Mendel Sachs's QM from GR
Jack
He is an intelligent thoughtful thinker and the book is interesting.
However, I remain unconvinced on his central argument that he is able to
derive an effective N-particle configuration space from his nonlinear
spinor field theory in ordinary 3-space in the limit of small
energy-momentum transfers. The key to his argument is in Ch 6 e.g. eqs
(6.14) to (6.1.7). I do not consider this really to be a rigorous
deduction. It is an Ansatz equivalent to the usual theory IMO. That is,
Sachs like everyone else is forced to posit configuration space in his
(6.1.5). I do not see that he deduces it from his nonlinear theory in
ordinary space. His nonlinear theory may be interesting, however, for
other reasons, but not for this one. For one thing the class of
multiparticle states in (6.17) is only a subset of possible entangled
states that include non-identical particles beyond the special case of
the Pauli exclusion principle.
A few other points. Sachs defines the "vacuum" as flat spacetime. That
is, he says matter is necessary for curvature i.e. he says zero
curvature without a stress energy tensor. However, this is not true as
Wheeler showed in his book Geometrodynamics with "geons" as "mass
without mass". That is, the nonlinearity in Einstein's field equations
even with zero stress energy tensor everywhere and when can have
non-flat solutions that are curved vacuums.
Also Sach's does not have torsion although his "spin affine connection"
may be generalized to torsion. In that case, it is not clear if his
conclusion of a positive definite inertial field ,i.e. no anti-gravity,
will survive in the presence of torsion. That is, his conclusion that
that the inertial field is the positive-definite modulus of a complex
function may itself only be an approximation based on assumptions no
longer true if torsion is present.
Sachs does use Wheeler-Feynman action at a distance source
electrodynamics without independent photon fields and with advanced
causation. So there are no virtual photons in Sach's theory. Problem is,
are there near fields in Sach's theory? If everything is on the light
cone how do you have near fields? This would apply also to the original
Wheeler-Feynman model of 1940. Also he says there is no real
electron-positron annihilation only deeply bound states of zero charge.
Therefore, Sach's theory is incompatible with the Haisch-Rueda-Puthoff
EM ZPF origin of inertia idea as a fundamental theory distinct from a
phenomenology. In this regard, Basil Hiley's student M. R. Brown at
Birkbeck, University of London has shown implicitly how the EM ZPF
origin of inertia is a "momentum dispersion energy" of the Bohm
"super-quantum potential" whose material "Bohm point" is the classical
electromagnetic field configuration that includes the near fields as
well as the far fields. Brown's paper is quant-ph/9703007 "The quantum
potential: symplectic breakdown and dispersion". The key word for ZPF is
"dispersion".
--
"But the real glory of science is that we can find a way of thinking
such that the law is evident. ... For a successful technology, reality
must take precedence over public relations, for Nature cannot be
fooled." Feynman
"I want to know God's thoughts ... the rest are details. ... Great
Spirits have always encountered violent opposition from mediocre minds.
... Quantum mechanics is very impressive. But an inner voice tells me
that it is not yet the real thing. The theory produces a great deal but
hardly brings us closer to the secrets of the old one." Einstein
"It's the end of the line, and I feel a paradigm about to shatter. Let's
get to the heart of the Grey Matter." Pamela Stonebrooke
http://www.well.com/user/sarfatti/
Jack
-------- Original Message --------
Subject: Re: Mendel Sachs's QM from GR
Date: Thu, 18 May 2000 15:56:10 -0400
From: "Bill Page" <bill....@sympatico.ca>
To: "Jack" <sarf...@well.com>
CC: "David Cyganski" <cyga...@ece.WPI.EDU>,"Mendel Sachs"
<msa...@acsu.buffalo.edu>
Jack,
On Thursday, May 18, 2000 10:52 AM you wrote:
>...
>The key to his argument is in Ch 6 e.g. eqs (6.14) to (6.1.7). I do not
>consider this really to be a rigorous deduction. It is an Ansatz
>equivalent to the usual theory IMO. That is, Sachs like everyone else
>is forced to posit configuration space in his (6.1.5). I do not see that
>he deduces it from his nonlinear theory in ordinary space.
[Page]
"Eqs. 6.1.4 are deduced from 6.1.1' in the limit where the interaction
functional approaches 0. In this limit (the free field approximation)
the
coupled non-linear equations in 6.1.1' become "uncoupled". Eq.
6.1.5 is just the sum over the separate eqs. 6.1.4."
[Jack]
No, it is not deduced in any sense. He does not do anything wrong, but
he does not deduce anything. He simply makes the same Ansatz everyone
else does. Also the entangled states are not at all limited to small
energy-momentum transfers.
>His nonlinear theory may be interesting, however, for other reasons,
>but not for this one. For one thing the class of multiparticle states in
>(6.17) is only a subset of possible entangled states that include
>non-identical particles beyond the special case of the Pauli exclusion
>principle.
[Page]
Can you give an example of a state that is not in the class defined
in 6.1.7?
[Jack]
Easy. For example 1, a hydrogen atom consisting of a proton p and
electron e and a radiation field with oscillators 1,2,3 ....
The states of the proton are the complete set {|pi>} of simultaneous
eigenfunctions in a relevant maximal commuting subalgebra of the Lie
algebra of Hermtian observables for the proton. Similarly for the
electron {|ej>} and for the photon field configuration in its Fock space
representation including all 4 polarization states (i.e. near + far
field). We can generalize to any number of hydrogen atoms. So the Pauli
exclusion principle is not directly relevant here, but entanglement
certainly is.
The general state |p,e, EM field> will be entangled of the form
Sum over i, sum over j, sum over n1, n2, n3 ... of
|pi>|ej>|n1,n2,n3....><pi|<ej|<n1,n2,n3...|p,e, EM field>
Example 2 is p. 9 May 2000 Physics Today "Entanglement of 4 particles"
with four beryllium ions, using a laser pulse "the four ions were driven
through their coupled motion into an entangled superposition of being
all spin down and all spin up .... the technique can be used to entangle
many more than four partilces, with evident usefulness for quantum
information technologies .. Nature, 404, 256 (2000)
i.e.
|psi> = (1/sqrt2){|++++> + |---->}
There are, obviously, an infinity of possible examples. Entanglements of
many-particle systems whose Bohm points move through configuration space
on a quantum de Broglie-Bohm pilot field lanscape are much more general
than the very special case of the Pauli exclusion principle for N
identical elementary spinors.
Mendel Sachs has simply given a heuristic plausibility argument that
there is no conceptual incompatibility between his nonlinear spinor
theory in 3D space and the conventional quantum formalism of entangled
states whose domain is classical mechanical configuration space and
whose range is the tensor products of the component Hilbert space of
wave functions of the separate parts that entangle into the organic
non-mechanical whole in the sense of Hermann Weyl, Bohm and Hiley etc.
>
>A few other points. Sachs defines the "vacuum" as flat spacetime.
>That is, he says matter is necessary for curvature i.e. he says zero
>curvature without a stress energy tensor. However, this is not true as
>Wheeler showed in his book Geometrodynamics with "geons" as
>"mass without mass". That is, the nonlinearity in Einstein's field
>equations even with zero stress energy tensor everywhere and when
>can have non-flat solutions that are curved vacuums.
[Page]
I think it is necessary to define carefully what is meant by "flat".
That is the essence of Shipov's theory based on A4 (which is
flat is a specific technical sense).
[Jack]
Mendel is very clear that he means "flat" in the sense of special
relativity. His book is interesting and has some interesting maverick
ideas worth thinking about. However, as I suspected, you oversold the
rigor of his argument that the fundamental theory is in 3D space and
that higher dimensional configuration space is not "funda-MENTAL"
(Hameroff's term). I am not at all persuaded by what I read. His
argument is quite weak logically IMO and what he sets out to prove is
not the general case of entanglement in quantum theory, but a special
case, albeit an important special case.
[Page]
I agree that perhaps Sachs
has not fully appreciated the sense in which Einstein's eqs. are
based on the Riemann tensor which does not represent curvature
in the more general case, i.e. the curvature of A4 is zero by
definition.
>
>Also Sach's does not have torsion although his "spin affine
>connection" may be generalized to torsion.
[Page]
I think it is equivalent. See especially Shipov's spinor representation
in chapter 6 of his book and eq. (6.30).
[Jack]
It cannot be if Shipov is consistent and knows what he is talking about.
I know, for certain, that Shipov fervently believes that his A4 torsion
field theory will permit an effective "anti-gravity" in the sense of
"flying saucer" reports. I have discussed this directly with Gennady
several times. Therefore, Mendel and Gennady cannot be both correct on
this particular important point. That much I can say for sure.
"No possible doubt whatever." Gondoliers, Gilbert & Sullivan
>In that case, it is not clear if his conclusion of a positive definite
>inertial field ,i.e. no anti-gravity, will survive in the presence of
>torsion. That is, his conclusion that that the inertial field is the
>positive-definite modulus of a complex function may itself only
>be an approximation based on assumptions no longer true if
>torsion is present.
It seems to me that this is equivalent to Shipov's eqs. (2.65) through
(2.72). I do not think that "no anti-gravity" is one of Mendel Sachs'
conclusions.
[Jack]
Sure it is. Shipov says, on basis that his inertial lambda field is the
intrinsically positive modulus of a complex function that gravitational
repulsion is not possible in principle. Also it is not at all clear that
Mendel's particular form of the spin affine connection is as general as
Gennady's. Remember, Gennady's corresponds to the anholonomic case in
which the rotational 4D curl of the tangent vector flow fields does not
vanish. That is, the assumption that
dx^i = eu^i(q)dq^u
is an exact differential corresponding to an integrable
x^i = x^i(q)
is false in the presence of anholonomic torsion fields corresponding to
non-Riemannian geometry. That is, there is no unique path-independent
irrotational streamline flow of the tangent vector fields (tetrads) as
there is in Riemannian geometry on which Einstein based his original
1915 general theory of the gravity metric field on. There is of course
elastic curvature which is the path-dependent nonintegrability of the
partial derivatives of the holonomic torsion-free irrotational
streamlines of Einstein's 1915 theory. It is quite obvious that Mendel
did not include non-Riemannian geometry, with plastic rotational torsion
signaling breakup of irrotational streamlines with good wavefront
surfaces normal to the streamlines, in his particular nonlinear spinor
theory. The aether hydrodynamic picture allowing use of V, I Arnold's
"singularity" theory for the plastic torsion gap rotational turbulence
of the tetrad flow patterns, giving Kiehn's "irreversibility" is a good
intuitive model to use. Who said God did not know how to solve
turbulence? God may not know, but V I Arnold may! :-)
>
>Sachs does use Wheeler-Feynman action at a distance source
>electrodynamics without independent photon fields and with advanced
>causation. So there are no virtual photons in Sach's theory. Problem is,
>are there near fields in Sach's theory? If everything is on the light
>cone how do you have near fields? This would apply also to the original
>Wheeler-Feynman model of 1940.
[Page]
I think your question presumes a "particle mentality". I don't see why
"near fields" are impossible. This is just one more aspect of the
solutions of the field equations.
[Jack]
It has to be shown explicitly. I think Wheeler-Feynman, Hoyle and
Narlikar ignored near fields in the classical limit at least. On the
other hand, if they get the Feynman propagators in the quantum case, the
near fields are there as coherent states off the mass shell of whatever
source configurations give them. If the radiation far-fields correspond
to both advanced and retarded actions at a distance confined to the
light cone, the near fields must correspond to actions at a distance
between sources and absorbers not on the light cone. Classical near
fields as found in any electrical circuit with capacitors and
inductances etc would have to be coherent superluminal actions at a
distance. In any case, I need to look at this issue. It is not obvious.
