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CATEGORY:
Questioning the Foundations Essay Contest (2012)
[back]

TOPIC: Questioning the Postulates of Quantum Field Theory by Peter Warwick Morgan [refresh]

TOPIC: Questioning the Postulates of Quantum Field Theory by Peter Warwick Morgan [refresh]

There have already been many attempts in the literature to modify the Wightman or Haag-Kastler axioms to be closer to the empirically successful Lagrangian approach to quantum field theory. It is suggested here that insofar as one fundamental difficulty of both Wightman and Lagrangian QFT is the postulate that the quantum field is an operator-valued distribution ---a linear map from a linear space of test functions to a linear space of operators---, we are motivated to consider taking a quantum field to be a *non*-linear map from a linear space of test functions to a linear space of operators, an approach that to my knowledge has not previously been proposed. Constructively, some of the non-linear possibilities for the scalar field case are introduced and discussed. The introduction of non-linearity widens the range of well-defined theories enough that they may provide worthwhile effective field models even if they cannot provide ultimately correct models. [I apologize that I cannot yet make the mathematical level be that of Nature or SciAm.]

I have been trying to "understand" quantum field theory for 20 years, more-or-less. I have focused on interacting QFT for approximately the last 5 years.

I would be interested in any references relevant to Section III of my paper. It seems unlikely that such a simple derivation isn't already in the literature. Thanks.

"[I apologize that I cannot yet make the mathematical level be that of Nature or SciAm.]"

In my opinion, some of the essays in the contest could use a tad more mathematical links to mainstream assumptions but this reads very much like a specific journal article. Were you not concerned it might be too far outside the realm of the average Nature or Scientific American reader? I am sure that you are well qualified to write this, but could you explain in simpler terms what this means towards a foundational assumption? I would hate to skip over a great essay simply because I lacked some small concept.

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In my opinion, some of the essays in the contest could use a tad more mathematical links to mainstream assumptions but this reads very much like a specific journal article. Were you not concerned it might be too far outside the realm of the average Nature or Scientific American reader? I am sure that you are well qualified to write this, but could you explain in simpler terms what this means towards a foundational assumption? I would hate to skip over a great essay simply because I lacked some small concept.

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Indeed, Community Rating may not work out well for this, but I think it's a curious essay for anyone who knows their QFT. I may put it on the arXiv as well, and I can publish it or not after the competition has run its course, so there is life after FQXi spits it out undigested. AFAICT, all the interesting essays so far are expounding ideas that are already in the literature in quite similar form,...

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Dear Peter Warwick Morgan,

Perturbative corrections, that proceeds with the notations of Wightman axioms in QFT is indicative of the unfathomable supersymmetry that arises from matter-antimatter asymmetry.

Time paradox expressional with Minkowski spacetime that proceeds with the notations of Haag-Kastler axiomatic framework is indicative of ambiguous extra dimensions in that the emergence of time within systems is inexpressive in entirety.

Thus we may have to redefine the dimensionality with string dynamics in that a different quantum mechanics may be applied with quark-gluon plasma.

With best wishes,

Jayakar

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Perturbative corrections, that proceeds with the notations of Wightman axioms in QFT is indicative of the unfathomable supersymmetry that arises from matter-antimatter asymmetry.

Time paradox expressional with Minkowski spacetime that proceeds with the notations of Haag-Kastler axiomatic framework is indicative of ambiguous extra dimensions in that the emergence of time within systems is inexpressive in entirety.

Thus we may have to redefine the dimensionality with string dynamics in that a different quantum mechanics may be applied with quark-gluon plasma.

With best wishes,

Jayakar

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Hi JJJ,

Thanks for your comment. I suppose I take a different approach, in that I'd like to clarify our understanding of interacting QFT a little before trying to understand the even deeper mysteries and complexities of Mathematics such as QCD and string theory that I take to depend on QFT. I hope one can say something interesting about fundamental Physics without taking into account the finest details of hadronic matter and gravity, even if they are undeniably omnipresent, but it's good to have people on both sides of weighty dichotomies.

