Dear Janko,

Thanks for your interest and comments. I reply to some of them below.

>As generally it bother me at all contestants that Zeilinger-Brukner theory

>of atomization of information is not mentioned here. Feynman also

>mentioned similarly as they. So the essence is in discrete world. Almost >obvious existence of Planck's space-time shows similarly. It would be

>well, that all contestants should mentioned this - I think on proponents

>and opponents of digital physical world. I have not read all essays, does

>anyone mentioned this?

I, for one, have not mentioned this theory because I do not know much about it. I take your comment as a suggestion for learning more about it. Thanks.

>It is a general argument (also yours) that quantum field theory is >continuous, and that field is more important than particles.

well, in a sense you are right. But indeed, this is what current quantum field theory seems to teach us. And I think we have to first of all take seriously what we currently know about the universe, before moving beyond it. But indeed, one needs to be careful in the assumptions made, and flexible enough to question any current wisdom.

> But we should not ignore that final version of QFT is in discrete Planck's >space.

I am not sure what you mean by this. We do not know at present, if space at the Planck scale is (best described as) discrete or continuous. We are entitled to make our favorite assumptions and see where they lead us, but we simply do not know. Indeed, my essay tried to paint a picture of quantum space that is more complex than this.

>You mentioned richness of those models. But we should be aware that there

>is also richness of possibility of simple models.

I fully agree with this. What I wanted to stress is that the set of possible 'phases' and regimes of the physical system corresponding to quantum space can be very diverse, so to make the answer to the question whether space is discrete or continuous not univocal. I do not know if this richness is to be encoded in 'complicated' mathematical models, or can be reproduced on the basis of simple ones. Only further research can tell us.

>It is expected that quantum gravity should be a simple theory.

By whom? opinions about this, as far as I know, are various. In any case,

>You gave a comparison with condensed matter. This can be also a rich

>topic, but this is not necessary for foundations of this. And, foundations

>of condensed matter and quantum gravity are different.

I suggested a point of view on quantum space based on what we know from (or at least from how I interpret) recent results in quantum gravity research; this point of view is inspired by the 'analogy' with condensed matter. Nothing more than this.

>You mentioned that you begin with quantization of space. It should be well

>to mention that space-time without matter does not exist, so this is a >quantization of matter. (But from your graphs it seems, that this is your >standpoint.)

The possibility of giving physical meaning to spacetime without matter is indeed questionable and questioned in both philosophy and physics. However, vacuum spacetimes can and are studied in General Relativity, so they make sense at least in some approximation. On whether and how matter should be incorporated in or shown to emerge from this description of quantum space, see my reply to another comment above.

>You mentioned that wave function exists in a every node. It seem to me,

>that wave function is only a thing of continuous space. I speculate this >after reading Brukner-Zeilinger interpretation (quant-ph/0212084).

In the models I considered, GFTs, indeed one can define an compute wave functions associated to discrete chunks of quantum space, individual nodes of graphs. So this definition at least does not need a continuous space, in a physical sense.

>I was late for this contest, so my ideas can be read here. http://>vixra.org/pdf/1103.0025v1.pdf

>I have also an article, which is not speculative and it is a base for the >above article. http://vixra.org/pdf/1012.0006v3.pdf There are also

>additional claims about connections between matter and space-time. I need >someone who will be the arxiv endorser for this article. So that I will

>get opportunity, that my theories will be discussed.

As I am trying to read as many essay as possible, I, of course, try to read as much available literature as possible on this topic. So, thanks a lot for your suggestion.

Best,

Daniele

Dear Daniele,

I really appreciated your essay which bring very interesting and innovative ideas while still being of perfectly scientific level. I share your view of the cosmological phase transition instead of a big bang. My own work totally agree with that thesis. Quantum space is now crystallized (as an hyperdiamond) and should have emerged from a liquid or gaseous phase. It is made of a trivalent graph, evolving through pachner moves, and quantized as spin foam. The crystallographic structure embed standard model through e8 roots.

Best regards

Ray

    • [deleted]

    Hi,

    thanks a lot. I am happy to see that similar ideas are shared by people coming from different paths. It can still be we are all wrong, of course, but at least it serves as an encouragement to keep working.

    Best,

    Daniele

    • [deleted]

    Dear Johan,

    thanks again for your comments. It is so refreshing to see your amount of certainties and firm convictions, when everybody I know in the field of quantum gravity (and beyond) is always so cautious and tentative in his/her suggestions, proposals and sometimes even results.

    I comment below to some of your comments.

    >The problem of quantum gravity is to give a description of nature which is >in principle valid on all scales (this is by no means in contradiction >with renormalization). So your answer that it depends upon the scale or >system is unfortunately not valid.

    First, a brief comment: as far as I understand it, the problem of quantum gravity is to give a description of gravity and spacetime that works beyond the scales we have already tested, that goes beyond GR and possibly solves physical issues in that theory like singularities etc. Moreover, it is widely believed and quite likely, that it will still be based on some form of quantum mechanics, possibly modified to deal with a peculiar system like spacetime itself, whence the name. If it is valid at all scales or simply at a new range of scales, after which we have to find an even better theory, we do not know yet. Second, even if we have a theory that formally is valid at all scales, in the sense that the theory itself does not break down, this does not imply that it is the best description of things at all scales. An example would be QCD. On the one hand, formally the theory is valid at any energy scales; on the other hand, one uses a lattice formulation of it at strong coupling, and a continuum formulation at weak coupling; then, still at strong coupling, one has different phases, e.g. the quark-gluon plasma, that require different 'effective' formulations, and similarly at weak coupling it is better to use other effective formulations. Further still, at super-high energies, despite the fact that the theory itself does not break down, we know or at least believe that new degrees of freedom should start play a role, so that QCD is not the whole story, for example quantum gravity effects. So what is the best (formulation of the) theory and what is the best way to describe a certain physical system does depend on the scale and the regime and the phase that one is considering. This is not very controversial, I think. I was simply pointing out that we do not have any reason to expect something different from quantum gravity, plus I was taking this expectation seriously in its more conceptual implications (as I see them, of course) regarding the discrete/continuum nature of space. In particular, I point out that GFT are continuum field theories, whose quanta are discrete 'chunks of space'.