If there is no way to describe near fields in
Wheeler-Feynman-Hoyle-Narlikar then it is a strong argument that their
idea is, if not wrong, seriously incomplete. They are focused on the
light cones and far field radiation in a transaction between source and
absorber. I simply have to take a closer look at their formalism. It's
been a while and this question will resolve itself easily.
>Also he says there is no real electron-positron annihilation only deeply
>bound states of zero charge. Therefore, Sach's theory is incompatible
>with the Haisch-Rueda-Puthoff EM ZPF origin of inertia idea as a
>fundamental theory distinct from a phenomenology.
[Page]
Yes, I think that is true.
>In this regard, Basil Hiley's student M. R. Brown at Birkbeck, University
>of London has shown implicitly how the EM ZPF origin of inertia is a
>"momentum dispersion energy" of the Bohm "super-quantum potential"
>whose material "Bohm point" is the classical electromagnetic field
>configuration that includes the near fields as well as the far fields.
[Page]
I don't see how this relates to Sachs' theory.
[Jack]
Bohm's theory is a covering theory for the Haisch et-al theory. If
Mendel has a fundamental theory his theory must cover Bohm's. This is by
no means obvious. Also, Mendel's theory is admittedly "deterministic".
My theory transcends determinism for self-organizing self-determination,
hence conscious intent with morally responsible free will is part of the
post-quantum physical paradigm.
>Brown's paper is quant-ph/9703007 "The quantum potential: symplectic
>breakdown and dispersion". The key word for ZPF is "dispersion".
Thanks for the reference.
Regards,
Bill Page.
Jack
Jack wrote:
"lanscape" should be "landscape"
>
>
> [Page]
> (2.72). I do not think that "no anti-gravity" is one of Mendel Sachs'
> conclusions.
>
> [Jack]
>
> Sure it is. Shipov says, on basis that his inertial lambda field is the
> intrinsically positive modulus of a complex function that gravitational
> repulsion is not possible in principle.
Change "Shipov" to "Sachs" above.
>
>
Jack
Paul Zielinski wrote:
Jack wrote:
> I finally got Mendel Sach's "Quantum Mechanics from General Relativity".
> He is an intelligent thoughtful thinker and the book is interesting.
> However, I remain unconvinced on his central argument that he is able to
> derive an effective N-particle configuration space from his nonlinear
> spinor field theory in ordinary 3-space in the limit of small
> energy-momentum transfers. The key to his argument is in Ch 6 e.g. eqs
> (6.14) to (6.1.7). I do not consider this really to be a rigorous
> deduction. It is an Ansatz equivalent to the usual theory IMO. That is,
> Sachs like everyone else is forced to posit configuration space in his
> (6.1.5). I do not see that he deduces it from his nonlinear theory in
> ordinary space.
Of course statistical correlations in general always refer to multiple random
variables. Presumably you mean something stronger than that here?
Stronger. Mendel simply makes the Ansatz ad hoc
psi(x1,t) psi(x2,t) ... psi(xN,t) after some neither there nor here handwaving IMHO.
> His nonlinear theory may be interesting, however, for
> other reasons, but not for this one. For one thing the class of
> multiparticle states in (6.17) is only a subset of possible entangled
> states that include non-identical particles beyond the special case of
> the Pauli exclusion principle.
Do you mean "non-identical" or "distinguishable identical" particles?
The former, like an electron entangled with a proton.
There
is a lot of slipping and sliding around this terminology in textbooks and
in the literature.The "special class" satisfying the Pauli principle is of course a subset of
the available pure entangled states for N *indistinguishable* identical particles
in standard QM (which transform as irreducible representations of S[N]).
Those are in turn a subset of the available pure states for N *distinguishable*
identical particles.Do you agree?
Yes. That is my point.
> A few other points. Sachs defines the "vacuum" as flat spacetime. That
> is, he says matter is necessary for curvature i.e. he says zero
> curvature without a stress energy tensor. However, this is not true as
> Wheeler showed in his book Geometrodynamics with "geons" as "mass
> without mass". That is, the nonlinearity in Einstein's field equations
> even with zero stress energy tensor everywhere and when can have
> non-flat solutions that are curved vacuums.
If Sach's assumption is a physical hypothesis, it cannot be refuted by
pointing out that it is *mathematically* possible to have curvature in
the absence of "massive" matter. Or is Sachs claiming that this is
ruled out for purely mathematical reasons?
I have not read the entire book only up to Ch 6 and I did not read
his stuff on quantum theory history. So far I have not seen any evidence
that he is aware of this? I could be wrong.
> Also Sach's does not have torsion although his "spin affine connection"
> may be generalized to torsion. In that case, it is not clear if his
> conclusion of a positive definite inertial field ,i.e. no anti-gravity,
> will survive in the presence of torsion. That is, his conclusion that
> that the inertial field is the positive-definite modulus of a complex
> function may itself only be an approximation based on assumptions no
> longer true if torsion is present.
>
> Sachs does use Wheeler-Feynman action at a distance source
> electrodynamics without independent photon fields and with advanced
> causation. So there are no virtual photons in Sach's theory. Problem is,
> are there near fields in Sach's theory? If everything is on the light
> cone how do you have near fields? This would apply also to the original
> Wheeler-Feynman model of 1940. Also he says there is no real
> electron-positron annihilation only deeply bound states of zero charge.
Yes, you would find his stuff interesting he is competent and more thoughtful than most mainstream theorists. I do not think he is correct however. For one thing, his starting point is too narrow IMHO.I have to agree this seems like interesting stuff, even if ultimately it doesn't
work.
>
> Therefore, Sach's theory is incompatible with the Haisch-Rueda-Puthoff
> EM ZPF origin of inertia idea as a fundamental theory distinct from a
> phenomenology. In this regard, Basil Hiley's student M. R. Brown at
> Birkbeck, University of London has shown implicitly how the EM ZPF
> origin of inertia is a "momentum dispersion energy" of the Bohm
> "super-quantum potential" whose material "Bohm point" is the classical
> electromagnetic field configuration that includes the near fields as
> well as the far fields. Brown's paper is quant-ph/9703007 "The quantum
--
Jack
Paul Zielinski wrote:
> Jack wrote:
>
> >
> >
> > Stronger. Mendel simply makes the Ansatz ad hoc
> >
> > psi(x1,t) psi(x2,t) ... psi(xN,t) after some neither there nor here handwaving IMHO.
>
> Well, *mathematically* we can form products of one-particle states and apply the
> superposition principle to those product functions. Since the resulting correlated
> N-particle states will then automatically satisfy a Schrodinger equation, this suggests
> a rather natural interpretation of the N-particle psi function as a *physical wave* that
> propagates in the N-particle configuration space. I imagine it is this *physical* aspect
> that you have in mind here.
[Jack]
Yes, that's what Sachs does at the crucial step. It's the same thing everyone does. In no sense is he
logically forced to do it by his nonlinear field theory in 3D space. It is a logically independent
postulate he adds ad hoc to his theory. Bill Page oversold the reality when he said that Mendel Sachs
proved that configuration space is not a fundamental quantum concept but can be derived from classical
theory in ordinary space. The difference in the classical and quantum roles of configuration space is in
Bohm's quantum potential specifically in the nonseparability of Bohm's quantum potential when there is
entanglement, in its form-dependence, its intensity-independence, its nonlocality, and its
non-mechanical context dependence i.e. no pre-assigned interactions among the entangled source particles
and force fields as in classical physics.
Jack
Bill Page wrote:
> Jack,
>
> On Friday, May 19, 2000 10:33 AM you wrote:
> >
> >Paul Zielinski wrote:
> >
> >> Jack wrote:
> >>
> >> > Stronger. Mendel simply makes the Ansatz ad hoc
> >> >
> >> > psi(x1,t) psi(x2,t) ... psi(xN,t) after some neither there nor here
> >> > handwaving IMHO.
> >>
> >> Well, *mathematically* we can form products of one-particle states and
> >> apply the superposition principle to those product functions. Since the
> >> resulting correlated N-particle states will then automatically satisfy a
> >> Schrodinger equation, this suggests a rather natural interpretation of
> >> the N-particle psi function as a *physical wave* that propagates in the
> >> N-particle configuration space. I imagine it is this *physical* aspect
> >> that you have in mind here.
> >
>
> I think Paul used the correct keyword here: interpretation. Such an
> interpretation goes beyond the requirements of the theory.
I am not sure what the argument is in that case. My only point is that there is
no mathematical necessity to do what Mendel did when he gets to the Pauli
exclusion principle. In no sense is he forced to do it by the structure of his
nonlinear field theory whose configurations are limited to 3D space unlike the
Bohm quantum potential Q. He simply puts in the quantum superposition principle
in configuration space adhoc as a postulate, same as everyone else does since it
is required to agree with experiments. I see no justification for any claim that
Sach's nonlinear spinor field theory in 4D spacetime derives quantum theory's
reliance on configuration space and entangled states in Hilbert space as a
limiting case for small energy-momentum transfers between the separated pieces
of the whole. The quantum superposition principle (summing weighted products of
single-particle eigenfunctions of relevant observables) is a separate postulate
not already demanded by his prior formulation of his theory.
>
>
> >[Jack]
> >
> >Yes, that's what Sachs does at the crucial step. It's the same thing
> >everyone does.
>
> No. The important steps come before this. It is the fact that the
> coupled non-linear field equations can be represented in certain
> cases (approximately) as uncoupled linear equations that is the
> crucial step.
This is trivial and obvious and in no way impinges on my point. To show
uncoupled linear equations in a certain limit, is not, by any stretch of the
imagination, a logical justification for the necessity of introducing
"entanglement", i.e coherent superposition of products of single particle
functions whose domain is configuration space and whose range is the tensor
product of irreducible representations of single particle systems as shown in
detail, for example, by Hermann Weyl in "Theory of Groups in Quantum Mechanics"
(Dover).
Indeed, take one of Mendel's uncoupled linear equarions for say particle labled
1. Since the partial differential equation for particle 1 is linear, we are
certainly justified in superposing fi(x1,t) single particle eigenfunctions.
That is if fi(x1,t) are solutions then so is
F(x1,t) = Sum over i of ci fi(x1,t)
a solution.
However, the claim in the quantum many-body problem is more than that. First of
all, it is never claimed, as Mendel claims, that the energy-momentum transfers
between the particles is "weak'. It is never claimed that there are separate
uncoupled equations one for each particle. Indeed, that defeats the very idea of
the many-body problem in orthodox quantum physics as shown in any standard text
book on the subject.
One has a Hamiltonian with sum of single particle kinetic energies and usually a
sum of pair static potentials like the Coulomb potential and a EM vector
potential all in the minimal gauge invariant way even if the EM field is not
quantized but only the particle motions are quantized in the semi-classical SED
for example used by Haisch et-al.
The quantum superposition principle in the Galilean relativity many-body
problem is
PSI(x1,x2,x3, ... xN, t) = Sum i1.... iN C(i1.... iN)
fi1(x1,t)fi2(x2,t)fi3(x3,t).... fiN(xN,t)
This is obviously a physically independent new postulate not at all dependent on
any approximation of uncoupled equations.
This is general. In addition, if you want the Pauli exclusion principle you need
to add still more postulates!
You need to add the notion of nonlocal permutation symmetry from the irreducible
representations of the finite symmetric group SN for which there are many Young
Patterns of parastatistics.
Then you need to specialize. You need to impose complete antisymmetry (a
particular Young Pattern of a single row of boxes in the usual notation) for
identical fermions.
None of this is in Mendel's theory in 3D space. Its role is not even recognized
by him at least as far as I read to Ch 6 in his book. For this reason his claim
and yours is completely naive mathematically as a look at Weyl's classic book on
the subject clearly shows.
>
>
> >In no sense is he logically forced to do it by his nonlinear field theory
> >in 3D space. It is a logically independent postulate he adds ad hoc to
> >his theory.
>
> It is not a postulate of Sachs' theory.
It is if one wants to make sense of his theory as I show above.
