A glance beyond the quantum model

[DrChinese]

I wanted to follow up on a couple of specific points that were raised in another thread, and felt it would be better to split the discussion off here. The references for the discussion are:

A glance beyond the quantum model, Navascues and Wunderlich (2009)

"One of the most important problems in Physics is how to reconcile Quantum Mechanics with General Relativity. Some authors have suggested that this may be realized at the expense of having to drop the quantum formalism in favor of a more general theory. However, as the experiments we can perform nowadays are far away from the range of energies where we may expect to observe non-quantum effects, it is difficult to theorize at this respect. Here we propose a fundamental axiom that we believe any reasonable post-quantum theory should satisfy, namely, that such a theory should recover classical physics in the macroscopic limit. We use this principle, together with the impossibility of instantaneous communication, to characterize the set of correlations that can arise between two distant observers. Although several quantum limits are recovered, our results suggest that quantum mechanics could be falsified by a Bell-type experiment if both observers have a sufficient number of detectors. "

...And a recent comment on the above (by a PF member no less :)

Comment on "A glance beyond the quantum model", Peter Morgan (2010)

"The aim of "A glance beyond the quantum model" [arXiv:0907.0372] to modernize the Correspondence Principle is compromised by an assumption that a classical model must start with the idea of particles, whereas in empirical terms particles are secondary to events. The discussion also proposes, contradictorily, that observers who wish to model the macroscopic world classically should do so in terms of classical fields, whereas, if we are to use fields, it would more appropriate to adopt the mathematics of random fields. Finally, the formalism used for discussion of Bell inequalities introduces two assumptions that are not necessary for a random field model, locality of initial conditions and non-contextuality, even though these assumptions are, in contrast, very natural for a classical particle model. Whether we discuss physics in terms of particles or in terms of events and (random) fields leads to differences that a glance would be well to notice. "

----------

Of interest - and there has been recent discussion about several of these points - are the following:

a) Can you speak of particles without discussing the associated fields?

b) Are the fields themselves discrete or continuous?

c) It the correspondence between the macroscopic world and the microscopic world fundamental? Can we recover certain classical concepts - such as "no-signaling principle" or the introduced idea of "macroscopic locality" when a large number of particles are involved and our measurement devices fail to resolve discrete particles?

d) Are their low-energy Bell-type experiments that can set limits on the unification of quantum theory and gravity?

e) Anything else you might think of from the above...

 

[Peter Morgan]

Of interest - and there has been recent discussion about several of these points - are the following:

a) Can you speak of particles without discussing the associated fields?

b) Are the fields themselves discrete or continuous?

c) It the correspondence between the macroscopic world and the microscopic world fundamental? Can we recover certain classical concepts - such as "no-signaling principle" or the introduced idea of "macroscopic locality" when a large number of particles are involved and our measurement devices fail to resolve discrete particles?

d) Are their low-energy Bell-type experiments that can set limits on the unification of quantum theory and gravity?

e) Anything else you might think of from the above...

a) Not easily, but one can talk about measurement results (which one can say are properties of the measured systems, even though the systems themselves are not seen) in a finite-dimensional Hilbert space context, without introducing the Schrodinger equation or a quantum field. Indeed, quantum information lives very happily in this regime and often is thought to be fundamental.

b) One can work with either discrete or continuous mathematics. QFT on a lattice has certainly taught us stuff. Universality makes it difficult to make a categorical statement here, because discrete structure at the Planck scale would presumably be washed out at the scales at which we have any present hope of making measurements.

c) I think I take the Correspondence Principle to be a methodological requirement that comes from social issues in science. If one wants a new theory to get a running start, it helps to be able to point out how it is the same as and how it is different from the theories we currently take to be empirically effective. If one can show that the new theory can legitimately adopt a lot of the empirical effectiveness of an existing theory, it leaves less to do to establish how the new theory is better. The Correspondence Principle was used with stunning effectiveness by the founders of the new quantum theory in the late 20s to constrain quantum theory, so it seems worthwhile to attempt the same sort of approach now.

From a Correspondence Principle point of view, given that our current best theories are QFT and GR, it makes sense to stick with a field approach of some sort in attempts to construct new theories. The choice of an effective mathematical structure is important. Part of my enthusiasm for random fields is that they are a powerful generalization of classical differentiable fields that introduces the concept of probability in a mathematically correct way (whereas differentiable fields don't sit well with the measure theory), and which can be presented in a way that is very closely parallel to quantum fields. Retrospectively, a random field formalism might make a Correspondence Principle approach more possible.

However, this does not, to my more-or-less empiricist approach, entail that the world is continuous, only that it can be useful to use continuum mathematics, always supposing that we can get finite answers out, somehow.

d) Dunno. When I critiqued Navascués' and Wunderlich's assumptions I was careful not to get into the actual purpose of their paper because I know not much about QG.

e) Even less to say. Except that I believe the published version of the Navascués and Wunderlich paper is free to access on Proc. Roy. Soc. A, at http://rspa.royalsocietypublishing.org/content/466/2115/881" , and is preferable, from the point of view of my Comment, because they introduced classical fields into their paper only after the current arXiv version.

 

[strangerep]

a) Can you speak of particles without discussing the associated fields?

I've been wondering about a similar question in a different context,
namely the problem of IR divergences in QED, and correct identification
of the asymptotic dynamics, and hence also the asymptotic fields.

(I'm not sure whether what follows is tangential to your focus in this
thread, but I guess you'll tell me if so. :-)

In brief, I find it interesting that considering charged particles
together with their Coulomb fields seems to solve the IR problem in
QED in a much more physically satisfactory way than the typical
textbook treatments. This (imho) lends credence to the proposition that
it's better to treat particles together with their entourage of associated
fields, although such composite dressed entities are of course nonlocal.

For those who want more detail, here's an extract from a summary I've
been writing up for myself about it...

-----------------------------

Textbook treatments of the infrared (IR) divergences in quantum
electrodynamics (QED) typically introduce a small fictitious photon
mass to regularize the integrals. Allowing this mass to approach zero,
it becomes necessary to sum physically measurable quantities, such as
the cross sections for electron scattering, over all possible
asymptotic states involving an infinite number of soft photons, yielding
the so-called "inclusive" cross section.

The IR divergences are thus dealt with by restricting attention only to these
"IR-safe" quantities such as the inclusive cross section. However, various
authors have expressed dissatisfaction with this state of affairs in which
the cross sections become the objects of primary interest rather than the
S-matrix. The seminal paper of Chung (Chu) showed how one may
dress the asymptotic electron states with an operator familiar from the
Glauber theory of photon coherent states, thereby eliminating IR divergences
in the S-matrix to all orders for the cases he considered.

In a series of papers, Kibble (Kib1,Kib2,Kib3,Kib4) provided a much
more extensive (and more rigorous) development of Chung's idea, solving
the dynamical problem to show that IR divergences are eliminated by
dressing the asymptotic electron states by coherent states of soft
photons. Kibble constructed a very large nonseparable state space, within
which various separable subspaces are mapped into each other by the
S-matrix, but there is no stable separable subspace that is mapped into
itself.

Later, Kulish & Faddeev (KulFad) ("KF'" hereafter) gave a
less cumbersome treatment involving modification of the asymptotic
condition and a new space of asymptotic states which is not only
separable, but also relativistically and gauge invariant. They were
able to derive Chung's formulas without the laborious calculations of
Kibble, yet also obtained a more satisfactory generalization to the
case of arbitrary numbers of charged particles and photons in the
initial and final states.

KF emphasized the role of the nonvanishing interaction of QED at
asymptotic times as the source of the problems. This inconvenient fact
means that QED's asymptotic dynamics is not governed by the usual
free Hamiltonian $$H_0$$, so perturbative approaches starting from such
free states are singular (a so-called "discontinuous" perturbation).
Standard treatments rely on the unphysical fiction of adiabatically
switching off the interaction, but KF wished to find a more physically
satisfactory operator governing the asymptotic dynamics.

