Dear Johan,

thanks for you comments and interest, and sorry for the delay in my reply.

It is certainly true that the limitations of the essay format implied that I could not touch on all of the aspects of the problem that I would have like to, and that even those that I discussed could have been explained and treated in much more detail and more satisfactorily. However, it would not...

view entire post

Dear Johan,

thanks for you comments and interest, and sorry for the delay in my reply.

It is certainly true that the limitations of the essay format implied that I could not touch on all of the aspects of the problem that I would have like to, and that even those that I discussed could have been explained and treated in much more detail and more satisfactorily. However, it would not be honest to blame these limitations for any shortcoming of my essay. My own limitations in knowledge and expository skills are what I am more concerned with and what I, like everyone else, should try to improve on.

Let me try to clarify a bit more my thoughts on this matter by replying to your comments, which I am not sure I really understand though.

First, as a general comment on atoms, gas, fluids and condensed matter systems, I do not claim to have written anything original on any of this, in my essay. The parallel with atoms and condensed matter systems is indeed used only to exemplify, using familiar concepts, a certain picture of quantum space that cannot be as familiar, because of the more exotic nature of the subject, and the more limited comprehension of it we have.

So I agree with your comment that the limited, not absolute, purely effective nature of our description of atoms as discrete, of a gas as discrete or of a fluid as continuous is agreed upon by any physicist. Again, I am happy we agree on this because I was not trying to say anything original here. However, I also think that any physicist would agree that 'atoms are discrete' in the 'effective, limited' sense that there exists circumstances (e.g. relativistic effects should indeed by neglected to some extent) in which the physics of a system is well-described by a few discrete entities behaving like particles etc. Same for field theories around the Fock vacuum in flat space at low orders in perturbation theory etc. The fact that this effective description, valid in some circumstances, has to be replaced by another in which the same system is described by a continuous medium, for example, in other circumstances, is exactly the rationale behind my 'it depends' and, as I tried to explain, rests indeed on the characteristic properties of QFT.

Then you say something crucial: ''Fact is that QFT is defined on a continuum''. Indeed. This hints at the fact that it is this underlying continuum spacetime that one is considering as being 'fundamentally so' or, alternatively as 'fundamentally discrete' in nature, e.g. described by a causal set.

The main point of my essay is that one can 1) take the fundamentally discrete entities constituting spacetime at the quantum level in some approaches to quantum gravity (lattices, graphs, possibly also elements in a causal set, etc); 2) re-interpret them as 'particles', 'atoms' of space in analogy with the 'real' ones of condensed matter systems; 3) describe their dynamics in terms of a field theory that is not defined on any spacetime itself but rather on some internal, auxiliary, meta-space (call it as you like), the group manifold; 4) have as a result the same richness of different phases and effective descriptions (continuous, discrete etc) for spacetime that one has for condensed matter systems.

This means that the same limited validity of both the continuous and 'atomic' description of fields in QFT or of condensed matter systems will hold true for spacetime itself. Thus, the question of whether spacetime is discrete or continuous can only have answer 'it depends'. And the question whether it is either fundamentally one way or the other can only have answer 'no', because neither description would be fundamental, as you correctly say for atoms or gases or fluids.

To try to argue for the above point of view was the main goal of the essay.

You mention several important issues, related to the fundamental status of several features of QFT on flat space, like causality, locality, statistics, etc and ask whether GFT contributes to our understanding of them. For some of them it does, and I can only refer to the literature for all current work. The object of the essay, you would understand, could not be to address these issues. Certainly, GFT denies their validity at a more fundamental level, because they are very much tied to the background dependent description of ordinary QFT.

However, we are very far from being able to show how they emerge from a purely background independent description of space (e.g as the one of GFT). The theory is very incomplete, and indeed the main open problem, as far as I can tell, is to prove that a continuum description of spacetime and General Relativity (and thus special relativity) arises from GFT.

As you also say, nobody knows, at present, how to do this. However, I do not see why this inability should be mistaken for impossibility (either in principle or in practice) and thus invalidate the picture I tried to paint, beside the fact that obviously much more work is needed to validate it (and actually, also to refute it). Again, for all the current work on this issue, which I mentioned in the text, I refer to the literature (e.g. that on GFT renormalization, on the extraction of physics from spin foams, on the effective non-commutative field theories obtained as perturbations of GFT solutions, etc).

The comparison with condensed matter is indeed just an analogy, as I stressed in the text, possibly useful to guide us towards a better understanding of quantum space, but I agree it cannot be taken literally because our condensed matter theories are (as they should be, given that real condensed matter systems live in our labs) based on a fixed, flat spacetime.

