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.