S-matrix is pretty much the "observables" you get from ST, right? And while this is not subject to the critique above, it is subject to another critique, wether it makes any sense at all to consider information that needs to be collected at infinity?

I personally think that neither approach to what to count, and what the counting system is and how it's counted is satisfactory.

With Rovelli's reasoning, I really don't understand - WHO is counting and where is the counters (information encoded)?

With the asymptotic observables, the information seems counted and stored at the boundary. But does this really make sense? If so how. Yes it works fine for SM, but then recall that this is a very special case. The counting region is in a laboratory frame that is very controlled. This really explains why we do get away with this in such a case. But how does asymptotic observables possibly make any sense is a cosmological scale theory, where the observers are inside, rather than on hte boundary?

/Fredrik

 

[atyy]

ST OTOH, seems to also have an issue. I hope someone will correct me if I'm way wrong, but as far as I understand the S-matrix is pretty much the "observables" you get from ST, right? And while this is not subject to the critique above, it is subject to another critique, wether it makes any sense at all to consider information that needs to be collected at infinity?

Polchinski discusses that problem here, and an attempt to make progress on it. http://online.itp.ucsb.edu/online/qcdscat11/polchinski/

 

[Fra]

Thanks, it was a long talk, but not pdf I think. I'll try to check it later.

But if I am not totally mistaken, I think I've read somewhere that some prominent string theorists argued that the S-matrix is the only kind of "proper" observables that you can - in principle - expect out of a theory. I don't find the reference, or don't recall the arguments.

However it's not the boundary itself I object it, because with any realistic observer, tere is always a kind of communication channel or interaction interface, that can be understood as a boundary or horizon. The pathological part is when the boundaries are infinite or spread out to infinity, and that the observer-side of the boundary is effectively an infinite information sink. This corresponds to an infinite mass of the observer. This is how things are done in regular QM and QFT. The observer part, never introduces a cutoff in an way due to limiting Encoding capacity - like it should.

The difficulty to understand how a dynamical background can encode a mesaurement theory is avoided by instead sending the observer to the infinite boundary. Which may be a technical trick but I can't see what problem it solves.

In regular SM/QFT, the laboratory fame can for all practical purposes be thought of as the "infinity" at least relative to the interactions in a collider. But the success of this, due to the obvious assymmetry in the situation should not make us think this is a correct universal procedure.

/Fredrik

 

[marcus]

...
One interesting thing about the recent LQG developments (also see https://www.physicsforums.com/showthread.php?t=520125") is that the continuum may be reappearing, as an infinite refinement of a spin foam, produced when the Immirzi parameter flows to zero. This does look promising as a framework in which the particle physics perspective can be embedded.

I agree. This is currently one of the most interesting developments in loop gravity.
I'm not clear on how it comes up in this thread of Tom Stoer's about "A critical look at strings." But given that it has, I'll get some background.

This seems to be an essential element whenever one says "continuum limit" in the Lqg context. It is understood (or should be, I think) when one says j --> ∞.

Because by itself increasing the area and volume j labels (without letting gamma flow to zero) just increases the size of the network or foam without limit. It does not reduce the cell size (as in a continuum limit) in fact it does the opposite.

So anytime one is talking about the theory going to Regge GR or to GR itself in a j-->∞ limit assuming the overall size of the region stays the same that has to have gamma*j fixed.

A key paper is Rovelli's reference [71] on page 14 of his review. That is where he is talking about the evidence that the theory has the right limits. First two paragraphs of page 14, he cites [71] a couple of times and then says "The evidence for the emergence of the Regge action is now multifold. Several issues remain open. For instance..."

[71] is the May 2011 paper by Magliaro and Perini http://arxiv.org/abs/1105.0216.
They have now rewritten that and posted the final version published in EPL as
http://arxiv.org/abs/1108.2258 ("Emergence of gravity from spinfoams").

I notice that on page 5 of http://arxiv.org/abs/1108.0832 Rovelli cites a paper by Eugenio Bianchi and You Ding a couple of times in connection with convergence, classical limit, 2-point function or propagator amplitudes. This is at the bottom of page 5, reference [30]
Bianchi Ding "Lorentzian spinfoam correlation amplitudes."

My guess is that the convergence and GR limit picture is now taking definite shape and the next version of the review/status report (Zakopane lectures) will have a reference to Magliaro Perini 1108.2258 "Emergence of gravity" and also to Bianchi Ding "Lorentzian...amplitudes."

Both make use of what you called attention to---the double scaling limit (i.e. j-->∞ with gamma*j held fixed).

