Foundations of a theory of quantum gravity - Johan Noldus' book.

[Careful]

What I wrote is my impression of Hofstadter. But then I (as my PF name implies), I am just an amateur in the world of physics and math.

I did not mean anything by it (I am certainly not going to engage in a discussion about an author you just told me about), I just scrolled in his magnum opus on amazon and saw he talks about the same topics I do and at the end I noticed a paragraph in which he expresses scepticism regarding finding a machine which is equally intelligent than a human in the forseeable future. I am myself not a ''specialist'' in these issues either, which doesn't imply that what I say about it is rubbish.

 

[Careful]

Do you have any idea which principle could single out 4-dim. spacetime? I have one but it's still rather vague. It came to my mind as you mentioned the continuum as a crucial input.

Yes, the gravitational theory only works in 4-D in contrast to Einstein's which allows for higher dimensional extensions. The reason is that energy momentum as well as spin are incoorporated and the gravitational ''spin-field'' fluctuates between the 4 dimensions of the base-manifold and the eight dimensions of the tangent bundle. It is what Jadczyk calls a twisted Finsler geometry.

As far as I know, there is no reason for 4-D residing in the quantum theory; perhaps this is to be expected since gravitation dictates spacetime physics after all.

 

[Careful]

Thanks, I'll try to look again in this light. In particular chapter 3. The choice of headline for chapter 3 made me think it was not the starting point, but I'll read again ands see if things get clear.

I look forward to your fqxi paper to motivate those structures. When it's published please let us know. I want to read it.

/Fredrik

Well, you won't find a treatment of this issue in section 3; all I said is that section 3 contains the beginning of an outine of some principles a theory of quantum gravity should satisfy. In a sense, I have found a way to unite the vision of Einstein with that of Whitehead in a ''new'' mathematical framework.

 

[Careful]

@Careful: unfortunately I still didn't read you book carefully, but it seems that this is an important step. Classical actions or Hamiltonians may be a way to motivate the structures and symmetry principles of a quantum theory, but there are indications (which we discussed elsewhere) that it is impossible to derive the quantum theory rigorously from the classical one. The problem is that the quantum theory has much more structure which is "washed away" in the classical limit and can therefore not be reconstructed in doing a "quantization". The structure is not derived from classical physics but put in by hand via the quantization procedure. This must not necessarily be wrong, but one has to be aware of the fact that additional assumptions enter the scene.

Indeed, the real reason for disposing of the classical picture is not in the ambiguities of the quantization procedure (however these may signal that something is wrong) but the fact that these are all global techniques which break the space-time picture of relativity (covariance). Only a local, manifest covariant, formulation of quantum interactions will allow you to solve the problem of infinities. Note that relativity in the Einsteinian view has no problems with singularities, it is only the modern formulation which fails.

 

[Fra]

will allow you to solve the problem of infinities

Apart from the infinity issue; does your program/project at some point, contain a reconstruction also of unification of all interactions? where the actions of a generic system somehow are inferred or constrained from some constructing principles? or is your main focus on unifying the QM and GR frameworks - ontop of which a standard models (ie specific hamiltonians or lagrangians of matter) is put manually?

With this I mean that the QM or QFT framework as such, contains no statements of the action - as this is as is mentioned here simply taken from some classical picture (or experiment of course; except that there is no formalisation and theoretical level of taking serious this "experimental inference" beyond the poppian view; essentially meaning that the justification is that it works. This is of course correct, but it still leaves us with zero insight about this process).

/Fredrik

 

[Careful]

Apart from the infinity issue; does your program/project at some point, contain a reconstruction also of unification of all interactions? where the actions of a generic system somehow are inferred or constrained from some constructing principles? or is your main focus on unifying the QM and GR frameworks - ontop of which a standard models (ie specific hamiltonians or lagrangians of matter) is put manually?

The answer to that question is open at the moment. But let me tell you the following: what would you understand by a constraining principle ? I mean, what do these unified gauge group theoretical approaches such as E_8 explain ? If there exists a principled explanation for the particle content of the universe, then it has to be something which originates from Lorentz covariance; in either from the Clifford numbers. This is an old idea which goes back to at least 1960: I have some ideas in this direction, but it is open till now.

With this I mean that the QM or QFT framework as such, contains no statements of the action - as this is as is mentioned here simply taken from some classical picture (or experiment of course; except that there is no formalisation and theoretical level of taking serious this "experimental inference" beyond the poppian view; essentially meaning that the justification is that it works. This is of course correct, but it still leaves us with zero insight about this process).
/Fredrik

See my comment above; perhaps, this question is far more difficult than most people imagine it to be.