    >You seem to take the point of view that the observer(s) are somehow living >in ''meta space'' and that the theory should adapt to the ''glasses'' they >are looking through.

    I am not sure what you mean by this, nor where I have written something along these lines. The only time I mentioned 'metaspace' is in giving a label to the manifold on which the GFT field is defined, in order to clarify that this (continuum) manifold does not have itself the interpretation of spacetime. I think I mentioned 'glasses' only in referring to standard results in philosophy of science (Lakatos, Feyerabend, Popper, and many others) showing the extent to which observations and experiments are really much 'theory-laden', and not at all 'neutral' (it is not meant to be a bad thing, by the way).

    >Of course, this is what you get when you naively combine quantum mechanics >with general relativity which is what brings me to another point of yours >where you say that you do not understand how these issues make the whole >idea of ''quantum space'' unlikely. As I said, the main problem is how to >define ''local observables'' in a ''canonical way'': there exist very good >(read: almost conclusive) no go arguments against the mere possibility for >even doing this. This issue is intertwined with an observer living inside >or outside the universe and it would take pages to explain it in any >detail. What surprises me however is that you deny that while this is an >open problem for 80 years now (indeed, so long) it most likely implies >that it does not work that way (and indeed, I know it doesn't).

    the issue of defining local observables in classical and quantum gravity is a thorny one, and indeed I know of only a few 'solutions' to this problem, all requiring the introduction of matter fields. It is already a difficult task in classical GR, and quantum mechanics (especially in its standard interpretation) makes it even more difficult. And it is so in all approaches to quantum gravity I know (otherwise, of course, we would know at least some solutions to the issues), whether continuum or discrete (it has not to do with discrete space at all, but rather with general covariance, which is a necessary property, I think, of any theory of space taking into account the basic lessons of GR), euclidean or lorentzian, in 3 or 4 or higher dimensions, based on more or less standard quantum field theory or on something more exotic, etc. I am not denying anything, I think. Only, exactly because it is not tied to a specific approach to quantum gravity, but a very general problem, it also does not rule out any specific ways of approaching the construction of the theory, nor the general idea of a 'quantum space', given that this simply means a 'space manifesting some quantum properties' or 'a system that does not look like ordinary continuum classical space but reduces to one in some approximation'. Obviously, I would welcome any clear-cut and complete solution to this issue, but I simply am not aware of any.

    >Moreover, I guess you start from space and not space-time right?

    no. you could formulate (at least in principle) the 'states' of the GFT system to refer to d-dimensional timelike regions embedded in a d+1 spacetime. The distinction between 'states' and 'processes' is a rather general feature of any (quantum) mechanical theory, while the better understanding of the case in which states are associated to purely spacelike data is simply due to the fact that this is the simplest and most studied case. If even the standard distinction of state and processes is somehow felt to be unsatisfactory, then one can try to adopt, in GFT as in any other (quantum) mechanical theory, a more covariant, history formulation. In any case, what I wanted to say in the essay as well as the general features of GFT, do not depend much on this.

    >But even on a much simpler plane, you could insist that strict locality is >a property of nature; this immediately rules out all the exotics you are >willing to consider (so here you have a deep physical reason). The >problems with the kind of models you are considering are legio and most >importantly, they lack physical insight and motivation.

    You could insist on locality, yes. And clearly to maintain strict locality at all scales and for all descriptions of the physics of spacetime, classical and quantum, rules out a few alternatives and a few possible features of a quantum space. But 1) there are some reasons to doubt that such local description is really available in all circumstances (e.g. locality is defined in terms of a metric, and thus the very possibility of metric fluctuations or superpositions would imply fluctuations and superpositions in locality, and in turn would require to formulate your theory in a framework in which you do not rely on strict locality); 2) even if locality is somehow incompatible with other properties, this only shows that you have to make choices about the basic principles you implement in your theory; fine; indeed, different approaches to quantum gravity explore the consequences of making different assumptions; up to now, no set of assumptions has been proven to provide a theory free of difficulties, so the exploration and the attempt to solve these difficulties is still ongoing. When we will find one set of assumptions and a consequent framework that succeeds in giving a good account of the physics of quantum space, interesting predictions that are corroborated by experiments, we will all be happy and we will be convinced that we have found at least one good theory of quantum gravity. Until then, it is healthy and sensible to follow different approaches based on different assumptions. Your last statement is rather, how to say, weird, and I prefer not to comment.

    >Let me give you a few examples : free QFT on flat space-time is exactly >correct without any doubt.

    and also strictly speaking totally unrealistic. It would work exactly only if no interaction at all was present, which is clearly never the case in nature. Obviously, it is a very good approximation of phenomena where interactions are very weak, and indeed it is used in this spirit.

