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

[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.

 

[MTd2]

Well, given that you put unfair words in my hands, I will forward you Noldus' answer:

"The problems which plague gauge theory are adressed from several novel perspectives:
(a) Haag's theorem, which obstructs a nonperturabive formulation of QFT, is circumvented by means of generalized Fock bundles and giving up causality on spacetime.
(b) The quantum gauge theory he constructs is not the ordinary quantization of classical gauge theories.
(c) The way the renormalization problem is attacked is by abandonning causality and cluster decomposition, there are no apriori classical lagrangians and coupling constants only arise when solving the equations of motion; not by merely putting them in by hand.

Defining an effective S matrix and therefore calculating energy shifts and cross sections depends upon how you coarse grain the local particle notions. This is a very difficult task which is not even accomplished in a satisfactory way in classical relativity.

Concerning the 100 parameters, some of your points needs to be addressed: (a) they do not need to be small, there exist large scales in cosmology where GR also needs modification (b) 100 free parameters are not much compared to the extra degrees of freedom introduced in the landscape in string theory or LQG.

What spaces are you talking about ? The necessary functional analysis is developped in section seven partially. The sections are not unstructured and perhaps you should give it a chance. All sections stick closely together and build upon each other sequentially.

Why is this so ? There have been plenty of good QG physicists writing about the philosophical problems: these include Chris Isham and Karel Kuchar.

The first six chapters are crucial and by no means side issues. They provide the justification and motivation for the work to come. Again, please, give it a chance :).

Concerning the axioms, it was explained you in private several nice reasons why he chose not to write them in a full mathematical form:
(a) because physical axioms are much more general and powerful than mathematical ones.
(b) Because I did not want to commit the same error Von-Neumann made by unnecessarily overspecifying the mathematical context.

Actually, this does not make the work any less precise because it is clearly states in section seven that hard calculations will have to show which limitations can be imposed and which are unwarranted. This book is not finished and it not claimed to be. This the reason why the title is ''Foundations of a theory of quantum gravity''.

And yes, the theory depends upon the choices made, some of them which have no experimental impact. For example, the Unruh effect holds or not depends upon local versus quasi local particle notions, the latter which would require higher bundles. Now, the unruh effect is not going to be tested in the next 50 years probably. Nevertheless, the theoretical implications are huge. So this is one example why it was not not specified the full mathematical context, because there would not be a good reason to do so.

Concerning axiom 0, it must be understood that these concepts cannot be explained in one simple axiom or not even in section 8, because even this generalized definition of a Nevanlinna space takes 10 pages to explain, which happens in section 7. Again, be a nice guy with the paper! :)

Sure, TM is usually regarded as a natural fiber bundle whose manifold stucture is not canonically given. Actually there exist several different constructions : one could passively lift coordinate charts from M to TM as is usually done, or one could use a dynamical object such as the vierbein to define a dynamical atlas, which is what is done. Both differentiable structures give rise to different non-linear connections, so this is not canonical at all.

By coincidence or not, the generalized Fock bundles was invented again... It could be worse not having heard about them but not knowing how to use!

There is no inconsistency whatsoever concerning Axiom 3 because the generators of the local Poincare groups have to be split into two parts, one which is generated from Noether's theorem and contains all the matter degrees of freedom and the second part which gives the graviton sector. This literally mandatory due to the Weinberg-Witten theorem, which is a concept that is not trivial.

Regarding the axioms of consciousness, it is hard to tell them right away so easily.

I think it must be clear that you seem to be personally angry towards the author and perhaps missed some fundamental points, given the fact that of the carefully explained issues discussed in private communication. In case this line of argumentation is not forfeit, the author sees no reason to keep a discretionary attitude."

 

[A. Neumaier]

Well, given that you put unfair words in my hands,

I had only forgotten a pair of quotation tags; this is now corrected.

I will forward you Noldus' answer

I'd have been more interested in _your_ response to the paper in the light of my remarks.
Anyway, here are some comments on Noldus' reply:

(c) The way the renormalization problem is attacked is by abandonning causality and cluster decomposition, there are no apriori classical lagrangians and coupling constants only arise when solving the equations of motion; not by merely putting them in by hand.