 

[Fra]

See my comment above; perhaps, this question is far more difficult than most people imagine it to be.

I certainly agree. I do not expect something simple. I appreciate that as least your not trying to deny it :) This is whay I dislike when sometimes people try to pretend that some hard problems doesn't exist, or doesn't belong to science.

But let me tell you the following: what would you understand by a constraining principle ? I mean, what do these unified gauge group theoretical approaches such as E_8 explain ?

As far as I know these things, most people speaking of that use a completely different approach than me, and seems to be guided by some sort of mathematical simplicity or beauty that lacks physical justification. So to the extent I'm aware of I don't think they explain anything (or well, at least not NEAR as much as one would want). Either that, or I'm too stupid to get it.

But the constructing principle I expect is essentially in the form of an rational inference; which necessarily takes place within an observer. In this sense I think that there is a way to consider all interactions (not just gravity like verlinde suggests) as entropic in nature, BUT "entropic" in terms not of classical statistics but in terms of a new, not yet well defined, inference, where quantum logic naturally enters the picture, not as assuptions but as consequences of non-commutative structures, which in turn developes because it's the only way for systems to survive and be stable. So the selection principle is not deductive style consistency constraints, but softer evolutionary style rationality constraints.

To associate to your computer vs human issue, computers are information processing agents that follow a deductive type deterministic logic. Humans are not. This is why a comptuer can be superior of a human in specific, well defined tasks, such as computing decimals of pi :) while the human brain is way superior in creative and fuzzy tasks. This is just in line with I suggest as well. There is simply not much survival value in competing decimals pi at high speed.

Similarly I envision that there is actually a survival value in an information processing agent (subatomic matter) to implement quantum logic.

I believe this is possible, but it is complicate and the descrption of this properly, say in a paper to be publish, (which I also have in mind sometime in the future, if I can do this) unfortunately couples with several other problems (such as origina of complexity, which I consider to relate to the origina of gravit as well) that has to be solved in parallell, probably iteratively. There is simply no way to explain on part, while holding the other part fixed in the mainstream world. The new compelte picture need to be evolved together. I've thought and sketched quite a lot about this.

So while I see that this is a very complex task; it's somehow "in the end" what I expect out of any potential research program. If I at least can see it coming, or seeing that it's possible, then the program is interesting for me. Some programs OTOH, that doesn't even phrase, acknowledge, or even explicitly ignores this are not something that I find worty the time.

So what I like about your thinking is that even if I don't know your full picture, seem to have put some good thought into it and you don't seem to try to deny the issues. That's what I find to be the stronger points, making me curious too learn more.

/Fredrik

 

[A. Neumaier]

I once send you a summary and you found it full of buzzwords, while for QG physicists it was very clear what I wrote.

It is very easy to claim clarity. It is much more difficult to make it believable.

Please have some QG physicist comment here in PF on your book, to confirm your claim that for QG physicists it was very clear what you wrote.

 

[Careful]

It is very easy to claim clarity. It is much more difficult to make it believable.

Please have some QG physicist comment here in PF on your book, to confirm your claim that for QG physicists it was very clear what you wrote.

See post 61 for example. For the rest, personal communication is personal.

 

[A. Neumaier]

See post 61 for example. For the rest, personal communication is personal.

I know this due to personal communication. Why would I say this if this were not the case ?

Well, you mentioned Arkadius Jadzcyk. He is very active on PF (7.58 posts per day on average; the last post from arkajad is from January 26) but doesn't seem interested in discussing your book. Moreover, looking at his publication list http://arkadiusz-jadczyk.org/jadczyk_publications.html I wouldn't call him a QG physicist, though he has a few old (pre 1990) papers on Kaluza-Klein theory. (If you find this sufficient to make him a QG physicist, you could as well call me a quantum physicists - but you repeatedly emphasize that I am only a mathematician lacking the most elementary understanding of physics.)

You may actually check the forum and you will see that tom.stoer found an almost complete copy of this document helpful and actually requested for me to put it on the web (but this is not the communication I was talking about).

Yes. What you sent me was a draft of your book of about 80 pages. Of course, any shortening that cuts out the philosophical ramblings and concentrates on the formal aspects is _helpful_. (Though Tom Stoer didn't actually say this, neither in #61 nor in #90 - it was _you_ who commented - in #62 - that it might be helpful.)