Best wishes, Peter.

Thanks for your comment. I suppose I take a different approach, in that I'd like to clarify our understanding of interacting QFT a little before trying to understand the even deeper mysteries and complexities of Mathematics such as QCD and string theory that I take to depend on QFT. I hope one can say something interesting about fundamental Physics without taking into account the finest details of hadronic matter and gravity, even if they are undeniably omnipresent, but it's good to have people on both sides of weighty dichotomies.

Best wishes, Peter.

Dear Peter,

Problems like Haag's theorem seem indeed to be avoidable by allowing non-linearity. Taking the quantum fields to be non-linear maps from a linear space of test functions to a linear space of operators seem, after reading your essay, very promising in moving towards interactions. Do you think your approach can offer a better behavior for quantum fields on curved spacetime too? Could the desired non-linearity be obtained somehow from the general covariance?

Best regards,

Cristi Stoica

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Problems like Haag's theorem seem indeed to be avoidable by allowing non-linearity. Taking the quantum fields to be non-linear maps from a linear space of test functions to a linear space of operators seem, after reading your essay, very promising in moving towards interactions. Do you think your approach can offer a better behavior for quantum fields on curved spacetime too? Could the desired non-linearity be obtained somehow from the general covariance?

Best regards,

Cristi Stoica

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Hi Christi, and thanks.

I have thought about QFT-CST and about QG only a very little. So little, indeed, that I have a prejudice that I've so far been unable to shake from my head, in favor of working with torsion on an otherwise Minkowski space-time (something of the type of Einstein-Cartan, teleparallelism, or Poincaré gauge theory, but I know too little to know what formalism I would prefer), although perhaps only as an approach to local modeling, because Fourier transforms are so central to QFT, but difficult on a variable metric CST and impossible(?) if the background space-time is dynamical.

Within such a scheme, my first attempt would be to take the torsion tensor to be the dynamical object of a quantum field theory, insofar as the non-linear approach I suggest in my essay may be less concerned with the renormalizable/non-renormalizable distinction than is standard QFT. I don't know how well that would work out, of course.

That's not an answer to your question, but it's a vague answer to the question that your question suggests to me. Best wishes, Peter.

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I have thought about QFT-CST and about QG only a very little. So little, indeed, that I have a prejudice that I've so far been unable to shake from my head, in favor of working with torsion on an otherwise Minkowski space-time (something of the type of Einstein-Cartan, teleparallelism, or Poincaré gauge theory, but I know too little to know what formalism I would prefer), although perhaps only as an approach to local modeling, because Fourier transforms are so central to QFT, but difficult on a variable metric CST and impossible(?) if the background space-time is dynamical.

Within such a scheme, my first attempt would be to take the torsion tensor to be the dynamical object of a quantum field theory, insofar as the non-linear approach I suggest in my essay may be less concerned with the renormalizable/non-renormalizable distinction than is standard QFT. I don't know how well that would work out, of course.

That's not an answer to your question, but it's a vague answer to the question that your question suggests to me. Best wishes, Peter.

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Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Dear Peter,

I also have an essay questioning the postulate of quantum theory - "Is there really no reality beneath quantum theory by Hou Ying Yau". Just like you, I spend many years trying to understand physics. I hope you will find the paper interesting.

Sincerely,

Hou Ying Yau

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I also have an essay questioning the postulate of quantum theory - "Is there really no reality beneath quantum theory by Hou Ying Yau". Just like you, I spend many years trying to understand physics. I hope you will find the paper interesting.

Sincerely,

Hou Ying Yau

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Sadly not worthwhile to put a worthwhile paper on here. Hey ho.

