- #141
CarlB
Science Advisor
Homework Helper
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Careful said:
An example of this would be someone having you explain what "measurement" means when the standard model clearly doesn't have a clue.
Carl
Where we stand-Baez talk at Luminy
- Thread starter marcus
- Start date
In summary, John Baez gave a talk on fundamental physics, discussing the search for a small set of laws that can explain everything in the universe. He also talked about the current state of theoretical physics, addressing issues such as the string theory controversy and the lack of progress in theoretical physics in the last 25 years. Baez suggests that the root of the problem may lie in the way physics students are trained to think and the deep emotional investment they have in their field. He also mentions the danger of clinging to old ideas and the need for physicists to be open to new and surprising data. Overall, Baez's talk offers a thought-provoking critique of the current state of theoretical physics and highlights the need for a shift
An example of this would be someone having you explain what "measurement" means when the standard model clearly doesn't have a clue.
Carl
- #142
Careful
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**Careful what I would like from you is an arxiv link to one or several of your research papers, please. You have made your own research rejection by academia an issue. I want to know what it is. **
Oh no, Marcus I did not make that an issue at all : my background (as a person) here is entirely unimportant (and many of my papers were well received actually), let's stick to the content right ? I thought on this forum we can discuss physics and not be merely royalty watchers. When I spoke about realist papers I did not speak about myself in the first place. I am offering some specific general discussion points about background independent approaches and I get no response from you on these concrete fundamental issues.
**
the topic of this thread is Baez talk on the current situation in fundamental physics and looking ahead **
So, that means we can speak about fundamental issues in physics, no? :grumpy: Good, you don't like what I say, so please argue. In case you find yourself unable to do so, then we indeed better quit this discussion which has clearly no use then. For a change, can I ask you why you are so LQG oriented, you clearly are not aware of the details of many works, so how can you so confidently defend it ? Because you simply don't like the monopoly of string theory and you are in for some alternative ideas ?
Cheers,
Careful
Oh no, Marcus I did not make that an issue at all : my background (as a person) here is entirely unimportant (and many of my papers were well received actually), let's stick to the content right ? I thought on this forum we can discuss physics and not be merely royalty watchers. When I spoke about realist papers I did not speak about myself in the first place. I am offering some specific general discussion points about background independent approaches and I get no response from you on these concrete fundamental issues.
**
the topic of this thread is Baez talk on the current situation in fundamental physics and looking ahead **
So, that means we can speak about fundamental issues in physics, no? :grumpy: Good, you don't like what I say, so please argue. In case you find yourself unable to do so, then we indeed better quit this discussion which has clearly no use then. For a change, can I ask you why you are so LQG oriented, you clearly are not aware of the details of many works, so how can you so confidently defend it ? Because you simply don't like the monopoly of string theory and you are in for some alternative ideas ?
Cheers,
Careful
- #143
Careful
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CarlB said:
You got it :tongue:
- #144
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Careful said:The painful contradiction in this story is that really fundamental research in QM is frowned upon and almost forbidden; so far your liberty in academics
Cheers,
Careful
marcus said:
Careful said:
I have to repeat. Your apparent disatisfaction with the reception of your research is an issue. You have raised the business of academic freedom and suppression of approaches that arent somebody's (like 't Hooft's) pets. and you keep suggesting that you have the right approach and that whatever the QG community at large is pursuing is doomed to fail. It is too obvious that if your ideas can't be accepted then everybody else has to be wrong.
You clearly have an ax to grind. So show us the ax.
Show us the research which is presumably on the right track---since you act like you've shown all these other people to be on the wrong track.
All the time you have been here at PF there is only one person that I can remember whose research you have approved----it is Johan Noldus. Since I don't have your papers, I will use his as an example.
IIRC it was in the "List of new initiatives" thread, I will get the link. Your approval even in this case was very lukewarm, I must say. I would like to have a sample of your own, but lacking that I will go fetch some that I recall your speaking positively about.
================
here we are
https://www.physicsforums.com/showthread.php?p=852574#post852574
marcus said:
Careful said:
even here you are not very generous with your approval, Careful. But in the next you seem to warm up some:
https://www.physicsforums.com/showthread.php?t=103750
This last link here is the closest thing to praise from you of someone's research that I have seen.
If you think everybody else work is so hopeless (and to me your arguments seem forced, as if by a need to show it) then I would really like to see what you do yourself.
