Hi Moshe,

I managed to read your essay and liked it a lot. I won't manage to write you an appropriate reply to the various issues you raise now, but I'll try to do it (either here or in private) as soon as possible. There are several points I would like to make on them, some partial answers and some more confusion to share, but it takes some time. At least, I managed to vote for your essay!

Thanks again.

Daniele

  • [deleted]

Thanks Daniele. I am not sure for how long I'd check things here, so private email would be best. As I said, I am curious to hear your perspective on these issues.

  • [deleted]

>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.

>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.

This is false. Any deformation of the Lorentz (or Poincare) algebra I know of, in contrast to breakings of the same algebra, remain 10-dimensional at any energy and reduce to the standard algebra at low energies. This is exactly what is meant by deforming the algebra with respect to some additional parameter, unless you call any modification a 'breaking' but then you are using words in a rather loose sense, which is at danger of placing very different formalisms, with very different mathematical and conceptual structure, in the same pot. The Hopf algebra of k-Poincare is an example of what I said.

>All these type of ideas are ad hoc and lack foundational insight.

This may be true, but it is a matter of rather subjective taste; they have some motivations, even though of course there is a lot to be understood about them, both mathematically and physically, and in terms of their 'foundations'. In any case the right attitude seems to me to study them more, not to drop them, until everything is clear and they have been proven right or wrong. And I am happy that lots of clever people are doing so.

>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.

I do not agree. We do know a lot about them, in the context of non-commutative geometry, and at least for some 'groups', and progressively knowing more. If we stop working on them, as a community, because we have not yet found all the answers, we will never find them. And will miss a lot, I think.

>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.

I do not think of the poor Poincare group what you assume I do. As a general but therefore imprecise statement, what seems to be given up in non-commutative approaches, including those based on quantum group symmetries and thus Hopf algebras, is strict locality, and as a consequence a standard continuum manifold picture of spacetime (even though depending on the specific cases spacetime quantities like 'coordinates' may stay continuous). Homogeneity an isotropy are maintained, at least if you define them from an algebraic point of view (lacking a continuum manifold structure, it is not obvious what other definition one could use). Causality is tricky to define in this context, but seems to be compatible with the quantum group structure of symmetries. You may like it or not, but I am not trying to convince you to like them, only pointing out what I know of them.

>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.

One example of which is the attempts to define quantum mechanics in absence of isometries, in absence of background spacetime at all, and for arbitrary boundaries (compact, timelike, etc). All this is slowly being developed and should not, I think, simply dismissed. Obviously, all of the above also calls for a re-interpretation, as any quantum theory of space will, but it amounts indeed to much more than that. Again, I have never stated simple re-interpretations are enough.

>Finally your last message; well if you make basic errors, I tend to point them out, but I appreciate you like my succinct

>summary.

It was, as you know, a concern about your style of discussion, which I am happy to see you amended. Concerning the way science works, I am aware I have still to learn a lot, but I have read my Feyerabend and Lakatos, among others, and I do appreciate the important role that metaphysics, feelings, principles, etc play in the construction as well as in the justification of physical theories (by the way, it is also a basic result in philosophy and history of science, beside daily scientific practice, that science does not work by deducing consequences from foundational principles, and that 'principles' come -after- one has identified the 'right' theory, most of the time). If you read again my original statement, you will see only a confirmation of this awareness.

>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.

That a new understanding of locality is one of the open issues in most approaches is indeed a fact that I have stated from the very beginning. I also stated that there are good arguments (to me) that locality is indeed one of the concepts we have to re-think, when dealing with quantum gravity. I added that a revision of strict locality seems to be called for in all approaches I know of, whether discrete or continuum (even if of course details will change depending on the framework). I am working on this issue myself, as a testimony of my awareness of the issue, and my interest in it. I believe, as I stated above, that statement of naturalness or beauty of current attempts are important to direct ones' research, but prove nothing and are rather subjective (which is not meant to be a bad thing, but not much of a basis for convincing others). You seem to have a different judgement of the situation and on the role of locality in a more fundamental theory of spacetime. Fine. I have no problem with this. Keep working and everybody, as always, will judge from the results, of yours like of any other approach.

>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).