But there is a world of difference between clarity on the one side, and, on the other side, providing a reasonably short outline being helpful to understand what you write in your otherwise almost incomprehensible mix of philosophy, subjective comments, and formal development.

Even more helpful would be pointers to where you give precise definitions of the concepts you are using (in particular of things where you deviate from standard usage - like ''consciousness'', ''soul'', and ''Nevanlinna space''). Otherwise, a reader (like most) not willing to spend a month of full-time work to read the paper line by line will have severe difficulties to see what is going on and where to start.

 

[Careful]

e

Well, you mentioned Arkadius Jadzcyk. He is very active on PF (7.58 posts per day on average; the last post from arkajad is from January 26) but doesn't seem interested in discussing your book. Moreover, looking at his publication list http://arkadiusz-jadczyk.org/jadczyk_publications.html I wouldn't call him a QG physicist, though he has a few old (pre 1990) papers on Kaluza-Klein theory. (If you find this sufficient to make him a QG physicist, you could as well call me a quantum physicists - but you repeatedly emphasize that I am only a mathematician lacking the most elementary understanding of physics.)



Yes. What you sent me was a draft of your book of about 80 pages. Of course, any shortening that cuts out the philosophical ramblings and concentrates on the formal aspects is _helpful_. (Though Tom Stoer didn't actually say this, neither in #61 nor in #90 - it was _you_ who commented - in #62 - that it might be helpful.)

But there is a world of difference between clarity on the one side, and, on the other side, providing a reasonably short outline being helpful to understand what you write in your otherwise almost incomprehensible mix of philosophy, subjective comments, and formal development.

Even more helpful would be pointers to where you give precise definitions of the concepts you are using (in particular of things where you deviate from standard usage - like ''consciousness'', ''soul'', and ''Nevanlinna space''). Otherwise, a reader (like most) not willing to spend a month of full-time work to read the paper line by line will have severe difficulties to see what is going on and where to start.

Ok, I strongly advise you to quit at this point. You are clearly not interested in my work, do not have sufficient knowledge and your overall comments are silly. Why wouldn't I start a thread on the quantum mechanics of Arnold Neumaier ? I promise the reader upfront that there is not a single idea in it which you cannot find in textbooks or which is generally unknown to physicists and moreover, the mathematics is quite simple. Jadczyk is much more a physicist than you will ever be, so again your arrogance is simply of an unspeakable magnitude. And why would Arkadiusz speak here about my work if I had plenty of private conversations with him about it up to some point (actually even more than with you, with means a number larger than 150).

I do not respond anymore to you and ask you to leave it at this point. I am strongly against reporting, so I won't do that even if you next message is on the level of your previous ones.

Careful

 

[tom.stoer]

Ok, I strongly advise you to quit at this point. You are clearly not interested in my work, do not have sufficient knowledge and your overall comments are silly. Why wouldn't I start a thread on the quantum mechanics of Arnold Neumaier ? I promise the reader upfront that there is not a single idea in it which you cannot find in textbooks or which is generally unknown to physicists and moreover, the mathematics is quite simple. Jadczyk is much more a physicist than you will ever be, so again your arrogance is simply of an unspeakable magnitude. And why would Arkadiusz speak here about my work if I had plenty of private conversations with him about it up to some point (actually even more than with you, with means a number larger than 150).

I do not respond anymore to you and ask you to leave it at this point. I am strongly against reporting, so I won't do that even if you next message is on the level of your previous ones.

Careful

What a pitty. You have the chance to exchange your ideas with respected scientists - and all what you are doing is to disparage colleagues. I strongly recommend you to think about the difference to be right and to get right (I am not in the position to assess whether you are right, but I bet my a.. that you will not get right).

 

[A. Neumaier]

I do not respond anymore to you.

A noble promise that I heartily welcome.

Then the discussions in other threads on rigorous but standard quantum mechanics will no longer be disrupted by your attempts to belittle them and move them towards speculative generalizations.

 

[Careful]

What a pitty. You have the chance to exchange your ideas with respected scientists - and all what you are doing is to disparage colleagues. I strongly recommend you to think about the difference to be right and to get right (I am not in the position to assess whether you are right, but I bet my a.. that you will not get right).