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- #145
Kea
- 859
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My, my, haven't we all been busy? First, please permit me to define a few broad terms, as I believe they are commonly used.
Quantum Gravity: a very loose term meaning any theory capable of completely reproducing computational SM plus GR. This, of course, rules out conventional Strings, LQG and a large number of other proposals.
Background Independent: a property of a physical theory or model that must incorporate (1) independence of spacetime coordinates, and (2) a lack of any form of aether. This second condition is far more stringent. Even GR fails this test.
Logic: a not-necessarily-classical use of syntax with accompanying semantics involving truth-valued propositions and operations such as AND, OR, NOT, implication and quantifiers.
(Local) Observable: a mathematical construct representing the semantics of measurable numerical quantities. Clearly any theory that does not address the problem of measurement cannot hope to have a complete description of such operators.
Magic: entertainment involving well-trained tigers, hoops, mirrors, saws and people in shiny costumes.
In response to a couple of Careful's comments:
Not according to the definitions that I have given above. You have been using a more restrictive set of definitions, in response to the comments of others, but some readers reasonably appear to be finding this loose use of terms confusing.
I think I more or less or agree, although you have not been clear, but the fact that QM needs alteration does not necessarily mean that we need to throw QM intuition out the window. I wonder if it has occurred to you that your conclusions re the necessity of a classical direction here might in fact be wrong. The alternatives involve enlarging one's sphere of logic - seemingly dire perhaps - but alternatives in the spirit of QM all the same.
An article I like by d'Espagnat is Quantum logic and non-separability in the volume The Physicist's Conception of Nature, edited by Mehra for Dirac's 70th birthday.
Quantum Gravity: a very loose term meaning any theory capable of completely reproducing computational SM plus GR. This, of course, rules out conventional Strings, LQG and a large number of other proposals.
Background Independent: a property of a physical theory or model that must incorporate (1) independence of spacetime coordinates, and (2) a lack of any form of aether. This second condition is far more stringent. Even GR fails this test.
Logic: a not-necessarily-classical use of syntax with accompanying semantics involving truth-valued propositions and operations such as AND, OR, NOT, implication and quantifiers.
(Local) Observable: a mathematical construct representing the semantics of measurable numerical quantities. Clearly any theory that does not address the problem of measurement cannot hope to have a complete description of such operators.
Magic: entertainment involving well-trained tigers, hoops, mirrors, saws and people in shiny costumes.
In response to a couple of Careful's comments:
Not according to the definitions that I have given above. You have been using a more restrictive set of definitions, in response to the comments of others, but some readers reasonably appear to be finding this loose use of terms confusing.
I think I more or less or agree, although you have not been clear, but the fact that QM needs alteration does not necessarily mean that we need to throw QM intuition out the window. I wonder if it has occurred to you that your conclusions re the necessity of a classical direction here might in fact be wrong. The alternatives involve enlarging one's sphere of logic - seemingly dire perhaps - but alternatives in the spirit of QM all the same.
An article I like by d'Espagnat is Quantum logic and non-separability in the volume The Physicist's Conception of Nature, edited by Mehra for Dirac's 70th birthday.
- #146
Careful
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** You have raised the business of academic freedom and suppression of approaches that arent somebody's (like 't Hooft's) pets. and you keep suggesting that you have the right approach and that whatever the QG community at large is pursuing is doomed to fail. It is too obvious that if your ideas can't be accepted then everybody else has to be wrong. **
Ah marcus, you clearly did not understand how research works. When you are a young researcher who wishes to really solve conceptual problems, you have to sidestep for some amount of time with the consequence that one stops publishing. Those who do publish, are very much aware of these shortcomings I raised too (otherwise you do not deserve PhD in front of your name), they merely content themselves with the knowledge that one of their future heroes will solve it.
**
All the time you have been here at PF there is only one person that I can remember whose research you have approved----it is Johan Noldus. Since I don't have your papers, I will use his as an example.
IIRC it was in the "List of new initiatives" thread, I will get the link. Your approval even in this case was very lukewarm, I must say. **
Well, clearly this guy was only at the beginning of adressing the conceptual flukes in QM at that time - the retour to realism does not necessarily imply a negation of the Bell tests.
