[Paleopsych] zero point energy, pilot waves, reality and von Neumann
Paul J. Werbos, Dr.
paul.werbos at verizon.net
Mon Jan 3 16:22:54 UTC 2005
Good morning, folks!
This morning I feel I am finally beginning to make REAL sense of some of the
real fundamental issues suggested by the subject line here.
Some of you may wonder why it too me so long. But physics has become such a
huge
and tangled subject that being too quick to draw conclusions won't work so well
any more. Sorting out the tangle, while maintaining high standards of
understanding
things, is not so easy. Clearly there are many basic themes which no one
earth fully understands as yet.
So let me start with zero point.
I was cheered greatly when Jack started to emphasize the distinction
between two KINDS
of "energy from vacuum":
(1) the more classical notion of zero point energy (ZPE) based
effectively on the "(1/2)hw" terms which emerge in some formulations of
quantum field theory (QFT)
as H0- ::H0::,
the raw free Hamiltonian versus the normal form of that Hamiltonian. (The
exact same
ZPE noise is assumed in texts on semiclassical models of quantum optics.)
(2) more sophisticated but less definite ideas, such as vacuum breakdown or
forces
linked to dark energy or negative energy.
Jack has not always treated other people in an optimal way -- but I think
he is basically
right that the first seems very unlikely, while the second has a very real
chance of
working out somehow, someday, if we can figure out what is going on more
precisely and more completely.
NEVERTHELESS -- even though I do not believe that the (1/2)hw noise is
really there,
the first major theme of my cond-mat 2004 paper is description of a chip
that should
be able to prove that it is there and exploit its energy **IF** it should
be there.
(I like the idea of trying to do full justice to alternative viewpoints
even when I do
not really believe them.) All the information I have received so far, in
feedback
from that paper, has been very encouraging. (However, I do have some concern
that the chip simulation and design work should at least include quantum
effects in chips
enough to reflect such basic parameters as coherence length of the radiation.
Not all E&M or chip simulators do that. I think we are on course to do it
right,
but in real-world engineering one must be careful not to make too many
assumptions.)
Such a chip would be important scientifically, and possibly even useful, if it
does work, even if (1/2)hw ZPE does not exist.
Why am I so very, very skeptical that the (1/2)hw stuff is there? I'm sure
that Hal Puthoff has heard many reasons -- but mine go a bit beyond what
he has heard.
Someone on Jack's lists said a long time ago that "of course the vacuum
noise is there; it explains stuff like Lamb shifts, and we can't escape that.
Read..." (By the way, Jack, feel free to repost this on the most relevant
lists.
With the caveat that it does not represent my employers or anyone else,
and that it should be understood as informal Saturday morning stuff.)
I was very puzzled by that statement -- but went back to other business.
This week I think I understand what the key misunderstanding there was.
I was very lucky to have learned QFT initially from Mandl's old
but concise textbook Introduction to Quantum Field Theory.
(I think there is a kind of updated paperback version available from
amazon, but I haven't
bought it.) He simply lays out in a step by step way what all the main
contributions to the Lamb shift were back in the old days, and shows the
Feynman
diagrams for each contribution. When you look at the actual calculation,
laid out
in a straightforward and concise way, it is crystal clear that every term
results from
using the normal form Hamiltonian, ::H::, and that the supposed (1/2)hw terms
have no relation at all to the results.
But -- this past month, since Mandl is back at work, I looked at some other
books to review
the Lamb shift stuff. And I was astounded to see that another very standard
text by Bjorken
and Drell really does invoke intuitive (1/2)hw arguments, and describes how
it is following
the original historic development of the understanding of Lamb shifts. A
more modern
canonical treatment in Weinberg's QFT text is so utterly formal that it
does not provide clear
intuition one way or the other. Probably the generation of physicists who
learned QFT
from Boglyubov or Zuber would know what I learned from Mandl's text, but it
seems that
a lot has been lost here and there.