Much earlier, Dirac (Dir55) took some initial steps in
constructing a manifestly gauge-invariant electrodynamics. The dressing
operator he obtained is a simplified version of those mentioned above
involving soft-photon coherent states, but he did not
address the IR divergences in this paper. Neither Chung, Kibble, nor
Kulish and Faddeev cite Dirac's paper, and the connection between explicit
gauge invariance and resolution of the IR problem did not emerge until
later. (Who was the first to note this??) In 1965 Dirac noted (Dir65, Dir66)
that problems in QED arise because the full gauge-invariant Hamiltonian is
typically split into a "free" part $$H_0$$
and an "interaction" part $$H_I$$ which are not separately
gauge-invariant. Indeed, Dirac's original 1955 construction had
resulted in an electron together with its Coulomb field, which is
clearly a more physically correct representation of electrons at
asymptotic times: a physical electron is always accompanied by its
Coulomb field.

More recently, Bagan, Lavelle and McMullan (BagLavMcMul-1, BagLavMcMul-2)
("BLM" hereafter) and other collaborators have developed these ideas
further, applying them to IR divergences in QED, and also QCD in which
a different class of so-called "collinear" IR divergence occurs. (See
also the references therein.) These authors generalized Dirac's
construction to the case of moving charged particles. Their dressed
asymptotic fields include the asymptotic interaction, and they show
that the on-shell Green's functions and S-matrix elements for these
charged fields have (to all orders) the pole structure associated with
particle propagation and scattering.

--------------------------------------------
Bibliography for the above:

\bibitem{BagLavMcMul-1}
E. Bagan, M. Lavelle, D. McMullan,
"Charges from Dressed Matter: Construction",
(Available as hep-ph/9909257.)

\bibitem{BagLavMcMul-2}
E. Bagan, M. Lavelle, D. McMullan,
"Charges from Dressed Matter: Physics \& Renormalisation",
(Available as hep-ph/9909262.)

\bibitem{Bal} L. Ballentine,
"Quantum Mechanics -- A Modern Development",
World Scientific, 2008, ISBN 978-981-02-4105-6

\bibitem{Chu}
V. Chung,
"Infrared Divergences in Quantum Electrodynamics",
Phys. Rev., vol 140, (1965), B1110.
Also reprinted in (KlaSkag).

\bibitem{Dir55}
P.A.M. Dirac,
"Gauge-Invariant Formulation of Quantum Electrodynamics",
Can. J. Phys., vol 33, (1955), p. 650.

\bibitem{Dir65}
P.A.M. Dirac,
"Quantum Electrodynamics without Dead Wood",
Phys. Rev., vol 139, (1965), B684-690.

\bibitem{Dir66}
P.A.M. Dirac,
"Lectures on Quantum Field Theory",
Belfer Graduate School of Science, Yeshiva Univ., NY, 1966

\bibitem{Dol}
J. D. Dollard,
"Asymptotic Convergence and the Coulomb Interaction",
J. Math. Phys., vol, 5, no. 6, (1964), 729-738.

\bibitem{Kib1}
T.W.B. Kibble,
"Coherent Soft-Photon States \& Infrared Divergences. I.
Classical Currents",
J. Math. Phys., vol 9, no. 2, (1968), p. 315.

\bibitem{Kib2}
T.W.B. Kibble,
"Coherent Soft-Photon States \& Infrared Divergences. II.
Mass-Shell Singularities of Green's Functions",
Phys. Rev., vol 173, no. 5, (1968), p. 1527.

\bibitem{Kib3}
T.W.B. Kibble,
"Coherent Soft-Photon States \& Infrared Divergences.
III. Asymptotic States and Reduction Formulas.",
Phys. Rev., vol 174, no. 5, (1968), p. 1882.

\bibitem{Kib4}
T.W.B. Kibble,
"Coherent Soft-Photon States \& Infrared Divergences.
IV. The Scattering Operator.",
Phys. Rev., vol 175, no. 5, (1968), p. 1624.

\bibitem{KlaSkag}
J. R. Klauder \& B. Skagerstam,
"Coherent States -- Applications in Physics \& Mathematical Physics",
World Scientific, 1985, ISBN 9971-966-52-2

\bibitem{KulFad}
P.P. Kulish \& L.D. Faddeev,
"Asymptotic Conditions and Infrared Divergences in Quantum
Electrodynamics",
Theor. Math. Phys., vol 4, (1970), p. 745

-----------------------------

 

[strangerep]

Part of my enthusiasm for random fields is that they are a powerful generalization of classical differentiable fields that introduces the concept of probability in a mathematically correct way (whereas differentiable fields don't sit well with the measure theory)

It's been a while since I looked at your papers, and I don't remember the point about
"random fields ... introducing the concept of probability in a mathematically correct way".
Could you elaborate on the details of this point, and/or give specific places in your
earlier papers where you discuss this, please?

 

[Peter Morgan]

I found your discussion of IR divergences interesting, and I've bookmarked it both for the discussion and for the references, but I regret that I can't speak to it at this point, except to say that I've never seen anything that makes dressed particles look conceptually simple enough (or, more specifically, algebraically simple enough -- though that's not a conceptual direction one necessarily has to take).

It's been a while since I looked at your papers, and I don't remember the point about "random fields ... introducing the concept of probability in a mathematically correct way". Could you elaborate on the details of this point, and/or give specific places in your earlier papers where you discuss this, please?

I've had considerable trouble getting this across to anyone, although it seems clear as day to me, so I'm happy to try again. If one introduces a path integral approach for particles (though the same fact can be expressed in Hamiltonian formalisms), the path integral is dominated by nowhere differentiable paths (I've just seen this cited from Reed & Simon, which I don't have, but it ties in with my understanding of Hamiltonian methods). This works OK for particle trajectories, but notoriously, people have trouble making path integral methods rigorous in the field context, where there are more infinite limits to be taken. In the field context, I would say that no-one has really adequate mathematical control of the procedure, although some people are happy to say that renormalization is adequate mathematical control.

For a quantum field, some mathematical control (but not enough) is achieved by defining the quantum field to be an operator-valued distribution, not an operator-valued field, so that to construct an operator one has to "average" the quantum field over a finite region. As we consider smaller regions, the variance of such operators diverges, so if we try to talk about the quantum field at a point we find that, more-or-less, we would always observe either +infinity or -infinity, which isn't a good start for constructing a differentiable function. For the vacuum state of a free quantum field, the two point correlation function $$\left\langle 0\right|\widehat{\phi}(x)\widehat{\phi}(y)\left|0\right\rangle$$ is finite for $$x-y$$ non-zero, but diverges as $$x\rightarrow y$$, which is to say that the variance $$\left\langle 0\right|\widehat{\phi}(x)^2\left|0\right\rangle$$ is infinite. It's also to say that the correlation coefficient between the observed values at x and y is finite/infinity=zero, if we relinquish decent control of what limits we're taking. For interacting fields this only gets much worse, of course.

For classical fields, when we introduce the classical probability density $${\normalfont exp}(-\beta H(\phi))$$ of a thermal state we also find ourselves working with classical fields that are nowhere differentiable. I shouldn't say that there's no other way to deal with the situation, it can be managed, but random fields do deal with it pretty well, without introducing anything relatively exotic such as nonstandard analysis, for example.

I've taken it to be useful to consider random fields because they can be presented as random-variable-valued distributions, or even as mutually commutative operator-valued distributions, which are close enough to quantum fields to make comparison of random fields and quantum fields very interesting. In comparison of classical differentiable fields with quantum fields it's hard to know how to start. Part of why this is good to do is that it does give a new way to think about quantum fields, even if the more ambitious hopes I have for my program don't work out.