Dear Tom,

Arnold and I have a pretty repetitive history; many of the things you hear here I have listened to at least a couple of times. Moreover, he is a mathematician and therefore discussions are very limited; I actually hoped at one point that his different perspective may become useful but alas the gap is too large. Moreover, my work will not be judged on PF, neither do I advertise it here; I merely try to respond in a helpful way to questions which show genuine interest. If the work is as good as I think it is, it will become known sooner or later. I am not in a hurry.

Johan

 

[Fra]

Hopefully the thread won't tilt until I get around to skimming more.

I still maintain this hope ;)

/Fredrik

 

[tom.stoer]

If the work is as good as I think it is, it will become known sooner or later. I am not in a hurry.

I wish you much success

 

[Fra]

Here are some more simple starting points, and the purpose here to to find the starting point, initial premises etc.

From previous threads:

1) Is it ok to assume that you by conscious beeing = any physical observer. (ie. any physical system, that observers it's environment?)

Yes, here I go further than Penrose and ''dead matter'' can have a minimal form of consciousness too.

Then I jump to your starting points 3.

The starting point is the philosophical section three.

Now let me explain why this is not in conflict with the notion of free will, but first let me clarify how I see ’quasi local consciounesses’ make ’quasi local’ measurements. Let \psi be the state of the universe written down in the ontological orthogonal local basis constituting the realities in the path integral formulation. The reality as seen by a quasi local conscious observer is not given by \psi but can be constructed from \psi by inserting the quasi local identity operator written down in terms of the irreducible projection operators coming from the spectral decomposition of the quasi local Hamiltonian.

What do you mean by ontological local basis? and what does the realities in PI refer to?

What I mean is, where is the observer, encoding this state? Or do you assume this to just exist in the realist, or superobserver sense?

Can you clarify? Somehow I THINK you mean that there are one observer, observing another observer. So that the first observer takes the role of a "superobserver" except of course, it's not, it's just a normal obsever. So that the "quasi local" observer you refer to, are the "secondary observer" distinguished as coherent subsystem living withing the image of the first observer? Is this right? or do you mean something else?

/Fredrik

 

[Careful]

What do you mean by ontological local basis? and what does the realities in PI refer to?

Ontological basis = basis of states which are supposed to be ''real''. If you write out the path integral formulation of say field theory, then the classical field configurations are preferred hidden variables.

Can you clarify? Somehow I THINK you mean that there are one observer, observing another observer. So that the first observer takes the role of a "superobserver" except of course, it's not, it's just a normal obsever. So that the "quasi local" observer you refer to, are the "secondary observer" distinguished as coherent subsystem living withing the image of the first observer? Is this right?

More or less, this picture is much more refined and complicated in section 8 (where there is a continuum of super observers). But in section 3, the issue I raise is the following : where does consciousness of macroscopic observers come from ? Why do ants, humans and so on have this gift but say fullerene molecules probably don't (to any reasonable extend)? I want a dynamical theory of consciousness, one in which the material configuration feeds consciousness and consciousness feeds the material configuration. This requires a dynamical theory of a superobserver, but alas it cannot be written into a symbolic language (it can however to a good approximation, but not exactly). However, once a conscious individual observer has been formed, it has all the ''powers'' ascribed to by Von-Neumann.

 

[Fra]

Ontological basis = basis of states which are supposed to be ''real''. If you write out the path integral formulation of say field theory, then the classical field configurations are preferred hidden variables.

Mmm, it sounds like I may have some issues with this.

My question is how an observer can infer this "real basis". Unless you have something special in mind, this is a "realist construct" that I have hard to accept as a starting point.

What I mean is: How do you define; in terms of something inferrable and representable, this "real" states from the more subjective basis of an observer?

Of course these problems are existing already in QM, I'm just trying to see how you view them, and if you carry them over.

Edit: I think normally this real basis is defiend relative to an effectively classical and objective environment. Ie. the LABORATORY, which is orders of magnitues more massive and stalbe than say the tiny "inside observers" in the subatomic system in question.

More or less, this picture is much more refined and complicated in section 8 (where there is a continuum of super observers).

Ok I'll look at this later. But my issues here, will apply also to the continuum. How is the continuum inferred. I distinguish what's mathematically possible, and what's encodable by an observer.

But in section 3, the issue I raise is the following : where does consciousness of macroscopic observers come from ? Why do ants, humans and so on have this gift but say fullerene molecules probably don't (to any reasonable extend)? I want a dynamical theory of consciousness, one in which the material configuration feeds consciousness and consciousness feeds the material configuration.