Likewise -- the old papers by Coleman and Mandelstam on Sine-Gordon and
Massive Thirring Model
show a very clear and strong understanding of the role of the NORMAL FORM
Hamiltonian
in quantum field theory. Coleman seems to adopt the attitude that of course
everyone knows
that the normal form Hamiltonian is what we use, in all field theories, so
it is beneath
our dignity to emphasize the point... but in fact, a lot of the best people
in axiomatic field
theory do not really know, and it is not always spelled out in the
textbooks. It is as if
people were working in group theory and forgot to mention half the axioms,
and didn't
really care about the resulting confusion.
As for the OTHER concepts of energy from vacuum ... I think we need to
know/understand
more about how such things work, before we can harness them. And that's why
it's important for more of us to work on the basic understanding...
--------------
Pilot waves....
I have to admit I feel a bit of envy for those of you who have had a chance
to really work with people
like Vigier (really, De Broglie), Hoyle and Sudarshan. Gold is not Hoyle and
Vigier was not DeBroglie, but they do represent some very critical
understanding. I
did have the pleasure of good correspondence with DeBroglie many years
ago... and
I regret that it took so long for me to make sense of questions that he and
I both felt
the same about. People become annoyed when they need to keep asking the
same question for
more than a decade or two... but if it hasn't been answered yet, we still
have to face up to it.
(Of course, some would say we can always give up on reality and go pray in
a monastery,
but even the abbots might question that approach.)
Once we allow for backwards-time effects, all the Bells Theorem objections
to a local realistic
model of physics go away. (See my quant-ph papers for lots of explanation.)
But how
does one represent the electron then?
The electron as just a wave does not make sense. DeBroglie was clear about
that long ago,
and his book with Vigier remains reasonable on that point. Furthermore, the
kind
of statistical behavior we get from continuous wave fields matches BOSONIC
QFT, not fermionic. (Again, see quant-ph. See also
chapter 4 of Walls and Milburn, and chapter 3 of Howard Carmichael's book
on statistics of quantum optics. I really do HIGHLY recommend studying both
those chapters.
This empirically-grounded work has an element of reality and clarity far beyond
what I have seen in texts which are supposedly more general. Yet it is
far more solid and theoretically grounded than more seat-of-the-pants
optics work.)
And finally, the electron self-energy renormalization and "Rutherford
scattering" analysis
of the electron all looks a lot more like a point particle; it doesn't fit
the idea of a
smooth soliton big enough to explain the mass of the electron (and it
doesn't explain how
the electron would hold together anyway in the face of self-repulsion).
DeBroglie was equally clear that a pure point particle model does not work
either,
because of the well-known double slit (actually diffraction grating) kind
of experiment.
Since neither model of the electron could work, he simply proposed a kind
of COMBINATION --
a "point particle" (actually, a tiny zone of nonlinear energy
concentration) and a "pilot wave"
(actually an asymptotic linearized solution of the nonlinear wave equations),
BOTH propagating over ORDINARY 3+1-D Minkowski space-time. Again, his book
with Vigier was quite clear. Only much later, as DeBroglie failed to find
a good account for the spectrum of helium, did people like Bohm and even Vigier
start to "defect to Fock space" because of the difficulty of OPERATIONALIZING
De Broglie's vision. How to translate the VISION in the book by DeBroglie
and Vigier
into real mathematics, without defecting to Fock space?
Again, my papers in quant-ph, the chapter in Walls-Milburn and the chapter in
Carmichael, all develop the kind of mathematics which really makes it
possible to operationalize all this --
FOR BOSONIC QFTs. (Section 3e of my cond-mat 2004 paper fills in a critical
gap, and
the 1984 paper in Physics Reports by Hillery, OConnell, X and Wigner is
also critical.
OConnell is alive and well in Louisiana, and might have something to
contribute here.)
Now... here is a critical point, which I see very clearly today.