>
>
> >Bill Page oversold the reality when he said that Mendel Sachs proved
> >that configuration space is not a fundamental quantum concept but can
> >be derived from classical theory in ordinary space.
>
> When did I say that configuration space can be derived from classical
> theory? I don't believe that I did.
Oh, I thought you did. I thought that was the whole point. If that's not what
you claimed, then I do not know what the dispute was about? It is clearly what
Mendel is claiming I think.
> Also, I never argued whether not
> configuration space was "a fundamental quantum concept". Certainly
> it plays a fundamental role in quantum theory. What I said was (more or
> less) that it apparently wasn't a fundamental *physical* concept, i.e.
> that acceptable and sufficiently complete (relative to conventional
> general relativity and quantum mechanics) theories exist (such as
> Mendel Sachs' theory) that do not incorporate configuration space
> as a fundamental concept.
A delicate distinction! (Gilbert and Sullivan)
>
>
> >The difference in the classical and quantum roles of configuration space
> >is in Bohm's quantum potential specifically in the nonseparability of
> >Bohm's quantum potential when there is entanglement, in its form-
> >dependence, its intensity-independence, its nonlocality, and its non-
> >mechanical context dependence i.e. no pre-assigned interactions
> >among the entangled source particles and force fields as in classical
> >physics.
>
> The same nonseparability occurs in Mendel Sachs' field theory.
>
> Regards,
> Bill Page.
>
> PS. For your reference I attach the email where I think this thread
> started. I still stand by what I said then.
Well I do not understand the significant difference in your
"What I said was (more or
less) that it apparently wasn't a fundamental *physical* concept, i.e.
that acceptable and sufficiently complete (relative to conventional
general relativity and quantum mechanics) theories exist (such as
Mendel Sachs' theory) that do not incorporate configuration space
as a fundamental concept."
Perhaps Paul Zielinski can figure out the difference?
Jack
Bill Page wrote:
> Jack,
>
> On Thursday, May 18, 2000 7:23 PM you wrote:
>
> >...
> >[Page]
> >
> >"Eqs. 6.1.4 are deduced from 6.1.1' in the limit where the interaction
> >functional approaches 0. In this limit (the free field approximation)
> >the coupled non-linear equations in 6.1.1' become "uncoupled".
> >Eq. 6.1.5 is just the sum over the separate eqs. 6.1.4."
> >
> >[Jack]
> >
> >No, it is not deduced in any sense. He does not do anything wrong,
> >but he does not deduce anything.
>
> I don't want to get bogged down in semantics here. Mendel Sachs'
> claim is that n-particle quantum mechanics can be arrived at as a
> particular *approximation* to his theory of matter. So in that sense
> you are right. Similarly, one could claim that one does not *deduce*
> Newtonian mechanics from general relativity nor from quantum
> mechanics. However we know that we can relate both of these
> theories to Newtonian mechanics is certain limited ways. Sachs is
> saying that we can recover the formalism of n-particle quantum
> mechanics (as expressed in 4n dimensional configuration space)
> from his theory (which expresses n-particles as field "modes"
> over a single space-time) as a similar kind of limit.
I think he is even wrong about that. Specifically, his claim that the quantum
many-body problem is limited to small energy-momentum transfers between the
parts of the whole giving uncoupled linear equations for the isolated monadic
single particles. I don't buy that. One can have non-perturbative solutions in
the nonrelativistic manybody problem. Indeed, the gap equation in the BCS model
of superconductivity is a sum of an infinite number of Feynman diagrams, so
small energy-momentum transfers in the sense of using only a few Feynman
diagrams is not required. It depends precisely on what Sach's really means by
"uncoupled" and "small". Certainly, the permutation symmetry is an additional
postulate whose role Mendel is not explicit about in his formulation of the
basics of his theory. The use of the intrinsically nonlocal symmetric group SN
flies in the face of any purely local 3D or 4D theory. Without SN you have
complete disagreement with many experimental facts. Case closed IMO. Weyl calls
this a fundamental reciprocity between the irreducible representations of the
continuous Lie groups and their finite groups. Weyl obviousl ysees this as a
physical principle that anticipates Bohm's later "implicate order".
All of you guys are stuck in the local objective explicate Cartesian order.
Einstein was right about objective reality, but not about the completeness or
suffciency of the explicate order.
Bohr was right about nonlocality, but wrong about nonobjective reality.
Einstein was right about objective reality, but wrong about nonlocality.
Bohm and Bell corrected both of them with nonlocal objective reality. Post
quantum physics is a self-determining nonlocal objective reality theory with
signal-nonlocality violating both orthodox quantum physics and Bohm's
deterministic causal theory version of it.
>
>
> >He simply makes the same Ansatz everyone else does.
>
> What is this "Ansatz"? Can you give an example of its use?
I did in previous communications today.
>
>
> >Also the entangled states are not at all limited to small
> >energy-momentum transfers.
>
> I think that is true. What is your point? In chapter 6, Sachs is talking
> about the limit of small energy-momentum transfers only as one
> means by which to recover conventional QM from his theory. He
> has not stated that entanglement only occurs in this situation -
> in fact, quite the opposite - one can interpret Sachs' theory as
> saying that everything is "entangled" all the time. The extent to
> which we can interpret a particular solution of the field equations
> as a set of independent particles is as an approximation. And a
> quantum mechanically entangled set of particles is still an
> approximation, albeit, a better one.
I think Sach's idea here is not relevant to the real problem. I will have to
read the rest of his book of course. While I think Sachs is a good thoughtful
guy, I think he is on a quixotic quest to derive quantum nonlocal realism from
Einstein's original classical local realism. Bell showed that cannot be done
IMO.
>
>
> >
> >>His nonlinear theory may be interesting, however, for other reasons,
> >>but not for this one. For one thing the class of multiparticle states in
> >>(6.17) is only a subset of possible entangled states that include
> >>non-identical particles beyond the special case of the Pauli exclusion
> >>principle.
> >
> >[Page]
> >Can you give an example of a state that is not in the class defined
> >in 6.1.7?
> >
> >[Jack]
> >
> >Easy. For example 1, a hydrogen atom consisting of a proton p and
> >electron e and a radiation field with oscillators 1,2,3 ....
> >
> >The states of the proton are the complete set {|pi>} of simultaneous
> >eigenfunctions in a relevant maximal commuting subalgebra of the Lie
> >algebra of Hermtian observables for the proton. Similarly for the
> >electron {|ej>} and for the photon field configuration in its Fock space
> >representation including all 4 polarization states (i.e. near + far
> >field). We can generalize to any number of hydrogen atoms. So the
> >Pauli exclusion principle is not directly relevant here, but entanglement
> >certainly is.
> >
> >The general state |p,e, EM field> will be entangled of the form
> >
> >
> >Sum over i, sum over j, sum over n1, n2, n3 ... of
> >
> >|pi>|ej>|n1,n2,n3....><pi|<ej|<n1,n2,n3...|p,e, EM field>
> >
>
> (6.1.7)
> Psi = (1/n!)^(1/2) Sum_p exp(i alpha_p) Product_u Psi^(m_u)(x_u)
>
> Although the notation is different, it seems to me that your example is
> included in eq. 6.1.7. Note (top page 92): "the indices above, (u), for
> each of the field solutions, stand for the set of quantum numbers {m_u},
> that relate to the Hilbert space of functions for each of these solutions.".
> Your pi, ej and nk are among Sachs' m_u. Sachs did not write spin
> states explicitly, but it seems clear that they can be included (take Psi
> as an appropriate spinor solution to the field equations).
The point is that use of permutation symmetry is a separate nonlocal postulate
of the theory. A particular nonlocal permutation symmetry is used for fermions.
Another is used for Bosons. Anyons use still another. How can Sachs account for
that? He can't, not without extending his local realism to nonlocal realism. So
he has done nothing new unless he can show some data in high energy physics that
only his theory can explain.
>
>
> >Example 2 is p. 9 May 2000 Physics Today "Entanglement of 4 particles"
> >with four beryllium ions, using a laser pulse "the four ions were driven
> >through their coupled motion into an entangled superposition of being
> >all spin down and all spin up .... the technique can be used to entangle
> >many more than four particles, with evident usefulness for quantum
> >information technologies .. Nature, 404, 256 (2000)
> >
> >i.e.
> >
> >|psi> = (1/sqrt2){|++++> + |---->}
> >
>
> Why would you think this was not included?
He only argues for the special case of the Pauli-exclusion principle. I see no
explict recognition of entanglement in general? If it is there which pages?
Which formulas?
>
>
> >
> >There are, obviously, an infinity of possible examples. Entanglements
> >of many-particle systems whose Bohm points move through configuration
> >space on a quantum de Broglie-Bohm pilot field landscape are much more
> >general than the very special case of the Pauli exclusion principle for N
> >identical elementary spinors.
>
> Who said they were identical?
>
> Your terminology: "Bohm points move through configuration space on a
> quantum de Broglie-Bohm pilot field landscape" seems to me to be just a
> colorful interpretation. I have no problem with the notions of "Bohm points"
> and "pilot fields". I agree that it is a useful intuitive model.
One that fits the pictures of complexity theory, neural nets, Kauffman's new
biology ...
> But they
> are not an intrinsic (nor empirically verifiable) part of the theory.
They are in the post-quantum case! That's my point! Yes, in the quantum case the
situation is moot as you say.
> That
> is why Bohm and other authors have consistently used the word
> "interpretation" rather than "theory". I know that you have attempted to
> extend quantum mechanics to what you call PQM and have subsumed
> this interpretation within your theory. But it is not Mendel Sachs intention
> (in QMGR, at least) to show that his theory necessary has a limit which
> is compatible with this sort of extension of quantum mechanics.
I know. My claim is that Mendel's claim of parsimony, that he does the same with
less is not justified.
>
>
> >
> >Mendel Sachs has simply given a heuristic plausibility argument that
> >there is no conceptual incompatibility between his nonlinear spinor
> >theory in 3D space and the conventional quantum formalism of entangled
> >states whose domain is classical mechanical configuration space and
> >whose range is the tensor products of the component Hilbert space of
> >wave functions of the separate parts that entangle into the organic
> >non-mechanical whole in the sense of Hermann Weyl, Bohm and Hiley
> >etc.
>
> In what sense is Sachs' argument in chapter 6 only heuristic? I think
> you need to read the rest of chapter 6.
Perhaps.
>
>
> > ...
> >[Page]
> >I think it is necessary to define carefully what is meant by "flat".
> >That is the essence of Shipov's theory based on A4 (which is
> >flat is a specific technical sense).
> >
> >[Jack]
> >
> >Mendel is very clear that he means "flat" in the sense of special
> >relativity. His book is interesting and has some interesting maverick
> >ideas worth thinking about. However, as I suspected, you oversold the
> >rigor of his argument that the fundamental theory is in 3D space and
> >that higher dimensional configuration space is not "funda-MENTAL"
> >(Hameroff's term). I am not at all persuaded by what I read. His
> >argument is quite weak logically IMO and what he sets out to prove is
> >not the general case of entanglement in quantum theory, but a special
> >case, albeit an important special case.
>
> Actually, Sachs' theory is expressed in a generalized Riemann space-
> time.
Yes, of course. That does not contradict what I said. His "vacuum" in only in
the flat spacetime of zero stress energy tensor. However there are curved vacuum
"geon" solutions when there is zero stress energy from real matter as in
Wheeler's "mass without mass".
> Mental phenomena and consciousness are certainly beyond the
> scope of the material in QMGR. I don't know whether they are beyond
> the scope of the theory. My opinion about the strength of his argument
> and what he intends to prove is quite different than yours. In the end, it
> isn't necessary that we should agree.