Writing equations of motions are a way to propose a theory, but as long as one hasn't begun to solve it, one doesn't know that renormalization problems are absent. For example, the equations of motions written down for QED in the early days of quantum mechanics appeared quite innocent but turned out to lead to divergences in second order perturbation theory, indicating the need for renormalization.

Noldus hasn't presented any evidence that his equations of motions can be solved without recourse to renormalization. But he states on p.95: ''the theory constructed here
is extremely ambitious, it does not only want to solve technical ”details” such as renormalizability but it also claims to address long standing conceptual issues
in quantum mechanics.'' -- Maybe he wants, but he doesn't do it. His paper is full of ideas and suggestions but far from having demonstrated the ''logically consistent and precise theory of quantum gravity'' the abstract promises.

Concerning the axioms, it was explained you in private several nice reasons why he chose not to write them in a full mathematical form:

The private exchange was so little convincing that I copied many of my email remarks on the prior 90 page preprint that we had discussed into the preceding post - none of my criticism had any influence on the current form of the manuscript.

This book is not finished and it not claimed to be.

I measured the paper on the preprint server by its abstract. If the current version does not satisfy what is promised in the abstract, the abstract is misleading.

I think it must be clear that you seem to be personally angry towards the author

I deliberately waited with my post assessing the whole paper till the emotionally heated part of the discussion was over.

 

[MTd2]

Alright, so this is an answer he sent me. I do not have an opinion on his work yet.

"You were not sent a 90 page preprint, bu one about 130 pages thick.

Noldus : But, on the other hand, as I said, I do not have a standard
dynamical system. I don't have a (global) Hamiltonian, my formulation is
much more like the standard 4-covariant formulation of general relativity.

Neumaier : Of course, one cannot have a global Hamiltonian in a diffeomorphism
invariant theory. Nevertheless, one still has a symmetric hyperbolic
structure, and this is what allows one to formulate an initial-value
problem in local covariant coordinates. Solving that will most likely
bring up renormalization issues.


Noldus : No, there are several ways of understanding this; let me give you two reasons why covariant formulations are better suited:
(a) in GR if you work in a physical gauge such as the Gaussian gauge, then usually you run into inconsistencies because of the physics of GR (focal points); any physical gauge in GR suffers from similar problems. Of course, if you take suitable coordinate systems, nothing happens. The best example is that of the original Schwartzschild solution which blows up at the event horizon, but the physics doesn't and indeed going to Eddington-Finkelstein coordinates gives you a very different picture. So, the idea here is that renormalization problems in QFT show up because of a bad ''physical gauge choice'' (and I will explain in a minute why my theory proves this to be the case) ; the Heisenberg equations of GR are generally covariant, but the Heisenberg commutation relations are not. They are attached to a physical ''gauge'', that is the hypersurfaces of equal ''time'' should be spacelike. Now, you may think of causality (the commutation relations) as kind of an ''initial value formulation'' of a fully relativistic dynamics. But my theory proves that is wrong. There is not so much freedom to pick initial data on an initial hypersurface, the only freedom is given by a data on a holographic two-sphere at infinity. So, my suspicion is that the ordinary formulation of interacting QFT is **overconstrained** and that's why you run into troubles, you ''gauge fix'' more than there are ''gauge'' degrees of freedom.
(b) Another way is a more technical one, and I have explained it already to you (but it boils down to the same thing). If you would fix causality **a priori** (the commutation relations), then you must go over to field theory (see Weinberg). In the interaction picture, this leaves you with a number of free coupling constants and you assume them to be small, so you expand order by order in the coupling constants and treat each order separately. There is *no* freedom here, the physics is fixed and must come out *finite*, but it doesn't. This leads you to two problems: the renormalization of the separate terms and the non-analyticity of the series expansion.
Now, it is long time well known that there exists ways to do the summation differently and mix different orders of the coupling constant (infinities cancel out this way much better, actually, this is the rationale behind the asymptotic freedom program of Saueressig, Benedetti and co). However, within standard field theory, there is no good motivation for this and you don't really know what you are doing physically. Now, in my theory, there are no coupling constants, but each term in front of a monomial of normal ordered creation and annihilation operators comes with free functions in terms of the Lorentz covariant four momenta, physical polarization vectors and spacetime coordinates. So, when calculating the unitary potential, the appropriate expansion is in monomials of the creation and annihilation operators (and all those terms are of the right type since the number of integrals equals the number of operators minus one - hence formally satisfying the cluster decomposition principle). So, if we ignore the clifford terms you have the same number of free functions as you have terms to make finite: indeed, delta functions do show up since the product of two terms of n -1 + m - 1 = n + m - 2 so, that is precisely one integration short (these terms give singular operators) - if you, by normal ordering replace a creation and annihilation operator by one delta function, you again have n + m - 3 integrals for n + m - 2 operators which is fine, n + m - 4 integrals for n + m - 4 operators is still well defined but more contractions give again singular operators. So, the point is that higher order coefficient functions in the Hamiltonian do get involved in the lower order coefficients of the unitary expansion while those terms are usually thought of as being higher order in the coupling constant. So, it is a very different scheme, with plenty of more freedom and no a priori constraints due to causality.