This is where it is starts to get unclear. So I do not quite ask this question. I probably partially associate to this; except your way of phrasing the question seems a little more existential than how I see it. Even if you have good thinking, I think a lot of people may shrug by notions like "theory of consciousness".

They way I phrase this is just how a physical system can encode, and act upon it's own state (incorporating informatio nabout the environment). In this, I see no principal difference between humans and electrons except orders of magnitude in complexity and levels of organisation of the complexion set where the view of the environment is encoded.

The word conscioussness isn't something I would use here, although as I understand you, I would probable label this thing just "self-reflection" or selfinteraction. It just would mean that a system responds to it's own state, and this (in my view) ALL systems do, even an atom. And I picture it to related to a connection between the holography and the action, since an quantum systems evolution; in the abscence of perturbation; is simply a function of it's own initial state. It's a kind of self-interaction only. I connect this to the foundations of the logic of inference and the foundations of probability theory and QM logic.

I have a feeling that you might have (apart from some of the "reality" notions where I'm not sure what you mean) a somewhat similar perspective as me, but the fact that you keep using words like conscioussness for things I would lavel (self-interaction, or self evolution of inference systems) makes me a little confused.

What I have in mind has nothing to do with human intelligence, it's just a basic property of an evolution information processing agent, that I do think is describable(in the future!) in terms of an inference model (generalization of inductive probability with non-commutative sets). This is what I would avoid associating to human mind and pscyhology. Even if there may be at some leveal an coupling, pointing it out, I think rather than clarify may caused more technical people to misunderstand it.

/Fredrik

 

[Careful]

Mmm, it sounds like I may have some issues with this.

My question is how an observer can infer this "real basis". Unless you have something special in mind, this is a "realist construct" that I have hard to accept as a starting point.

Yes, one more or less can. Locally, there is of course the standard basis associated to local representations of the Poincare algebra. To glue these together is a non-unique procedure, but I am fairly confident it can be done in a reasonable way. All I wanted to say in that section is that path integrals start from such an ontological basis which has no physical significance and that this is a severe limitation (classical thought which should not be there).

Ok I'll look at this later. But my issues here, will apply also to the continuum. How is the continuum inferred. I distinguish what's mathematically possible, and what's encodable by an observer.

The continuum just is for very good reasons. Your quantum attitude cannot be consistently applied to all levels of ''reality''.

This is where it is starts to get unclear. So I do not quite ask this question. I probably partially associate to this; except your way of phrasing the question seems a little more existential than how I see it. Even if you have good thinking, I think a lot of people may shrug by notions like "theory of consciousness".

I don't care about people's problems with words they should use because they feel it might be unscientific to do so.

They way I phrase this is just how a physical system can encode, and act upon it's own state (incorporating informatio nabout the environment). In this, I see no principal difference between humans and electrons except orders of magnitude in complexity and levels of organisation of the complexion set where the view of the environment is encoded.

The word conscioussness isn't something I would use here, although as I understand you, I would probable label this thing just "self-reflection" or selfinteraction. It just would mean that a system responds to it's own state, and this (in my view) ALL systems do, even an atom. And I picture it to related to a connection between the holography and the action, since an quantum systems evolution; in the abscence of perturbation; is simply a function of it's own initial state. It's a kind of self-interaction only. I connect this to the foundations of the logic of inference and the foundations of probability theory and QM logic.

Your logic is way too limited here and the standard classical atomistic point of view. The problem is that in GR, the universe is holistic: there are no identities a priori, no I's and therefore no ''self-reflection'' or self interaction at the basic level. You view the world as an ensemble of interacting subsystems, each with their own Hilbert space and well defined state. In my view this is totally wrong and certainly completely contradictory to Mach's philosphy and QFT as well. Indeed, the notion of a single extended particle within a curved spacetime is not even sharply defined, it is only so ultralocally. And, the extend to which it is not so, depends upon interactions with the rest of the universe. So, identity is something which should be ''born'' out of grandiose holistic view. It should be created, just like your identity is created when your mother's egg met your father's sperm. This requires a superobserver(s) of some kind and there is no way out of this.

What I have in mind has nothing to do with human intelligence, it's just a basic property of an evolution information processing agent

But it is more than information processing! It is also information creating.

 

[arkajad]

I wouldn't call him a QG physicist

Certainly I am not. Neither quantum nor classical.