 

[strangerep]

For a quantum field, some mathematical control (but not enough) is achieved by defining the quantum field to be an operator-valued distribution, not an operator-valued field, so that to construct an operator one has to "average" the quantum field over a finite region. As we consider smaller regions, the variance of such operators diverges, so if we try to talk about the quantum field at a point we find that, more-or-less, we would always observe either +infinity or -infinity, which isn't a good start for constructing a differentiable function. For the vacuum state of a free quantum field, the two point correlation function $$\left\langle 0\right|\widehat{\phi}(x)\widehat{\phi}(y)\left|0\right\rangle$$ is finite for $$x-y$$ non-zero, but diverges as $$x\rightarrow y$$, which is to say that the variance $$\left\langle 0\right|\widehat{\phi}(x)^2\left|0\right\rangle$$ is infinite.

Yep... standard stuff so far. $$\widehat{\phi}(x)$$ are not operators, therefore applying
them to a state vector is technically illegal. They must be smeared with test functions to
give bonafide operators. OK.

I've taken it to be useful to consider random fields because they can be presented as random-variable-valued distributions, or even as mutually commutative operator-valued distributions, which are close enough to quantum fields to make comparison of random fields and quantum fields very interesting.

You didn't really answer the question I asked about how random fields
introduce the concept of probability in a "mathematically correct way".
My perception of your random fields (or should we say "Lie fields"?)
is as an inf-dim Lie algebra parameterized by spacetime points,
as we discussed a while back. But obviously I'm missing some crucial
connection between this and probability. I need you to be more explicit/expansive
on this point if I'm to understand...

 

[Peter Morgan]

You didn't really answer the question I asked about how random fields introduce the concept of probability in a "mathematically correct way".
My perception of your random fields (or should we say "Lie fields"?) is as an inf-dim Lie algebra parameterized by spacetime points, as we discussed a while back. But obviously I'm missing some crucial connection between this and probability. I need you to be more explicit/expansive on this point if I'm to understand...

Perhaps a more abstract approach? A set of operators $$\{\widehat{\phi}_{f_i}\}$$ generates a *-algebra (to which we add an operator 1, which acts as a multiplicative identity in the *-algebra). A state $$\omega(\widehat{A})$$ over the *-algebra is positive on any operator of the form $$AA^\dagger$$, $$\omega(AA^\dagger)\ge 0$$, and $$\omega(1)=1$$, which allows us to use the GNS-construction of a Hilbert space. We take $$\omega(\widehat{A})$$ to be the expected value associated with the random variable A, corresponding to the operator $$\widehat{A}$$. The sample space associated with A is the set of eigenvalues of $$\widehat{A}$$, and the probability density in the state $$\omega$$ can be written as $$P(x)=\omega(\delta(\widehat{A}-x.1))$$. From this we can generate the characteristic function associated with that probability density as a Fourier transform $$\widetilde{P}(\lambda)=\omega(exp(i\lambda\widehat{A}))$$.

All that is standard QM, albeit not in elementary terms. When we introduce joint observables $$\widehat{A}$$ and $$\widehat{B}$$, the difference between QM and random fields is only whether they always commute, which they do not for QM, but they do for a random field. In the random field case, the function $$\widetilde{P}(\lambda,\mu)=\omega(exp(i\lambda\widehat{A}+i\mu\widehat{B}))$$ is a joint characteristic function, whereas it is not (in general) the Fourier transform of a positive function in the QM case (unless $$[\widehat{A},\widehat{B}]=0$$, which will be the case if the two operators are constructed using only quantum field operators associated with mutually space-like regions).

I hope this is at an appropriate level and helpful? I'm not sure it's an answer even if the level is OK, in which case sorry.

I realize now that I should also note that IMO a random field and a quantum field are better considered as indexed by smooth functions on space-time, not indexed by space-time points. I find it helpful to think of the index functions as "window functions", which is the name this concept is given in signal processing. Learning to work intuitively with the concept of operator-valued distributions took me several years, but it seems obvious enough by now that I have trouble explaining. Sorry.

 

[strangerep]

[...] the probability density in the state $\omega$ can be written as $$P(x)=\omega(\delta(\widehat{A}-x.1))$$ .

I thought I was conversant with the algebraic approach,
but what is your $\delta$ in the above expression?

 

[meopemuk]

Hi strangerep,

Thank you very much for the interesting review of IR divergences and references. I am very interested in combining these ideas with the dressed particles approach of Greenberg and Schweber. Do you have any suggestions?

Eugene.

 

[strangerep]

I am very interested in combining these ideas with the dressed particles
approach of Greenberg and Schweber. Do you have any suggestions?

I'm wrestling with related questions, but it's too soon for me to say anything.
(And it would probably be too speculative for Physics Forums anyway. :-)

Perhaps after you've had a look through the referenced papers we could
discuss further in a separate thread, or privately.

 

[Peter Morgan]

I thought I was conversant with the algebraic approach,
but what is your $\delta$ in the above expression?

Hee! It's a Dirac delta, perhaps too quick and dirty as a way to construct a probability density. It's also, formally, the inverse Fourier transform of the characteristic function that follows,
$$\omega(exp(i\lambda\widehat{\phi}_f))= \omega(\sum_{k=0}^{\infty}\left[\frac{(i\lambda\widehat{\phi}_f)^k}{k!}\right])$$.
Except, urp, that there should be a factor of $2\pi$. That seems a better way to introduce it. The expected values of $\widehat{\phi}_f^k$ are the moments of the vacuum state's probability density over $\widehat{\phi}_f$, giving us the characteristic function, which we can formally inverse Fourier transform to obtain the probability density. In practice, one constructs the characteristic function as a scalar function of $\lambda$, which for the free field vacuum would be a Gaussian, which inverse Fourier transforms into a Gaussian probability density.

It does seem that what you have to say about IR divergences and dressed particles is pretty vague at the moment. A "discuss these papers" thread would seem reasonable to me, however, and it's generally a helpful discipline to pay attention to how speculative what we're doing is and to look for ways to rein it in. Indeed, I think that the path to my getting papers into journals is very much about that process, partly because anything that looks speculative is often picked on by referees as a reason to reject a paper that they only have general misgivings about. If you make no speculations, the referee's rejection letter is generally much more helpful, because they have to engage more with the paper to give a clear reason to reject it. At a grosser level, which I have often visited, editors can spot speculative from about a light-year away, so one then doesn't get as far as relatively more detailed feedback from a referee. Getting papers published is just making the speculation look well reasoned --- not getting rid of it, which IMO often makes for a boring paper.

 

[Peter Morgan]

Hee! It's a Dirac delta, perhaps too quick and dirty as a way to construct a probability density. It's also, formally, the inverse Fourier transform of the characteristic function that follows,
$$\omega(exp(i\lambda\widehat{\phi}_f))= \omega(\sum_{k=0}^{\infty}\left[\frac{(i\lambda\widehat{\phi}_f)^k}{k!}\right])$$.
Except, urp, that there should be a factor of $2\pi$.

A citation is possible, page 119 of Itzykson & Zuber, Section 3-1-2, eq. (3-63) does exactly this (in a 1980, McGraw-Hill paperback edition; I don't know whether there are substantially different editions, which is why I'm over-specifying).

 

[strangerep]

page 119 of Itzykson & Zuber, Section 3-1-2, eq. (3-63) does exactly this [...]

OK, so let's see if I now understand what your random fields are...

Your random fields (and their noncommutative quantum generalization) are basically
a generalization of certain concepts in classical statistical mechanics. Actually, let me
quote some stuff from the draft book of Neumaier & Westra, arXiv:0810.1019v1,
that (I think) relates to this way of looking at things...

(This is from their sect 1.2...)

An important ingredient in statistical mechanics is a phase space density ρ playing the
role of a measure to calculate probabilities; the expectation value of a function f is given
by
$$\langle f \rangle ~=~ \int \rho f ~~~~~~~~~~~~~~ (1.1)$$
where the integral indicates integration with respect to the so-called Liouville measure in
phase space.

In the quantum version of statistical mechanics the density ρ gets replaced by a linear
operator ρ on Hilbert space called the density matrix, the functions become linear opera-
tors, and we have again (1.1), except that the integral is now interpreted as the quantum
integral,
$$\int f ~=~ tr f, ~~~~~~~~~~~~~~ (1.2)$$
where tr f denotes the trace of a trace class operator. We shall see that the algebraic
properties of the classical integral and the quantum integral are so similar that using the
same name and symbol is justified.