The original DeBroglie idea of a continuous pilot wave and a nonlinear
"core" -- approximated
as a continuous field and a point particle -- WILL NOT WORK in getting us
to derive
the predictions of quantum electrodynamics (QED). It will not work because
the continuous pilot wave as DeBroglie envisioned would HAVE to be quantized
in a bosonic form. Even as an approximation it is not adequate. The physics
is fundamentally different.
After a lot of very complex OTHER analysis, my conclusion is as follows: the
only mathematics which works is to assume that the "pilot wave," instead
of being a normal continuous field, is a highly chaotic kind of wave motion,
analogous to the wave form of ordinary AM radio waves, where two
frequencies are BOTH present. The duality of "wave-like"
(more continuous) and "particle-like" (very small radius) behavior
of the electron can be explained as a duality very similar to that between the
high (RF) and low (audio) frequencies in an ordinary radio wave.
----------------------
Of course, these words -- like the book of DeBroglie and Vigier itself --
require
a mathematical formulation to be of any value whatsoever. In fact...
it is the analysis of the mathematics which led me to believe these words.
The mathematics is what I begin to understand more clearly today.
------------
Back in the quant-ph papers, I reasoned as follows. If a realistic
continuous field model
has exact equivalence to any desired BOSONIC QFT -- we could explain
the success of the standard model of physics in neoclassical terms by
finding a bosonic quantum field theory equivalent to the standard model.
There is a HUGE mainstream literature on "bosonization" and
"nuclear democracy" and "duality" which suggests that this should not be
too hard.
For example, Vachaspati (see arXiv.org) has lots of papers on a bosonic
dual standard model.
However -- when you really try to rely on the mainstream, you learn of its
feet of clay
even more than you do from a distance...
In the end...after hundreds of papers... it all seems to come back to the
old idea
of Alfred Goldhaber (and Wilczek) that sometimes a bound state of two bosonic
magnetic monopoles ends up being a fermion. I have seen lots of nice
abstract reasoning about this...
but not earthy examples. To construct a real (and reliable) theory we need
earthy examples.
(And Schwinger's way of generalizing monopoles into "dyons" is important in
extending
this, in principle, as are many ideas in The Skyrme Model by Makhankov,
Rybakov and Sanyuk.)
So we need a more constructive mathematical version of these ideas.
One might ask: "why do you bother with all this? Why not just represent the
electron as a point
particle, in the obvious and natural mathematical implementation of the
ideas in section 3e
of your cond-mat 2004 paper?" There are two main reasons why I don't regard
this as the most promising
approach: (1) point particle QED MUST be represented as a kind of limit (as
in QED regularization itself!),
because of things like infinite electron self-repulsion -- and we need a
rational basis for choosing
a "regularization,' in effect; and (2) there are still the old DeBroglie
arguments against a classical
type of point particle model.
After learning to think in terms of coherent fields, as in quantum optics
and bosonic statistics...
it takes some adjustment to get back into particle-like thinking again.
For example, we must recall that:
psi(x1,s1; x2,s2;... xn,sn) =
psi1(x1...sn)*psi2(x1...sn)
defines a totally symmetric (bosonic) wave function
when psi1 and psi2 are totally antisymmetric (fermionic).
When electric charge is like a totally conserved and quantized topological
charge,
we can safely "truncate" or project the statistics of a bosonic field into
subspaces of "definite charge." Thus the statistics of the classical
bosonic field theory basically give us something a lot like traditional
"one electron" (or "N" electrons for a charge of N) wave functions,
EXCEPT that we must include virtual electron/positron pairs, which are
no different from what QED really assumes.
One way of interpreting Goldhaber's ideas more constructively is to say...
a bound state of two monopoles is a lot like a simple hydrogen atom,
a bound state whose wave function can be represented as the PRODUCT
of "two wave functions," because of the way that the separation
of variables works. THIS IS NOT like the kind of multiplication
of wave functions that QM typically uses for two uncoupled
particles; it is just an artifact of the way we exploit separation of
variables.