    >For example, it almost canonically follows from: (a) locality (b) >causality (c) isotropy and homogeneity of the >vacuum (d) 4 dimensions (e) >cluster decomposition (f) Hilbert space representations of the symmetry >group (g) positive energies (h) statistics. If you think about it for a >while, then you recognize that every single requirement is physically >mandatory for the limit of zero interactions. Therefore, you have to think >about how you are going to build an interacting theory but the latter >should have many foundations in common with the free one.

    I agree with everything except the last statement. What the first part shows is only, I think, that whatever more fundamental theory we have, and whatever its foundations are, we should be able to show that it has free field theory as a limit in the approximation of very weak interactions. For example it is clear that no flat space symmetry group (i.e. Poincare) can exist on a generically curved space, even if classical, but one should indeed recover it in the limit of flat space, i.e. no gravity. At the same time, one should not build the global poincare' group in the foundations of the more general theory, where indeed it is replaces by a more local, approximate, version.

    >Just as plain Minkowski is the short scale limit of general relativity, >the free theory should be the short scale limit of the interacting one - >so we should have asymptotic freedom and not merely asymptotic safety.

    As a general line of thought, it could make sense, but we know that quantum gravity treated as a more or less standard quantum field theory obtained from general relativity, treated as a more or less standard field theory, is simply not asymptotically free. Now (and there are then two possibility, either it is still a more or less conventional field theory and it is asymptotically safe (that's the route followed by the asymptotic safety approach to quantum gravity, and in some interpretation by some lattice gravity approaches), or it is not, at a more fundamental level, a standard field theory at all (or does not come from general relativity strictly), because spacetime is not a continuum anymore, or because the degrees of freedom are not encoded in a metric, etc (this is the line of thought followed by several other approaches). Anyway, I am just saying that even taking your argument for granted, it leaves a lot of room for developing the theory in different directions, in my opinion.

    >A first step in that direction would consist in giving interacting quantum >theory itself an Einsteinian (meaning local and fully covariant) >formulation. This is a necessary exercise in order to put both theories on >the same level. You may imagine that the interacting theory will not be >causal, have more exotic statistics and not satisfy the cluster >decomposition, but all this should by dynamical: it should follow from the >physical requirements of covariance, asymptotic freedom, locality + the >conditions on the free theory.

    what you seem to be suggesting is what people working on 'algebraic quantum field theory' have been trying to obtain rigorously (apart from the requirement of asymptotic freedom, which I fail to see the necessity of nor the realistic implementation). It can indeed be seen as a necessary first step, and it is without doubt of great interest and value, but there is a rather unanimous consensus (including among researchers working on it) that 1) in itself would not address any of the deeper issues (conceptual or physical) that a complete quantum theory of gravity and spacetime is supposed to address, and 2) at the same time it should indeed represent a good approximation of any more fundamental theory, in some regime. The two things are in no way in contradiction, as far as I can see.

    >GFT probably satisfies none of those requirements (including covariance!) >and I haven't seen a good principled analysis nowhere in the literature.

    I encourage you to look more carefully at the literature; it may not answer all the question you may have (indeed these models are in many way underdeveloped), but it may give you a better idea of what they are about and what are their motivations and goals. More precisely, let me only say that a) GFT renormalization has just started to be investigated, so we do not know if any given GFT model is renormalizable or not, asymptotically free or safe or whatever; b) the condition of 'free theory' is certainly and trivially satisfied, if you simply mean that the GFT free theory should be reproduced in the limit of the GFT coupling constant going to zero (i.e. what happens in ordinary field theory on fixed spacetime); c) the GFT is local in the sense that it deal directly with local 'chunks' of space, which are the fundamental (interacting) quanta of the theory. Being a theory -of- spacetime and not a theory -on- spacetime, however, the standard notions of locality, causality, short and long distance scale, etc etc, are necessarily to be modified or re-interpreted. This is inevitable, to some extent, and we should be mentally flexible enough, I think, to do it when needed.

    >So, what do people do? They go in defense mode. They even start to deny >that the free theory is a physical limit. This of course is utter rubbish, >why in principle should nature not be capable of playing around with the >gravitational constant (or the Planck constant or the speed of light) ? >You may think about c as a definition of a second starting from a meter, G >as a conversion between mass and a meter and hbar as setting the scale for >the meter itself. So again, it appears totally obvious to me that the >limit of zero G in theory space should exist (as well as the limit of zero >interactions) and it is the knowledge of that limit which should be a >foundation of your theory just as special relativity is for general >relativity in the Palatini formalism and just like classical mechanics is >for quantum mechanics in the deformation quantization approach. This is >actually also the case for the thermodynamic limit of absolute zero; there >have been numerous attempts like stochastic vacuum field fluctuations as >an alternative to QED and a big chunk of the physics is determined by the >T = 0 limit. This is something which is fundamentally lacking in all >approaches to quantum gravity (except one) and it is a big mistake.

    none of what you wrote above is controversial, nor in any contradiction with the fact that we have to go beyond this limiting case in defining conceptually and mathematically our more fundamental theory of quantum gravity, just as we had to go beyond special relativity, encoding it as a limiting case only, in constructing general relativity. We are trying to do just that, bringing in as much as we can of current theories in building new and more general ones, based necessarily on different assumptions (or at least a reformulation of the same assumptions in a different more general context), but recovering the old assumptions in well controlled approximations.

    Different approaches to quantum gravity take different route from known physics towards new, unknown physics, exploring different assumptions and ideas, but I think all agree with the above remarks of yours.