That is all I have to say."

 

[A. Neumaier]

You were not sent a 90 page preprint, bu one about 130 pages thick.

I was only discussing the 90 page version he sent me first (on December 12). I didn't read the later versions he sent me since it was clear that it was still work in progress and much more was to come. Since I didn't want to spend so much time on a half-baked manuscript, I preferred to wait for the public version now on the arXiv. Unfortunately, this online version is still only half-baked.

I grant that the paper contains lots of potentially interesting ideas. But it sells the plan of a house for the actual building. To advertise beliefs, hopes, or expectations as achievements is very poor scientific practice. The proper thing to do would be to modify the abstract, reducing the claims to what is actually proved, and to moderate in the bulk of the work the tone of superiority about unproved items.

I am looking forward to seeing on the arXiv a revised version v3 that is much improved in this respect...

Noldus : But, on the other hand, as I said, I do not have a standard
dynamical system. I don't have a (global) Hamiltonian, my formulation is
much more like the standard 4-covariant formulation of general relativity.

Neumaier : Of course, one cannot have a global Hamiltonian in a diffeomorphism
invariant theory. Nevertheless, one still has a symmetric hyperbolic
structure, and this is what allows one to formulate an initial-value
problem in local covariant coordinates. Solving that will most likely
bring up renormalization issues.

Noldus : No, there are several ways of understanding this; let me give you two reasons why covariant formulations are better suited:
(a) in GR if you work in a physical gauge such as the Gaussian gauge, then usually you run into inconsistencies because of the physics of GR (focal points); any physical gauge in GR suffers from similar problems. Of course, if you take suitable coordinate systems, nothing happens. The best example is that of the original Schwartzschild solution which blows up at the event horizon, but the physics doesn't and indeed going to Eddington-Finkelstein coordinates gives you a very different picture. So, the idea here is that renormalization problems in QFT show up because of a bad ''physical gauge choice'' (and I will explain in a minute why my theory proves this to be the case) ; the Heisenberg equations of GR are generally covariant, but the Heisenberg commutation relations are not. They are attached to a physical ''gauge'', that is the hypersurfaces of equal ''time'' should be spacelike. Now, you may think of causality (the commutation relations) as kind of an ''initial value formulation'' of a fully relativistic dynamics. But my theory proves that is wrong. There is not so much freedom to pick initial data on an initial hypersurface, the only freedom is given by a data on a holographic two-sphere at infinity. So, my suspicion is that the ordinary formulation of interacting QFT is **overconstrained** and that's why you run into troubles, you ''gauge fix'' more than there are ''gauge'' degrees of freedom.
(b) [...] Now, in my theory, there are no coupling constants, but each term in front of a monomial of normal ordered creation and annihilation operators comes with free functions in terms of the Lorentz covariant four momenta, physical polarization vectors and spacetime coordinates. [...] So, it is a very different scheme, with plenty of more freedom and no a priori constraints due to causality.

I don't think these comments improve the quality of the overall argument. My response (originally happening on December 15) was (spelling amended):

... to point (a) of this dialogue:
''I don't find QED overconstrained. If it were, it could make no predictions since it would produce immediate contradictions. This is the case for the old QED of the 1930s but not for the successful (renormalized) QED of today.
And renormalization has nothing to do with gauge fixing. You also have it in Phi^4 theory where there is no gauge group. And indeed, you have it in much simpler systems, e.g., in the system consisting of a single particle in an external delta function potential.''