But (iiuc) a difference between this approach and yours is that, whereas classical
quantities f are normally interpreted as functions over phase space (hence the
Liouville measure above), your random fields are just over 4D spacetime (or rather
over a space of test functions over 4D spacetime). (?)

So I'm now trying to follow your criticism of Navascues and Wunderlich more carefully...
But... in the online version (arXiv:0907.0372), which is all I have access to right now,
I can't relate your quotes to their section numbering. I also can't find the mention
of "continuous fields"? Is the Proc Roy Soc version different from the online version,
and you were commenting on the former?

 

[Peter Morgan]

But (iiuc) a difference between this approach and yours is that, whereas classical quantities f are normally interpreted as functions over phase space (hence the Liouville measure above), your random fields are just over 4D spacetime (or rather over a space of test functions over 4D spacetime). (?)

Yes, my definition and constructions are manifestly Lorentz and translation invariant. The usual definition is Lorentz and translation invariant, but not manifestly so. The usual phase space approach, is only possible if only mass shell components of a test function contribute. The restriction to only a single mass shell (if that's what is wanted) is implemented in my approach by the inner product having a delta function restriction to the mass shell.

So I'm now trying to follow your criticism of Navascues and Wunderlich more carefully... But... in the online version (arXiv:0907.0372), which is all I have access to right now, I can't relate your quotes to their section numbering. I also can't find the mention of "continuous fields"? Is the Proc Roy Soc version different from the online version, and you were commenting on the former?

The Proc. Roy. Soc. A version is different, which I didn't discover until after I submitted my comment. The Proc. Roy. Soc. A version is available for free, I think because of the Royal Society's anniversary celebrations. Go to http://dx.doi.org/" . [You won't find any citation to the arXiv version in my paper, the arXiv administration added it to the arXiv abstract, in their wisdom.]

 

[strangerep]

[...] the Proc. Roy. Soc. A page,
http://rspa.royalsocietypublishing.org/content/466/2115/881" .

OK, so now I'm confused about what your objection really is.
At the end of your comment paper, you say:

Navascués and Wunderlich have done something rather remarkable. By introducing the
idea of continuous fields in their paper they have laid themselves open to a criticism that they
must introduce random fields, and encourage a discussion that would otherwise have been
mpossible. If they had introduced fields without daring to go “beyond” the standard model, they
would equally have been conventionally impervious. Navascués’ and Wunderlich’s paper
requires a vigorous condemnation where something less ambitious would have gone
unchallenged. Finally, this comment does not touch Navascués’ and Wunderlich’s argument;
their paper’s flaw, I think, and such little as it is, is to have introduced a classical field
metaphysics and not to have thought enough of it. [...]

In this one paragraph, you say "requires a vigorous condemnation" but then say
"this comment does not touch Navascués’ and Wunderlich’s argument". So... you're not
actually arguing against the essential results of NW's paper? But only the "little" flaw
of using the phrase "continuous fields" rather than "random fields" ?

 

[Peter Morgan]

In [the last] paragraph, you say "requires a vigorous condemnation" but then say "this comment does not touch Navascués’ and Wunderlich’s argument". So... you're not actually arguing against the essential results of NW's paper? But only the "little" flaw of using the phrase "continuous fields" rather than "random fields"?

Mixed messages indeed. I was cross at Navascués’ and Wunderlich’s assumptions, not at their argument. When I saw your quote, "requires a vigorous condemnation", I thought you might have quoted me out of context, because I thought I surely must have mentioned that it was their assumptions that require a vigorous condemnation, but I see that I was vigorous at their whole paper.

Getting the politeness right in a critical comment apparently evaded me, but I do think these are serious Physicists, running with a respectable idea, that we might look at what the Correspondence Principle might tell us about the Planck scale and beyond. I think it's a good idea to do that in principle, but I'm telling them that "Oh, I wouldn't start from there". That could be boring.

What saves their paper, I think, and what made it possible for me to make my comment constructive, I hope, is that they introduce classical continuous fields. They do it half-heartedly, and they might even have been made to introduce fields because the referee said, "well, but what about fields?", but they do it. This is a potentially significant development, because the ways in which classical fields might be used to model Physics is underdeveloped. Good math approaches to QFT take it almost for granted that QFT is about
fields, not about particles, particularly because of the Unruh effect, since about 20 years ago, say.

Very few Physicists, however, take the obvious next step, which is that in that case we'd better find ways to talk about fields instead of about particles. A notable exception is Art Hobson, whose web-site has available a copy of the paper of his that I cite. He's concerned with how to teach QFT, and proposes to do it by emphasizing a field perspective. Andrei Khrennikov, who is a Mathematical Physicist who turned seriously to foundations of Physics about ten years ago, takes a similar line, but his mathematical methods and mine are very different. 't Hooft's approach is also similar but different, as also for Wolfram. Elze and Wetterich are two other hard Mathematical Physicists who are developing entirely different formalisms. Khrennikov, Elze, and Wetterich are developing fairly traditional stochastic differential equation methods, 't Hooft and Wolfram are developing finite automata models, in which the statistics are generated by simulation; I'm the only one, to my knowledge, who is seriously developing an algebraic presentation of random fields. A friend, Ken Wharton, is developing a view based on classical fields, with me trying to persuade him that he has to introduce probability in a mathematically decent way, and him dragging his heels, perfectly reasonably, because he doesn't like a metaphysics that includes probability. If I have a metaphysics, it is a metaphysics of statistics and ensembles rather than of probability, with my being content with a relatively loose, somewhat post-positivist relationship between observed statistics and the mathematics of probability, but we've been negotiating this fine point for a while. All this move to fields, and lattices, has more-or-less started to happen in the last ten years (although there's also Stochastic Electrodynamics, dating from the 60s, and Nelson's approach, too, from the 70s, but these are arguably problematic because they are preoccupied with fermions being particles, bosons being fields, and these programs, although I believe always continuing, have had significant hiatuses).

As far as all these different approaches are concerned, I consider that mine has the most to gain from comparison with QFT, in a Correspondence Principle sort of way, because I can even show that a free complex quantum field is empirically equivalent to a free random field, so I'm especially happy to see NW talking about CP. Nonetheless, I would only claim that my approach gives a useful counterpoint to stochastic or lattice methods, not that my approach is correct. I wish not to claim that the world is continuous rather than discrete, for example. A random field, properly speaking, is only an indexed set of random variables, it is only associated with a continuous space-time if we specifically take the index set to be the Schwarz space of functions on space-time (or some other well enough controlled function space on space-time).

So why should NW be pulled up for this rather than someone else, given that almost no-one pays any attention to how their use of particle-talk conditions their thinking? Their fault, I suppose, is that they mention fields so glibly, without thinking about how rich the seam is, and proceed with a discussion that would make almost no sense if they tried to accommodate both particle and field ways of thinking. At the very least, their conclusions would have to be hedged with a statement such as "if we think only in terms of particles, ...".

NW's discussion of Bell inequalities is similarly conventional. If they did the job properly, they would know that the flow of ideas surrounding Bell inequalities has been shifting dramatically over the last 10 years, with roots that go back to about 1980. The relative significances of contextuality and of locality are gradually being teased out more and more clearly. Anybody trying to talk about Bell inequalities should at least acknowledge those currents, and again they should either accommodate the various possibilities or explicitly hedge their conclusions.

As the last sentence of the abstract says, "Whether we discuss physics in terms of particles or in terms of events and (random) fields leads to differences that a glance would be well to notice." Perhaps I might add, even more facetiously, "or at least what is not noticed ought to be mentioned", but that would go far enough that I imagine the editors would have sent it back to me unrefereed. As it is, my comment is with referees; I hope they see that my criticism is constructive.

 

[strangerep]

"classical fields" [...] "continuous fields" [...] "random fields" [...]