Finally, I am well aware of the many philosophical issues raised by the very notion of quantum space, and of all those intertwined with every aspect of quantum gravity research (and even before that, with Genera Relativity and Quantum Mechanics themselves). However, first, I do not see how these issues (all currently and hotly debated among philosophers and physicists) make the 'whole idea' unlikely; second, to discuss these issues was not the scope of my essay, focused on a much more limited question and trying to achieve a a more limited goal: to present and argue for the general picture I outlined again above, in the hope that it could be stimulating and inspiring for further research of others as it is for mine.

Thanks again for you interest and comments and do not hesitate to put forward more of them or any specific doubt or question. I would be happy to discuss any such specific issue.

Best,

Daniele

view post as summary

Dear Daniele,

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

view entire post

Dear Daniele,

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. 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. 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).

Moreover, I guess you start from space and not space-time right? 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. Let me give you a few examples : free QFT on flat space-time is exactly correct without any doubt. 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. 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. 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. GFT probably satisfies none of those requirements (including covariance!) and I haven't seen a good principled analysis nowhere in the literature.

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.

Kind regards,

Johan

PS: I do not care about how you write things, expository skills are a matter of social convention and I have never cared too much about what others ''think''. 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.

view post as summary

>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...

view entire post

>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.

view post as summary

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....

view entire post

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

view post as summary

>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...

view entire post

>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!

view post as summary

>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...

view entire post

>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.

view post as summary

>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...

view entire post

>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.

view post as summary

>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...

view entire post

>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.

view post as summary

>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...

view entire post

>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.

view post as summary

Dear Sir,

Mr. Peter Jackson, one of the finalists had asked us some clarifications. We think it may be of interest to you. Hence we post the reply to him below your Essay.

First let us answer to your question regarding how direct observation could be different. Since you are fond of spectroscopy, we will give you an example from that branch. Look at the mechanism behind the emission...

view entire post

Dear Sir,

Mr. Peter Jackson, one of the finalists had asked us some clarifications. We think it may be of interest to you. Hence we post the reply to him below your Essay.

First let us answer to your question regarding how direct observation could be different. Since you are fond of spectroscopy, we will give you an example from that branch. Look at the mechanism behind the emission spectra and absorption spectra. Both the emitter and the observer are in the same bigger frame of reference linking both and separated by the field. You will admit that the scattering in the medium causes the difference.

You say: “direct light hitting the eye is also scattered.” In our theory, different forces co-exist. Thus, it is not scattering, but comparison like when we measure (compare) the length of a rod by a scale. The scale is not scattered by the rod. When you say “it can be apparent when we move”, you are falling into the trap laid by Einstein. We have discussed it elaborately earlier by giving the example of Eddington.

You have not defined dark matter or dark energy precisely. The phenomena cited by you as proof is indirect and not direct. We can explain those phenomena differently. You also admit this possibility indirectly when you say: “The plasma does the precise job our imaginary 'dark matter' does, and in the same places!”

You say: “The references again show that curved space time exactly matches the effects of diffraction (gentle refraction delays and path curvature) via scattering in plasma.” We have given our interpretation of “curved space-time”, which is different from GR and it can also explain the effects of diffraction equally correctly.

You say: “The separate terms plasma-sphere and ionosphere are really misnomers”. But you admit their difference when you say: “they are a graded whole, proton rich low down and electron rich higher up.” The grading is not smooth, but shows the same distribution like the arrangement of protons and electrons in an atom. Since protons and electrons are placed differently in nucleus and orbits, the plasma-sphere and ionosphere have to be treated as different. We divide the electric and magnetic fields into four types each based on their gradient. That, along with the interaction with the Solar wind will explain the rest of your comments.

Now we will explain 'velocity of the field', which also will explain the constancy of ‘c’. We have already explained that the basic nature of the field is equilibrium. The basic nature of forces is displacement. This gives rise to two different types of inertia: inertia of motion due to forces and inertia of restoration (elasticity) due to the field. This leads to both these inertia acting against a point of equilibrium to create locally confined structures. These structures, which are nothing but confined field is called “rayi”. Both the inertias further act on “rayi”. In such a scenario, the combined effect leads to repeated confinement around the point of equilibrium. The confined structures in which inertia of restoration dominates, is called particle (moorty). In the opposite case, it is called “amrita”. This can be considered as your DFM.

The confinement could be strong, weak or loose, which leads to the formation of solids, fluids (including gases) and plasma. We call these ‘dhruva”, “dhartra” and “dharuna” respectively. Where the inertia of motion dominates, it appears as heat. Depending upon the nature of the particles, the propagation of heat is also classified into three categories. In solids, plasma and fluids, these are done by conduction, radiation and convection. We call these as “nirbhuja”, “pratrirnna” and “ubhayamantarena” respectively. The third category gives rise to the electric field. Thus, electric behaves like a hot fluid.

