On the Depth of Quantum Space by Daniele Oriti

Dear Daniele, Thank you for your thoughtful reply and the solid approach you take towards analyzing models. I gave it a high rating. I realize there is only one day left, but I hope you will have a chance to read my essay that takes a different perspective to analyze a possible reason for particle energy.

Kind regards, Russell

Hi Daniele. I used the opportunity of this essay competition to write what I feel is the burden of proof for all condensed matter models where Lorentz invariance is emergent, which are presumably rich enough to include the standard model matter content. If you are interested it is here

http://www.fqxi.org/community/forum/topic/856

I am curious about your thoughts, either in the context of your model, or in general.

Best,

Moshe

Thanks Daniele. Feel free to send me an email, even after tomorrow.

Dear Daniele,

Regarding your first reply, you still seem to deny my statement that what you say is not relevant as an answer to the contest; I do not see why you don't because many people I know do understand so.

Concerning your classical boundaries in a ''partially quantum universe'', I do not see any logical reasoning behind it apart from the desire to have classical boundary structures in order to define observables. For example, how large are these chunks, what physical principle decides upon that ? Moreover, for ordinary particle theory in curved spacetime, no such boundaries are present (and would destroy the coherence of the theory) except at asymptotic infinity which is held flat or de Sitter.

Third, the inclusion of matter needs to break general covariance in one of the following senses:

(a) either you have a diffeomorphism invariant dynamics (that is a new constraint algebra containing the matter variables) but you have to resort to partial observables.

(b) the quantization of gravity with matter will induce anomalies in the algebra.

Concerning the constraint algebra, this question has not even been settled in pure gravity theory because the quantization procedure treats the Hamiltonian different from the spacelike diffeomorphism constraints. Concerning (a), this is physically nonsensical because I do not see how you would retrieve an arrow of time in this way.

Fourth, I did not say that pure gravity was ill defined, I simply said it has no observables; it is an empty theory from the physical point of view, while the limit of zero gravity is not and that is actually the correct vacuum.

Fifth, I do not know of any standard approach to quantum theory which is not grounded in a classical theory. The path integral approach has the classical action as starting point and likewise so for the Hamiltonian one. The only kind of reasoning which departs from quantum concepts partially (but not fully) can be found in the book of Weinberg.

Asymptotic freedom is just the physical idea that on short distance scales the theory becomes a free one. This is a well defined concept in a quantum as well as classical setting.

Finally, relativity was found by reasoning in terms of a new principle. Einstein clearly thought about general covariance and there exist plenty of historical documents to prove that. I am not sure about the person, but I remember he told to Planck about a generally covariant law for gravitation and the response was that nobody would be interested in that.

Moreover, you completely miss the point that finding principles is very difficult because it implies that your really know what you are doing physically.

Kind regards,

Johan

Dear Daniele,

Concerning your second mail, I will only mention the points I think are wrong. The deformations of the Lorentz group do break Lorentz invariance at high energies, that is why we call it a deformation. All these type of ideas are ad hoc and lack foundational insight. Moreover, the representation theory of these deformed Lorentz groups has still to be developed so that we obtain a new non commutative space-time picture; we are still nowhere near that. So what I would like to see is a new set of physical priniples; the Poincare group is derived from continuum, homogeneity, isotropy and causality of the vacuum. Therefore, if you think the Poincare algebra is a piece of shit because you are overpowered by renormalization problems, tell me which one of these principles fails and what type of new symmetry structures you will recover. I doubt whether these structures have anything to do with Hopf algebra's.

Concerning your comments about quantum mechanics, we need much more than just a reinterpretation, if it were only that simple. We need new mathematical structures, and no they are fairly unique and not fexible at all.

Best,

Johan

Finally your last message; well if you make basic errors, I tend to point them out, but I appreciate you like my succinct summary. Furthermore, there is no correct notion of locality in background independent approaches; there are however plenty of ansatze for what you would like locality to be. The problem is that none of these definitions are natural and resemble what an engineer does when has has to repair an ill constructed building.

Concerning your evaluation towards discrete approaches, I have worked on these issues for many years and actually most of the researchers I know share my opinion on this (at least in private).

Enjoy your chicken, I think the pepper sauce we just prepared will do fine.

Kind regards,

Johan

>Concerning your classical boundaries in a ''partially quantum universe'', I do not see any logical reasoning behind it apart

>from the desire to have classical boundary structures in order to define observables. For example, how large are these chunks,

>what physical principle decides upon that ? Moreover, for ordinary particle theory in curved spacetime, no such boundaries are

>present (and would destroy the coherence of the theory) except at asymptotic infinity which is held flat or de Sitter.