When I first read NW's sentence where they mention "continuous fields"
my first thought was "what _precisely_ do they mean by that phrase"?
(Such pedantic detail becomes important in discussions about
"introducing probability in a mathematically correct way"...)

So let me ask you the question...

You've explained in earlier posts what you mean by a random field
(i.e., an inf-dim commutative *-algebra, with basis elements indexed
from a space of well-behaved functions over spacetime, such that
state functionals over this algebra make sense).
What then are your definitions of the phrases "classical field"
and "continuous field" ?

 

[Peter Morgan]

When I first read NW's sentence where they mention "continuous fields" my first thought was "what _precisely_ do they mean by that phrase"?
(Such pedantic detail becomes important in discussions about "introducing probability in a mathematically correct way"...)

So let me ask you the question...

You've explained in earlier posts what you mean by a random field (i.e., an inf-dim commutative *-algebra, with basis elements indexed from a space of well-behaved functions over spacetime, such that state functionals over this algebra make sense). What then are your definitions of the phrases "classical field" and "continuous field" ?

Including their context, NW say, "Now, in order to establish a connection with classical physics, Alice and Bob should not regard these intensities as fluxes of discrete particles, but rather as continuous fields". I think from this they mean continuous fields simpliciter, although I suppose that if they were given a second try and were more careful, they might say differentiable or possibly second differentiable fields. The question that I think is impossible for anyone except them to answer is "what would they say if they were being careful?". If they took the kind of criticism I have raised seriously, would they retreat to a space of functions defined in terms of measurability, or would they keep to a space defined in terms of continuity or differentiability?

If NW take the kind of criticism I have raised seriously, then they could fairly easily retreat to a point that would be recognizably quite similar to mine, in that they would introduce some kind of mathematics that would allow probability to be introduced decently. I don't much care whether they retreat to a stochastic processes approach to introducing probability or to an algebraic approach, but I would hope that they might recognize that a classical continuous field is not as good a starting point for constructing a meaningful Correspondence Principle as a classical probabilistic mathematical structure of some kind would be. I don't know, of course, how embarrassed they will feel at being called out in this way, and how annoyed they will be at whatever embarrassment they may feel, which could easily affect how they respond.

I sent a copy of my Comment to Navascués, who is the corresponding author, last Wednesday. I haven't heard back from them, but I consider them to be within their rights not to respond at any point. I'm curious whether, supposing my comment is accepted by Proc. Roy. Soc. A, they might not exercise their right to reply in Proc. Roy. Soc. A. Even if Proc. Roy. Soc. A were to publish my Comment, I think there is a good chance that it will die from lack of attention. I think there is a move of the zeitgeist towards fields, enough that the editors sent my Comment to referees, but, even if I'm right that the zeitgeist is moving, 2010 may still be too early on the wave for there to be a serious debate. I think, in any case, that the state of development of the mathematics, understanding, and presentation of random fields is currently too fragmentary to persuade anyone who doesn't want to be persuaded that there is a curious and novel alternative to existing interpretations of QFT/QM here in prospect.

Thanks for pushing me on this, Strangerep. I hope I'm getting better at arguing the case, thinking of new, more interesting ways of discussing the issues. I hope I'm not just getting better at rambling on and on. Time will tell, if no-one else does.

 

[strangerep]

I don't know, of course, how embarrassed [NW] will feel at being called out in this way, and
how annoyed they will be at whatever embarrassment they may feel, which could easily
affect how they respond.

Or they might just wonder "what on Earth is this guy on about?".

I think there is a move of the zeitgeist towards fields [...]

I now find the whole particle-vs-field debate quite bizarre, since the message I take
from both (modern) classical mechanics and (modern) quantum theory is
that the important thing is (tensor products of) irreducible representations
of certain groups. Field theoretic stuff is then just the inf-dim version of this.

BTW, if you can find the time, you might be interested in some of the other
non-obvious threads woven through that book of Neumaier & Westra which I
mentioned earlier. One such thread concerns the not-well-known similarities
between classical and quantum physics, as an improved way of unifying the two.
(But one must read quite a lot, and not get turned off by math, to follow it.)

I hope I'm not just getting better at rambling on and on.

Well, er, yes, you do have a tendency for that, if I may say.

Case in point: you didn't answer the other part of my question about
how you define "classical field" and "continuous field"... (?)

 

[Peter Morgan]

I don't know, of course, how embarrassed they will feel at being called out in this way, and how annoyed they will be at whatever embarrassment they may feel, which could easily affect how they respond.

Or they might just wonder "what on Earth is this guy on about?".

If they don't get it at all, if they don't feel embarrassed because they think my criticisms are nonsense, I have more work to do, as always.

I now find the whole particle-vs-field debate quite bizarre, since the message I take from both (modern) classical mechanics and (modern) quantum theory is that the important thing is (tensor products of) irreducible representations of certain groups. Field theoretic stuff is then just the inf-dim version of this.

OK, but then to get from a symmetry group to probabilities of given measurement results, I suppose one needs a positive linear form of some kind, which gets us to a particular von Neumann algebra, right? Do we give an abstract presentation of the symmetry group in terms of commutation relations between unbounded operators in a *-algebra, or do we give an abstract presentation of a C*-algebra of bounded operators? If we do the latter, then we have work to do to make contact with the empirically successful presentation of QFT as states over an unbounded algebra, which lead fairly directly to S-matrices and to cross-sections, etc. One little remarked aspect of QFT is the importance of the vacuum projection operator, which is used everywhere to construct projection operators, corresponding to probabilities of events in detectors. The use of the vacuum projection operator as part of the algebra of observables makes it seriously nonlocal, but this is a vital part of the empirical success of QFT.

I think we have to ask whether there are some vector spaces that support representations of a given symmetry group (so, modules) that seem more natural than other modules, given that we have to make contact with classically presented information about experimental results. I think it's a reasonable question whether particular internal symmetry groups emerge as a mathematically natural consequence of some other mathematics. A place to look, in the first instance, is in the geometry of Minkowski space, its tangent manifold, etc., perhaps torsion with a trivial metric connection. In the second instance, if Minkowski space is not enough, one might look at the geometry of higher dimensional spaces, ... , but then the naturalness of the construction becomes gradually more remote. One wants the simplest structure that is explanatory and that is consistent with experiment. I won't bore you with more speculations.

I'm not certain that gauge groups are necessarily a feature of future theories. I particularly worry that fermion fields are not a happy mathematical definition because they are supposed to be operator-valued distributions, but only sesquilinear forms of the fermion field at a point are gauge invariant observables. Since gauge invariance is specifically tied to this improper structure, I would prefer to introduce interactions in a mathematically better defined way. I would prefer to work with the observables associated with fermion fields instead of working with the fermion fields. Which I have (lots of) work to make happen.

BTW, if you can find the time, you might be interested in some of the other non-obvious threads woven through that book of Neumaier & Westra which I mentioned earlier. One such thread concerns the not-well-known similarities between classical and quantum physics, as an improved way of unifying the two. (But one must read quite a lot, and not get turned off by math, to follow it.)

I didn't focus on the Neumaier & Westra, but I have now downloaded it. I didn't notice this when it came out on arXiv, which surprises me. It's long enough to keep me out of trouble.

Well, er, yes, you do have a tendency for that, if I may say.

If I give you a rope to hang me with, ... . I use PF for conversation about developing ideas, so it's inevitably more prolix than an attempt at a published paper.

Case in point: you didn't answer the other part of my question about how you define "classical field" and "continuous field"... (?)

Briefly, solutions of a differential equation, so a first or second differentiable function of position in Minkowski space. So of course no general covariance.

I'm feeling worn out by a week or so of intensively being here on PF. Time, soon, to go back to the longer wave of calculations instead of so much speculation. Thanks for the various reality checks, Strangerep. Good luck with your own work.