**If you think everybody else work is so hopeless (and to me your arguments seem forced, as if by a need to show it) then I would really like to see what you do yourself. **
As I said, career safety desicions often inforce a more or less conventional research topic upon you - unless you work in a math institute, then you basically can commit a reasonable amount of heresy. Your hero smolin has also adressed this problem several times.
But, again, tell me why you are such a LQG believer ??
Cheers,
Careful
Ah marcus, you clearly did not understand how research works. When you are a young researcher who wishes to really solve conceptual problems, you have to sidestep for some amount of time with the consequence that one stops publishing. Those who do publish, are very much aware of these shortcomings I raised too (otherwise you do not deserve PhD in front of your name), they merely content themselves with the knowledge that one of their future heroes will solve it.
**
All the time you have been here at PF there is only one person that I can remember whose research you have approved----it is Johan Noldus. Since I don't have your papers, I will use his as an example.
IIRC it was in the "List of new initiatives" thread, I will get the link. Your approval even in this case was very lukewarm, I must say. **
Well, clearly this guy was only at the beginning of adressing the conceptual flukes in QM at that time - the retour to realism does not necessarily imply a negation of the Bell tests.
**If you think everybody else work is so hopeless (and to me your arguments seem forced, as if by a need to show it) then I would really like to see what you do yourself. **
As I said, career safety desicions often inforce a more or less conventional research topic upon you - unless you work in a math institute, then you basically can commit a reasonable amount of heresy. Your hero smolin has also adressed this problem several times.
But, again, tell me why you are such a LQG believer ??
Cheers,
Careful
- #147
f-h
- 272
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Welcome to the fry. ;)
What do you mean by aether? Especially in the context of classical GR? All LQG people I know seem to consider classical GR to be BI. So your definition seems to be stricter then general usage.
Hmmmm... I think I disagree, we can construct localized observables for QM, we do it all the time. Every Heisenberg Operator is an observable with a localisation in time. That is possible because, while we do not have a consistent description of meassurement there are many things we do know about the process and how it appears in the formalism. This allows us to do physics *effectively*. The operationalists never had a problem with QM after all.
Kea said:
What do you mean by aether? Especially in the context of classical GR? All LQG people I know seem to consider classical GR to be BI. So your definition seems to be stricter then general usage.
Kea said:
Hmmmm... I think I disagree, we can construct localized observables for QM, we do it all the time. Every Heisenberg Operator is an observable with a localisation in time. That is possible because, while we do not have a consistent description of meassurement there are many things we do know about the process and how it appears in the formalism. This allows us to do physics *effectively*. The operationalists never had a problem with QM after all.
- #148
Careful
- 1,670
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**
Background Independent: a property of a physical theory or model that must incorporate (1) independence of spacetime coordinates, and (2) a lack of any form of aether. This second condition is far more stringent. Even GR fails this test.**
That is not correct Kea (but it is funny to notice that the meaning of ``background independence´´ causes confusion) : background independent means any construction which does not depend upon the choice of a background *metric*. Now, if you would choose (1) as axiom, then I can dynamically prefer Minkowski as well as geodesic coordinates (without giving up on covariance !). (2) is probably unphysical, this is something which goes back to Maxwell, through what medium do the waves travel ? Actually, the background metric version can also be criticised similarly : as is well known, the lapse and shift function in the ADM formulation of gravity serve as lagrange multipliers, so why would it be forbidden to add a background metric through lagrange multipliers? As I once commented, background independence is not so clear cut (as our conversation proves again ). Really, it is instructive to read Kretchmann's comments upon the issue of general covariance and how even Newtonian physics can be reformulated in a (ugly) covariant way.
**Logic: a not-necessarily-classical use of syntax with accompanying semantics involving truth-valued propositions and operations such as AND, OR, NOT, implication and quantifiers. **
Clearly a mathematician, but then you can go any side you want to with, say, fuzzy logic.
** (Local) Observable: a mathematical construct representing the semantics of measurable numerical quantities. Clearly any theory that does not address the problem of measurement cannot hope to have a complete description of such operators. **
Well, a *local* observable is rather more than that no.
**Magic: entertainment involving well-trained tigers, hoops, mirrors, saws and people in shiny costumes. **
Nah, these things can all be explained by local physics, the measurement problem cannot unless you do it in MWI.
**Not according to the definitions that I have given above. You have been using a more restrictive set of definitions, in response to the comments of others, but some readers reasonably appear to be finding this loose use of terms confusing.**
Ah, then I was still teasing f-h (what I clearly stated later on).