My claim here about PQM is that I can compute objective numbers
1 sec duration of conscious moment
10^18 critical qubit complexity to generate a conscious moment
5 milliwatts dissipation for each Hertz in the consciousness channel
all 3 above experimental numbers for objective correlates of consciousness
dependent on the observed Hubble flow
1/H = 13 billion years.
>
>
> >> ...
> >>Also Sach's does not have torsion although his "spin affine
> >>connection" may be generalized to torsion.
> >
> >[Page]
> >
> >I think it is equivalent. See especially Shipov's spinor representation
> >in chapter 6 of his book and eq. (6.30).
> >
> >[Jack]
> >
> >It cannot be if Shipov is consistent and knows what he is talking about.
> >I know, for certain, that Shipov fervently believes that his A4 torsion
> >field theory will permit an effective "anti-gravity" in the sense of
> >"flying saucer" reports. I have discussed this directly with Gennady
> >several times.
>
> What someone believes about flying saucer reports seems irrelevant
> to me (or at the very most: of very little value).
This is wrong. Physics is supposed to based on empirical evidence. Observations
of flying saucers are facts that need to be explained. One can argue particular
cases of course. You are like the Cardinals who refused to look through
Galileo's telescope.
> Physics is an empirical
> science. And the mathematical equivalence (or not) of Sachs' and
> Shipov's theories can be determined (in principle) completely within
> the realm of mathematics.
>
> >Therefore, Mendel and Gennady cannot be both correct on
> >this particular important point. That much I can say for sure.
> >
>
> What does this have to do with spin-affine connections versus
> torsion?
I said Sach's particular formula for the spin connection is Riemannian therefore
excludes torsion.
>
>
> >...
> > [Jack]
> >
> >>In that case, it is not clear if his conclusion of a positive definite
> >>inertial field ,i.e. no anti-gravity, will survive in the presence of
> >>torsion. That is, his conclusion that that the inertial field is the
> >>positive-definite modulus of a complex function may itself only
> >>be an approximation based on assumptions no longer true if
> >>torsion is present.
> >
> > [Page]
> >
> >It seems to me that this is equivalent to Shipov's eqs. (2.65) through
> >(2.72). I do not think that "no anti-gravity" is one of Mendel Sachs'
> >conclusions.
> >
> >[Jack]
> >
> >Sure it is. Sachs says, on basis that his inertial lambda field is the
> >intrinsically positive modulus of a complex function that gravitational
> >repulsion is not possible in principle.
>
> Where does he say that? On page 63 Sachs writes:
>
> "... the spinor matter field equations of the Dirac form are derived from
> a consideration of a particular mapping of time-reversed two-component
> spinor variables in a Riemannian space-time. The geometrical relation
> was seen to be in terms of a positive-definite field variable, gamma, since
> it is the modulus of a complex function. The implication of this result in
> general relativity theory, together with the principle of equivalence, is
> that gravitational forces, *in the Newtonian limit* of Einstein's field
> theory applied to gravity, can only be attractive -- thereby accounting
> for the empirical facts, in the Newtonian limit."
>
> It seems clear to me that he is not talking about the general case.
So you say that later on Sach's talks about antigravity? Where?
>
>
> >Also it is not at all clear that Mendel's particular form of the spin
> >affine connection is as general as Gennady's. Remember, Gennady's
> >corresponds to the anholonomic case in which the rotational 4D curl of
> >the tangent vector flow fields does not vanish. That is, the assumption
> >that
> >
> >dx^i = eu^i(q)dq^u
> >
> >is an exact differential corresponding to an integrable
> >
> >x^i = x^i(q)
> >
> >is false in the presence of anholonomic torsion fields corresponding to
> >non-Riemannian geometry.
>
> I do not see where Sachs' makes the assumption that dx^i (or the
> equivalent in his approach, the quaternion dL. See below) is an
> exact differential.
He assumes Riemannian geometry and Einstein's standard 1915 metric theory.
That's where.
>
>
> >It is quite obvious that Mendel did not include non-Riemannian
> >geometry, with plastic rotational torsion signaling breakup of
> >irrotational streamlines with good wavefront surfaces normal to
> >the streamlines, in his particular nonlinear spinor theory.
>
> What is "plastic rotational torsion signaling ..."? Your sentence is
> almost undecipherable to me.
You misinterpreted "signalling". I did not mean signaling with torsion fields -
another topic. There should have been a comma i.e.
"with plastic rotational torsion, signaling the breakup of
irrotational streamlines
I am referring to Haken Kleinert's point, where the difference between holonomic
elastic curvature Riemannian geometry and anholonomic plastic torsion
non-Riemannian geometry is analogous to the onset of turbulence in the breakup
of irrotational streamline flow in fluids. This becomes even more clear in V. I.
Arnold's topological hydrodynamics.
>
>
> But I think you are wrong when you say that Mendel Sachs theory does
> not generalize Riemannian geometry. Since in QMGR the subject is
> quantum mechanics and Sachs' route to that is through Dirac's equation,
> most of the material in QMGR is based on the special relativity limit of
> Sachs' general theory. His previous book "General Relativity and Matter"
> (GRM) deals in much more detail with the general case. However,
> chapter 4 and in particular section 4.3 "Spinor variables in general
> relativity" provides a quick overview of the general theory. Sachs points
> out that second rank spinors (such as used by Shipov in chapter 6 of
> his book) are algebraically equivalent to the quaternions.
>
> In GRM (page 59), Sachs writes the metric in the "factored" form:
>
> (3.58) dL = q^mu(x) dx_mu
>
> (3.59) ds^2 = dL dL~
>
> where q^mu(x) are a set of four quaternion field variables. dL~ is the
> quaternion conjugate of dL. Sachs calls dL "the invariant line element" -
> a generalization of what is usually meant by ds in the conventional theory.
> "Thus, dL is a geometric invariant, although is is algebraically a
> quaternion. The latter feature is equivalent to that of a second-rank
> spinor ... at each space-time point, dL has spin degrees of freedom in
> addition to its dependence on the space-time co-ordinates x."
Yes, but is dL integrable? That is, is there a "potential" L ( a finite
coordinate) of which dL is an exact differential with path-independence in going
from the differential to the finite?
That is, is there a non-trivial first order homology group in Sach's theory in
which the factor group of closed forms dL over exact forms dL' is non-trivial,
i.e. not the identity?
Einstein's torsion free diffeomorphic Riemannian geometry is the simply
connected homology with all closed 1 forms of the line element also exact forms.
Torsion gaps are from non-trivial multiply connected homology.
>
>
> If you refer to Shipov chapter 6, eq. (6.30), and eq. (5.11), you can see
> that this is equivalent to Shipov's "A4 in a spinor basis" which in turn
> is equivalent to conventional tetrad formulation (Shipov chapter 5).
>
> In section 3.13 of GRM, Sachs' develops quaternion calculus, for
> example, defining the "line integral" over dL. Of course there are
> conditions for the existence of such an integral. But if the integral
> exists, then the "path" defined by this integral is more general than
> that considered in Riemann geometry. Sachs writes:
>
> "... the path int(dL) is parameterized by a four element set, rather than
> a single element set {s}, as we have for the path of the standard
> formulation in Riemann geometry. That is, in the quaternion formulation,
> at each point along a path in space-time one needs four numbers
> (rather than one) to specify a further infinitesimal translation along
> this path. These four parameters then play the role of the (single time)
> parameterization of the Newtonian trajectory in Euclidean space, of
> the Einstein trajectory in the standard formulation of general
> relativity that utilizes the tensor calculus."
Begs the key question of integrability of dL - is there path independence or
not?
>
>
> "This generalization of the trajectories in a Riemann space, in terms
> of a 4-parameter set characterizing a generalized 'proper time' in
> terms of a quaternion algebra, was not introduced in an ad hoc fashion.
> It is a result of fully exploiting the symmetry group that underlies the
> general theory of relativity - and it appears in conformity with Hamilton's
> expectations when he invented the quaternion algebra ..."
Still begs the question.
>
>
> >...
> > [Jack]
> >
> >>In this regard, Basil Hiley's student M. R. Brown at Birkbeck, University
> >>of London has shown implicitly how the EM ZPF origin of inertia is a
> >>"momentum dispersion energy" of the Bohm "super-quantum potential"
> >>whose material "Bohm point" is the classical electromagnetic field
> >>configuration that includes the near fields as well as the far fields.
> >
> >[Page]
> >
> >I don't see how this relates to Sachs' theory.
> >
> >[Jack]
> >
> >Bohm's theory is a covering theory for the Haisch et-al theory. If
> >Mendel has a fundamental theory his theory must cover Bohm's.
>
> Bohm's *theory* is just conventional quantum mechanics. In that
> sense, Sachs' intends in QMGR to demonstrate that his theory does
> "cover" Bohms.
He fails to justify that goal IMO.
> Bohm's *interpretation* of this theory is of course
> quite different than the conventional Copenhagen interpretation, but
> the ontology (holism, the physical reality of the wavefunction, etc.)
> developed in Bohm's interpretation is surprisingly similar to that
> developed by Sachs' in relation to his own theory.
>
> That inertia has an "electromagnetic" explanation should hardly
> seem controversial in the context of Shipov's and Sachs' theories
> since both inertia and electromagnetism arise from the torsion
> of space.
A separate issue. Does Sachs claim an electromagnetic origin to gravity with
actual equations? Pages? Eq numbers? My purpose here was only the claim that
configuration space and permutation symmetry etc could be completely understood
in terms of 4D or 3D classical nonlinear field theory. I still think that is a
false claim.
>
>
> >This is by no means obvious. Also, Mendel's theory is admittedly
> >"deterministic". My theory transcends determinism for self-organizing
> >self-determination, hence conscious intent with morally responsible
> >free will is part of the post-quantum physical paradigm.
>
> This is beyond the scope of QMGR.
Agreed.
Jack
Bill Page wrote:
> Jack,
>
> On Friday, May 19, 2000 1:10 PM you wrote:
> >...
> >My only point is that there is no mathematical necessity to do what
> >Mendel did when he gets to the Pauli exclusion principle. In no sense
> >is he forced to do it by the structure of his nonlinear field theory whose
> >configurations are limited to 3D space unlike the Bohm quantum
> >potential Q.
>
> You are still missing the main point: The solution to Sachs' nonlinear
> field equations is a field defined over space-time. (My present contention
> is also that this is the same field defined by what Shipov calls the
> structural equations of A4, i.e. we have a 2nd rank spinor = quaternion
> field or equivalently an anholonomic tetrad defined over all space-time.)
> This is the essential content of Sachs' theory. Everything is ultimately
> to be described in terms of this field.
So what? It is one thing to say that you have a quaternion classical field over
all of spacetime, holonomic or not. It is quite another thing to say that one
can deduce, without any additional physical interpretive postulates, the
characteristic nonlocal entanglements and special permutation symmetries among
spatially separated soliton concentrations of this nonlinear classical field.
The key phrase here please note "without any additional physical interpretive
postulates" especially "without any". By the way, my objection here also applies
to Shipov's A4 theory as well as Sach's. The difference is that Shipov
acknowledges the correctness of my point here. My objection is general and
applies to any claim that a classical nonlinear local field theory written only
as a configuration in 3D space that evolves dynamically, can account for the
peculiar entanglements and special permutation symmetries that require a
nonclassical central objective role for both configuration space as domain and
for tensor products of single-particle Hilbert spaces as range for the
many-soliton solutions of the nonlinear field in 3D space. Now if one can show
how the subtratum of nonlinearity in 3D creates these nonlocal connections of
entanglement and special spin-dependent permutation symmetries for
indistinguishable solitons, that would be fine, but I see nothing like that even
remotely done mathematically in Sach's book. If I am wrong please point me to
the relevant mathematics?
>
>
> Sachs' argument is that *if* we make an approximation to these non-
> linear field equations as a linear system of differential equations, *then*
> they necessarily have the same Hilbert space form (expressed as
> wavefunctions over configuration space) as found in quantum mechanics.