Till now we were discussing about the confinement of “rayi” (where inertia of restoration dominates). In the opposite case, where inertia of motion dominates, “rayi” gives rise to three corresponding forces of cold confinement. These can explain the effects of the so-called “dark matter and dark energy”. Magnetism belongs to this category. Thus, magnetism is a cold confining force. Since both these are different states of “rayi”, electricity and magnetism are two sides of the same coin.

Till now we were discussing “rayi”, which is a part of the primordial field dominated by inertia of restoration. The other part is dominated by inertia of motion, which we call “praana”. The effect of this is felt by other bodies. Hence this gives rise to force. Depending on their effects on different bodies, these forces are classified into different groups discussed earlier. While strong, weak, electromagnetic and radioactive disintegration forces belong to this category associated with inertia of motion and heat, gravitational interaction is associated with inertia of restoration and cold. Thus, they cannot be united.

After a part of the primordial field is confined within “rayi”, inertia of restoration in the field becomes weak and inertia of motion dominates. Thus, the field generates waves that expand rapidly in all directions. You call this big bang. The effects of “rayi” and “praana” in the primordial medium create the bow shock effect. This leads to reduced velocity of the wave, which ultimately stabilizes, cutting off a vast volume which we call universe. Since there is no reason to believe that it happens only in our locality, we believe in multiverses, which are similar universes and not as described by MWI.

After the bow shock comes to rest, the forces of inertia of motion and inertia of restoration cancel each other leading both to a superposition of states. We call this “maayaa”. But the equilibrium is momentary, since the balance between “rayi” and “praana” within the confinement of “maayaa” has not been equated, the next moment inertia of restoration dominates and there is massive contraction. You call this inflation. We call this force “dhaaraa”. This creates further interaction, which leads to structure formation. We call this “jaayaa”. Outside the structures, the inertia of restoration still dominates. You call it the cosmic microwave back ground radiation. We call it “aapah”. Thus, the universe can be picturised as an ocean containing many islands. The galaxies can be imagined to float in an “ocean” called “saraswaan”, the stars can be imagined to float in an “ocean” called “nabhaswaan”, and the Earth like planets can be imagined to float in an “ocean” called “samudra arnava”.

Just like the Earth orbits the Sun and spins around its own axis due to the combined effects of the Sun’s movement and that of the inter-stellar medium that move in different directions on the one hand, the different magnetic fields on the other hand (in a broader scale, these are the effects of “rayi and praana” and “dhaaraa and jaayaa”), the Universe as a whole also moves within the confines of “maayaa”. This appears as the receding galaxies, just like the planets sometimes appear to move away from each other. This movement of the Universal field is constant for all structures. This is what you describe as “space has inertia and angular momentum.”

It is well known that objects are perceived only during transition. The transition can be of two types: the object can move or the field containing the object can move while the object is stationary (both together are also possible, but they fall into these two groups). In the case of electromagnetic field in space, it is the field that moves at a constant velocity. You also admit it when you say: “ALL matter in motion is in motion with respect to a LOCAL background. Light entering the galaxy is Doppler shifted by the Halo to the galaxies 'c', again at the heliopause to the Sun's 'c', and at the Ionosphere to the Earths 'c', and on ad infinitum.” The only difference is that you presume the particle is moving at ‘c’ with respect to the back ground, which you take as at rest. We take the opposite view of the background with us moving at ‘c’. Like we do not experience the motion of the Earth, but think the Sun and the stars are orbiting it, we do not experience the motion of the back ground since we are also moving with it. But the effects in both cases are the same.

Regarding the 3 frames, you are on the right track. Here we quote from one of our posts under the Essay of Mr. Rafael Emmanuel Castel, where we had commented elaborately about Einstein’s 1905 paper.

Einstein: We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:

3. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.

4. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous stationary clocks located at different places, and have evidently obtained a definition of “simultaneous”, or “synchronous”, and of “time”. The “time” of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.

Our comments: Einstein sets out in the introductory part of his paper: “…the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate…”. The “Principle of Relativity” is restricted to comparison of the motion of one frame of reference relative to another. Introduction of a third frame of reference collapses the equations as it no longer remains relativistic. The clock at B has been taken as a privileged frame of reference for comparison of other frames of reference. If privileged frames of reference are acceptable for time measurement, then the same should be applicable for space measurement also, which invalidates the rest of the paper.