**
I think I more or less or agree, although you have not been clear, but the fact that QM needs alteration does not necessarily mean that we need to throw QM intuition out the window. **
Well, I have added somewhere the ``deduction´´ where the background *metric* would appear (so although I started off from a more restrictive definition, I think they are effectively equivalent). I agree that it was not crystal clear - in the sense that it is not written in elaborate mathematical form (which would consume more than 20 pages) - but if you would care about following the details (by trying out each particular step yourself) then you will see the conclusion I made there is hard to escape.
**
I wonder if it has occurred to you that your conclusions re the necessity of a classical direction here might in fact be wrong. **
Of course I have considered this. The point is that a classical attempt can logically solve the ``big´´ problems at hand in a conceptually clear intuitive way. I have no crystal ball in which I can predict if one can recover all experimental output in a *nice* way, but my private attempts so far give me any reason to believe that it will; neither is there any historical record about the implausible character of such enterprise.
**
The alternatives involve enlarging one's sphere of logic - seemingly dire perhaps - but alternatives in the spirit of QM all the same.
**
I agree (with both statements).
Cheers,
Careful
Background Independent: a property of a physical theory or model that must incorporate (1) independence of spacetime coordinates, and (2) a lack of any form of aether. This second condition is far more stringent. Even GR fails this test.**
That is not correct Kea (but it is funny to notice that the meaning of ``background independence´´ causes confusion
) : background independent means any construction which does not depend upon the choice of a background *metric*. Now, if you would choose (1) as axiom, then I can dynamically prefer Minkowski as well as geodesic coordinates (without giving up on covariance !). (2) is probably unphysical, this is something which goes back to Maxwell, through what medium do the waves travel ? Actually, the background metric version can also be criticised similarly : as is well known, the lapse and shift function in the ADM formulation of gravity serve as lagrange multipliers, so why would it be forbidden to add a background metric through lagrange multipliers? As I once commented, background independence is not so clear cut (as our conversation proves again ). Really, it is instructive to read Kretchmann's comments upon the issue of general covariance and how even Newtonian physics can be reformulated in a (ugly) covariant way. **Logic: a not-necessarily-classical use of syntax with accompanying semantics involving truth-valued propositions and operations such as AND, OR, NOT, implication and quantifiers. **
Clearly a mathematician, but then you can go any side you want to with, say, fuzzy logic.
** (Local) Observable: a mathematical construct representing the semantics of measurable numerical quantities. Clearly any theory that does not address the problem of measurement cannot hope to have a complete description of such operators. **
Well, a *local* observable is rather more than that no.
**Magic: entertainment involving well-trained tigers, hoops, mirrors, saws and people in shiny costumes. **
Nah, these things can all be explained by local physics, the measurement problem cannot unless you do it in MWI.
**Not according to the definitions that I have given above. You have been using a more restrictive set of definitions, in response to the comments of others, but some readers reasonably appear to be finding this loose use of terms confusing.**
Ah, then I was still teasing f-h (what I clearly stated later on).
**
I think I more or less or agree, although you have not been clear, but the fact that QM needs alteration does not necessarily mean that we need to throw QM intuition out the window. **
Well, I have added somewhere the ``deduction´´ where the background *metric* would appear (so although I started off from a more restrictive definition, I think they are effectively equivalent). I agree that it was not crystal clear - in the sense that it is not written in elaborate mathematical form (which would consume more than 20 pages) - but if you would care about following the details (by trying out each particular step yourself) then you will see the conclusion I made there is hard to escape.
**
I wonder if it has occurred to you that your conclusions re the necessity of a classical direction here might in fact be wrong. **
Of course I have considered this. The point is that a classical attempt can logically solve the ``big´´ problems at hand in a conceptually clear intuitive way. I have no crystal ball in which I can predict if one can recover all experimental output in a *nice* way, but my private attempts so far give me any reason to believe that it will; neither is there any historical record about the implausible character of such enterprise.
**
The alternatives involve enlarging one's sphere of logic - seemingly dire perhaps - but alternatives in the spirit of QM all the same.
**
I agree (with both statements).
Cheers,
Careful
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- #149
Careful
- 1,670
- 0
**
What do you mean by aether? Especially in the context of classical GR?