I know that's what he says. However, I do not see that actually does it in any
convincing way beyond the additional postulates he makes, perhaps unconsciously,
that are the same in the standard theory.
>
> Again, this is his deduction: If we start with the full non-linear theory
> involving fields over just space-time *and* if we insist on the best
> linear approximation to these equations, then the result is quantum
> mechanics over configuration space.
Again I say this is an unjustified claim that my critical reading of Sach's text
does not support. I see no "there" there, no new parsimony or same with less in
terms of conceptually independent interpretive postulates needed to get from 3D
field theory to configuration space as used in standard quantum theory for
several particles whether indistinguishable or not.
> In other words: configuration
> space in quantum mechanics is just the way that quantum mechanics
> uses to cope with the fact that the underlying phenomena is essentially
> non-linear.
That's a nice idea, but I see no convincing rational proof or even coherent
argument why it might be true from Sach's Ch 6. I am not saying it is not true
only that I cannot follow Sach's argument that it is true sans additional
postulates.
>
>
> Similarly to Bohm's quantum potential, the functional PSI in eq. (6.1.5)
> in QMGR "is a limiting form of a functional which, generally, represents
> a [non-local] connective relation between the elements of the set of
> solutions {Psi^(u)}of the coupled nonlinear equations (6.1.1')."
Correct, and that's my point. There is no justification for that functional
apart from the usual postulates made in quantum theory. Sachs sticks it in
through the back door like in a shell game. As soon as he posits that he is no
longer strictly using a local 3D field theory. Nonlinearity makes no difference
here.
>
>
> >He simply puts in the quantum superposition principle in configuration
> >space ad hoc as a postulate, same as everyone else does since it
> >is required to agree with experiments.
>
> It is not a postulate of Mendel Sachs' theory.
Sure it is, though he may not be conscious that he makes it. As soon as you
admit "Similarly to Bohm's quantum potential" it's check mate and you lost.
>
>
> >I see no justification for any claim that Sach's nonlinear spinor field
> >theory in 4D space-time derives quantum theory's reliance on
> >configuration space and entangled states in Hilbert space as a
> >limiting case for small energy-momentum transfers between the
> >separated pieces of the whole.
>
> Sachs' theory starts with the assumption that everything is represented
> by a single field defined over space-time by a set of non-linear field
> equations.
And he is inconsistent as soon as he introduces "a functional which, generally,
represents
a [non-local] connective relation between the elements of the set of
solutions {Psi^(u)}of the coupled nonlinear equations (6.1.1')."
> Thus it has the notion of "entangled states" built-in from the
> very beginning. If there is only one field, then everything must somehow
> be an aspect of this single field.
Depends what you mean by "somehow". Lots swept under the rug in that "somehow".
If the "somehow" is limited to retarded signals along the forward light cone
then it won't work. Sachs does admit advanced solutions along the past light
cone and from that he needs to show explicitly how entanglements and permutation
symmetries arise. For example, he needs to show how the spin-statistics
connection emerges from his theory, and why other parastatistics (Young patterns
with mixed permutation symmetries) may arise in lower space dimensions like in
quantum wells, wires and dots.
> All of these (approximately separate)
> aspects are necessarily entangled (contingent on each other) to the
> extent required by the fact that the field as a whole is a solution of the
> field equations.
Handwaving. Not good enough.
>
>
> >The quantum superposition principle (summing weighted products of
> >single-particle eigenfunctions of relevant observables) is a separate
> >postulate not already demanded by his prior formulation of his theory.
>
> I agree. It is also not required in his theory. It is only required in the
> linear approximation to his theory that is quantum mechanics.
There is no evidence whatsoever, that quantum theory is violated in the specific
sense of his theory. Correct me if I am wrong.
>
>
> >
> >> >[Jack]
> >> >
> >> >Yes, that's what Sachs does at the crucial step. It's the same thing
> >> >everyone does.
> >> [Bill Page]
> >> No. The important steps come before this. It is the fact that the
> >> coupled non-linear field equations can be represented in certain
> >> cases (approximately) as uncoupled linear equations that is the
> >> crucial step.
> >
> >This is trivial and obvious and in no way impinges on my point.
> >To show uncoupled linear equations in a certain limit, is not, by any
> >stretch of the imagination, a logical justification for the necessity of
> >introducing "entanglement", i.e coherent superposition of products
> >of single particle functions whose domain is configuration space
> >and whose range is the tensor product of irreducible representations
> >of single particle systems as shown in detail, for example, by Hermann
> >Weyl in "Theory of Groups in Quantum Mechanics" (Dover).
>
> No, this is wrong. The entanglement is introduced by Sachs in the initial
> formulation of his nonlinear field equations. That is can be expressed
> (approximately) as a "coherent superposition of products of single particle
> functions whose domain is configuration space and whose range is the
> tensor product of irreducible representations of single particle systems"
> is what Sachs demonstrates in chapter 6.
Well then there is no disagreement. You just admited Sachs postulates it. The
whole debate here is similar to earlier attempts to derive Euclid's fifth
postulate of a unique parallel to a line passing through a point not on the line
from his first 4. This could not be done and so non-Euclidean geometries were
discovered leading to Riemannian and non-Riemannian geometries. Similarly, you
seemed to be claiming that the postulate of configuration space and its
entanglements and permutation symmetries (in special cases) were not like
Euclid's fifth independent postulates, but were theorems provable from a purely
local nonlinear classical field theory with localized particle like soliton
solutions from the nonlinearity. This you and Sachs have not done IMO.
>
>
> > ...
> >However, the claim in the quantum many-body problem is more than that.
> >First of all, it is never claimed, as Mendel claims, that the energy-
> >momentum transfers between the particles is "weak'.
>
> Mendel Sachs claims that his theory and quantum mechanics make essentially
> the same predictions when the energy-momentum transfers between "particles"
> is weak. He says the predictions of the two theories will differ in the case
> of stronger interactions.
Give a specific example that is testable in principle. Even if such an example
is given, it really does not prov, without further analysis, that generic
entanglements and specialized permutation symmetries are provable from only a
local nonlinear classical field, even if it is a quaternion field. That is, it
does not prove that 3D is more fundamental than configuration space in more
space dimensions.
>
>
> >It is never claimed that there are separate uncoupled equations one for
> >each particle. Indeed, that defeats the very idea of the many-body problem
> >in orthodox quantum physics as shown in any standard text book on the
> >subject.
>
> Sachs makes no such claim.
Then what is his claim? I think we are spinning our wheels on this. His claim is
very vague and carries no logical necessity to my mind.
>
>
> >...
> >The quantum superposition principle in the Galilean relativity many-body
> >problem is
> >
> >
> >PSI(x1,x2,x3, ... xN, t) = Sum i1.... iN C(i1.... iN)
> >fi1(x1,t)fi2(x2,t)fi3(x3,t).... fiN(xN,t)
> >
> >
> >This is obviously a physically independent new postulate not at all
> >dependent on any approximation of uncoupled equations.
>
> This is not a postulate of Sachs theory.
So you claim it is a theorem? Where is the proof?
>
>
> >
> >This is general. In addition, if you want the Pauli exclusion principle you
> > need to add still more postulates!
>
> Sachs shows in chapter 6 is mathematical detail that this is not true.
No he did not. All he did there is some vague handwaving. There is no rigorous
proof there to my mind. Only a kind of shell game that pretends to be different
from the standard intepretive postulates but in fact is not different according
to my standards of rigor.
>
>
> >
> >You need to add the notion of nonlocal permutation symmetry from the
> >irreducible representations of the finite symmetric group SN for which
> >there are many Young Patterns of parastatistics.
>
> These are a consequences of the specific non-linearity of the theory.
Show me in special cases. Show me parastatistics in spaces of lower space
dimensions as are now done routinely experimentally in solid state physics
"anyons". That is show, in Sach's theory, how the dimensionality of space
affects the permutation symmetry.
Also, prior to that, show why the basic spin 1/2 solitons of the nonlinear 3D
field must have complete antisymmetry rather than complete symmetry? Show that
without adding new postulates to the theory. I say it cannot be done.
>
>
> >
> >Then you need to specialize. You need to impose complete antisymmetry
> >(a particular Young Pattern of a single row of boxes in the usual notation)
> >for identical fermions.
>
> You are correct that this is an additional postulate in conventional
> quantum mechanics.
And in Sach's theory as well. All he did was to handwave on this point.
>
>
> >
> >None of this is in Mendel's theory in 3D space. Its role is not even
> >recognized by him at least as far as I read to Ch 6 in his book. For
> >this reason his claim and yours is completely naive mathematically
> >as a look at Weyl's classic book on the subject clearly shows.
> >
>
> You need to study the rest of chapter 6 more carefully.
>
> >> ...
> >> >Bill Page oversold the reality when he said that Mendel Sachs proved
> >> >that configuration space is not a fundamental quantum concept but can
> >> >be derived from classical theory in ordinary space.
> >>
> >> When did I say that configuration space can be derived from classical
> >> theory? I don't believe that I did.
> >
> >Oh, I thought you did. I thought that was the whole point. If that's not
> >what you claimed, then I do not know what the dispute was about?
>
> You do not seem to be willing to consider Mendel Sachs' theory
> as a viable alternative to quantum mechanics.
I am willing to consider it, but, so far, I see no convincing rational argument
that it is so. All I see is handwaving and unconscious adoption of postulates.
>
>
> > It is clearly what Mendel is claiming I think.
>
> I don't think so.
>
> >
> >> Also, I never argued whether not configuration space was "a fundamental
> >> quantum concept". Certainly it plays a fundamental role in quantum
> >> theory. What I said was (more or less) that it apparently wasn't a
> >> fundamental *physical* concept, i.e. that acceptable and sufficiently
> >> complete (relative to conventional general relativity and quantum
> >> mechanics) theories exist (such as Mendel Sachs' theory) that do not
> >> incorporate configuration space as a fundamental concept.
> >
> >A delicate distinction! (Gilbert and Sullivan)
> >
>
> Not so subtle, I think. You only need to have less of an intellectual
> commitment to only one theory. Physics is a complex subject. All
> answers are provisional.
>
>
Indeed, including Mendel's. :-)
Jack
Paul Zielinski wrote:
>
>
>
> > > Jack,
> > >
> > > On Friday, May 19, 2000 10:33 AM you wrote:
> > > >
> > > >
> > > >
> > > >> Jack wrote:
> > > >>
> > > >> > Stronger. Mendel simply makes the Ansatz ad hoc
> > > >> >
> > > >> > psi(x1,t) psi(x2,t) ... psi(xN,t) after some neither there nor here
> > > >> > handwaving IMHO.
> > > >>
> Paul Zielinski wrote:
> > > >> Well, *mathematically* we can form products of one-particle states and
> > > >> apply the superposition principle to those product functions. Since the
> > > >> resulting correlated N-particle states will then automatically satisfy a
> > > >> Schrodinger equation, this suggests a rather natural interpretation of
> > > >> the N-particle psi function as a *physical wave* that propagates in the
> > > >> N-particle configuration space. I imagine it is this *physical* aspect
> > > >> that you have in mind here.
> > > >
> > > Bill Page wrote:
> > > I think Paul used the correct keyword here: interpretation. Such an
> > > interpretation goes beyond the requirements of the theory.
> > Jack wrote:
> > I am not sure what the argument is in that case. My only point is that there is
> > no mathematical necessity to do what Mendel did when he gets to the Pauli
> > exclusion principle. In no sense is he forced to do it by the structure of his
> > nonlinear field theory whose configurations are limited to 3D space unlike the
> > Bohm quantum potential Q.
> Paul Zielinski wrote:
> This is an important point about Bohmian theory: in TUU the quantum potential is
> defined in such a way that it provides an integral physical basis for quantum entanglement,
> as opposed to applying the superposition principle to many-body wavefunctions
> in a purely formal *ad hoc* manner.