The key idea here is as follows: for a continuous nonlinear field theory,
like the classical Skyrme model or a system of two bound classical dyons,
we may find no TRUE separation of variables, but we MAY find
a separation of variables at asymptotic distances from the core or center
of the system (aka chaotic soliton). Thus in the asymptotic limit,
or as "soliton radius r goes to zero", the set of solutions
for the system OR FOR the matrix of statistical covariances of the system,
my converge to a product,
like psi=psi1*psi2, where psi1 is "broad"
(like the center of gravity wave function for a nonlocalized hydrogen atom)
and psi2 is "narrow" (like the wave function of electron RELATIVE to proton
in that hydrogen atom). Even if psi is naturally
a single-valued function, it may happen to be REPRESENTED
as a product of two two-valued (fermionic) functions in this process.
Thus the mysterious fermionic weirdness discussed by Goldhaber
and by Makhankov, Rybaov and Sanyuk may be
disentangled and presented in a more straightforward Von-Neumann-like
way by deriving it in this kind of context. Yes, we still have to
consider spatial rotations in explaining why CERTAIN PDE
yield these kinds of asymptotic solutions, but this is how it works.
And then.. translating it into a physical picture... it is almost like saying
the electron is really more LIKE a point particle, but that it uses a kind
of AM radar system to pilot itself through double slits and the like.
The fact that the math works out is what ultimately guarantees the match to
experiment... and we do need to take all this and get the equations all down
on paper and so on. (One more week of vacation left to me... maybe enough,
maybe not...). The word "chaotic" sounds messy .. but the analysis
in terms of matrices of statistical moments is extremely orderly.
And then, another curious issue emerges. IN THIS CONTEXT, a very different
kind of "zero point" fluctuation becomes much more interesting and
plausible as a modification of the basic model I have just outlined.
In the "nonlinear core zone" of such a chaotic electron model,
a very special kind of white noise in space (limited to what perturbs the
core zone locally) or thermal fluctuation across space-time becomes possible.
Normally, in fields, simple diffuse white noise is very messy, because
of issues of positive-definiteness of covariance matrices in Minkowski
space (whose metric is not definite in sign). But within "world line"
(or, better, world-channels) of massive particles like electrons, it is a
different story.
Can this be made mathematically meaningful an relativistic? Sure:
consider additions to curvature of a world-line. I wonder whether this addition
to the model may be crucial, in the end, to really
understand what goes on in tunneling, at the Josephson junction.
Perhaps a lot of that rigorous work by Kunio Yasue on stochastic point
electrons
may indeed turn out to be crucial piece of the final rigorous unified story
here.
But.. one step at a time. All of this needs to be put down mathematically
(the no-noise and particle-noise versions), and used to fill in the details
of part 3e of cond-mat 2004. If any of you can do this better or faster than I,
I will be delighted (at least if you do cite the useful but incomplete
contribution I have made so far). Given the approach of
return to work, and return to some rather urgent life-or-death
government policy issues... I may not have time to fill in all details here.
Happy New Year...
Paul
P.S. For the "thermal" variation of the particle-noise idea,
I have one image of treating collisions in space time in
a way analogous to today's treatments of molecules
in space, in closing a stoichiometric kind of statistical argument.
In the end, it may all be a kind of approximation, as is
traditional first-order chemical thermodynamics... but it may be
very useful as a starting point, in much the same way.
Before we can get to second order thermodynamics -- as in
cond-mat 2004 chips! -- we must develop the space-time
analogue of first-order thermodynamics!
At least, that is one possible way to go, after the
simpler noise-free fermionic PDE statistics are worked out
per the asymptotic separation of variables concepts.
And of course, the separation of variables is not isotropic
in this case. Like a classical dipole expansion.
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