    >PS: I do not care about how you write things, expository skills are a >matter of social convention

    no, expository skills are important skills, and I care about improving in those as in others

    >and I have never cared too much about what others ''think''.

    I do care what others think, because I can learn from them, not always, but often

    >What I do care about is what you write and as far as I can see, you repeat >all the hopes and ''misconceptions'' I have heard for more than 10 years.

    thanks a lot for your criticisms. I encourage you to read more carefully the quantum gravity literature of the last 10 (actually, 80) years, because I think you can find a good deal of interesting ideas and results. On my part, I look forward to read your essay and other published work, hoping for the enlightenment and wisdom that clearly the rest of the quantum gravity researchers and articles could not provide.

    Dear Johan,

    here are some more comments.

    >Now that I see, I did not respond yet to a few points of yours. So, you >admit the notion of a particle becomes superfluous in the context of >relativity: therefore, why are you doing your best to reinstate this >concept in a theory of quantum gravity?!

    I am not, if not as an analogy.

    >Shouldn't you just do the opposite and move even further away (that is >further weaken) from the concept of a particle than it is the case in QFT >on Minkowski?

    Indeed. If you look at it carefully, GFTs are conceptually very far away from ordinary QFT, as much as it gets; to start with, they are not even defined on a spacetime.....

    >Furthermore you imply that conditions like causality, positive energy and >statistics are background dependent concepts... they are not by any means. >You confuse the principle here with its implementation in QFT on >Minkowski; actually, from the latter we know they are independent issues >even in this weakened context. By this, I mean that, for example, one can >drop positive energies and still get a causal QFT with the right >statistics. If you think about it deeper, you will need a principle for >having an arrow of time (positive energies) and independently you will >need to specify the statistics (that is the very nature of quantum >mechanics). Probably, you would need to specify the spin-statistics >relation (all research to a spin statistics theorem in quantum gravity >points in that direction) as well. So, you still need three independent >principles and you haven't gained anything.

    I am not sure I understand what you are trying to say. The notion of causality as such is indeed not necessarily dependent on a background, although we know how to implement it completely only in such case. Still, it can be taken as a definition of a background geometry, but more fundamental than this, as in causal sets or in some formulations of spin foam models. THe notion of energy, on the other hand, is necessarily tied to the existence of a timelike isometry, and thus to a given spacetime, so much that no such notion exist for matter fields on generic geometries or for geometry itself. Statistics refers to the behaviour of the wavefunction

    under certain discrete groups, usually coming from the motion group of objects embedded in some fixed space (at least as a topology). I do not deny that they are all important principles in all known physics, nor that some version of these concepts will be useful or even necessary in a more fundamental quantum theory of spacetime dynamics. I do believe, though, that their more fundamental form will be very different than the usual one, which is indeed background dependent, so much so that it is unclear to me to what extent one will still be able to talk about 'causality' or 'energy' as one understands them in standard background dependent, classical physics. I am not sure what the controversy is, here.

    >The problem is that you assume a priori that gravity has to be quantized >like any ''particle'' does.

    I have never stated anything like this, and I certainly do no assume it.

    >You care to give a good physical motivation for this, apart from saying >that ''quantum theory as we know it should be universally applicable?''.

    Again, I have never stated this as a matter of principle. In fact, I do believe that a drastic re-interpretation of quantum mechanics, if not a formal modification of it, will be necessary to understand properly the physics of quantum space. This will probably be true, again, even if the mathematical formulation of our quantum gravity models turn out to be formally rather conventional quantum mechanical theories, simply because, beyond their formal aspects, they aim to describe physics 'in absence' of spacetime, exactly because they want to describe the physics 'of' quantum spacetime.

    >Why do you assume that probably nobody has ''authority'' in this kind of >question?

    I simply mean that I am full of respect for anyone has studied carefully these issues (philosophical, mathematical, physical), thought hard about them, and understood already some aspects of them, but I am reluctant to grant 'authority' to anyone because 1) it is 'ideas' and 'results' that can have authority, not people, in science; 2) the subject is so difficult and our current understanding so incomplete (even if often tantalizing and exciting) that even ideas and results can only be taken as tentative and partial, so have even less 'authority'.

    >Moreover, what would you consider to be a satisfying answer ? If I tell >you that local realism cannot be excluded by any experiment, would you say >(a) that this is false (b) it is true (c) it is true, but not reasonable?

    if something 'cannot be excluded by any experiment' it is not a scientific fact, but at best a fertile philosophical hypothesis. Fine, follow it and let us see what scientific theory one can construct on its basis, and then how it compares with experiments and with other theories. If you simply mean that no existing experiment contradicts local realism, I would say that this is good, but does not imply that much, as it simply means that it should be reproduced in some approximation.

    >Now suppose I would say that there is no good reason to abandon the >continuum and that there exist strong arguments for it such as locality >and local Lorentz covariance. Would you say then that (a) this might be >true, but it doesn't prove that space-time is continuous since there is an >extremely tiny possibility that my assumptions fail (b) this is true and >probably means that space-time is a continuum (c) I exaggerate (and you >explain why). Moreover, take now into account the ''failure'' of discrete >space-time after 30 years and the impossibility of defining local >observables for the gravitational field (even in classical gravity), how >would you balance these facts?