>
> At the same time, it is hard to see how Bohmians can claim that the symmetrization
> postulate (including the Pauli principle) "drops out" of their theory.
[Jack]
I am not aware that they make such a claim? My understanding is that the spin-statistics
connection is simply assumed as an independent postulate in the Bohm ontology.
Paul Zielinski wrote:
> As far as I
> am aware this was never satisfactorily explained in Bohmian terms -- although of
> course Bohmian theory is no worse off in that respect than is conventional QM.
[Jack]
Agreed.
>
> > He simply puts in the quantum superposition principle
> > in configuration space adhoc as a postulate, same as everyone else does since it
> > is required to agree with experiments.
Paul Zielinski wrote:
> So in this respect Sachs is pulling even?
[Jack]
No, because according to Bill Page, Sach's claim is much stronger. He claims to be deriving
Pauli principle, though even if he does that is not good enough to cover all the nonlocal
quantum phenomena.
>
> [Jack]
> > I see no justification for any claim that
> > Sach's nonlinear spinor field theory in 4D spacetime derives quantum theory's
> > reliance on configuration space and entangled states in Hilbert space as a
> > limiting case for small energy-momentum transfers between the separated pieces
> > of the whole.
> Paul Zielinski wrote:
> I think this is too strong. Sachs need only claim that the *numbers* agree in the
> limiting case. The theoretical meaning of those numbers may be quite different in his
> framework. As long as he can reproduce the correlations associated with
> quantum entanglement on an empirical level, any introduction of configuration
> space in order to express those correlations may simply be a matter of
> mathematical convenience, as opposed to playing an essential physical role as
> in Bohmian theory.
>
> > The quantum superposition principle (summing weighted products of
> > single-particle eigenfunctions of relevant observables) is a separate postulate
> > not already demanded by his prior formulation of his theory.
Paul Zielinski wrote:
> Yes, but I believe Sachs' burden is only to show how the empirical success
> of the QM formalism is *not inconsistent* with his theory.
[Jack]
I have no problem with that. In fact that is what I think is the valid part. However, Bill Page
at least, insists on a much stronger claim.
Paul Zielinski wrote:
> Evidently, his premise
> is that the success of the quantum superposition principle is an artifact of a linear
> approximation to a fundamentally non-linear theory of nature.
[Jack]
Yes. However, "linear" is used in different ways. The Hamiltonian is highly nonlinear in the
second quantized field operators , yet the Hamiltonian is a linear operator on the Fock space
whose basis are the number eigenstates in which the superposition principle applies. I think
Page and Sachs may be confounding these two different meanings of "linear"/"nonlinear" and
"superposition". Classical nonlinearity does not imply quantum nonlinearity as my example here
shows. You can have a nonlinear classical field theory that maps into a linear quantum field
theory. The classical nonlinear terms map to scatterings and absorptions and emissions of the
field quanta, but these terms are still linear operators in the Fock space!
The Landau-Ginzburg model is different. There you do have nonlinear partial differential
equations of the order parameter. You can even map that into the linear second quantized
picture however.
>
>
> > > >[Jack]
> > > >
> > > >Yes, that's what Sachs does at the crucial step. It's the same thing
> > > >everyone does.
> > >
> > > No. The important steps come before this. It is the fact that the
> > > coupled non-linear field equations can be represented in certain
> > > cases (approximately) as uncoupled linear equations that is the
> > > crucial step.
> >
> > This is trivial and obvious and in no way impinges on my point. To show
> > uncoupled linear equations in a certain limit, is not, by any stretch of the
> > imagination, a logical justification for the necessity of introducing
> > "entanglement", i.e coherent superposition of products of single particle
> > functions whose domain is configuration space and whose range is the tensor
> > product of irreducible representations of single particle systems as shown in
> > detail, for example, by Hermann Weyl in "Theory of Groups in Quantum Mechanics"
> > (Dover).
>
> No, but it may show that the additional independent hypothesis can be consistently
> joined with his theory.
[Jack]
Yes, this is exactly what I say is really going on, but Page disputes that.
[Paul]
> That is not insignificant, even if what you say is correct.
[Jack]
OK, agreed.
[Paul]
> Right.
[Jack]
Page disputes this point because it knocks the wind out of Sach's sails - or should I say
"sales"? $168 a book! :-)
>
> [Jack]
> > You need to add the notion of nonlocal permutation symmetry from the irreducible
> > representations of the finite symmetric group SN for which there are many Young
> > Patterns of parastatistics.
[Paul]
>
> First you impose the "indistinguishability postulate": [A, P] = 0 for any observable
> A and any permutation P of N identical particles, on the *observables*. I think
> it is important to recognize that this an *assumption*, contrary to what is asserted
> in most textbooks.
[Jack]
Yes, that is one of my points here.
>
> [Paul]
> This fractures the incoherent N-particle Hilbert space into quasi-coherent subspaces
> between which the relative phases of state vectors are not measurable in principle. It
> also implies that the dynamics of the system cannot transform the N-particle psi
> function from one such subspace to another, since the Hamiltonian is an observable.
[Jack]
Right, so this is "broken supersymmetry".
>
> [Jack]
> > Then you need to specialize. You need to impose complete antisymmetry (a
> > particular Young Pattern of a single row of boxes in the usual notation) for
> > identical fermions.
[Paul]
> The only *fully coherent* subspaces of the raw N-particle Hilbert space are those
> transforming as one-dimensional IR's of the permutation group S[N], and there is no
> complete set of commuting observables in the higher subspaces (i.e. those transforming
> as higher-dimensional IR's of S[N]). This leads to serious ambiguities in the physical
> interpretation of the more complex symmetry species which it appears can only be
> resolved by a deeper theory of quantum measurement.
>
> > None of this is in Mendel's theory in 3D space. Its role is not even recognized
> > by him at least as far as I read to Ch 6 in his book. For this reason his claim
> > and yours is completely naive mathematically as a look at Weyl's classic book on
> > the subject clearly shows.
>
> Although you must agree that there is also a strong element of "ad hocness" in
> the alternatives on this issue.
[Jack]
Of course, and I have been saying this. But the others make no pretense to such intellectual
elegance, parsimony and scholarship sublime as Page did for Sachs.
>
>
> > > >In no sense is he logically forced to do it by his nonlinear field theory
> > > >in 3D space. It is a logically independent postulate he adds ad hoc to
> > > >his theory.
> > >
> > > It is not a postulate of Sachs' theory.
> >
> > It is if one wants to make sense of his theory as I show above.
> >
> > >
> > >
> > > >Bill Page oversold the reality when he said that Mendel Sachs proved
> > > >that configuration space is not a fundamental quantum concept but can
> > > >be derived from classical theory in ordinary space.
> > >
> > > When did I say that configuration space can be derived from classical
> > > theory? I don't believe that I did.
> >
> > Oh, I thought you did. I thought that was the whole point. If that's not what
> > you claimed, then I do not know what the dispute was about? It is clearly what
> > Mendel is claiming I think.
>
[Paul]
>
> He may be claiming something just a little different -- as per my remarks above.
[Jack]
You can come over some time to look at the book it's not mine. We need to distinguish Page's
claim about Sachs from Sachs I agree.
>
>
> > > Also, I never argued whether not
> > > configuration space was "a fundamental quantum concept". Certainly
> > > it plays a fundamental role in quantum theory. What I said was (more or
> > > less) that it apparently wasn't a fundamental *physical* concept, i.e.
> > > that acceptable and sufficiently complete (relative to conventional
> > > general relativity and quantum mechanics) theories exist (such as
> > > Mendel Sachs' theory) that do not incorporate configuration space
> > > as a fundamental concept.
> >
> > A delicate distinction! (Gilbert and Sullivan)
> >
> > >
> > >
> > > >The difference in the classical and quantum roles of configuration space
> > > >is in Bohm's quantum potential specifically in the nonseparability of
> > > >Bohm's quantum potential when there is entanglement, in its form-
> > > >dependence, its intensity-independence, its nonlocality, and its non-
> > > >mechanical context dependence i.e. no pre-assigned interactions
> > > >among the entangled source particles and force fields as in classical
> > > >physics.
> > >
> > > The same nonseparability occurs in Mendel Sachs' field theory.
>
> If Sachs can get any kind of entanglement effect out of his theory without
> relying on ad hoc assumptions that would be something.
[Jack]
I agree it would be stupendous. In fact, he has done no such thing IMO.
>
>
> > > Regards,
> > > Bill Page.
> > >
> > > PS. For your reference I attach the email where I think this thread
> > > started. I still stand by what I said then.
> >
> > Well I do not understand the significant difference in your
> >
> > "What I said was (more or
> > less) that it apparently wasn't a fundamental *physical* concept, i.e.
> > that acceptable and sufficiently complete (relative to conventional
> > general relativity and quantum mechanics) theories exist (such as
> > Mendel Sachs' theory) that do not incorporate configuration space
> > as a fundamental concept."
> >
> > Perhaps Paul Zielinski can figure out the difference?
>
> Vide supra...
>
> Paul Zielinski
Jack
Paul Zielinski wrote:
>
>
> [Page]
> > Sachs' theory starts with the assumption that everything is represented
> > by a single field defined over space-time by a set of non-linear field
> > equations. Thus it has the notion of "entangled states" built-in from the
> > very beginning.
[Jack]
Let's focus on these two above sentences. I think Bill is totally confused here.
Let f(xyzt) be the classical field over spacetime (xyzt) linear or nonlinear. There
is some mapping q of f to a Hilbert space h(1) of single-particle quantum wave
functions that form a basis psik(xyz) for this Hilbert space. The total energy of
the classical field f maps to a field Hamiltonian H that becomes a linear operator
on the Hilbert space. The amount of classical nonlinearity reflected in the
Hamiltonian H is completely irrelevant. Neither Page nor Sachs seem to understand
this mathematical idea.
We have not yet gotten to entanglement!
To review:
Start with classical field f(xyzt) whose nonlinearity is as strong as one likes.
Quantize that classical field. This gives a field-Hamiltonian H (i.e. a 3D space
integral of a quantum field Hamiltonian density) with nonlinear terms i.e. products
of the classical field now transformed to a quantum operator. The field theory is
"local" if these nonlinear products in the Hamiltonian density are at the same
spacetime events. A truly nonlocal field theory would have nonlinear field products
connecting different events in spacetime. Sachs makes no such claim!
Now to get to generic entanglement, without specializing to Paul exclusion
principle, form tensor products of the Hilbert space
h(2) = h(1)xh(1)
h(3) = h(1)xh(1)xh(1)
etc.
For example, a possible entangled pair state |2> in h(2) is of the form, in the
configuration space representation
<xyz,x'y'z',t|2> = Sum over k of ck(t) psik(xyz)psik(x'y'z')
There is no way to derive this deductively from Sach's model alone IMO.
> [Paul]
>
> At least it has the potential for entanglement effects built into its core
> physical assumptions. Whether we can actually get the correspondence
> equivalent of quantum entanglement out of Sachs' theory is a more
> difficult question.
> [Page]
> > If there is only one field, then everything must somehow
> > be an aspect of this single field. All of these (approximately separate)
> > aspects are necessarily entangled (contingent on each other) to the
> > extent required by the fact that the field as a whole is a solution of the
> > field equations.
[Jack]
"Spare me from metaphysics!" Newton -- and excess verbal baggage. Page's remark
yearns, as if yearning replaces learning, but the precise problem here needs to be
mathematically expressed as I have begun to do above.
>
> >
> > >The quantum superposition principle (summing weighted products of
> > >single-particle eigenfunctions of relevant observables) is a separate
> > >postulate not already demanded by his prior formulation of his theory.
> >
> > I agree. It is also not required in his theory. It is only required in the
> > linear approximation to his theory that is quantum mechanics.