 

[Halcyon-on]

dear Peter Morgan, you missed another approach inspired to the Elze's idea of stroboscopic quantization, to the 't Hooft's idea of particles moving fast in a circle and which inspired your friend Wharton's work on the Hamiltonian's principle. Maybe it requires a little bit of conceptual effort. Or maybe it doesn't involve assumptions compatible with the Star-Trak fiction. Or maybe it doesn't need to involve the Planck scale, nor hidden variables, nor many universes. Or maybe it reproduces exactly the canonical and the Feynman formulation of quantum mechanics without involving any conjecture but only through rigorous mathematical demonstrations. Maybe the solution to the problematics of quantum mechanics are given by a simple and unexplored assumption that put all the pieces in the right place. To have a more complete vision of the possibilities beyond quantum mechanics you should try to really understand the following two papers: http://arxiv.org/abs/1001.2718 and http://arxiv.org/abs/0903.3680 .

 

[Peter Morgan]

dear Peter Morgan, you missed another approach inspired to the Elze's idea of stroboscopic quantization, to the 't Hooft's idea of particles moving fast in a circle and which inspired your friend Wharton's work on the Hamiltonian's principle. Maybe it requires a little bit of conceptual effort. Or maybe it doesn't involve assumptions compatible with the Star-Trak fiction. Or maybe it doesn't need to involve the Planck scale, nor hidden variables, nor many universes. Or maybe it reproduces exactly the canonical and the Feynman formulation of quantum mechanics without involving any conjecture but only through rigorous mathematical demonstrations. Maybe the solution to the problematics of quantum mechanics are given by a simple and unexplored assumption that put all the pieces in the right place. To have a more complete vision of the possibilities beyond quantum mechanics you should try to really understand the following two papers: http://arxiv.org/abs/1001.2718 and http://arxiv.org/abs/0903.3680 .

Hi, Halcyon-on,
I'm sorry to say that I can't see how I might use your mathematical methods, because we're using considerably different mathematics. For the kind of algebraic approach I have taken to the relationship between random fields and quantum fields, you might see my http://dx.doi.org/10.1209/0295-5075/87/31002" . I will understand if you, in return, can't use my algebraic methods, since in my experience it is all too often the case that people who work in Foundations of Physics are too wrapped up in their own approaches to be able to see ways to use other people's approaches. My attempt at understanding QFT has focused on finding classical mathematics that is as close as possible to the mathematics of QFT, which, if slavishly followed, demands algebraic methods of generating probability densities that are closely parallel to the algebraic methods of QFT. I worry that my algebraic approach obscures significant conceptual issues, from myself as much from other people, which I think your approach also suffers from, albeit for different reasons, as it seems to me.

 

[strangerep]

I'm feeling worn out by a week or so of intensively being here on PF. [...]

Sounds like you don't want to continue this conversation too much further,
so I'll just mention a couple of things briefly that occurred to me while
reading your previous post.

I now find the whole particle-vs-field debate quite bizarre, since the
message I take from both (modern) classical mechanics and (modern) quantum
theory is that the important thing is (tensor products of) irreducible
representations of certain groups. Field theoretic stuff is then just the
inf-dim version of this.

OK, but then to get from a symmetry group to probabilities of given
measurement results, I suppose one needs a positive linear form of some kind,
which gets us to a particular von Neumann algebra, right? Do we give an
abstract presentation of the symmetry group in terms of commutation relations
between unbounded operators in a *-algebra, or do we give an abstract
presentation of a C*-algebra of bounded operators? If we do the latter, then
we have work to do to make contact with the empirically successful
presentation of QFT as states over an unbounded algebra, which lead fairly
directly to S-matrices and to cross-sections, etc.

One can perhaps do a bit better than the above by using generalized
coherent states since they're much closer to the group and its Lie
algebra. Are you familiar with triangular decomposition of Lie algebras
(which underpins the general construction of coherent spaces)?

One little remarked aspect
of QFT is the importance of the vacuum projection operator, which is used
everywhere to construct projection operators, corresponding to probabilities
of events in detectors. The use of the vacuum projection operator as part of
the algebra of observables makes it seriously nonlocal, but this is a vital
part of the empirical success of QFT.

It's interesting that in Dirac's treatment of QFT (as expounded in the
"Lectures on QFT" reference I mentioned earlier), the concept of vacuum
is altered. (He works in the Heisenberg picture, having shown how it's
_not_ equivalent to the Schrodinger picture, and that the Schrodinger
picture is a "bad" picture for QFT, as he puts it.)

[...] I'm not certain that gauge groups are necessarily a feature of
future theories. I particularly worry that fermion fields are not a
happy mathematical definition because they are supposed to be
operator-valued distributions, but only sesquilinear forms of the
fermion field at a point are gauge invariant observables. Since gauge
invariance is specifically tied to this improper structure, I would
prefer to introduce interactions in a mathematically better defined
way. I would prefer to work with the observables associated with
fermion fields instead of working with the fermion fields. [...]

This whole problem is why I'm interested in Dirac's (and others')
attempts to formulate a gauge-invariant electrodynamics using
redefinitions of the basic fields which are explicitly gauge-invariant.
(I also mentioned this with references in my earlier post about IR stuff.)
It seems to me that gauge freedom is nothing more than unphysical
splitting of the total Hamiltonian. E.g., if we write
$$H ~=~ H_0 + H_I$$
then we can also write
$$H ~=~ (H_0 + foo) ~+~ (H_I - foo)$$
where foo is a gauge term and obviously quite artificial.

 

[Halcyon-on]

Hi, Halcyon-on,
I'm sorry to say that I can't see how I might use your mathematical methods, because we're using considerably different mathematics. For the kind of algebraic approach I have taken to the relationship between random fields and quantum fields, you might see my http://dx.doi.org/10.1209/0295-5075/87/31002" . I will understand if you, in return, can't use my algebraic methods, since in my experience it is all too often the case that people who work in Foundations of Physics are too wrapped up in their own approaches to be able to see ways to use other people's approaches. My attempt at understanding QFT has focused on finding classical mathematics that is as close as possible to the mathematics of QFT, which, if slavishly followed, demands algebraic methods of generating probability densities that are closely parallel to the algebraic methods of QFT. I worry that my algebraic approach obscures significant conceptual issues, from myself as much from other people, which I think your approach also suffers from, albeit for different reasons, as it seems to me.

Dear Peter,

the greatest problem in modern physics is exactly that everyone speaks so much without nothing original to say. In this way there is the risk that new ideas are not taken under serious consideration. That's would be a shame! Concerning those papers it seems to me that the only mathematic used is the discrete Fourier transform, the normal mode expansion, the relativistic field equation, the de Broglie relation, the Path integral formulation and some integration by parts. Are these too much involute mathematic methods? Physics can't be done only by reading the abstract of the papers, new ideas must deserve special attention.

 

[Peter Morgan]

Sounds like you don't want to continue this conversation too much further, so I'll just mention a couple of things briefly that occurred to me while reading your previous post.

Why would I want to go away when you say such interesting things?

One can perhaps do a bit better than the above by using generalized coherent states since they're much closer to the group and its Lie algebra. Are you familiar with triangular decomposition of Lie algebras (which underpins the general construction of coherent spaces)?

No. I'm too much of a hedgehog. When you work for more than ten years on trying to understanding quantum fields through their relationships to random fields, its difficult to go deep and stay wide. Gotta get out more! Do you have a reference, or perhaps this will be in the Neumaier & Westra, which I haven't looked at yet? Thanks in advance.

It's interesting that in Dirac's treatment of QFT (as expounded in the "Lectures on QFT" reference I mentioned earlier), the concept of vacuum is altered. (He works in the Heisenberg picture, having shown how it's _not_ equivalent to the Schrodinger picture, and that the Schrodinger picture is a "bad" picture for QFT, as he puts it.)

I've requested this from the Yale library. From my point of view, the Heisenberg picture is much more appropriate, given that the state is timeless (formally, as a mathematical model, without metaphysical commitment, at least from me). I definitely want to see Dirac's argument. Thanks again!