    I would say that I do not find the arguments for the continuum as a fundamental description of space so compelling as you seem to do, but also that there are indeed interesting approaches to quantum gravity (e.g. asymptotic safety) based on continuum spacetime and that they should be pursued and developed to see what they teach us. Once we have one or more complete formulations of quantum gravity, we will see what assumption or picture of spacetime was more useful or correct. If by 'failure' you mean that no approach to quantum gravity has proven successful after 30 years, I would point out that 1) this includes both discrete and continuum approaches, so that past 'failures' do not lend support neither to continuum nor to discrete approaches as such; 2) that 'failure' is a misnomer because we have learnt a great deal from all of them (including the one that failed most definitely, i.e. perturbative quantization of gravity around flat space in the continuum), and we are building up on their partial successes as well as on their 'failures'.

    >To make myself crystal clear; suppose you have to bake a chicken and >someone would actually make a fire and bake it on a plate, or someone else >would put it on a plate and leave it in the sun holding a magnifying glass >over it. Would you encourage the second option, knowing the benefits of >the first?

    Being (I think) a moderately sane person, I would certainly eat happily the baked chicken; I am happy to taste any type of baked chicken recipe (also because I don't think I know what the perfect and correct recipe is, even if there was a single one). Unfortunately, up to now, all those that have come to me with a purported perfectly baked chicken have either misunderstood what a chicken is, and brought all sorts of less palatable animals, or misunderstood what baking and cooking means, and brought a chicken that was still completely raw, or entirely burnt, or with a disgusting sauce, or even still alive and running. So, I keep waiting for those who are trying to bake the proper animal in a proper way, aware of the difficulties in doing so, and willing to do mistakes but not to call a way too early (and thus disappointing) dinner.

    • [deleted]

    Dear Daniele,

    As a first comment, you seem to confuse my certainty about what does not work with the attitude that I know how it works. Maybe even this last statement is true, but that remains to be seen; in contrast to you, I am not justifying my own shortcomings by relating them to the weaknesses of others.

    In the first paragraph you say nothing I disagree with, the point I made was that it has nothing to do with the question of the contest whatsoever which obviously seems to be : ''if we have a theory valid at all scales, does its prescription require a continuum or not? Is it a theory in which space-time is actually measured or not?''. If it were just a matter to simply push the theory to some higher energy scale, we could as well be pleased with perturbative quantum gravity.

    What I mentioned with the observers in ''meta space'' simply was that if you take space-time as quantum, the theory is not closed; an observer would have to measure things from the outside which brings along many difficulties which you might want to think about deeper.

    Concerning local observables; yes in GR and standard approaches, this is a problem of general covariance which is usually circumvented by breaking it through adding point matter (which is of course the wrong thing to do). However, even at this level, you need to be careful what you mean: do you think about quantum covariance or classical covariance (even within quantum gravity)? Anyhow, this problem simply means that you are asking the wrong questions; there are no physical observables in vacuum gravity (even at the classical level). One cannot claim really that the Dirac observables are so. This means that you never measure geometry and that is in my opinion the correct interpretation of classical relativity where you could get local observables from studying relationships between planets expressed in their physical eigentimes. My ideas concerning this still go a few steps further and really avoid the problem too in the quantum theory.

    Concerning my insisting on the free theory, you do not comprehend what I say. Obviously, the free theory is unrealistic just like absolute zero is in thermodynamics (that is actually a law). However, this does not preclude that this theory should exist as a limit of your theory and actually even more, that it might serve as a basis for your theory. I gave you the example of stochastic electrodynamics where the stochastic background field is exactly the defining property of the thermodynamic limit T=0. The whole physics at T > 0 is crucially influenced by this feature in the sense for example that the orbit of a classical point like electron around a nucleus can be computed to be stable and that in the case of hydrogen, the probability distribution of the corresponding ground state actually coincides with the predictions of non-relativistic quantum mechanics. Another example like that is how we build QFT and compute cross sections. You may not like this, but there are deep physical reasons for why a theory is build like this. And of course, I was not thinking about the GLOBAL Poincare group like string theorists do, but about LOCAL Poincare groups, something which you could have learned by now by reading my little work.

    Concerning the asymptotic freedom, it is just not an ''argument'' but a deep realization how to bypass Haag's theorem and how GUT's in general behave. Actually, classical gravity is also asymptotically safe by means of the equivalence principle. And no, if you combine asymptotic freedom with strict locality, all the exotic possibilities you imagine do not exist anymore. So your freedom of ideas is an illusion.

    AQFT is just a reformulation of the same theory in a different mathematical language, so it is not very pleasing. What I say is that standard QFT is even wrong at the level of interactions and free theories in curved space-time. This requires a different theory and not some mathematical masturbation of the old one.

    Btw, I do know the literature quite well and nothing what you say has anything to do with a principled analysis which means : formulate physical principles and study its mathematical representations.

    Again, concerning the free theory; what you say is rather misplaced. GR did not start from special relativity, it actually required new math and a physical principle why special relativity would hold locally. Nothing of that sort is done in GFT as far as I see, where the rules are heuristic and derived from some approaches resulting from QM GR.

    By the way, nothing published in the last 10 years comes even close to answering the issues I adressed.

    Kind regards,

    Johan

      • [deleted]

      Dear Daniele,

      To respond to your second mail, yes you do reinstate ''particles'' by considering discrete chunks of ''space-time''. Concerning causality, you indeed do not understand what I say. Even in quantum field theories on a background space-time you have two different notions. First you have the light-cones which give you a distinction between what we call future and past (as well as the conformal scale) and second you have the Heisenberg commutation relations. One question is whether these two notions should coincide even for interacting quantum theories on Minkowski. But that was not my point. Nobody knows what causality means in the context of quantum gravity (even not Rafael Sorkin) and the point I made was that it should not be a fundamental principle here. This means that you have to modify somehow quantum mechanics itself unless you want to break local Lorentz covariance.