Dear Peter Morgan,

I have read what I can of your essay. You have chosen a problem to analyse that I am not sure is a wrong basic physical assumption but may be something to do with the best mathematical representation of nature. Not having studies QFT I was not even aware of the problem that you chose to write about.The level of mathematics that you included is a barrier to clear communication with those who do not have a background in mathematics and maybe not even physics.

There are other entrants talking about mathematical approaches, such as Julian Barbour, who have non the less produced very accessible papers that can be understood by non specialists, are educational and enjoyable. Searching For New Mathematics by Ivars Peterson This article may help explain the problem for non mathematicians.

Those who do have a good grounding in mathematics, (T H Ray, Lawrence Crowell and Joy Christian spring to mind), might be able to give give a valuable critique. Perhaps you could introduce yourself to them if you have not already and they might also be able to suggest other people who would find your essay accessible and something that they would be able to discuss with you.

I am sorry I can not be more helpful. You no doubt feel very strongly about what you are doing as do many of the entrants, myself included. Good luck to you in getting the constructive feedback you are seeking.

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I have read what I can of your essay. You have chosen a problem to analyse that I am not sure is a wrong basic physical assumption but may be something to do with the best mathematical representation of nature. Not having studies QFT I was not even aware of the problem that you chose to write about.The level of mathematics that you included is a barrier to clear communication with those who do not have a background in mathematics and maybe not even physics.

There are other entrants talking about mathematical approaches, such as Julian Barbour, who have non the less produced very accessible papers that can be understood by non specialists, are educational and enjoyable. Searching For New Mathematics by Ivars Peterson This article may help explain the problem for non mathematicians.

Those who do have a good grounding in mathematics, (T H Ray, Lawrence Crowell and Joy Christian spring to mind), might be able to give give a valuable critique. Perhaps you could introduce yourself to them if you have not already and they might also be able to suggest other people who would find your essay accessible and something that they would be able to discuss with you.

I am sorry I can not be more helpful. You no doubt feel very strongly about what you are doing as do many of the entrants, myself included. Good luck to you in getting the constructive feedback you are seeking.

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Thanks for reading through it, Georgina. I figured out weeks ago that I had misjudged the nature of the contest. I saw up front that it clearly asks for a level between Scientific American and Nature, but I'm not at a point in my research at which I can do that, so I did what I could. Of course if someone doesn't understand an essay, they can hardly give it a high community rating, and indeed it's reasonable for them to give it a low community rating for not hitting one of the contest specifications, of getting the right level. Now I can see that it was not worthwhile trying to do my research here; I suppose one can only present a much more complete idea.

If one is arguing for something that has been in the literature as an idea for a while, as is the case for Julian Barbour, then a non-mathematical way of stating the issues has probably developed. An idea that hasn't yet become old enough to have a non-mathematical statement is probably wrong, as has always been true of my many previous ideas and approaches and as is probably true of my proposal here.

To some extent there's a catch-22 here, which I suppose means that the winner is not likely to achieve the principle aim of the contest as I think of it, the pointing out of an assumption that genuinely hasn't been noticed and that can *usefully* be teased into a different form. AFAICT, the assumption I address is the only assumption questioned in all the essays here, mathematical or not, that I have not seen questioned many times before.

I suppose everyone dies with less constructive criticism than they need. Best not to get too frustrated about it. It's perhaps ironic that I pretty much agree with everything that Peterson says in the interesting article that you link to (which definitely constitutes constructive feedback), but that does not mean that I ever succeed when I try to write lucidly.

Thanks again. Peter.

If one is arguing for something that has been in the literature as an idea for a while, as is the case for Julian Barbour, then a non-mathematical way of stating the issues has probably developed. An idea that hasn't yet become old enough to have a non-mathematical statement is probably wrong, as has always been true of my many previous ideas and approaches and as is probably true of my proposal here.

To some extent there's a catch-22 here, which I suppose means that the winner is not likely to achieve the principle aim of the contest as I think of it, the pointing out of an assumption that genuinely hasn't been noticed and that can *usefully* be teased into a different form. AFAICT, the assumption I address is the only assumption questioned in all the essays here, mathematical or not, that I have not seen questioned many times before.

