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]

  • Post #28

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]

    • Post #29

    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]

      • Post #30

      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]

          • Post #38

          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]

            • Post #39

            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]

              • Post #40

              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

                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]

                • Post #42

                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]

                • Post #43

                >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.