There is certainly one unjustified extrapolation in Johan's paper. At the end he wrote:
"...to Arkadiusz Jadczyk for the gigantic effort to have read the entire manuscript with a magnifying glass."

While the magnifying glass corresponds to reality, "the entire manuscript" is an extrapolation without any experimental evidence. Johan has an evidence only for ca 90 pages.

Moreover, most of my over 100 exchanges with Johan were around a single topic of his paper. He asked me not to write publicly about it before publishing his paper. Now that his paper is out, I may write about it - in due time.

 

[Careful]

Johan has an evidence only for ca 90 pages.

That is true, but given your enthousiasm, I anticipated that you would finally get to page 160. I hope my premature extrapolation did not turn out to be unjustified. If you insist, I will change entire to 60%.

Moreover, most of my over 100 exchanges with Johan were around a single topic of his paper. He asked me not to write publicly about it before publishing his paper. Now that his paper is out, I may write about it - in due time.

You already did partially on your blog when writing about non-linear connections. Words I only learned about because of you and as far as I know you learned them because of me (in either by digging into the literature for correspondance of my geometrical structures to already published work).

 

[arkajad]

You already did partially on your blog when writing about non-linear connections.

That's only an introduction. There will be follow-ups. But indeed, the discussion with you was a good boost to my long-standing, but pure Platonic, interest in Finsler-like geometries and nonlinear connections.

 

[Fra]

The continuum just is for very good reasons. Your quantum attitude cannot be consistently applied to all levels of ''reality''.

I look forward to your later arguments to why the continuum is there from start. But my hunch is that I will disagree. But I'm curious to see the arguments. It could again be words.

I don't question the utility of the continuum and calculus of course. it's clear. But I refer to it having a place in the reconstruction. This is at least "less clear" to be more diplomatic here.

I don't care about people's problems with words they should use because they feel it might be unscientific to do so.
...
But it is more than information processing! It is also information creating.

a) sure, I don't either, it was just a feedback on impression from your paper. Maybe I'm not the only one that's confused. But I certainly try to not confuse the message with choice of words.

b) yes I agree. more on that later in discussions.

Your logic is way too limited here and the standard classical atomistic point of view. The problem is that in GR, the universe is holistic: there are no identities a priori

No, this is not my view :) Then you read me wrong. Possibly the misunderstanding is mutual here.. More later. I'm not an atomist, not even close. But I think I see what you may think so, the "atomism" I think you see is a relative atomism. Each observer, at any instant sees an "atomic world", due to information bounds. This isn't to be confused with that the world really IS atomic in some objective sense - it's not. not in my view.

About GR, GR is also a realist theory. My vision does change both QM and GR; they need each other even, since gravitation and inertia are lreated, and in my view this translates to entropic gradients vs resistance to chance of opinon (inertia of information). In my view, the corresponding Einsteins equation corresponds to an equilibrium (except technically equiblirium is misleading, I mean "equilibrium" but relative to a new inference, not classical statistics of course).

/Fredrik

 

[DarMM]

Nobody so far had a good answer to Coleman-Mandula, Weinberg-Witten and Haag theorem... these are the cornerstones of quantum gravity.

How is Haag's theorem a cornerstone of quantum gravity?

 

[Careful]

How is Haag's theorem a cornerstone of quantum gravity?

Haag's theorem is extremely problematic for QFT; hitherto, it should be adressed in a theory of quantum gravity. If you know another way out of Haag than I do, you may want to adress it.

 

[DarMM]

Haag's theorem is extremely problematic for QFT; hitherto, it should be adressed in a theory of quantum gravity. If you know another way out of Haag than I do, you may want to adress it.

Well, there is no "way out of" Haag's theorem. It's just a theorem. In perturbation theory it isn't a problem and nonperturbatively you just build the theory in a different Hilbert space.

 

[Careful]

Well, there is no "way out of" Haag's theorem. It's just a theorem.

Sure it presents a problem for QFT which is by definition a perturbative game (at least if you follow the treatment of Weinberg). In that sense, Haag's theorem forces you to find a very different set of physical principles behind QFT.

nonperturbatively you just build the theory in a different Hilbert space.

But that doesn't make any physical sense you see, Fock space is motivated from very good principles. You reason like a mathematician without any physical guideline; I have told the same to another mathematician on this forum once. There is nothing wrong with Fock space and if you think there is, please motivate yourself. Haag's theorem points towards a much deeper shortcoming in my opinion.