I suppose everyone dies with less constructive criticism than they need. Best not to get too frustrated about it. It's perhaps ironic that I pretty much agree with everything that Peterson says in the interesting article that you link to (which definitely constitutes constructive feedback), but that does not mean that I ever succeed when I try to write lucidly.

Thanks again. Peter.

Hi Peter,

I feel compelled to echo Georgina's opinion that it would be very difficult to find a referee for your work among the denizens here. (Don't look at me -- I've had Weinberg's 3-volume QFT text for years and every book is in pristine condition.)

If it's worth anything to hear -- I don't think there will ever be a plain language version of QFT; the subject is clearly specialized for experts. Any continuous field theory that attempts quantization has already jumped the comprehensibility barrier of common language -- because we all understand "things," not fields. I suspect that's how string theory captured the popular imagination; the public at large doesn't have a clue of supersymmetry or the field excitations that the theorist derives from QFT, but they know what kind of thing a string is.

I did see your request for someone to find an existing derivation of section 3 weeks ago, but I'm not up to that research, and I couldn't tell you who is.

FWIW, I think your theme suffers from the difficulty of understanding in physics that probability theory has in mathematics -- i.e., not really much is known about it except in formal language. So doing a calculation ends up having a meaning of its own independent of any constructive meaning that the problem it purportedly solves, is trying to convey. That's the reason I switched from number theory to complex systems science, where the problems are clearly correspondent to the real world.

Nevertheless, of the parts of your paper that I understand I am seeing some potentially valuable insights into quantum vaccum field solutions that could very well end up explaining how the field varies so radically from point to point yet sums to zero. That definitely brings things back to reality -- or rather, reality back to "things."

All best wishes, Peter, in the contest and in your further research.

Tom

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I feel compelled to echo Georgina's opinion that it would be very difficult to find a referee for your work among the denizens here. (Don't look at me -- I've had Weinberg's 3-volume QFT text for years and every book is in pristine condition.)

If it's worth anything to hear -- I don't think there will ever be a plain language version of QFT; the subject is clearly specialized for experts. Any continuous field theory that attempts quantization has already jumped the comprehensibility barrier of common language -- because we all understand "things," not fields. I suspect that's how string theory captured the popular imagination; the public at large doesn't have a clue of supersymmetry or the field excitations that the theorist derives from QFT, but they know what kind of thing a string is.

I did see your request for someone to find an existing derivation of section 3 weeks ago, but I'm not up to that research, and I couldn't tell you who is.

FWIW, I think your theme suffers from the difficulty of understanding in physics that probability theory has in mathematics -- i.e., not really much is known about it except in formal language. So doing a calculation ends up having a meaning of its own independent of any constructive meaning that the problem it purportedly solves, is trying to convey. That's the reason I switched from number theory to complex systems science, where the problems are clearly correspondent to the real world.

Nevertheless, of the parts of your paper that I understand I am seeing some potentially valuable insights into quantum vaccum field solutions that could very well end up explaining how the field varies so radically from point to point yet sums to zero. That definitely brings things back to reality -- or rather, reality back to "things."

All best wishes, Peter, in the contest and in your further research.

Tom

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Peter,

While I sympathize with your inability to stir up an audience, I have to agree with Georgina that the audience you require is extremely select. There is the unhelpful Catch 22 that such detail oriented work requires equally detail oriented observers to analyze it and nature contains far more detail than observers. If you notice some of the other threads, many are not even participating in discussions of their own ideas.

I have something of the opposite problem with my entry. It is so elementally basic that no one takes it seriously. It is simply that we assume the effect of time, sequence of events, is fundamental, rather than the action causing them. That it is not the present moving from past to future, but the changing configuration of what exists, turning future into past. For example, the earth doesn't travel the fourth dimension from yesterday to tomorrow, but tomorrow becomes yesterday because the earth rotates. One effect of this you might consider is that it turns time from a linear dimension into a non-linear dynamic, since duration doesn't transcend the present moment, but is the state of the present between the occurrence of events.