All LQG people I know seem to consider classical GR to be BI. So your definition seems to be stricter then general usage. **
What does it mean that GR is BI ?? All this can mean is that GR is a reparametrization invariant theory (that is defined independent of coordinates), this has *nothing* to do with the meaning of BI. The ``idea´´ behind BI orginated from the observation that perturbative quantum gravity is not perturbatively renormalizable around Minkowski. So either, this means that GR as a QFT is ill defined (a conclusion string theorists draw) or it means that Minkowski is just a bad background to do perturbation theory around and that it might be that GR as a QFT around a *different* background could be non-perturbatively renormalizable (you still have to explain then why it goes wrong when perturbing around minkowski of course).
**
Hmmmm... I think I disagree, we can construct localized observables for QM, we do it all the time. Every Heisenberg Operator is an observable with a localisation in time. That is possible because, while we do not have a consistent description of meassurement there are many things we do know about the process and how it appears in the formalism. This allows us to do physics *effectively*. The operationalists never had a problem with QM after all. **
Sure, the ``working´´ interpretation of QM is perfectly fine, it just does not solve anything (you still have to go to MWI if you do not wish to improve upon it).
If I were you f-h, I would start by properly learning *classical* GR before you wish to attend a barbecue in my honor. It is clear that I wish to maintain my identity as Careful, please respect that and argue scientifically.
Cheers,
Careful
What do you mean by aether? Especially in the context of classical GR?
All LQG people I know seem to consider classical GR to be BI. So your definition seems to be stricter then general usage. **
What does it mean that GR is BI ?? All this can mean is that GR is a reparametrization invariant theory (that is defined independent of coordinates), this has *nothing* to do with the meaning of BI. The ``idea´´ behind BI orginated from the observation that perturbative quantum gravity is not perturbatively renormalizable around Minkowski. So either, this means that GR as a QFT is ill defined (a conclusion string theorists draw) or it means that Minkowski is just a bad background to do perturbation theory around and that it might be that GR as a QFT around a *different* background could be non-perturbatively renormalizable (you still have to explain then why it goes wrong when perturbing around minkowski of course).
**
Hmmmm... I think I disagree, we can construct localized observables for QM, we do it all the time. Every Heisenberg Operator is an observable with a localisation in time. That is possible because, while we do not have a consistent description of meassurement there are many things we do know about the process and how it appears in the formalism. This allows us to do physics *effectively*. The operationalists never had a problem with QM after all. **
Sure, the ``working´´ interpretation of QM is perfectly fine, it just does not solve anything (you still have to go to MWI if you do not wish to improve upon it).
If I were you f-h, I would start by properly learning *classical* GR before you wish to attend a barbecue in my honor.
It is clear that I wish to maintain my identity as Careful, please respect that and argue scientifically.Cheers,
Careful
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- #150
f-h
- 272
- 0
Most people, I think, go by the way it's defined, for example, in Wald: General covariance and no nondynamically defined objects (aether). That's how I understood Kea. But then of course GR is Background Independent.
- #151
Careful
- 1,670
- 0
f-h said:
But the entire subtlety in the argument is what you call ``kinematical´´ and ``dynamical´´ (is the topological/differentiable structure of the manifold ``kinematical´´ at the classical level (I would think it is) ? ); Kretchmann showed that even Newtonian physics can be given a covariant formulation ; any background frame or eather can be dynamically implemented as constraints on the equations of motion. A nice, recent example of this is how 't Hooft implements dissipation at the quantum level through constraints on the states. In this way, you can start out from a classical harmonic oscillator (using an unconvential Hamiltonian whose quantized version is the same as the classical one) and end up with a free quantum particle or a quantum harmonic oscillator *depending* upon the constraints you use.
If you really want to inforce the idea that you must find a quantum version of general covariance, then you have to solve the quantum constraint algebra. Otherwise, what becomes the true meaning of BI?
BTW if I follow your definition of BI literally, then isn't is justified to state that the construction of local observables by Dittrich and Rovelli is *not* BI ? Remember: you explicitely said that the ``reference frame´´ was KINEMATICAL.