      Second, the notion of energy is indeed thight to timelike isometries in the conventional way of thinking. That is why the conventional way of thinking is wrong (and again you will find an answer to this in my little paper). Third statistics has nothing to do with the wave function, it is a the heart of quantum theory itself; it actually determines the dynamics ! Even more than this, the statistics question is only well posed on Minkowski because swapping free particles there is physically a well defined and path independent operation. The question itself even doesn't make any sense in a curved space-time (even one with a killing symmetry). So what I say is that QFT is even wrong in these cases. The controversy here is that all these principles are the corner stones of quantum theory itself and your favorite approaches leave quantum mechanics itself virtually untouched. That cannot be if you imagine the substitute principles to be very different.

      Kind regards,

      Johan

        • [deleted]

        Dear Daniele,

        I start to doubt whether you understand the basics of science. No idea can be proven wrong, a concrete realization can but the principle itself not. The whole scientific enterprise consists of the delicate art of balancing between principles, representations, ontology and experiment. For example, in case of Bell's theorem, most people would say it excludes local realism assuming the experiments favor quantum predictions but this is manifestly false, strictly speaking. Morally, however, I think it is true; by this I mean that a local realist theory matching nature would not be very natural and complicated.

        Furthermore, you do not seem to realize the depth of locality and local poincare invariance as fundamental principles of nature (which leads to the continuum). Both are tied to the definition of the vacuum state, something your favorite approaches fail in.

        Third, no, by failure I meant failure of discrete approaches. We are actually almost nowhere yet. Nobody knows how to properly construct a smooth effective geometry from a discrete spaghetti, nobody knows even to define the equivalent of a d'Alembertian on random discrete structures and so on... These are merely questions one should try to understand on the kinematical level first and all these difficulties are not present in the continuum approach. I guess you haven't thought too much about these things.

        About chickens, there exist plenty of possibilities: either you don't understand what the animal is, or you have prejudices about what it should be. Or perhaps, your palet is not as refined as one would expect it to be from an italian. Anyway, if you do not go and look for the chicken itself and keep on waiting, chances are high you will eat an earthworm in the end.

        Kind regards,

        Johan

          >As a first comment, you seem to confuse my certainty about what does not >work with the attitude that I know how it works. Maybe even this last

          even this type of certainty is something I quite envy. I am not certain even about the incorrectness of any of the many approaches to quantum gravity I know of. Obviously, I have my own preferences, which I try to base as much as I can on careful reasoning, and I am forced, as a professional working in this area, to place my bets on what I feel has the best chances of working.

          >statement is true, but that remains to be seen; in contrast to you, I am >not justifying my own shortcomings by relating them to the weaknesses of >others.

          that's rather gratuitous. anyway, it does not alter much the content of the discussion, so I do not need to comment further.

          >In the first paragraph you say nothing I disagree with, the point I made >was that it has nothing to do with the question of the contest whatsoever >which obviously seems to be : ''if we have a theory valid at all scales, >does its prescription require a continuum or not? Is it a theory in which >space-time is actually measured or not?''. If it were just a matter to >simply push the theory to some higher energy scale, we could as well be >pleased with perturbative quantum gravity.

          good we agree on what I wrote. My point was that even if a theory is valid in principle at all scales, for example a theory of spacetime, this does not mean that it is 'ultimate' or 'most fundamental' nor that it would give a univocal answer to the discrete/continuum question for spacetime. GFT could well be in principle valid at all scales, but, I argue, admits or would admit a variety of descriptions for spacetime at different scales and in different phases. At a more established and mundane level (and maybe less directly relevant to the spacetime issue), QCD is valid at all scales but its prescription requires a discrete spacetime in the non-perturbative regime, and a continuum one at weak coupling, to be useful in any way.

          >What I mentioned with the observers in ''meta space'' simply was that if >you take space-time as quantum, the theory is not closed; an observer >would have to measure things from the outside which brings along many >difficulties which you might want to think about deeper.

          on this:

          1) I am not arguing for the treatment of spacetime as a whole (the universe) as a quantum system (more than, possibly, at some very coarse level of approximation), somehow to be measured from the outside in the standard interpretation of quantum mechanics. Indeed, this is physically highly dubious. And in fact, one thing I find attractive in GFT (and other approaches) is that it allows you to consider 'local' chunks of spacetime, and to ask question about what an outside observer would measure at the boundary of such regions. It is still true, of course, that we are far from being able to reconstruct a continuum space (as we should at least in some limit) from this description and to check if it gives reasonable physics. I do not think I claimed the opposite.

          2) I am aware of (and I stated) the difficulties in applying quantum mechanics as we know it to spacetime, as I am aware of the difficulties in developing suitable modifications (whether mathematical or interpretational) of it that would make application to spacetime easier.

          I do agree that there is also a logical possibility that one should not apply any form of quantum mechanics at all to spacetime, but rather leave it classical or try to define it altogether from the interactions of (quantum) matter fields or similar (e.g. strings), without treating it as a physical system in itself that exist outside matter. In fact, I am interested in any approach that tries to do so, either philosophically or physically. However, I have not seen yet any satisfactory theory constructed on this basis, and on the other hand I am more convinced by the logical alternatives.

          >Concerning local observables; yes in GR and standard approaches, this is a >problem of general covariance which is usually circumvented by breaking it >through adding point matter (which is of course the wrong thing to do).

          the inclusion of (not necessarily point-like) matter does not break any covariance. And it does not sound wrong, given that we do observe matter around us.