... and to point (b):
''But how do you achieve any predictivity with so many degrees of freedom. QED is very predictive just because it is so restrictive: one one knows the electron mass m and charge e, you can predict everything of interest.
In your scheme, you apparently need to know many more degrees of freedom before you can predict anything specific (such as the Lamb shift).''

 

[MTd2]

Noldus sent me this email to show that he sent the 134 page version and not the 90page one:

"

Hi,

My way of doing nonperturbative QED would be based upon what you can find in sections 8,9,10 of the paper below. There is no renormalization at all, and nothing is based upon action principles. Note, this is a draft version of my work and nothing may be used or transmitted to third parties. If you are interested in having some more explanations/discussion about it, I would be happy to provide you with. This work has already been discussed partially with Rafael Sorkin and Arkadiusz Jadczyk.

Especially in section 10, you can understand how such computations would need to be done.
Could you please send me back a confirmation of receipt ?

All the best,

Johan Noldus

approach quantum gravity.pdf
707K Visualizar Baixar"


I opened the file and it is dated 12th december, 2010. It has 134 pages.

He later sent me this message:

"Concerning my promises; at least I give plenty of plausibility arguments. Rovelli for example writes a book ''Quantum Gravity'' and there is not even a theory inside it (no proposal for a dynamics even), Smolin writes ''three roads to quantum gravity'' and he does not even outline a single road in any detail. In version 3, there will be no word changed, on the contrary, more evidence will be provided that these claims are correct. Bold conjectures are OK as far as they are reasonable. Mathematics is full of them, see the Poncare or Fermat conjecture or the Riemann hypothesis... they are the driving force of the field."

 

[Fra]

Concerning my promises; at least I give plenty of plausibility arguments. Rovelli for example writes a book ''Quantum Gravity'' and there is not even a theory inside it (no proposal for a dynamics even), Smolin writes ''three roads to quantum gravity'' and he does not even outline a single road in any detail. In version 3, there will be no word changed, on the contrary, more evidence will be provided that these claims are correct. Bold conjectures are OK as far as they are reasonable. Mathematics is full of them, see the Poncare or Fermat conjecture or the Riemann hypothesis... they are the driving force of the field."

Too bad Careful doesn't post more in this thread.

If anyone spots the paper where the motivation for the continuum structures that is his startingpoitn please notify. I think it was suppose to be in some fqxi contest.

I intended to keep skimming his ideas, but to make it in the order I prefer to see the motivation for the starting points before it makes sense to study the constructions based on it.

/Fredrik

 

[Fra]

Smolin writes ''three roads to quantum gravity'' and he does not even outline a single road in any detail

I was some year ago HOPING that the book that Smoling and R. Unger was supposed to release, might outline a little more in detail the "philosophy" that Smolin has advocated in several talks and papers.

But for some reason...the book still not out... I'm starting to think that this book won't come, and if it comes, it will be a more another popular style book rather than reconstruction of new formalism. I fear that that in order to see such a book, I someone else just have to write it ,worse case I'll have to try write it myself.

I suppose I'm curious to find out if Carefuls book will make some contribution here. But more important than anything to start with IMHO is to try to understand the reasoning. This is why I see the next step as the motivation behind his starting point.

/Fredrik

 

[A. Neumaier]

Noldus sent me this email to show that he sent the 134 page version and not the 90page one:
[...] I opened the file and it is dated 12th december, 2010. It has 134 pages.

In this case, I read the 134 pages; I can't check it anymore since I delete attachments from my mailbox. In any case, this doesn't affect at all the content of my comments.

"Concerning my promises; at least I give plenty of plausibility arguments.

But they are misleadingly announced in the abstract as being ''logically consistent''.

Rovelli for example writes a book ''Quantum Gravity'' and there is not even a theory inside it (no proposal for a dynamics even), Smolin writes ''three roads to quantum gravity'' and he does not even outline a single road in any detail.

Did they claim to do that? If not, they are faithful to their promises.

 

[A. Neumaier]

Too bad Careful doesn't post more in this thread.

As you can see, he still does post, through the address of MTd2. But it is borderline to violating the rule of PF that states:

''(iii) Only one person per account/username--accounts are not to be shared.''