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While I sympathize with your inability to stir up an audience, I have to agree with Georgina that the audience you require is extremely select. There is the unhelpful Catch 22 that such detail oriented work requires equally detail oriented observers to analyze it and nature contains far more detail than observers. If you notice some of the other threads, many are not even participating in discussions of their own ideas.

I have something of the opposite problem with my entry. It is so elementally basic that no one takes it seriously. It is simply that we assume the effect of time, sequence of events, is fundamental, rather than the action causing them. That it is not the present moving from past to future, but the changing configuration of what exists, turning future into past. For example, the earth doesn't travel the fourth dimension from yesterday to tomorrow, but tomorrow becomes yesterday because the earth rotates. One effect of this you might consider is that it turns time from a linear dimension into a non-linear dynamic, since duration doesn't transcend the present moment, but is the state of the present between the occurrence of events.

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Peter,

This is in reply to your post on my thread. Since you sound more respectfully considerate, than genuinely interested, I repost it here:

Peter,

Thank you for the reply. I would first have to agree we are on opposite sides of a significant fence and I can understand why you might see my side as lacking necessary detail to be informative. My position is that while your...

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This is in reply to your post on my thread. Since you sound more respectfully considerate, than genuinely interested, I repost it here:

Peter,

Thank you for the reply. I would first have to agree we are on opposite sides of a significant fence and I can understand why you might see my side as lacking necessary detail to be informative. My position is that while your...

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I think I have to say that I know it's built on sand. I'm no Platonist, to think that I build my models of anything else (though I've no way that I know of to gainsay someone who thinks Mathematics transcends our experience). You'll have to read between the lines of my various web presences to realize that there isn't much ivory in my tower.

It looks as if your "there is a cycle of...

view entire post

It looks as if your "there is a cycle of...

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Peter,

Thank you for the thoughtful and considerate response. I have to say I generally get a more emotional and negative reaction when I try to push the buttons of others in the field.

For me, the concepts basic physics deals with; Energy, order, structure, expansion/contraction, attraction/repulsion, complexity/simplicity, etc. underlay and manifest all aspects of existence. Every person alive, from some kid kicking a soccer ball, to an astronaut, has to understand physics. We live what theorists analyze.

Obviously there are levels of understanding, but there is no clear line between what people experience and theorists try to divine. Which is to say that I feel I have a stake in the field, even if my thoughts don't meet with approval by those more directly engaged in the various disciplines.

While you are quite right to say our understanding starts with what is, my strongest impulse is that we stand over the abyss of mortality, so the "nothing" is as much a feature to explain, as complexity.

For me, I accept there is an infinite amount of complexity I can never conceive, from quantum math, to biological and neurological functions and so the best I can do, is to sense those general patterns and how they interact and manifest in different ways. This gives me some foundation to deal with the unknown.

I would say life is a game where the goal is to figure out the rules and the first rule is that many rules are subject to circumstance.

Good luck with putting together your work and finding the right audience.

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Thank you for the thoughtful and considerate response. I have to say I generally get a more emotional and negative reaction when I try to push the buttons of others in the field.

For me, the concepts basic physics deals with; Energy, order, structure, expansion/contraction, attraction/repulsion, complexity/simplicity, etc. underlay and manifest all aspects of existence. Every person alive, from some kid kicking a soccer ball, to an astronaut, has to understand physics. We live what theorists analyze.

Obviously there are levels of understanding, but there is no clear line between what people experience and theorists try to divine. Which is to say that I feel I have a stake in the field, even if my thoughts don't meet with approval by those more directly engaged in the various disciplines.

While you are quite right to say our understanding starts with what is, my strongest impulse is that we stand over the abyss of mortality, so the "nothing" is as much a feature to explain, as complexity.