          >However, even at this level, you need to be careful what you mean: do you >think about quantum covariance or classical covariance (even within >quantum gravity)? Anyhow, this problem simply means that you are asking >the wrong questions; there are no physical observables in vacuum gravity >(even at the classical level). One cannot claim really that the Dirac >observables are so. This means that you never measure geometry and that is >in my opinion the correct interpretation of classical relativity where you >could get local observables from studying relationships between planets >expressed in their physical eigentimes. My ideas concerning this still go >a few steps further and really avoid the problem too in the quantum >theory.

          It is well possible that the consideration of vacuum space is but a idealization, and I agree that the inclusion of matter is necessary in any model of (classical and quantum) gravity to extract physical result. See the answer I gave above to another contributor. I have no problem with this. I do not agree on the implication that the consideration of vacuum space and gravity is wrong even as an idealization, and necessarily leads to the use of the wrong mathematical or conceptual structures. But again, I think everybody would welcome any solid advance whatever point of view it is based on.

          >Concerning my insisting on the free theory, you do not comprehend what I >say. Obviously, the free theory is unrealistic just like absolute zero is >in thermodynamics (that is actually a law). However, this does not >preclude that this theory should exist as a limit of your theory and >actually even more, that it might serve as a basis for your theory. I gave >you the example of stochastic electrodynamics where the stochastic >background field is exactly the defining property of the thermodynamic >limit T=0. The whole physics at T > 0 is crucially influenced by this >feature in the sense for example that the orbit of a classical point like >electron around a nucleus can be computed to be stable and that in the >case of hydrogen, the probability distribution of the corresponding ground >state actually coincides with the predictions of non-relativistic quantum >mechanics. Another example like that is how we build QFT and compute cross >sections. You may not like this, but there are deep physical reasons for >why a theory is build like this.

          I have no problem with any of the above, but I do not see how it changes the point of the discussion. The fact that a theory exists as a limit of another does not imply (although in some cases it is true) that the other should be built on the same conceptual or physical foundations.

          An example is any quantum theory, which has some classical theory as a limit, but is built on entirely different conceptual foundations. Some new features may also arise (and even be taken as foundational) in the weak coupling limit of a more general theory not based on them. Unless you simply mean that well tested, if approximate theories, should be reproduced necessarily as a consistency check on newer ones. With this, I obviously agree.

          >And of course, I was not thinking about the GLOBAL Poincare group like >string theorists do, but about LOCAL Poincare groups, something which you >could have learned by now by reading my little work.

          I did not have time to read it, indeed. I look forward to do so. Let me note that even the local Poincare' group could be a feature that arise only in some approximation (e.g. if anything like 'deformed special relativity' is true in some semi-classical regime), and it is not obvious to me that it should be taken as a foundational principle.

          >Concerning the asymptotic freedom, it is just not an ''argument'' but a >deep realization how to bypass Haag's theorem and how GUT's in general >behave. Actually, classical gravity is also asymptotically safe by means >of the equivalence principle.

          I guess you mean 'asymptotically free' here. Although I do not understand your application of the terms to a classical theory, given that I know of their definition and application only to quantum field theories. I'll check again the literature.

          >And no, if you combine asymptotic freedom with strict locality, all the >exotic possibilities you imagine do not exist anymore. So your freedom of >ideas is an illusion.

          Once more, even if what you say was true, it would merely imply the incompatibility of assuming asymptotic freedom and strict locality, with assuming other basic principles or structures. Ok. Useful. But it would not say much, I think, on the validity of one over the others, which would have to be decided on other grounds (e.g. mathematical first and experimental then). In order to do so, I think it is important to encourage freedom of ideas and the possibility to pursue even mutually incompatible ones, until one acquires more weight that others. I do not think we are there yet.

          >AQFT is just a reformulation of the same theory in a different >mathematical language, so it is not very pleasing. What I say is that >standard QFT is even wrong at the level of interactions and free theories >in curved space-time. This requires a different theory and not some >mathematical masturbation of the old one.

          Fine. So we need a new theory of gravity, because GR admits vacuum solutions and dynamics, which cannot be truly physical, and new theories of matter, because the ones we have are based on interacting quantum field theories, which are also wrong. Still, we need to recover them in some approximation, since they have proven useful and physically correct to some extent. This seems to leave us with quite a task. But I still do not understand your proposal. It should be quite something, though, given the task, so I look forward to read your essay.

          >Btw, I do know the literature quite well and nothing what you say has >anything to do with a principled analysis which means : formulate physical >principles and study its mathematical representations.

          Physics, for what I see, does not always work in such simple way, unfortunately, and sometimes we have to work in a much more tentative way, until we discover or realize what the correct 'principle' formulation of our theory should be. Actually, I do not think that any theory has been ever developed in such 'principled' way, even though it could maybe be presented this way -after- it has been fully developed. Not even relativity was found this way, and nobody has ever been so clear in his logical thinking than Einstein...

          >Again, concerning the free theory; what you say is rather misplaced. GR >did not start from special relativity, it actually required new math and a >physical principle why special relativity would hold locally. Nothing of >that sort is done in GFT as far as I see, where the rules are heuristic >and derived from some approaches resulting from QM GR.

          It is true that we do not have a principle-based formulation of GFT, and that we should try to understand better what its basic principles are or should be, also to guide any future development. If this is what you mean... but so what? Unfortunately, to identify some principles one can trust and simply follow them is not the rule of the game. I wish it was so simple!