 

[Fra]

Polchinski discusses that problem here, and an attempt to make progress on it. http://online.itp.ucsb.edu/online/qcdscat11/polchinski/

Witten at least mentions some of the difficulties in this 2001 paper.

Quantum Gravity In De Sitter Space

"[snip from abstract]...We discuss the difficulties in defining any precisely calculable or measurable observables in an asymptotically de Sitter spacetime, and explore some meta-observables that appear to make mathematical sense but cannot be measured by an observer who lives in the spacetime...[snip]"

-- http://arxiv.org/abs/hep-th/0106109, E. Witten

For example he seems to come to the probable conclusion that the best attempts to define observables are still not inferrable (computable and measureable) from an observer inside the universe.

In that sense, the object that we have described is perhaps better characterized as a meta-correlator, computable and interpretable only by an observer external to the spacetime. This makes its interpretation obscure. We turn next to the question of what, if anything, an observer in the spacetime can measure in a precise way.

We are accustomed to physical theories that make, within the rules set by quantum mechanics, predictions of arbitrary precision that can be tested experimentally, in principle, with any required accuracy. For example, we customarily assume that the g-factor of the electron is a well-defined real number. It is true that any given experiment only measures g with some limited (but perhaps very good) precision. But one customarily assumes that there is no bound to the precision with which g could be measured, in principle, given the necessary time, resources, and skill.

Of course the flaw is in the condition here, the necessary time, resources and moreover INFORMATION simply AREN'T given.

...In an eternal universe, in the absence of gravity, with a constant free energy supply
generated by stars, this makes perfect sense. In a more realistic description of nature,
taking the expansion of the universe into account, there are many pitfalls...

It is thus just as well that the only candidates we can see for quantities that might
be calculable with arbitrary precision are the meta-observables, which extend beyond any
one horizon.

Where does this leave string theory? Like physics as we know it, string theory as we know it deals in precisely defined quantities, such as the S-matrix in an asymptotically flat spacetime, or the correlation functions of the boundary conformal field theory for the case of negative cosmological constant. If quantities with this degree of precision do not exist – which seems to be the case in de Sitter space if one rejects the meta-observables – then it is not clear just what one should aim to compute. This question has nothing specifically to do with string theory, and any answer to it that makes sense might make sense in string theory.

I think he is right that this is not specific to string theoy, but that is no excuse for not addressing it. A research can from scratch try to, or not try to address it. It's at least good to see that Witten raises these concernts in this paper!

He mentions the above briefly at the last 4 pages, and it seems he is inconclusive what to do about this situation. But he seems to acknowledge it as a problem, but says that it's not specific to string theory, which I think is correct.

My question would be, is this "issue" serious enough to be taken more seriously, in the constructing principles of a research program, or is it OK to sort of ignore it by the argument that "everyone has this problem"?

/Fredrik

 

[Fra]

So let's assume that this is a relevant issue:

any answer to it that makes sense might make sense in string theory.

I have to admit that to the extent I understand the constructing principles of ST as well as LQG, ST might have better chances of making sense out of an answer, although it's far from obvious.

My personal opinion is that this issue with what is observable - and thus "what do we compute" from the theory, really coincides with the issue of how to really understand a theory, in the context of a scientific method.

After all, it IS possible, that there really ARE not fully proper observables that can be inferred (measured or computed) by a finite observer inside the universe with full precision? (and I think this is close tot he truth; indeed all other theories like LQG too includes "non-inferrable" things, but Rovellis solves this by considering it to be elements of structural realism; but the problem is the that these structures are hardly unique).

If this is so, what do we make of the situation? Then how do an observer inside the universe falsify this theory? Can it even be done? If not, is there a different way to understand falsification?

Anyway, I think in the discussion that could now follow, one what is a theory, and what does a theory or theory, or a landscape of theories mean? Ie. could this even be the otherwise problematic thing, that adds up with the lack of perfect observables to give a NEW somewhat coherent picture of this? Maybe? And then it seems to me that ST does have a slighly better chance than say LQG so cope with it.

If ST fails to cope with it, I think it's either because the lanscaoe is too small! and/or that the constructing principles of ST completely fails to arrive at an selection principle in the landscape.

Very generically, the space of theories is not an unattractive trait, my worry is more wether this space is generated in the right way (byt the right constructing principles) and wether a selection principles is allowed without completely violating it's own constructing principles.

They way I understand it, none of this was on the map originally when ST was started. IT seems more like something they've stumbled on, or have been forced upon the program dued to failure of finding a unique theory.

/Fredrik