I have never mentioned classical boundaries, nor partially quantum universes, whatever that means. I wrote that the formalism allows to consider finite open regions of 'spacetime', with their boundary (quantum) geometry and topology fixed, and bulk geometry and topology fluctuating and dynamical. Indeed, a better understanding of classical and quantum field theories in such generalized context is needed, together with the corresponding possible generalization of standard quantum mechanics. Such generalization, however difficult, seems interesting, if not necessary, to me also beyond this specific approach.

>Third, the inclusion of matter needs to break general covariance in one of the following senses:

>(a) either you have a diffeomorphism invariant dynamics (that is a new constraint algebra containing the matter variables) but

>you have to resort to partial observables.

> (b) the quantization of gravity with matter will induce anomalies in the algebra.

>Concerning the constraint algebra, this question has not even been settled in pure gravity theory because the quantization

>procedure treats the Hamiltonian different from the spacelike diffeomorphism constraints. Concerning (a), this is physically

>nonsensical because I do not see how you would retrieve an arrow of time in this way.

none of the above is correct, in my understanding. The use of partial observables is a more convenient way to deal with Dirac observables, and to understand their meaning as correlations of measured (but not diffeo invariant) quantities. It does not imply any lowering of standards with respect to covariance. One can produce explicit quantizations of the constraint algebra of gravity plus matter which are free of anomalies, and the real question is whether the corresponding quantization has the correct classical limit and produces the correct physics. But there is no obstacle of principle.

>Fourth, I did not say that pure gravity was ill defined, I simply said it has no observables; it is an empty theory from the

>physical point of view, while the limit of zero gravity is not and that is actually the correct vacuum.

I did not question the fact that pure (classical and quantum) gravity is non-physical, because we lack local observables, although I would not be so clear-cut; and in fact I said that this gives one more reason, beside the obvious physical motivation, to introduce matter. I wrote that just as in classical GR pure gravity does represent an idealized case from which we learn things, the same could be true in the quantum case. The limit of zero gravity is physical provided you are not interested in gravity (classical or quantum), which is a shame. As soon as you want to say something about gravity, this limit becomes at best an approximation, as one does in any interacting field theory, and all the problems re-appear and have to be dealt with.

>Fifth, I do not know of any standard approach to quantum theory which is not grounded in a classical theory. The path integral

>approach has the classical action as starting point and likewise so for the Hamiltonian one. The only kind of reasoning which

>departs from quantum concepts partially (but not fully) can be found in the book of Weinberg.

sure. and in fact -any- approach to quantum gravity I know of (including GFT) rests to some extent, in motivation, type of structures used, basic principles that one tries to carry over to the quantum theory, etc on classical GR. again, I never stated that one should somehow invent a quantum theory of gravity and/or spacetime without ever considering GR. so what?

>Asymptotic freedom is just the physical idea that on short distance scales the theory becomes a free one. This is a well defined

>concept in a quantum as well as classical setting.

in my understanding the concept makes real sense only in a quantum theory in which coupling constants run with scales, otherwise you are using the term in a rather non-standard way. Then, QCD is asymptotically free while QED is not, and none of the two is 'asymptotically free' at the classical level, given that there the coupling constants are whatever one sets them to be. In any case, Gravity, treated as a standard quantum field theory, is not asymptotically free, although it could be asymptotically safe. This is true, of course, unless you treat it as a non-standard quantum field theory or you intend the terminology in a non-standrad way. Fine, but you should then clarify what you mean, and then one can check whether what you mean makes sense or not.

>Finally, relativity was found by reasoning in terms of a new principle. Einstein clearly thought about general covariance and

>there exist plenty of historical documents to prove that. I am not sure about the person, but I remember he told to Planck about

>a generally covariant law for gravitation and the response was that nobody would be interested in that.