 

[A. Neumaier]

Sure it presents a problem for QFT which is by definition a perturbative game (at least if you follow the treatment of Weinberg). In that sense, Haag's theorem forces you to find a very different set of physical principles behind QFT.

How little such considerations matter for perturbative quantum field theory can be seen from the fact that Weinberg mentions neither Haag's theorem nor inequivalent representations of the CCR.

It only matters for an endeavor which you (unlike people like Jaffe and Witten) find utterly irrelevant - that of putting QFT on a mathematically rigorous footing.

In other words: Perturbation theory and other ways of avoiding rigor are the standard and time-honored ways of bypassing Haag's theorem.

Your book is not innovative in this respect.

 

[A. Neumaier]

http://arxiv.org/abs/1101.5113
Foundations of a theory of quantum gravity
Johan Noldus
[...]
This paper/book was uploaded today. I put his name on google and saw that marcus put him on an observation list a few years ago:
https://www.physicsforums.com/showthread.php?t=102147

Yes. He wrote, among others:

Now I see that this PF forum can actually sometimes serve as an OUTLAW CAFE in some of its threads. We can help compensate for deficiencies in the system.

One way to do this is simply to LIST the divergent QG approaches and to try our best to shoot them down. [...]

If these novel approaches are natural allies, not rivals, then why should we concentrate on shooting them down? BECAUSE THAT IS WHAT YOU ALWAYS TRY TO DO WITH PHYSICS IDEAS, and it is GOOD FOR THEM. [...]

Also NOLDUS, whom I just noticed. What is wrong with Noldus ideas. He has a way to reform quantum mechanics from what he calls a "diehard" gen rel perspective. Well at least on the surface that sounds great. The possibility really should be seriously considered that whatever is keeping QM from merging with GR is basically QM's fault. People are reluctant to look at it this way, but Noldus attempts to bend QM into shape [...]

This thread was attended by Garrett Lisi, Thomas Larson and Careful. It seems that careful also keeps track of this author, as google point out his participation explaining Johan Noldus' ideas on other threads.

This is kind of a surprise to me.

yes, Careful discussing himself...

Now that he is no longer shaping the discussion about Noldus' work, let me make some comments on the latter (referring to version 1101.5113v2 from February 5, 2011).

Reading the thick book in great detail seems not warranted, given its present quality.

Though the author claims in the abstract that ''a logically consistent and precise theory of quantum gravity is presented'', and ''This novel theory automatically incorporates an extended form of gravity as well as a quantum gauge theory'', I can't see anything that would solve the problems that plague current gauge field theory.

Presented is a proposal for a new framework, but no quantum calculations are done (apart from generalities). No renormalization calculation or the absence of UV divergences, no discussion of infrared problems or their absence -- i.e., all the things where the usual quantum field theory faced difficulties are still unresolved, mostly even unaddressed.

It also remains a mystery how the standard model or standard QED should arise in some limit. No spectrum or energy shift is calculated, no scattering cross section, no thermodynamic potential, so it remains unknown whether the theory can predict anything, let alone predict it correctly.

On p.127 (10 lines from below), he apparently states that his theory has around 100 free parameters. To be predictive of anything, these parameters must either be determined from experiment or shown to be irrelevant at energies far below the Planck scale. He doesn't even indicate how to do either of the two.

Considerations precisely defining the spaces of interest with the appropriate topology
are virtually absent (except for a superficial discussion of some such issues on p.86-88, already on p.90, the author uses subjunctive language about what should hold rather than what he can prove.)


The exposition is also very far from satisfying.

The book consists of long, unstructured chapters, in which it is not easy to navigate. This forces the reader to read through the whole text in a linear fashion, which few are prepared for such a long text.

The material would be much more readable if only the construction and what one can conclude from it about observables, dynamics, and known physics were given, rather than a somewhat incoherent mix of historical and philosophical remarks, dead ends, and formal developments. Mixing model development in quantum gravity with philosophical
considerations of free will and consciousness makes one suspicious.

The first six chapters (comprising 75 of the 161 pages) discuss side issues - the axioms (i.e., the formal development) starts in Section 8, with Section 7 preparing the stage by introducing a prerequisite needed, ''quantum field theory on indefinite Hilbert space'' (though a Hilbert space cannot be indefinite; meant is a Clifford-bimodule equipped with a compatible indefinite inner product).