          >By the way, nothing published in the last 10 years comes even close to >answering the issues I adressed.

          I am somehow happy that I am not the only one to disappoint your expectations. And if you really -address- all those issues, univocally, solidly and satisfactorily, well, I am sure your work will be welcomed by the community, so keep up with the work!

          >To respond to your second mail, yes you do reinstate ''particles'' by >considering discrete chunks of ''space-time''.

          as an analogy, indeed. But as such it does not contradict anything we know about existence or non-existence, validity or not validity of the particle concept, in flat or curved spaces etc.

          >Nobody knows what causality means in the context of quantum gravity (even >not Rafael Sorkin) and the point I made was that it should not be a >fundamental principle here. This means that you have to modify somehow >quantum mechanics itself unless you want to break local Lorentz >covariance.

          I agree that the notion of causality is dubious in a quantum gravity context, and in fact I think I have stated this at some point in this discussion. I also think that locality as well is of difficult application in a quantum gravity context, and not obviously to be used as a foundational principle. In particular, in any framework in which spacetime is somehow emergent or the metric fluctuates, then it is almost necessary that locality should be at least re-interpreted very differently. Alternatively, one can decide to stick to the usual notion of locality and therefore do not follow any approach that necessarily leads to revising it or dropping it. Fine. I am simply not convinced we have such a solid argument for preferring this line of thought. Moreover, let me briefly point out that 'breaking of lorentz covariance' is not the only option, as in some approaches one tries to implement a deformation of the same, still based on 10-dimensional symmetries, only represented by quantum groups rather than lie algebras.

          >Second, the notion of energy is indeed thight to timelike isometries in >the conventional way of thinking. That is why the conventional way of >thinking is wrong (and again you will find an answer to this in my little >paper). Third statistics has nothing to do with the wave function, it is a >the heart of quantum theory itself; it actually determines the dynamics ! >Even more than this, the statistics question is only well posed on >Minkowski because swapping free particles there is physically a well >defined and path independent operation. The question itself even doesn't >make any sense in a curved space-time (even one with a killing symmetry). >So what I say is that QFT is even wrong in these cases. The controversy >here is that all these principles are the corner stones of quantum theory >itself and your favorite approaches leave quantum mechanics itself >virtually untouched. That cannot be if you imagine the substitute >principles to be very different.

          Beside the fact that I do not agree with some of your statements above, this is not so important. If your point is simply that standard quantum mechanics is based on several assumptions and mathematical ingredients that in turn rest on the existence of a (usually flat) background spacetime, I agree with this. If you infer from this that we will need at the very least a drastic re-interpretation of quantum mechanics in a quantum gravity context, I also agree. Unfortunately, this does not say much about how we should modify it nor implies that much about how or to what extent we can rely on it in developing new theories of spacetime or whatever substitutes it at a more fundamental level. We should work a bit harder, try applying some elements of it, or developing new formulations of it, and see what we get. The approaches I work with are quite flexible as to what formulation or interpretation of quantum mechanics is best suited to them, and will in any case force us a drastic re-interpretation of it, if only because, as I stressed, they are not based on any spacetime in their definition.

          >I start to doubt whether you understand the basics of science.

          I see you are not able to avoid personal statements. That is bad. But I think I can still manage to do so, which is good because they are not very useful.

          >No idea can be proven wrong, a concrete realization can but the principle >itself not. The whole scientific enterprise consists of the delicate art >of balancing between principles, representations, ontology and experiment.

          Thanks for this brief summary of the last centuries of philosophical thinking.

          >Furthermore, you do not seem to realize the depth of locality and local >poincare invariance as fundamental principles of nature (which leads to >the continuum). Both are tied to the definition of the vacuum state, >something your favorite approaches fail in.

          it could well be that I fail to appreciate fully these principles. However, I have been working also on identifying the basic symmetries and the correct notion of locality that applies, in absence of a background spacetime, to the kind of models I like, and how these characterize the GFT (perturbative) vacuum state. It must mean that I somehow sense, in all my limitations, the importance of them, for any physical theory.

          >Third, no, by failure I meant failure of discrete approaches. We are >actually almost nowhere yet. Nobody knows how to properly construct a >smooth effective geometry from a discrete spaghetti, nobody knows even to >define the equivalent of a d'Alembertian on random discrete structures and >so on... These are merely questions one should try to understand on the >kinematical level first and all these difficulties are not present in the >continuum approach. I guess you haven't thought too much about these >things.

          Beside once more irrelevant personal statements, I guess I disagree on the evaluation of what we have achieved and understood, up to now, in the different continuum and discrete approaches to quantum gravity. Never mind. There are plenty of clever people I disagree with and others I agree with.

          >About chickens, there exist plenty of possibilities: either you don't >understand what the animal is, or you have prejudices about what it should >be. Or perhaps, your palet is not as refined as one would expect it to be >from an italian. Anyway, if you do not go and look for the chicken itself >and keep on waiting, chances are high you will eat an earthworm in the >end.

          I agree with all of the above, if you meant it as a general statement; I still fail to appreciate it, if you intended it as referring to me personally.

          Now, please excuse me....I have a chicken in the oven....

          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

            Hi Moshe,

            thanks for your message and interest. I had already downloaded your essay, of course, but I didn't manage to read it yet. I hope t be able to do it by tomorrow.

            If I have anything interesting to say, I'll send you my comments.

            Best,

            Daniele

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

            • [deleted]

            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

              • [deleted]

              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

                • [deleted]

                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