>
[Paul]
> By correspondence. Sorry, don't mean to labor this point, but I think
> that is the meta-theoretic key to this dispute.
[Jack]
I have already said as much, but Page persists in disputing this point.
>
>
> > >> >[Jack]
> > >> >
> > >> >Yes, that's what Sachs does at the crucial step. It's the same thing
> > >> >everyone does.
> > >> [Bill Page]
> > >> No. The important steps come before this. It is the fact that the
> > >> coupled non-linear field equations can be represented in certain
> > >> cases (approximately) as uncoupled linear equations that is the
> > >> crucial step.
> > >
> > >This is trivial and obvious and in no way impinges on my point.
> > >To show uncoupled linear equations in a certain limit, is not, by any
> > >stretch of the imagination, a logical justification for the necessity of
> > >introducing "entanglement", i.e coherent superposition of products
> > >of single particle functions whose domain is configuration space
> > >and whose range is the tensor product of irreducible representations
> > >of single particle systems as shown in detail, for example, by Hermann
> > >Weyl in "Theory of Groups in Quantum Mechanics" (Dover).
> >
[Page]
> > No, this is wrong. The entanglement is introduced by Sachs in the initial
> > formulation of his nonlinear field equations. That is can be expressed
> > (approximately) as a "coherent superposition of products of single particle
> > functions whose domain is configuration space and whose range is the
> > tensor product of irreducible representations of single particle systems"
> > is what Sachs demonstrates in chapter 6.
[Jack]
Which is to say that Sachs has not done anything really new or parsimonious. He
simple sticks in configuration space entanglement adhoc at the beginning. Where
exactly do you say he does that? What exact page and line? Also, you say
"approximately" I say no such qualification is needed. This is a significant
difference of principle.
>
> >
> > > ...
> > >However, the claim in the quantum many-body problem is more than that.
> > >First of all, it is never claimed, as Mendel claims, that the energy-
> > >momentum transfers between the particles is "weak'.
[Jack]
Well you are wrong. I quote Sachs
"following as a necessary consequence of its axioms ... a set of coupled, nonlinear
spinor field equations, that has an asymptotic limit that corresponds to the
many=particle quantum mechanical theory. The limit corresponds to the assumption of
sufficiently small energy-momentum transfer among the component elements ..." p. 39
Ch 3
Now Bill do you mean to quibble that "small" is not the same as "weak"? So it is
"never claimed"? I caught you with your pants down and your hand in the cookie jar
on this one.
>
> >
> > Mendel Sachs claims that his theory and quantum mechanics make essentially
> > the same predictions when the energy-momentum transfers between "particles"
> > is weak. He says the predictions of the two theories will differ in the case
> > of stronger interactions.
[Jack]
More bait and switch - a real shell game.
[Paul]
>
> So that the empirical content could find expression in terms of an N-body
> configuration space and an extended superposition principle, although such
> elements are not native to Sach's theory. That would make sense to me.
[Jack]
Agreed, but that is not what is being claimed.
>
>
> > >It is never claimed that there are separate uncoupled equations one for
> > >each particle. Indeed, that defeats the very idea of the many-body problem
> > >in orthodox quantum physics as shown in any standard text book on the
> > >subject.
> >
> > Sachs makes no such claim.
> >
> > >...
> > >The quantum superposition principle in the Galilean relativity many-body
> > >problem is
> > >
> > >
> > >PSI(x1,x2,x3, ... xN, t) = Sum i1.... iN C(i1.... iN)
> > >fi1(x1,t)fi2(x2,t)fi3(x3,t).... fiN(xN,t)
> > >
> > >
> > >This is obviously a physically independent new postulate not at all
> > >dependent on any approximation of uncoupled equations.
> >
> > This is not a postulate of Sachs theory.
[Jack]
If it's not a postulate, then it must be a theorem. Where is the proof the theorem
from a purely local 3D model? If it is not in Sach's theory at all, then Sach's has
not reproduced quantum theory as claimed.
>
> >
> > >
> > >This is general. In addition, if you want the Pauli exclusion principle you
> > > need to add still more postulates!
> >
> > Sachs shows in chapter 6 is mathematical detail that this is not true.
> >
> > >
> > >You need to add the notion of nonlocal permutation symmetry from the
> > >irreducible representations of the finite symmetric group SN for which
> > >there are many Young Patterns of parastatistics.
> >
[Page]
> > These are a consequences of the specific non-linearity of the theory.
>
> OK *that* I would really like to see.
[Jack]
So would I, but there is nothing there. Page is speaking through his hat, blowing
hot air. There is no reference to SN in the index, no reference to Young Patterns
or parastatistics.
[Paul]
> It is significant enough that regardless
> of how it comes out mathematically, it would be an interesting result. So IMO
> it is probably worth the effort to grok his math.
[Jack]
Page's promise is not kept.
>
>
> > >
> > >Then you need to specialize. You need to impose complete antisymmetry
> > >(a particular Young Pattern of a single row of boxes in the usual notation)
> > >for identical fermions.
> >
> > You are correct that this is an additional postulate in conventional
> > quantum mechanics.
>
> So everyone agrees on that.
>
> > >None of this is in Mendel's theory in 3D space. Its role is not even
> > >recognized by him at least as far as I read to Ch 6 in his book. For
> > >this reason his claim and yours is completely naive mathematically
> > >as a look at Weyl's classic book on the subject clearly shows.
> > >
> >
> > You need to study the rest of chapter 6 more carefully.
[Jack]
I have tried to no avail. You need to explain it clearly.
>
> >
> > >> ...
> > >> >Bill Page oversold the reality when he said that Mendel Sachs proved
> > >> >that configuration space is not a fundamental quantum concept but can
> > >> >be derived from classical theory in ordinary space.
> > >>
> > >> When did I say that configuration space can be derived from classical
> > >> theory? I don't believe that I did.
> > >
> > >Oh, I thought you did. I thought that was the whole point. If that's not
> > >what you claimed, then I do not know what the dispute was about?
> >
> > You do not seem to be willing to consider Mendel Sachs' theory
> > as a viable alternative to quantum mechanics.
>
[Paul]
>
> Again, I think the communication problem here revolves around the
> correspondence realationship between the limiting cases of Sachs' theory
> and the configuration-space expression of quantum entanglement.
[Jack]
Correct. Also, I am beginning to think that Sachs has simply garbled the two
distinct meanings of "nonlinearity/linearity" and "superposition" in the passage
from classical physics to quantum physics. In general classical nonlinearities
violating classical superposition map to quantum linear operators with quantum
superposition/entanglement. The classical nonlinearites are simply scattering terms
in the Hamiltonian that is a linear operator on the Hilbert space.
In special cases of emergence of phase-coherent order parameters from collective
motions, like superconductivity, lasers, and non-equilibrium synergetics (Haken)
one has effective nonlinear partial differential equations to solve for these
collective many-particle modes.
>
>
> > > It is clearly what Mendel is claiming I think.
> >
> > I don't think so.
> >
> > >
> > >> Also, I never argued whether not configuration space was "a fundamental
> > >> quantum concept". Certainly it plays a fundamental role in quantum
> > >> theory. What I said was (more or less) that it apparently wasn't a
> > >> fundamental *physical* concept, i.e. that acceptable and sufficiently
> > >> complete (relative to conventional general relativity and quantum
> > >> mechanics) theories exist (such as Mendel Sachs' theory) that do not
> > >> incorporate configuration space as a fundamental concept.
> > >
> > >A delicate distinction! (Gilbert and Sullivan)
> > >
> Paul Zielinski
> But an important one.
[Jack]
What Page says is false. That is, it is not true that "acceptable and sufficiently
> >> complete (relative to conventional general relativity and quantum
> >> mechanics) theories exist (such as Mendel Sachs' theory) that do not
> >> incorporate configuration space as a fundamental concept."
>
>
>
>
> > Not so subtle, I think. You only need to have less of an intellectual
> > commitment to only one theory. Physics is a complex subject. All
> > answers are provisional.
>
> >
> >
> > Regards,
> > Bill Page.
Jack
Paul Zielinski wrote:
>
> > [Jack]
> > Yes, and my point is that this is an independent postulate beyond 3D space + 1D time
> > as the fundamental arena for physics. Sachs slips it in through the back door in his
> > I think third postulate though in an obscure way which still leaves a false
> > impression that his theory is pure 3D + 1D.
>
> Well, either he does, or he doesn't. But for sure, if he does not offer a solid
> mathematical proof, he is not even wrong here.
[Jack]
Right.
>
>
>
> > [Jack]
> >
> > No, this is completely irrelevant. I know Sachs thinks it is a profound insight. I do
> > not. My claim is that entanglement, i.e. coherent superposition of products of
> > one-particle eigenfunctions of observable one-particle linear operators on Hilbert
> > space with complex number weights, does not depend on any such weak-coupling limit as
> > Sachs claims without any relevant justification.
> >
> > >
> > >[Page]
> > > This is one of the many interesting things that come out of non-linear
> > > mechanics.
[Jack]
Would that it were so. Show me. How?
>
>
> >
> > [Jack]
> > What is also unclear, in fact what I think is false, is Sachs allegation that "EPR
> > entanglement and permutational symmetry effects" are consequences of a weak coupling
> > limit with small energy-momentum transfers among the parts of the whole. That, to me,
> > is an implausible conjecture.
> [Paul]
>
> However implausible, the question is can he do it mathematically.
[Jack]
I see no evidence that he did. Perhaps you will if you read the book.
[Paul]
> It is a purely
> mathematical question, once his core physical principles are articulated. The
> proper approach here is to grok the math and decide the issue before jumping
> in at the deep end.
[Jack]
I tried. Your turn.
>
>
> > Suppose I have a Galilean relativistic nonlinear partial differential equation in the
> > variables xyz, x'y'z' and t I can posit an entangled solution of the form
> >
> > PSI( xyz, x'y'z' t) = Sum j = 1 to n cn(t) fn(xyz)gn(x'y'z')
> >
> > without requiring any weak coupling between terms depending on xyz and terms
> > depending on x'y'z' in the structure of the nonlinear partial differential equation.
> >
> > Indeed, suppose I had one particle in 3D space, why not turn Sachs's argument in on
> > itself and say we need "weak coupling" between the x, y, and z degrees of freedom of
> > the same particle! This clearly shows that his argument is nonsense IMO.
> >
> > True, we cannot use the classical superposition principle in a nonlinear equation in
> > the sense that the linear superposition of separate solutions to the nonlinear
> > equation is still a solution. However that is not the essential physical meaning of
> > the quantum entanglement principle. That is, whether or not the separate terms
> >
> > cn(t) fn(xyz)gn(x'y'z')
> >
> > in the sum are individually solution of the nonlinear equartion is physically
> > irrelevant.
> >
> > There are subtle physical differences in the use of "superposition" in classical and
> > quantum physics.
>
> The essential physical meaning of entanglement is the ability to alter correlations
> between the results of measurement on well-separated components of a quantum
> system where there can be no question of a physical disturbance in the conventional
> sense. It is not clear that this effect can *only* be accounted for by reference to
> N-body configuration space, which is what you seem to claim.
[Jack]
There is no formal alternative to configuration space as the domain of entangled states for
N separated particles. Show me a mathematical counter example to what I just said.
Given the pair entangled state
|A,B> = (1/2^1/2)[|A+>|B+> + |A->|B->]
The "position representation" is formally meaningless without 6D "configuration space" i.e.
xyz,x'y'z' beyond ordinary classical 3D space. That is,
<xyz,x'y'z't|A,B> = (1/2^1/2)[<xyzt|A+><x'y'z't|B+> + <xyzt|A-><x'y'z't|B->]
The entanglement persists with observable physical consequences violating local realism
even when there is no common support, no overlaps between the separated wave packets
<xyzt|A> and <x'y'z't|B> etc. as shown by John Bell and later others as in GHZ quantum
teleportation beyond the statistical limitations of Bell's locality inequality. Now,
formulate that without configuration space!