This whole problem is why I'm interested in Dirac's (and others') attempts to formulate a gauge-invariant electrodynamics using redefinitions of the basic fields which are explicitly gauge-invariant. (I also mentioned this with references in my earlier post about IR stuff.) It seems to me that gauge freedom is nothing more than unphysical splitting of the total Hamiltonian. E.g., if we write
$$H ~=~ H_0 + H_I$$
then we can also write
$$H ~=~ (H_0 + foo) ~+~ (H_I - foo)$$
where foo is a gauge term and obviously quite artificial.

I think I'm going to pursue my own approach to this for now, in terms of a Lie random field without any Fermionic structure, because Fermion fields are not directly observable. Even though I suspect it's unlikely to work I hope to learn something from the process. I look forward to seeing whatever you can get out of your approach, however. I'm not clear whether you mean to introduce a particular kind of structure for $foo$, or whether you mean that you want to sidestep this type of approach to deforming the Hamiltonian?

From my block world point of view, the complete structure of an interacting field is specified by the inner product on the function space, by the Lie field structure functional, and by the vacuum state. The Hamiltonian is then a derived structure, by the introduction of active transformations, instead of being fundamental, so the issue you mention doesn't come up in the same way.

A major reason I haven't buckled in and worked out how a Lie random field works out with a Fermion field added in is my unhappiness with the Fermionic structure as a whole, particularly relative to the empirical content of the theory. The other major reason is fear of the number of minus signs there would be.

 

[Peter Morgan]

Dear Peter,
The greatest problem in modern physics is exactly that everyone speaks so much without nothing original to say. In this way there is the risk that new ideas are not taken under serious consideration. That's would be a shame! Concerning those papers it seems to me that the only mathematic used is the discrete Fourier transform, the normal mode expansion, the relativistic field equation, the de Broglie relation, the Path integral formulation and some integration by parts. Are these too much involute mathematic methods? Physics can't be done only by reading the abstract of the papers, new ideas must deserve special attention.

Sorry, Halcyon-on. I read the whole of your most recent paper. Not both, it's true. I regret that I couldn't find anything about your paper that I feel I might be able to use. The next person you show this to may like it a lot, in which case you'd be best to show it someone else.

When people say no to me, which they usually do by not answering at all, my response is to ask what I haven't done. Why has this person or this whole group not understood how brilliant my ideas are? Why is everyone so stupid? Why haven't they even read my paper? What's wrong with the abstract that they didn't read the paper? What's wrong with the title that they haven't read the abstract? It used to take me weeks or months to get over myself, but nowadays it usually takes me only a couple of days to get used to the idea that yes, I do have to spend another year or two learning other things, changing the whole basis of my thought again, as much as I'm able, usually introducing more sophisticated mathematics that I thought I would never understand (boy, am I dreading the moment when I finally accept that I have got to learn how to use category theory! I think that's likely to be five year's work, at my rate of math acquisition.) This works for me, but it may be irrelevant or unhelpful for you, in which case my apologies for this riff on (my) method. Best wishes, in any case. It's a wilder ride than anything else I've found in life, but there sure are downs as well as ups.

 

[Peter Morgan]

I've had a very open-handed e-mail from Navascués. I hope I can be as generous. I have to think very hard about an answer. Of course it remains the case that my Comment is very unlikely to be published in Proc.Roy.Soc.A. Indeed, because of Navascués' e-mail I can see several more reasons why the editors might reject the paper.

There is, however, a curiosity that can be seen by going to my academia.edu "keywords" page, http://yale.academia.edu/PeterWMorgan/Keywords" (I've checked, and I believe that anyone can see this web-page, but the effects of cookies and other tracking might possibly be significant). This feature sends me an e-mail when someone uses a search engine and then clicks through to one of my academia.edu pages. Academia.edu maintains a list of what search terms were used and the approximate location of the person or the proxy server who did the search. In the last 14 months, 123 searches have found my academia.edu pages. It's kind of nice to know that someone in Australia thought to look me up on January 28th. I wonder what they thought.

The question is, how deliberate was the choice of search terms that was used yesterday morning? And how deliberate was the choice to click through to academia.edu? Go see.

I can delete the search term if I want. But yes, my abilities are limited. I don't think I've done anything apart from submitting this Comment to Proc.Roy.Soc.A in the last week or two that could have led to this, but if someone is willing to 'fess up here or privately, I would be glad to make their acquaintance. Thanks.

If anyone would like to give me a little anonymous support, for which I would be grateful, or second the motion just referred to, which I hope I will accept gracefully, think of your own search term and click through to my academia.edu page. If there are already lots of new entries on the Keywords page, please be gentle with my e-mail inbox.

 

[Halcyon-on]

Hi, Halcyon-on,
I'm sorry to say that I can't see how I might use your mathematical methods, because we're using considerably different mathematics. For the kind of algebraic approach I have taken to the relationship between random fields and quantum fields, you might see my http://dx.doi.org/10.1209/0295-5075/87/31002" . I will understand if you, in return, can't use my algebraic methods, since in my experience it is all too often the case that people who work in Foundations of Physics are too wrapped up in their own approaches to be able to see ways to use other people's approaches. My attempt at understanding QFT has focused on finding classical mathematics that is as close as possible to the mathematics of QFT, which, if slavishly followed, demands algebraic methods of generating probability densities that are closely parallel to the algebraic methods of QFT. I worry that my algebraic approach obscures significant conceptual issues, from myself as much from other people, which I think your approach also suffers from, albeit for different reasons, as it seems to me.

Sorry, Halcyon-on. I read the whole of your most recent paper. Not both, it's true. I regret that I couldn't find anything about your paper that I feel I might be able to use. The next person you show this to may like it a lot, in which case you'd be best to show it someone else.

When people say no to me, which they usually do by not answering at all, my response is to ask what I haven't done. Why has this person or this whole group not understood how brilliant my ideas are? Why is everyone so stupid? Why haven't they even read my paper? What's wrong with the abstract that they didn't read the paper? What's wrong with the title that they haven't read the abstract? It used to take me weeks or months to get over myself, but nowadays it usually takes me only a couple of days to get used to the idea that yes, I do have to spend another year or two learning other things, changing the whole basis of my thought again, as much as I'm able, usually introducing more sophisticated mathematics that I thought I would never understand (boy, am I dreading the moment when I finally accept that I have got to learn how to use category theory! I think that's likely to be five year's work, at my rate of math acquisition.) This works for me, but it may be irrelevant or unhelpful for you, in which case my apologies for this riff on (my) method. Best wishes, in any case. It's a wilder ride than anything else I've found in life, but there sure are downs as well as ups.

You have perfectly confirmed what I was saying, the most difficult thing to do is a conceptual effort. Even rigorous mathematical demonstrations are useless without a minimal attention. I am not the author, I only know this work as other of the people that you cited. By the way I hope you do not referee papers in this way, without thinking more that few hours. That would be a shame! That's way nobody brings new ideas and the quant-ph arXiv's list becoming so boring. To me it seems that you are saying that do marketing of the same old ideas and "Shut up and calculate" is the more convenient way to publish and not perish. In the first reply you said that you are not familiar with the mathematics used in those papers, in this last reply you are suggesting to the author to use more involute mathematics to hide inconsistencies of the models. My opinion is that if you use the correct assumption everything turns out without invoking too much powerful mathematical weapons. As the history of physics demonstrates, if you use the correct key everything should pop up without efforts or paradoxes.

 

[Peter Morgan]

You have perfectly confirmed what I was saying, the most difficult thing to do is a conceptual effort. Even rigorous mathematical demonstrations are useless without a minimal attention. I am not the author, I only know this work as other of the people that you cited.

It's all true, Halcyon-on. In the last seven years I have downloaded just short of 4000 files into my "papers" and other folders on my computer. I imagine that I have not chosen well which of these papers I should really try to understand, but what I have chosen has been my choice, for which I am sure I will suffer. Do you begrudge me my own damnation?

By the way I hope you do not referee papers in this way, without thinking more that few hours. That would be a shame! That's way nobody brings new ideas and the quant-ph arXiv's list becoming so boring.