Simultaneity refers to occurrence of more than one action sequences, e.g.; events, which measure equal units in two similar action sequence measuring devices, e.g.; clocks, starting from a common reference point, e.g.; an epoch. It is the opposite of successive events. Synchronisation refers to the readings of more than one clock (or interval between event from an epoch), which do not require “clock correction”, i.e.; when such readings are compared with a common or identical repetitive action sequence or action sequence measuring devices, their readings match. It is not the opposite of successive events, but can also be simultaneous – for example, two clocks synchronised with each other will give similar readings simultaneously. If one of the clocks give 24 hour reading while the other gives 12 hour reading, then half of the time they will give readings that are synchronized and simultaneous, while half of the time they will not be so. Yet, the results can be made to synchronize by deducting 12 hours from any reading beyond it in the clock giving 24 hours reading. Here the clocks will be synchronized through out, but give simultaneous readings alternatively in succession or otherwise.

In the definition of simultaneity given by Einstein, the two clocks situated at two distant points in the same frame of reference (whether the frame of reference is inertial or not is not relevant as both the clocks and points P and P’ are fixed in the frame) are said to be synchronous, if their readings of the identical events in both clocks match. This only refers to the accuracy of mechanical functioning of the clocks and uniformity of the time unit used in both the clocks. This definition is nothing but telling the obvious in a complicated and confusing manner. Since the two clocks are synchronised, they should record equal time in both the frames of reference over equal interval.

We have also shown that if we follow the logic of Einstein, then we will land in a problem like the Russell’s paradox of set theory. In one there cannot be many, implying, there cannot be a set of one element or a set of one element is superfluous. There cannot be many without one meaning there cannot be many elements, if there is no set - they would be individual members unrelated to each other as is a necessary condition of a set. Thus, in the ultimate analysis, a collection of objects is either a set with its elements or individual objects, which are not the elements of a set.

Let us examine set theory and consider the property p(x) : x  x, which means the defining property p(x) of any element x is such that it does not belong to x. Nothing appears unusual about such a property. Many sets have this property. A library [p(x)] is a collection of books. But a book is not a library (x  x). Now, suppose this property defines the set R = {x : x  x}. It must be possible to determine if RR or RR. However if RR, then the defining properties of R implies that RR, which contradicts the supposition that RR. Similarly, the supposition RR confers on R the right to be an element of R, again leading to a contradiction. The only possible conclusion is that, the property “x  x” cannot define a set. This idea is also known as the Axiom of Separation in Zermelo-Frankel set theory, which postulates that; “Objects can only be composed of other objects” or “Objects shall not contain themselves”.

In order to avoid this paradox, it has to be ensured that a set is not a member of itself. It is convenient to choose a “largest” set in any given context called the universal set and confine the study to the elements of such universal set only. This set may vary in different contexts, but in a given set up, the universal set should be so specified that no occasion arises ever to digress from it. Otherwise, there is every danger of colliding with paradoxes such as the Russell paradox, which says that “S is the set of all sets which do not have themselves as a member. Is S a member of itself?” Or as it is put in the everyday language: “A man of Serville is shaved by the Barber of Serville id and only if the man does not shave himself?” Such is the problem in Special theory of Relativity.

Thus, “when we have to connect in time series of events occurring at different places, or - what comes to the same thing - to evaluate the times of events occurring at places remote from the watch”, we must refer to a common reference point for time measurement, which means that we have to apply “clock corrections” to individual clocks with reference to a common clock at the time of measurement which will make the readings of all clocks identical. (Einstein has also done it, when he defines synchronization in the para below). This implies that to accurately measure time by some clocks, we must depend upon a preferred clock, whose time has to be fixed with reference to the earlier set of clocks whose time is to be accurately measured. Alternatively, we will land with a set of unrelated events like the cawing of a crow and falling of a ripe date palm simultaneously. A stationery clock and a clock in a moving frame do not experience similar forces acting on them. If the forces acting on them affect the material of the clock, the readings of the clocks cannot be treated as time measurement. Because, in that case, we will land with different time units not related to a repetitive natural event - in other words, they are like individual elements not the members of a set. Hence, the readings cannot be compared to see whether they match or differ. The readings of such clocks can be compared only after applying clock correction to the moving clock. This clock correction has nothing to do with time dilation, but only to the mechanical malfunction of the clock.

There is nothing like empty space. Space, and the universe, is not empty, but full of the Cosmic Background Microwave Radiation from the Big-Bang. In addition to this, space would also seem to be full of a lot of other wavelengths of electromagnetic radiation from low radio frequency to gamma rays. This can be shown by the fact that we are able to observe this radiation across the gaps between galaxies and even across the “voids” that have been identified. Since the universe is regarded as being homogeneous in all directions, it follows that any point in space will have radiation passing through it from every direction, bearing in mind Olber’s paradox about infinite quantities etc. The “rips” in space-time that Feynman and others have written about are not currently a scientifically defined phenomenon. They are just a hypothetical concept - something that has not been observed or known to exist. Thus, “light signals, given out by every event to be timed, and reaching him through empty space” would be affected by these radiations and get distorted.

Regards,

basudeba

view post as summary