Cheers,
Careful
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- #152
hellfire
Science Advisor
- 1,051
- 1
As a layman that tries to understand some basic ideas about quantum gravity I am wondering about the confusion with the concept of background independence and I would expect some clarification from this discussion. If general relativity is background independent, then it seams to me that string theory must be also background independent, because the Einstein field equations can be derived from it's classical action making some low energy approximations (Is this right? Anyway, it is still a mistery to me how this is possible since it is not a theory of spacetime). However, everywhere one reads that string theory is not background independent. I had rather expected the usual definition of background independence to be related to the fact that a background is used to quantize perturbatively around it. Comments, please.
- #153
Careful
- 1,670
- 0
**As a layman that tries to understand some basic ideas about quantum gravity I am wondering about the confusion with the concept of background independence and I would expect some clarification from this discussion. **
This is even still a point of confusion between specialists.
** If general relativity is background independent, then it seams to me that string theory must be also background independent, because the Einstein field equations can be derived from it's classical action making some low energy approximations (Is this right? Anyway, it is still a mistery to me how this is possible since it is not a theory of spacetime). **
Yep, that is right.
** However, everywhere one reads that string theory is not background independent. I had rather expected the usual definition of background independence to be related to the fact that a background is used to quantize perturbatively around it. **
Well not entirely true, there is a priori nothing wrong with picking out a background, splitting the action in a free and interacting part around it and try to quantize it perturbatively. It is just that this procedure should *not* depend upon the chosen ``background´´ spacetime. If you could find another spacetime (not necessary a solution to the vacuum equations) around which such procedure is well defined and you can show that minkowski (and perhaps some other highly symmetric spacetimes) are ``singular´´ points, then you are done. It is simply so that the *physics* should not ``substantially´´ depend upon this procedure. My question is if the LQG people are *really* doing something which differs from such procedure (and my guess is not) *now*.
In the early days, background independence was called *quantum covariance*, i.e. quantization of the constraint algebra (wave function of the universe stuff) and that was definitely different from the stringy strategy, here you were trying to obtain a quantum version of diffeomorphism invariance (while diffeomorphism invariance is also present in QFT - the measure is covariant - but then at the kinematical level). The philosophy behind this being that diffeo invariance is a *dynamical* statement in GR (note: this is a particular interpretation) instead of a kinematical one. That is, calculate the Poisson brackets of the dynamical phase space variables with the smeared out constraints, evaluate the result on shell (that is plug in the equations of motion), and you will see that the result corresponds to the Lie derivative of this quantity with respect to the associated vectorfield (the traditional gauge transformations). However, this programme seems to be largely abandonned because of some very persistent problems showing up - apart from major conceptual difficulties (LOCAL observables !). ADDENDUM : for sake of clarity, this distinction was only stressed AFTER perturbation theory on Minkowski failed (not to be in blatant conflict with post 149).
So, what is the correct point of view here?? Is covariance really a kinematical aspect of the game, or a dynamical one? At the classical level, this makes no difference whatsoever and that what appears to be a ``kinematical construct´´ can be turned into a ``dynamical statement´´ and vice versa. I admit that covariance was an important guideline for Einstein in constructing his theory of general relativity, but is it really a substantial, fundamental part of it QUANTUM MECHANICALLY?
This, f-h is also something which Kuchar adresses regularly : the classical is entirely different from the quantum. So, that is why I say that general covariance is not such a clear cut notion.
Cheers,
Careful
This is even still a point of confusion between specialists.
** If general relativity is background independent, then it seams to me that string theory must be also background independent, because the Einstein field equations can be derived from it's classical action making some low energy approximations (Is this right? Anyway, it is still a mistery to me how this is possible since it is not a theory of spacetime). **
Yep, that is right.
** However, everywhere one reads that string theory is not background independent. I had rather expected the usual definition of background independence to be related to the fact that a background is used to quantize perturbatively around it. **
Well not entirely true, there is a priori nothing wrong with picking out a background, splitting the action in a free and interacting part around it and try to quantize it perturbatively. It is just that this procedure should *not* depend upon the chosen ``background´´ spacetime. If you could find another spacetime (not necessary a solution to the vacuum equations) around which such procedure is well defined and you can show that minkowski (and perhaps some other highly symmetric spacetimes) are ``singular´´ points, then you are done. It is simply so that the *physics* should not ``substantially´´ depend upon this procedure. My question is if the LQG people are *really* doing something which differs from such procedure (and my guess is not) *now*.