 

[MTd2]

This is why I see the next step as the motivation behind his starting point.

/Fredrik

Well, he posted an entry to this year's contest on FQXI:

http://www.fqxi.org/community/forum/topic/905

On that entry, you can post questions to the author, like in a forum's thread or blog post.

 

[MTd2]

As you can see, he still does post, through the address of MTd2.'

He doesn't use my account. Any admin can check that all IP acesses of my account comes just from my country, Brazil. I just forward part of what he answers, which I heavily edit, that is, I remove all strong words and observations that he likes to use here.

 

[Fra]

Well, he posted an entry to this year's contest on FQXI:

http://www.fqxi.org/community/forum/topic/905

On that entry, you can post questions to the author, like in a forum's thread or blog post.

Thanks! Will check it out.

I really suck at keeping track of news. That's in fact one of the things I like with PF. Alot of people, you included + Marcus and lots of other do a nice job at spotting new papers and bringing them up for discussion.


/Fredrik

 

[A. Neumaier]

He doesn't use my account. Any admin can check that all IP acesses of my account comes just from my country, Brazil. I just forward part of what he answers, which I heavily edit, that is, I remove all strong words and observations that he likes to use here.

Yes, through your mediation he comes across much more civilized. Thanks for filtering that out!

 

[MTd2]

Alright, I more or less understand what Noldus wants to say. I chatted daily with him for the last few weeks and I formed a personal view or opinion about what he is dealing with.

What he wants to do can be summarized by Feynman's view on quantum mechanics, but applied to gravity.

"Thirty-one years ago [1949], Dick Feynman told me about his "sum over histories" version of quantum mechanics. "The electron does anything it likes," he said. "It just goes in any direction at any speed, forward or backward in time, however it likes, and then you add up the amplitudes and it gives you the wave-function." I said to him, "You're crazy." But he wasn't.
Freeman J. Dyson, in a statement of 1980, as quoted in Quantum Reality : Beyond the New Physics (1987) by Nick Herbert"

So, we have to apply the most general structures possible within what is reasonable in gravity.

The tangent space must not only be just Lorentz invariant, but Poincaré invariant.
The geometry must not only be Riemann, but Finsler.
The quantum vector space must not only be Hilbert (definite norm), but Nevanlinna (indefinite norm).
The wave function must not only be complex, but consist of Clifford numbers.
There must be covariance, but just not only have curvature on space-time, but have torsion on the tangent space.
The statistics must be of the most general type, since it is not constrained anymore by coleman-mandula, because there is no restriction for causality when something is not observed.

 

[A. Neumaier]

Alright, I more or less understand what Noldus wants to say.
[...]
So, we have to apply the most general structures possible within what is reasonable in gravity.

The tangent space must not only be just Lorentz invariant, but Poincaré invariant.
The geometry must not only be Riemann, but Finsler.
The quantum vector space must not only be Hilbert (definite norm), but Nevanlinna (indefinite norm).
The wave function must not only be complex, but consist of Clifford numbers.
There must be covariance, but just not only have curvature on space-time, but have torsion on the tangent space.
The statistics must be of the most general type, since it is not constrained anymore by coleman-mandula, because there is no restriction for causality when something is not observed.

OK, this is a proposal of where to start. But the question is - if one does all this, does he end up with a theory that has a well-defined dynamics so that computations do not result in divergences?

Proposing a new dynamics is easy. But its possible virtues can be seen only after one has tried to solve it to some nontrivial approximation. Noldus hasn't done this - so his claims to success are not better founded than QED was in 1929.

Note that a proposed dynamics for QED was written down in 1929, but it turned out to be not solvable in perturbation theory because of divergences at second order. It took almost 20 more years to find out how to modify the dynamics through renormalization.

For gravity, we know already a number of schemes that lead to divergences,

We know how to renormalize canonical gravity - though with an infinite number of parameters - most of which are however suppressed by high powers of the Planck mass.

We know nothing at all about Noldus gravity - not even whether computations can be done at all. To claim success, any alternative to canonical gravity must be better than the latter. In particular, to show Noldus' method promising the least that must be shown is that some version of perturbation theory is finite without introducing infinitely many renormalization constants.

Since this hasn't been shown, Noldus' work is currently not more that a proposal of a new direction where one could hope to be successful one day.