>Moreover, you completely miss the point that finding principles is very difficult because it implies that your really know what

>you are doing physically.

when I read the historical texts or the original sequence of articles leading to GR, I see a much more complicated story, in which he arrived at the right principles only after a complicated sequence of trial and errors, partial results, later-to-be-discovered inconsistent foundations, glimpses of ideas, and even including formulations of the theory that were based on the very contradiction of the principle of general covariance. He did not first identify the principles and then deduced the results. Theoretical physics does not work like that, I think, unless principles are treated as working hypothesis, but then of course one should maintain a certain flexibility about them. This is exactly because identifying the right principles is difficult (again, I have never stated the contrary), and it is not even something that can be recognized as unique, if not much after the complete theory has been found. As a consequence, I do not feel I can blame any current approach to quantum gravity (a still incomplete theory, yet to be found, really) because it does not start from unique principles, or on already clear ones. Obviously, I also feel it is important to try to clarify the basic assumptions (''principles'') on which they are based, because indeed it may facilitate their development.

Dear Daniele,

If your formalism allows you to consider finite open regions of space-time, then this is equivalent to inserting a classical boundary. Basically what you are probably doing is taking some fixed discrete structure, promoting this as a ''boundary'' and allow for fluctuations inside. Of course all these concepts depend at least on a background topology such as the notions of inside, outside and so on. And yes, such ''boundary'' would be classical in the sense that the superposition principle does not apply there, even causal set people do regard one causal set as classical. Second, such states are highly unrealistic (and distributional); even in QFT, one has that the physical states do not have a finite support.

Towards your comments on covariance, they all appear to be wrong. First of all, nobody has ever constructed a quantum Dirac algebra in 4 dimensions; as I said, the way LQG deals with these issues probably breaks covariance. In 2+1 dimensions, I grant this has been done already. Second, we do measure partial observables all the time, and never ever do we measure Dirac observables. By definition, these last ones are globally defined only unless you really add POINT particles. But then you still break manifest diffeomorphism invariance not on space-time but on the parametrization space of the point particle itself (even the free relativistic particle on Minkowski has no manifest covariant quantization, that is why we need QFT). All you seem to say is that one could quantize this in principle and define Dirac observables; even if I think this is false in 3+1 dimensions, and of course you are welcome to provide me a reference which shows me wrong, still one has no local observables for matter fields. One could have local observables for point particles but that breaks manifest reparameterization invariance and of course it is not a correct theory (probably not even mathematically).

Well, I do say you need to construct a quantum theory for matter without reference to any classical matter theory.

Concerning the terminology of asymptotic freedom, nobody I explained this to had a problem with it. Classical vacuum GR clearly is asymptotically free due to the equivalence principle (except when you meet a physical singularity of course). Take any solution and zoom in, then in a neighborhood of a point, space-time will look flat. Now, classically, if you couple point matter to gravity then the theory is not asymptotically free anymore because the Newton potential does not have an extremum at zero distance.

Concerning Einstein, I do not doubt the fact that he first tried out noncovariant approaches as Whitehead and many others did after him. However, my point was that progress was only made once he understood general covariance was a key element. That has put him in communication with Cartan and Hilbert to learn the new mathematics. So,this does not invalidate anything I said; my point was that he was messing around until he had a new idea which relegated everything he did before to the trashbin. What I told you is that any unfounded approach will suffer the same destiny; actually, axioms are the result of deep, hard work and going through the mud first. If you say you are swimming in the mud now, you will have to hope for a really original idea sooner or later, or you will get nowhere. That is how theoretical physics works.

Best,

Johan

Dear Daniele,

Concerning your second mail, did I ever dispute the fact that the q-deformed algebra's are not closed ? All I said is that they seriously differ from the Poincare algebra at high energies. Moreover, it is not enough to have the algebra only, you need to have the entire deformed group with it's complicated topology. The reason is very simple, the quantization of spin is a property of the orthochronous Lorentz group and not the algebra. And yes, I use terminology in a loose way because we have no space-time understanding whatsoever yet of these deformed algebraic structures; I invite you to construct its representation theory.

Concerning the development of this mathematical theory; yes, I am also glad people do it and I have played with these things myself once upon a time.

The development of representation theory of these deformed algebra's is still in its infancy which again does not imply it should stop, but on the other hand (and that was my point) my intuition tells me that even this kind of mathematical structures are not broad enough yet.

Concerning your statements about the motivation for the deformation, I agree with what you try to say intuitively (not physically though). Of course, all this flies straight in the face of naturalness and moreover, your deformations should be fully dynamical. Haven't seen that anywhere yet...