In the early days, background independence was called *quantum covariance*, i.e. quantization of the constraint algebra (wave function of the universe stuff) and that was definitely different from the stringy strategy, here you were trying to obtain a quantum version of diffeomorphism invariance (while diffeomorphism invariance is also present in QFT - the measure is covariant - but then at the kinematical level). The philosophy behind this being that diffeo invariance is a *dynamical* statement in GR (note: this is a particular interpretation) instead of a kinematical one. That is, calculate the Poisson brackets of the dynamical phase space variables with the smeared out constraints, evaluate the result on shell (that is plug in the equations of motion), and you will see that the result corresponds to the Lie derivative of this quantity with respect to the associated vectorfield (the traditional gauge transformations). However, this programme seems to be largely abandonned because of some very persistent problems showing up - apart from major conceptual difficulties (LOCAL observables !). ADDENDUM : for sake of clarity, this distinction was only stressed AFTER perturbation theory on Minkowski failed (not to be in blatant conflict with post 149).
So, what is the correct point of view here?? Is covariance really a kinematical aspect of the game, or a dynamical one? At the classical level, this makes no difference whatsoever and that what appears to be a ``kinematical construct´´ can be turned into a ``dynamical statement´´ and vice versa. I admit that covariance was an important guideline for Einstein in constructing his theory of general relativity, but is it really a substantial, fundamental part of it QUANTUM MECHANICALLY?
This, f-h is also something which Kuchar adresses regularly : the classical is entirely different from the quantum. So, that is why I say that general covariance is not such a clear cut notion.
Cheers,
Careful
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- #154
f-h
- 272
- 0
Careful said:
In this sense, yes this is justified. Also, the differentiable structure is a background structure in the classical case (topology is more subtle). We start with a manifold and pick one of the infinitely many differentiable structures.
BI isn't a rigorous statement. Kretschmars objection is of course silly, one can write any theory in a more general way if one breaks down the generality of the language by introducing distinguished elements (non rotational invariant systems can be written as rotationally invariant + a distinguished vector for example).
I agree we need to implement the constraint algebra (or the part of it responsible for rendering a certain structure kinematical). Most of it is implements, the gauge and 3Diffeo constraints in particular.
And yes, the construction and interpretation of R/D involves kinematics, but only to supply interpretations, the resulting Observables are invariant under the full constraint algebra.
If there is nothing in your universe but the BI theory of the one field, then this localisation is of course of questionable physical validity. Luckily that's not the case.
- #155
Careful
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**In this sense, yes this is justified. Also, the differentiable structure is a background structure in the classical case (topology is more subtle). We start with a manifold and pick one of the infinitely many differentiable structures.**
Also topology is important since it can have curvature ramifications - the Gromov - Bishop theorems and so on...
**
BI isn't a rigorous statement. **
We are getting somewhere.
**
Kretschmars objection is of course silly, one can write any theory in a more general way if one breaks down the generality of the language by introducing distinguished elements (non rotational invariant systems can be written as rotationally invariant + a distinguished vector for example). **
It is not that simple, for example I can dynamically pick out a preferred coordinate system and thereby *appearantly* violating general covariance (see K. Kuchar work on quantisation in the gaussian gauge). I can write down a fully covariant action pricinciple which gives me Minkowski as a preferred background. On the other hand, I can write down GR as a gauge theory on Minkowski space time (see the work of Dorian, Hestenes and company), without having to worry about general covariance at all.
**I agree we need to implement the constraint algebra (or the part of it responsible for rendering a certain structure kinematical). Most of it is implements, the gauge and 3Diffeo constraints in particular. **
Well, also here you need to be careful, it is not so that the diffeomorphism *algebra* is implemented (your algebra does not exist due to the lack of weak continuity). So, it seems a very difficult task to be able to speak about a suitable interpretation of *spacetime* covariance (with the correct classical limit) here.
**
And yes, the construction and interpretation of R/D involves kinematics, but only to supply interpretations, the resulting Observables are invariant under the full constraint algebra. **
Ok, but that is at the *classical* level no big deal at all. Moreover, a hardcore relativist would expect local observables to be defined without kinematical background structure (and at the quantum level you have troubles with your Hamiltonian constraint) - so again you use a rather personal interpretation of BI here.