For me, I accept there is an infinite amount of complexity I can never conceive, from quantum math, to biological and neurological functions and so the best I can do, is to sense those general patterns and how they interact and manifest in different ways. This gives me some foundation to deal with the unknown.

I would say life is a game where the goal is to figure out the rules and the first rule is that many rules are subject to circumstance.

Good luck with putting together your work and finding the right audience.

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Dear Peter,

I thank you for a very useful contribution to an approach that needed to be explored. I am one of those who prefers to experiment with deviation from Lorentz covariance, but knowing some of the consequences and possibilities of changing other hypotheses is quite valuable.

Good luck with the contest, and take care,

Ben Dribus

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I thank you for a very useful contribution to an approach that needed to be explored. I am one of those who prefers to experiment with deviation from Lorentz covariance, but knowing some of the consequences and possibilities of changing other hypotheses is quite valuable.

Good luck with the contest, and take care,

Ben Dribus

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Taking Lorentz covariance to be broken at small scales is of course a much pursued option. I'm not against such ideas, but there seem to be so /many/ possibilities, and not, I think, quite enough empirical justification for any of them. I can't figure out which approach I like enough to work with.

On the other hand, the kind of nonlinearity I introduce here is not an attempt to change...

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On the other hand, the kind of nonlinearity I introduce here is not an attempt to change...

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Dear Peter,

I appreciate your response, and particularly your honesty. "Taste," (or intuition, as it might be called) is not to be dismissed out of hand. You may have noticed from my bio that I study algebraic geometry (mostly complex algebraic geometry), so nonmanifold models were not initially much to my taste either. The journey toward considering such things is not something one can put in a 12-page essay!

I think that your remarks about window functions are interesting, and I have great respect for approaches that make systematic use of scale. I studied harmonic analysis/wavelets a fair bit before going toward the algebraic side. Take care,

Ben

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I appreciate your response, and particularly your honesty. "Taste," (or intuition, as it might be called) is not to be dismissed out of hand. You may have noticed from my bio that I study algebraic geometry (mostly complex algebraic geometry), so nonmanifold models were not initially much to my taste either. The journey toward considering such things is not something one can put in a 12-page essay!

I think that your remarks about window functions are interesting, and I have great respect for approaches that make systematic use of scale. I studied harmonic analysis/wavelets a fair bit before going toward the algebraic side. Take care,

Ben

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I've eventually succumbed to commenting briefly (and not substantively for the purposes of the essay contest) on your more-or-less equating "taste" and "intuition". I think taste has an additional component, that of intention. That is, I think of taste in Mathematics/Physics as more colored by what we wish to achieve, whereas I think of intuition as more directed to how to achieve what we wish.

This is somewhat comparable to some ways of defining rationality in Philosophy; Wikipedia offers, inter alia, "A rational decision is one that is not just reasoned, but is also optimal for achieving a goal or solving a problem." That is, for my point here, /what/ goal or problem we choose to address is more a question of ethics, something that is not open to reasoning in the same way as is the /way/ in which we address the goal or problem that we choose.

Of course such boundaries are quite fluid in practice. We might well persuade someone, for example, that their goal of the moment does not further their achieving a more ultimate goal.

Your comments, of course, have been thoughtful and helpful, here and in the other places that I have seen; please take this as just a by the way.

Best wishes, Peter.

This is somewhat comparable to some ways of defining rationality in Philosophy; Wikipedia offers, inter alia, "A rational decision is one that is not just reasoned, but is also optimal for achieving a goal or solving a problem." That is, for my point here, /what/ goal or problem we choose to address is more a question of ethics, something that is not open to reasoning in the same way as is the /way/ in which we address the goal or problem that we choose.

Of course such boundaries are quite fluid in practice. We might well persuade someone, for example, that their goal of the moment does not further their achieving a more ultimate goal.