Good to know. But it changes nothing. I also work and have been working on these issues for some time, and hope to continue for longer. I also talk to researches both in public and in private. It also changes nothing. I see many different opinions, interesting issues being raised to both discrete and continuum approaches, clever criticisms etc. I like this because it drives our understanding and research further.

  • [deleted]

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

  • [deleted]

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

  • [deleted]

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

  • [deleted]

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.

  • [deleted]

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

    Dear Daniele Oriti,

    Congratulations upon your placing first in the community voting.

    Edwin Eugene Klingman

      Hi,

      and congratulations on your placing second! I think that finer differences do not really mean much, at this stage, and all those essays that classified roughly at the top have really been appreciated equally. Anyway, good to have our work somehow valued positively, isn't it?

      ciao

      Daniele

      Hi,

      believe me, the only reason why I could not read or comment all the essays that I would have wanted had nothing to do with competitive pressure, but only with the fact that I tried to keep doing good science. As a consequence, I do not have as much time as I would want.

      I'll try to read your essay, as you suggest, and let you know of comments, should I have any that could be of interest.

      best,

      Daniele

      Dear Daniele,

      I share Peter Jackson's view when he says "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 also hope that the top essay authors are still willing to consider the pesky questions of the dedicated amateurs. I have one for you which have I started with Ian Durham just recently incidentally:

      Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification, which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

        Dear Alan,

        thanks for your interest. As I replied to Peter, the reason why I did not reply and comment to all the submitted essays and contributed ideas is simply that, whatever their interest, I have not enough time to do so. I would like to, but I simply cannot. I do not know your model, and it will take some time to study and try to understand it. Therefore I cannot comment on it. As a general remark, I do of course agree that a theory that explains gravity at a more fundamental level, which is what models of quantum space or related quantum gravity models try to do, and that in addition explains electromagnetism (electrostatics is not enough) and possibly other interactions (i.e. nuclear ones) would be better than one that only explains gravity. Unfortunately, I do not know any such complete theory yet.

        Best,

        Daniele

        Hi Philip

        Thanks a lot for your encouraging comments, and for the useful references. I do have indications that this type of phase transitions can be realized also in complex models like GFTs, although of course they are indirect indications and indications only. One example is that of matrix models for 2d gravity, where exactly something like this happens and which are in both conceptual and mathematical terms the (very successful) precursors of GFTs. We even have very preliminary work in this direction, but it is way to early to say whether our results will hold after further scrutiny and development.

        Best,

        Daniele

        Thanks Daniele,

        I have plans to include the gravity force as well. You're all right, I need a working simualtion model that canb speak for itself.

        Kind regards,

        Alan

        • [deleted]

        Since Danielle Oriti declared having no time for replying to criticism, I will just add remarks:

        He wrote: "The idea of a cosmological phase transition of space itself, replacing the Big Bang singularity, may provide a novel way to look at the puzzles of very early cosmology (horizon problem, flatness problem, etc), currently address by inflation, itself in need for a better explanation".

        Such promise is of course welcome even without a tangible basis.

        Danielle Oriti admitted in reply to Wilhelmus de Wilde: "Concerning singularities, indeed, several if not all practicing scientists believe the notion of singularity is but a label for a physical situation we do not understand yet, but not something physical in itself. However, the task is then to build up a theory of what happens in such situations, and unfortunately to simply deny their realities is not enough. We all have to be able to do better."

        I do not just agree on that. My essay tries to show a way that does not need the coward and lazy "it depends". Instead it offers an admittedly highly unwelcome approach:

        In order to do better let's focus on possible flaws in very basics of mathematics and its relationship to physics.

        Admittedly I am guided by my experience as an engineer: I like using singularities - as tools -, not as something real. I am fully aware that there is no ideal line current and no ideal point charge.

        Eckard Blumschein

          True, I do not have as much time as I would like to reply to all messages. Despite this, I did reply to quite a few of them, and tried both to clarify my point of view, and to counterargue some criticisms. But let me understand: what is, exactly, your ciriticism? I have tried to present a point of view according to which the answer: ''it depends'' has a clear meaning (beside the ironic tone), and it is a shorthand for ''it depends on the specific phase and regime of approximation in which quantum space is and is probed, just like in any condensed matter system, and we may have a formalism for studying all these phases and approximations, we just have to work much harder and do it properly''. So, I don't see what is cowardly and lazy about it. Beside, I don't see the use of using this type of tone and empty statements.

          Daniele