**
If there is nothing in your universe but the BI theory of the one field, then this localisation is of course of questionable physical validity. Luckily that's not the case. **
Well, I am not sure what you mean here but in *any* case you need to make such identifications. If you include matter you have to color particle 1 red, particle 2 blue, particle 3 yellow and so on - so you will have many red spots in each universe and depending upon the questions you ask your ``consciousness´´ will be in different superpositions of universes - sorry I like to state this in a path integral language, it makes everything more ``visual´´. Now, you might say: well that works apart form the tiny facts that your number of orthogonal states blow up super exponentially and the small issue that you do not have properly understood the quantum constraint algebra yet. Moreover, in this way, you cannot setup a unification between matter and geometry (so again, this is not necessarily a virtue). In case you would be interested in such enterprise different point identifications will lead to different physics (different ``states´´ if you want to). In that case, it seems much more intelligent to start out from an interacting matter theory on Minkowski and to deduce your metric as an effective variable as EINSTEIN himself suggested (you see everyone uses some words of the old master in different ways and ignores with the same ease other equally important ideas ). I mean, good old Albert was never able to explain the measure stick (idealized and put on the tangent space), a theory of measurement physically originates from matter interactions and is weakly temperature dependent (in the old days they just counted the number of atoms in a stick, noted down the temperature, and used that as a reference). Really, even if this is not going to change anything for you, it is good to know of the difficulties (again with EM say) the view of the measurestick as fundamental variable carries in itself.
Cheers,
Careful
Also topology is important since it can have curvature ramifications - the Gromov - Bishop theorems and so on...
**
BI isn't a rigorous statement. **
We are getting somewhere.
**
Kretschmars objection is of course silly, one can write any theory in a more general way if one breaks down the generality of the language by introducing distinguished elements (non rotational invariant systems can be written as rotationally invariant + a distinguished vector for example). **
It is not that simple, for example I can dynamically pick out a preferred coordinate system and thereby *appearantly* violating general covariance (see K. Kuchar work on quantisation in the gaussian gauge). I can write down a fully covariant action pricinciple which gives me Minkowski as a preferred background. On the other hand, I can write down GR as a gauge theory on Minkowski space time (see the work of Dorian, Hestenes and company), without having to worry about general covariance at all.
**I agree we need to implement the constraint algebra (or the part of it responsible for rendering a certain structure kinematical). Most of it is implements, the gauge and 3Diffeo constraints in particular. **
Well, also here you need to be careful, it is not so that the diffeomorphism *algebra* is implemented (your algebra does not exist due to the lack of weak continuity). So, it seems a very difficult task to be able to speak about a suitable interpretation of *spacetime* covariance (with the correct classical limit) here.
**
And yes, the construction and interpretation of R/D involves kinematics, but only to supply interpretations, the resulting Observables are invariant under the full constraint algebra. **
Ok, but that is at the *classical* level no big deal at all. Moreover, a hardcore relativist would expect local observables to be defined without kinematical background structure (and at the quantum level you have troubles with your Hamiltonian constraint) - so again you use a rather personal interpretation of BI here.
**
If there is nothing in your universe but the BI theory of the one field, then this localisation is of course of questionable physical validity. Luckily that's not the case. **
Well, I am not sure what you mean here but in *any* case you need to make such identifications. If you include matter you have to color particle 1 red, particle 2 blue, particle 3 yellow and so on - so you will have many red spots in each universe and depending upon the questions you ask your ``consciousness´´
will be in different superpositions of universes - sorry I like to state this in a path integral language, it makes everything more ``visual´´. Now, you might say: well that works apart form the tiny facts that your number of orthogonal states blow up super exponentially and the small issue that you do not have properly understood the quantum constraint algebra yet. Moreover, in this way, you cannot setup a unification between matter and geometry (so again, this is not necessarily a virtue). In case you would be interested in such enterprise different point identifications will lead to different physics (different ``states´´ if you want to). In that case, it seems much more intelligent to start out from an interacting matter theory on Minkowski and to deduce your metric as an effective variable as EINSTEIN himself suggested (you see everyone uses some words of the old master in different ways and ignores with the same ease other equally important ideas ). I mean, good old Albert was never able to explain the measure stick (idealized and put on the tangent space), a theory of measurement physically originates from matter interactions and is weakly temperature dependent (in the old days they just counted the number of atoms in a stick, noted down the temperature, and used that as a reference). Really, even if this is not going to change anything for you, it is good to know of the difficulties (again with EM say) the view of the measurestick as fundamental variable carries in itself.Cheers,
Careful
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