Your comments, of course, have been thoughtful and helpful, here and in the other places that I have seen; please take this as just a by the way.

Best wishes, Peter.

Peter,

Your essay is far better than the middling status it has in the community rating. I have given it a basic read through, though I intend to give it more focused attention tomorrow. When I am done here I will give your essay a high score to bump it up the ranking.

You raise some interesting issues here. You write

Δ(x-z) = i(G_r(x,z) – G_a(x,z)) = [φ(x), φ(z)]

which time ordering is behind the commutivity. In my essay I argue on the basis of M-theory that field locality is to be removed. In effect [φ(x), φ(z)] =/= 0 even if x and z are spacelike. This is a departure from your work, but I am wondering if one can have a propagator equation

Δ(x-z) = i(G_r(x,y) – G_a(z,y)) = [φ(x), φ(z)]

Where x,y are timelike as are z, y. The equation 5

ξ(x) = T^†[e^{-iL}]φ(x)T[e^{-iL}]

would replace e^{-iL} with Jacobi theta functions.

I will probably have more comments directed more closely to your essay tomorrow.

Cheers LC

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Your essay is far better than the middling status it has in the community rating. I have given it a basic read through, though I intend to give it more focused attention tomorrow. When I am done here I will give your essay a high score to bump it up the ranking.

You raise some interesting issues here. You write

Δ(x-z) = i(G_r(x,z) – G_a(x,z)) = [φ(x), φ(z)]

which time ordering is behind the commutivity. In my essay I argue on the basis of M-theory that field locality is to be removed. In effect [φ(x), φ(z)] =/= 0 even if x and z are spacelike. This is a departure from your work, but I am wondering if one can have a propagator equation

Δ(x-z) = i(G_r(x,y) – G_a(z,y)) = [φ(x), φ(z)]

Where x,y are timelike as are z, y. The equation 5

ξ(x) = T^†[e^{-iL}]φ(x)T[e^{-iL}]

would replace e^{-iL} with Jacobi theta functions.

I will probably have more comments directed more closely to your essay tomorrow.

Cheers LC

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I doubt any bump will be enough, however the thought is welcome.

In your second equation here, I'm not sure what "y" is? There's something to bear in mind (at least within the axioms of AQFT), which is that if $\Delta(x-z)$ is a function only of the separation between the points identified by "x" and "z", then the field has to be a generalized free field (LICHT AL and TOLL JS 1961 Nuovo Cim. 21 346-51).

Do you mean by your last remark that you want a non-unitary evolution? I don't think you mean to replace e^{-iL} by something like ? What motivation do we have for adopting a Jacobi theta function in /this/ context?

In your second equation here, I'm not sure what "y" is? There's something to bear in mind (at least within the axioms of AQFT), which is that if $\Delta(x-z)$ is a function only of the separation between the points identified by "x" and "z", then the field has to be a generalized free field (LICHT AL and TOLL JS 1961 Nuovo Cim. 21 346-51).

Do you mean by your last remark that you want a non-unitary evolution? I don't think you mean to replace e^{-iL} by something like ? What motivation do we have for adopting a Jacobi theta function in /this/ context?

I was conjecturing a Δ(x,z) formed from retarded and advanced potentials with a common point y to the future (timelike or lightlike separation) of both x and z. The propagation from x to y in the retarded case and from y and z in the advanced case is replaced by the commutator. This of course would need to be derived by different means of course. Yet quantum gravity implies a nonlocality of...

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Dear Peter,

Your essay is interesting for me. I think you can find some of answers of your questions here:

essay

Best wishes

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Your essay is interesting for me. I think you can find some of answers of your questions here:

essay

Best wishes

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If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is and was the quantity of people which gave you ratings. Then you have of points. After it anyone give you of points so you have of points and is the common quantity of the people which gave you ratings. At the same time you will have of points. From here, if you want to be R2 > R1 there must be: or or In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Sergey Fedosin

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