Best,

Johan

Finally, glad you read so many books, I never studied what philosophers of science had to say about scientific practice. Scientists themselves should find that out. As a general comment to what you say, I think that your ideas apply to most people; however they are terribly outdated what I am concerned. Ultimately, progress always comes from a new idea which of course is grounded in the failure of an older one. But what usually happens is that the later generations forget about the idea and only learn the math; this is very problematic and completely outdated. Often it is so that a masterpiece of ''engineering'' leads to new abstract insights which by themselves open a whole new world. Far too often, this new world is not studied and people stick to the engineering example. The best examples here are general relativity and quantum theory. If you do not understand what I say, I will use more words for it.

The basic problem in all attempts to formulate a principle of locality for quantum spacetime is that in the continuum, this is a topological fact which has nothing to do with the dynamics. In algebraic approaches to quantum space-time you can see very easily where the problem resides; in kappa Minkowski for example the space coordinates commute and do not commute with the time coordinate. So, first you have to define an event, are you going to say that it corresponds to eigenvectors in a representation which diagonalize the position coordinates, so that an event is effectively non-local in time? Clearly such thing is not invariant under the deformed group because time and space mix. So an event will become ''coordinate dependent'', likewise will the notion of neighborhood be. Actually, depending upon your deformation parameter, one single event in one coordinate system may stretch out formidably in another. So the laws themselves will have a non-locality scale depending upon this stretching. Of course, all such approaches seriously tamper with diffeomorphism invariance which is very poorly understood in that context (Majid once made an attempt). In my book, that reads like having an effective class of coordinate systems.

Best,

Johan

Dear Sir,

You say that whether reality is digital or analog "refers, at least implicitly, to the 'ultimate' nature of reality, the fundamental layer." You admit that "I do not know what this could mean, nor I am at ease with thinking in these terms." Then how could you discuss the issue scientifically? Science is not about beliefs or suppositions. Your entire essay exhibits your beliefs and suppositions that are far from scientific descriptions. You admit it when you talk about "speculative scenario". This is one of the root causes of the malaise that is endemic in scientific circles. Thus, theoretical physics is stagnating for near about a century while experimental physics is achieving marvelous results.

Let us take the example of space. You have not defined reality since you admit you have no idea about it. You discuss space without defining it. Both space and time are related to the order of arrangement in the field, i.e., sequence of objects and events contained in them like the design on a fabric. Both space and time co-exist like the fabric and its back ground color. The perception of each sequence is interrupted by an interval however infinitesimal. The interval between objects is called space and that between events is called time. We take a fairly intelligible and repetitive interval and use it as the unit, where necessary by subdividing it. We compare the designated interval with this unit interval and call the result measurement of space and time respectively.

Since space and time have no physical existence like particles and fields, we use alternative symbolism of objects and events to describe them. Thus, what Euclid called space is not the interval between objects, but the basic frame of reference on which the objects are placed as markers. To this extent he is right. Dedekind and others did not know this concept. Hence they wrongly held that "it is possible to construct discontinuous spaces in which Euclidean geometry holds". Geometry is related to measurement of space and no measurement except distance (line) is possible in discontinuous spaces like in the interval between a point on Earth and another point on the Sun or Moon. However, this fallacy was not apparent to the others who built theories upon such invalid foundation. Since space is the interval between objects, the space is continuous throughout the Universe. Thus your definition of quantum space is fundamentally wrong. Hence it is no wonder that you conclude "the question has no absolute meaning, so no answer."

The rest of your essay also exhibits the same beliefs and suppositions. Thus, it is strange that it has been highly rated by the FQXi community. Possibly "novelty of presentation (which means talking admittedly vaguely)" and incomprehensibility are the Bench marks of scientific excellence these days.

Regrds,

basudeba.

Daniele, it is good to see you in this contest and doing well. I have admired the group field theory approach since its origins with people such as Boulatov. I mentioned it in my review if discrete space-time concepts back in arXiv:hep-th/9506171. I am pleased that you and your colleagues are keeping the idea alive and continuing to develop it.

As you say geometrogenesis goes back a long way. For example I discussed very similar ideas in arXiv:hep-th/9505089 but did not come up with such a great name or concrete realization. Even earlier forms of similar work are mentioned in my review. Fotini Markopoulous has done a great job of making the concepts much clearer in the context of quantum graphity. It would be be a big development if such phase transitions could be found in relation to a more mathematically rich approach such as group field theory. Do you see any indications of this being possible?

Daniele

I wish to warmly congratulate you on your provisional 1st place.

I hope now the 'competitive' pressure has gone we may return to good science. I'd be very appreciative if you read and genuinely commented on the model in my essay, which I beleive may be of major significance. http://fqxi.org/community/forum/topic/803

Very many thanks

Peter