Section 8 starts on p. 94 with the promise ''I shall ”axiomatize” a new quantum-gravity-matter theory''. I expected to see axioms stating the precise definitions and assumptions, and then some development using this. Indeed, the author sets very high standards: ''if one speaks about a fundamental theory, the latter has to be nonperturbatively well defined from the very beginning and have a clear ontology as well'' (p.95 top); ''the theory constructed here is extremely ambitious, it does not only want to solve technical ”details” such as renormalizability but it also claims to adress long standing conceptual issues in quantum mechanics'' (p.95 middle).

Instead, one still has to wade through pages of commentary that is only loosely related to the content but defends the choices against alternatives - as if the theory would be rated by the choices made rather than by the results produced.

Finally, on p.98 comes axiom 0, which (instead of starting from scratch, as the first axiom is supposed to do) refers to notation (e_a(x), {\cal L}, M) that is not explained; presumably it was introduced at an unknown place in the 97 pages before, and the reader is expected to have remembered it, since not even a back-reference is given. This makes it very hard for potential readers to follow. Lack of references to explanations things like the Guichardet construction or Haag's theorem (which are unlikely to be known to the average reader of a paper on quantum gravity) deepen the problem. Axioms should not depend on an extensive prior discussion but should provide the prior itself!

Moreover, Axiom 0 is not a statement of assumptions and definitions (as one would expect from an axiom), but a discussion of reasons (Since...) and considerations of possible continuations (cannot..., can...). I never saw an axiom system that mixes this.

Immediately after the statement of Axiom 0 comes talk about local Fock
spaces and a universal Hilbert space, which are introduced only 16 pages later.

Axiom 1 starts on p.99 and spans 4 pages (!). It begins by saying ''we regard TM as a manifold'' as if it could be regarded as something different. Again long justifications that make it hard to discern what are the actual things required and what is just commentary or conclusion. Apparently, what is assumed is a bundle structure with a Poincare group compatible with the the tangent manifold structure.

Axiom 2 appears on p.133 and requires what is called a Fock bundle structure (or something very similar; the description isn't very clear), discussed already in old work by Prugovecki (in the context of stochastic quantum gravity) and by Mickelsson (in the context of quantum gauge theories). Let me give some early references since Noldus gives none (and seems not to know about the concept).

@article{prugovečki1987geometro,
title={{Geometro-stochastic quantization of massive fields in curved space-time}},
author={Prugove{\v{c}}ki, E.},
journal={Il Nuovo Cimento A (1971-1996)},
volume={97},
number={6},
pages={837--878},
issn={0369-3546},
year={1987},
publisher={Springer}
}

@article{drechsler1996quantum,
title={{On quantum and parallel transport in a Hilbert bundle over spacetime}},
author={Drechsler, W. and Tuckey, P.A.},
journal={Classical and Quantum Gravity},
volume={13},
pages={611},
year={1996},
publisher={IOP Publishing}

@article{mickelsson1990commutator,
title={{Commutator anomalies and the Fock bundle}},
author={Mickelsson, J.},
journal={Communications in Mathematical Physics},
volume={127},
number={2},
pages={285--294},
issn={0010-3616},
year={1990},
publisher={Springer}

Axiom 3 (on p.114) makes some assumption, and disqualifies them in the next moment by stating (still as part of the axiom) that they are not entirely correct. Never before have I seen an axiom stating its own incorrectness!

Let me skip some axioms, and turn to Axiom 9. It introduce (on p.140) local reference frames in which consciousness operates, without saying what the latter means. It operates, hence seems to be an operator on the local reference frames. But the reader must find out the details for himself since the axiom doesn't tell. But it was promised on p.3 that ''I shall not hesitate to use a word like consciousness albeit I define it in a very precise and limited sense'' - something the author perhaps thinks is fulfulled with the informal Section 3; but I cannot recognize there precision in any sense.

The Axiom 10 presents (on p.141) the assumptions for ''a dynamical measurement theory, but again I will have to be somewhat handwaving here and merely explain in words what I have in mind''. Not a healthy sign for an axiom system!

The final Axiom 12 (on p.145) is the shortest and consists in the following:
''nature adapts its own laws and boundary conditions so that maximal structure formation occurs within the limitations of a well defined second law. There is no initial value problem nor landscape issue, the laws have a Darwinian purpose.''

Readers of this post should by now have enough impressions to know whether they should invest time into reading the whole 161 pages to understand the ''logically consistent and precise theory of quantum gravity'' promised in the abstract of the book.