Almost never am I asked to referee. I almost always do not accept, because I am generally not competent. When I have accepted, I have been so tentative in my conclusions that I have been useless to the journal editor.

To me it seems that you are saying that do marketing of the same old ideas and "Shut up and calculate" is the more convenient way to publish and not perish. In the first reply you said that you are not familiar with the mathematics used in those papers, in this last reply you are suggesting to the author to use more involute mathematics to hide inconsistencies of the models.

I don't like "shut up and calculate" much. Sometimes I feel it's a good idea for me to sit down and do some calculating, sometimes I feel it's better to talk, get myself in a little trouble by airing some faulty ideas, and discover a little which of my ideas seem good to others, sometimes I feel it's better to really try and mull over things, either with or without writing things down. I have a complicated relationship somewhere between caring what other people think, and doing the hard work that is needed to have papers published, and caring only what I think. But of course different people have different ideas about how to go forward.

I didn't think that I said that I am "not familiar with the mathematics used in those papers", I thought I said that I could not see a way to use it. I didn't think that I suggested that he "use more involute mathematics to hide inconsistencies of the models", I thought I suggested, as tentatively as I could find to say it, that he might consider the mathematics that I use, which I hope and suppose he could understand if he spent some time looking at it, but whether he spends his own time and effort I think is his own choice. I didn't think I suggested that his models might be inconsistent, because I did not engage enough with it to make such a stark judgment. How generously I read between the lines of whatever people are kind enough to say to me about my work makes a big difference, I think, to how much benefit I can derive from what they say.

My opinion is that if you use the correct assumption everything turns out without invoking too much powerful mathematical weapons. As the history of physics demonstrates, if you use the correct key everything should pop up without efforts or paradoxes.

Yes, a good key is rare but nice to find. For how much the effort might be, perhaps we should ask the people who did the finding.

I'm pleased that you like Donatello Dolce's work, and I hope you can find good ways to use it. I apologize that I assumed it was yours.

 

[Halcyon-on]

It's all true, Halcyon-on. In the last seven years I have downloaded just short of 4000 files into my "papers" and other folders on my computer. I imagine that I have not chosen well which of these papers I should really try to understand, but what I have chosen has been my choice, for which I am sure I will suffer. Do you begrudge me my own damnation?

Almost never am I asked to referee. I almost always do not accept, because I am generally not competent. When I have accepted, I have been so tentative in my conclusions that I have been useless to the journal editor.

I don't like "shut up and calculate" much. Sometimes I feel it's a good idea for me to sit down and do some calculating, sometimes I feel it's better to talk, get myself in a little trouble by airing some faulty ideas, and discover a little which of my ideas seem good to others, sometimes I feel it's better to really try and mull over things, either with or without writing things down. I have a complicated relationship somewhere between caring what other people think, and doing the hard work that is needed to have papers published, and caring only what I think. But of course different people have different ideas about how to go forward.

I didn't think that I said that I am "not familiar with the mathematics used in those papers", I thought I said that I could not see a way to use it. I didn't think that I suggested that he "use more involute mathematics to hide inconsistencies of the models", I thought I suggested, as tentatively as I could find to say it, that he might consider the mathematics that I use, which I hope and suppose he could understand if he spent some time looking at it, but whether he spends his own time and effort I think is his own choice. I didn't think I suggested that his models might be inconsistent, because I did not engage enough with it to make such a stark judgment. How generously I read between the lines of whatever people are kind enough to say to me about my work makes a big difference, I think, to how much benefit I can derive from what they say.
Yes, a good key is rare but nice to find. For how much the effort might be, perhaps we should ask the people who did the finding.

I'm pleased that you like Donatello Dolce's work, and I hope you can find good ways to use it. I apologize that I assumed it was yours.

Thank you for your kind replay. I know perfectly how dispersive can be try to find a good paper. My concern is that the mechanisms that establish the good or that bad works are not always fair. With the velocity of communication of the web, and the huge incrementation of the number of papers, the peer review process appear to be obsolete, slow and inefficient. Probably Physics Forum could represent a possible remedy to that problem. But the discussions should be less superficial... . I have already tons of interesting paper that I would like to study in more details but I hope to find time to understand your work as well.

 

[yoda jedi]

dear Peter Morgan, you missed another approach inspired to the Elze's idea of stroboscopic quantization, to the 't Hooft's idea of particles moving fast in a circle and which inspired your friend Wharton's work on the Hamiltonian's principle. Maybe it requires a little bit of conceptual effort. Or maybe it doesn't involve assumptions compatible with the Star-Trak fiction. Or maybe it doesn't need to involve the Planck scale, nor hidden variables, nor many universes. Or maybe it reproduces exactly the canonical and the Feynman formulation of quantum mechanics without involving any conjecture but only through rigorous mathematical demonstrations. Maybe the solution to the problematics of quantum mechanics are given by a simple and unexplored assumption that put all the pieces in the right place. To have a more complete vision of the possibilities beyond quantum mechanics you should try to really understand the following two papers: [B][PLAIN]http://arxiv.org/abs/1001.2718[/B][/url] and http://arxiv.org/abs/0903.3680 .

Wild Card Mr. halcion, Cogratulations !

that work was presented at
The 10th Symposium on the
Frontiers of Fundamental Physics.
School of Physics, The University of Western Australia
24th – 26th November 2009





------------------------
apart, there is a paper,that i can not find.
Field theory in compact space-time — Donatello Dolce —

The assumption of compact space-time dimensions for ordinary relativistic fields gives remarkable overlaps with the ordinary quantum theory. Formal, phenomenological and conceptual consequences of such assumption are briefly discussed.

 

[strangerep]

Why would I want to go away when you say such interesting things?

Really? That's the nicest thing anyone's said to me in quite a while. (Sad, huh?)

[...coherent states...] [...triangular decomposition...]

[...] Do you have a reference, or perhaps this will be in the Neumaier & Westra,
which I haven't looked at yet?

The basic stuff is in Neumaier & Westra, but is kinda spread out in various places.
The triangular decomposition concept is not difficult though. You could try this classic
review paper:

Zhang, Feng, Gilmore, "Coherent states: Theory and some applications",
Rev Mod Phys, vol 62, no 4, pp867-927, (1990)

It probably won't be at all obvious though why I mentioned this stuff
in the current context of algebras and probability. If so, feel free to bug
me again later.

I've requested [Dirac's "Lectures of QFT"] from the Yale library. From my point of view, the Heisenberg picture is much more appropriate, given that the state is timeless (formally, as a mathematical model, without metaphysical commitment, at least from me). I definitely want to see Dirac's argument.

If you have online journal access, you can get the basic idea from Dirac's
"QED without dead wood" paper. His "Lectures of QFT" are essentially an
elaboration of the ideas in that paper.

I'm not clear whether you mean to introduce a particular kind of structure for foo,
or whether you mean that you want to sidestep this type of approach to deforming the Hamiltonian?

I'm not clear about it either. :-)

From my block world point of view, the complete structure of an interacting field is specified by the inner product on the function space, by the Lie field structure functional, and by the vacuum state. The Hamiltonian is then a derived structure, by the introduction of active transformations, instead of being fundamental, so the issue you mention doesn't come up in the same way.

Sure, once one has the (non-perturbative) algebra of the interacting fields,
one has almost everything.

 

[Halcyon-on]

Wild Card Mr. halcion, Cogratulations !

that work was presented at
The 10th Symposium on the
Frontiers of Fundamental Physics.
School of Physics, The University of Western Australia
24th – 26th November 2009





------------------------
apart, there is a paper,that i can not find.
Field theory in compact space-time — Donatello Dolce —

The assumption of compact space-time dimensions for ordinary relativistic fields gives remarkable overlaps with the ordinary quantum theory. Formal, phenomenological and conceptual consequences of such assumption are briefly discussed.

I have no idea. The only papers I know are those above. The first one is an original and very long paper (not yet published on a journal, but I can imagine why). The second is a concise talk given in Sweden (QTRF5). I think he has impressing results and intriguing philosophical implications, which would be very interesting to discuss.