>
>
> > > > >In no sense is he logically forced to do it by his nonlinear field theory
> > > > >in 3D space. It is a logically independent postulate he adds ad hoc to
> > > > >his theory.
> > > >
> > > > It is not a postulate of Sachs' theory.
> > > >
> > > > >Bill Page oversold the reality when he said that Mendel Sachs proved
> > > > >that configuration space is not a fundamental quantum concept but can
> > > > >be derived from classical theory in ordinary space.
> > > >
> > > > When did I say that configuration space can be derived from classical
> > > > theory? I don't believe that I did. Also, I never argued whether not
> > > > configuration space was "a fundamental quantum concept". Certainly
> > > > it plays a fundamental role in quantum theory. What I said was (more or
> > > > less) that it apparently wasn't a fundamental *physical* concept, i.e.
> > > > that acceptable and sufficiently complete (relative to conventional
> > > > general relativity and quantum mechanics) theories exist (such as
> > > > Mendel Sachs' theory) that do not incorporate configuration space
> > > > as a fundamental concept.
> > >
> > > I think it is important to acknowledge that configuration space can be
> > > understood as a purely mathematical artifice, no different from any other
> > > abstract compound coordinate space (like, say, an RGB color space); *or*
> > > it can be understood as something that essentially supports a physical process --
> > > like the propagation of the psi-wave, which has not previously been explained
> > > as a physical process in sensible 3D space when there is more than one particle
> > > under consideration. It is the attachment of fundamental physical significance
> > > to this higher-dimensional wave process that in existing theory forces the
> > > reference to configuration space as something more than a mathematical artifice.
> > > In this sense, I think Jack's "configuration space is real" is shorthand for this
> > > interpretive move.
> >
> > [Jack]
> >
> > Exactly. And furthermore, it is a shell game, legerdemain, switch and bait, to claim
> > that this interpretive move is already demanded in some purely 3D+ 1D classical field
> > theory.
[Paul]
> But from what Bill has been saying Sachs may not be claiming this at all, and may
> not need to.
[Jack]
He is claiming that and he needs to claim that. The title of his book is "Quantum Mechanics
FROM General Relativity". (CAPS not in original). The "FROM" is key.
>
>
> > > > >The difference in the classical and quantum roles of configuration space
> > > > >is in Bohm's quantum potential specifically in the nonseparability of
> > > > >Bohm's quantum potential when there is entanglement, in its form-
> > > > >dependence, its intensity-independence, its nonlocality, and its non-
> > > > >mechanical context dependence i.e. no pre-assigned interactions
> > > > >among the entangled source particles and force fields as in classical
> > > > >physics.
> > > >
> > > > The same nonseparability occurs in Mendel Sachs' field theory.
> > >
> > > We need to see exactly how, with the aid of what auxilliary assumptions
> > > (if any) he is able to recapture the content of the Pauli principle from his
> > > theory. That is the acid test. It should be clear-cut.
> >
> > It should, but it's not. It's not because the claim is impossible IMO. Extraordinary
> > claims require extraordinary proof. I can see in a rough handwaving nonrigorous way
> > that a 3D based classical field theory with explicit faster than light action at a
> > distance could mimic (e.g. "Feynman zig zag") or perhaps be physically equivalent to
> > the usual configuration space formalism of quantum nonlocality. Sachs does use
> > advanced potentials in his S propagators, but the argument he gives from weak
> > coupling does not use that advanced S propagator and seems completely irrelevant
> > begging the question entirely.
[Paul]
>
>
> I do agree that hand-waving could hide a multitude of sins in this case.
[Jack]
And does.
Jack
Bill Page wrote:
> With more people involved in the discussion, it seems to me that we
> will have to proceed more carefully and slowly - maybe we should
> have anyway. <grin> It is obviously going to be hard to reply to specific
> points in each email. So instead of doing that, I think I will just pick
> a few and summarize the rest.
>
> First of all, I think that Paul's point about a "correspondence" is
> absolutely correct. What Sachs attempts to show is a correspondence
> between his theory in the linear limit and quantum mechanics. He
> does not say that one can deduce quantum mechanics directly from
> his theory. The example of special relativity and Newtonian mechanics
> is a very good one.
[Jack]
In that case, the argument is settled for now. Remember the title of his book is
"Quantum Mechanics from General Relativity"
"from" suggests "deduce". The title is not
"Quantum Mechanics compatible with General Relativity."
Now, in fact, Penrose made a big step in showing the connection between QM and
GR in his spinor theory. The Newman-Penrose symbols Sigmai^AB are the bridge
between explicate material world tensor indices i = t,x,y,z and pairs of
implicate mental spinor indices A,B = 0,1. This is "It from Bit" (Wheeler) For
example, a member of a tetrad ei is
ei = Sigmai^AB |A>|B>
Summation convention over A, B i.e.
ei = Sigmai^00|0>|0> + Sigmai^01|0>|1>+Sigmai^10|1>|0>+Sigmai^11|1>|1>
Now in Einstein's local theory, consider a point event P
ei(P) = Sigmai^00|<P|0>|<P|0> +
Sigmai^01<P|0><P|1>+Sigmai^10<P|1><P|0>+Sigmai^11<P|1><P|1>
We can generalize this to nonlocal field theory with two point events P and P'
ei(P,P') = 'Sigmai^00|<P|0>|<P'|0> + 'Sigmai^01<P|0><P'|1> +
'Sigmai^10<P|1><P'|0> + 'Sigmai^11<P|1><P'|1>
Note I use 'Sigma in the nonlocal equation, and Sigma in the local one. We may
need a spin connection analogous to a propagator connecting the events P and P'.
Locally, ei(P) is a tangent vector flow field. It is not yet clear what ei(P,P')
means? To my knowledge no one on this planet up to now has thought this thought.
> [Page]
> Jack also seems to agree with Paul's statement but apparently believes
> that I have claimed something more. I am sorry that I have given him that
> impression. Perhaps, at times, I have not been sufficiently careful to point
> out the limitations in what I have claimed.
>
> For example, I have probably written in the last few days that Sachs'
> theory makes the same empirical predictions as quantum mechanics.
> Taken on its on, this statement is probably both too strong (bold) and
> at the same time too vague (which version of QM? classical QM?
> with relativistic corrections? QED? etc.) It is true that such a statement
> might characterize Sachs' overall research program. But I do not
> mean that in this particular book, Sachs has done a point by point
> comparison. I mean only that he has shown some necessary results
> and made a plausible argument that his overall program is viable.
>
> One of these "necessary results" is, of course, how one can
> reconcile the use of configuration space in quantum mechanics
> with the fact that his theory (like general relativity) uses only one
> space-time. I agree that what Sachs considers in his book is only
> a subset of what been considered in quantum mechanics, but it
> does include the very necessary case of the Pauli exclusion
> principle.
[Jack]
I accept your sword Sir.
>
>
> Besides the two books that I have been talking about, during his
> career, Mendel Sachs has published over 150 articles in main
> stream physics journals showing the development of these ideas and
> expanding on various results that are presented only in summary form
> in the books. So it seems very surprising that he is apparently not very
> well known in theoretical physics!
>
> In spite of this a literature citation search also shows that he has not
> often been cited by other authors. So it is correct, perhaps, to
> characterize him as a maverick. But he is obviously a persistent and
> prolific one. Apparently his work is difficult to follow technically,
[Jack]
To put it mildly. David Bohm is a good clear writer and people like Evan Harris
Walker still don't understand him, and Evan is part of a crowd. So Mendel hasn't
a chance since he is not playing a very catchy melody on his trumpet. His memes
will not be assimilated easily like tough meat.
>
> perhaps because of his use of quaternion methods rather than the
> more common methods of differential geometry. Also it seems that
> unified field theories such as envisaged by Einstein have just not
> been in "vogue" in theoretical physics during the last half of the
> previous century which was largely devoted to attempting to complete
> the quantum mechanics program instead.
[Jack]
Before I forget:
"Now when a wite
Sits up all night,
Ill-natured jokes devising.
An all his wiles
Are met with smiles.
It's hard there's no denying.
Oh! Don't the days seem dank and long
When everything's right and nothing goes wrong.
And isn't your life extremely flat,
With nothing whatever to grumble at?
I offered toys to Altar Boys
And prayed they'd contradict me.
But would you know they were just so
Confoundedly politeful!"
King Gama (spoof on Richard III) in "Princess Ida" G&S
to be played by James Randi
>
>
> The following quotes are from Jack Sarfatti's email of Monday,
> May 22, 2000 5:42 PM
>
> >...
> >>
> >> [Page]
> >>
> >>> Sachs' theory starts with the assumption that everything is represented
> >>> by a single field defined over space-time by a set of non-linear field
> >>> equations. Thus it has the notion of "entangled states" built-in from
> >>> the very beginning.
> >
> >[Jack]
> >
> >Let's focus on these two above sentences. I think Bill is totally confused
> >here. Let f(xyzt) be the classical field over space-time (xyzt) linear or
> >nonlinear. There is some mapping q of f to a Hilbert space h(1) of
> >single-particle quantum wave functions that form a basis psik(xyz) for
> >this Hilbert space. The total energy of the classical field f maps to a
> >field Hamiltonian H that becomes a linear operator on the Hilbert space.
> >The amount of classical nonlinearity reflected in the Hamiltonian H is
> >completely irrelevant. Neither Page nor Sachs seem to understand
> >this mathematical idea.
>
> You are right. I do not understand what is relevant about the way you
> have formulated the problem above. Why do you presume that there
> should be a mapping of f to h(1)? The kind of correspondence between
> his theory and quantum mechanics that Sachs considers is much
> more involved than that.
[Jack]
What I am saying is quite standard. First let's start with particle mechanics.
The NR Hamiltonian H is in simplest case 1 space dimension, conservative force
field with a path independent potential V so the force 1-form dV is an exact
differential. This is the case N = 1
H(1) = p^2/2m + V1(x)
H(1) mutates into a linear operator on a Hilbert space h(1), with psi(x,t) a
member of h(1)
H(1)psi = ih&psi/&t
& means partial derivative.
Now suppose we have N = 2, a two particle problem. No assumption of identical
particles. One can be a proton, the other an electron.
The N = 2 Hamiltonian is now
H(1,2) = H(1) + H(2) + V(1,2)
The Hilbert space is NOT h(1) + h(2). That is a conceptual error. The Hilbert
space is
h(1,2) = h(1)xh(2) a tensor product!
A general member of h(2) is a pair-correlated entangled state
<x,x'|1,2> = Sum i1 Sum i2 <x|i1><x'|i2><i1,i2,t|1,2>
Where <i1,i2|1,2> are the time-dependent Einstein-Podolsky-Rosen-Bohm nonlocal
correlation coefficients (points in the complex plane) and (x,x') is the 2D
configuration space for the two point particles confined to one physical space
dimension. One can go to phase space by including the two linear momenta p and
p'. However, in Bohm theory, they are not independent of x and x' i.e.
p = Gradx S(x,x',t)
p' = Gradx' S(x,x',t)
S = action phase of the quantum pilot information field.
Next consider a classical field. Imagine N beads strung on a string with N ->
infinity for a finite length of string. That is essentially a classical field in
the simplest case. So field theory is N-point particle mechanics. Therefore,
each point on the line is a dimension of the field configuration space. In a
continuum the configuration space of the field is noncountable infinite
dimensional even though the field acts in 3D space.
So we have H(x) for each point in space. This is the field Hamiltonian density.
The field theory is local if there are no Hamiltonian densities like H'(x,x') or
still worse H"(x,x',x") etc. requiring multiple integrals over space.
We then have an integral over space of H(x).
That is the total field Hamiltonian is global. It is an integral over all space.
In general,
H(x) is of the form f(P(x)) + g(X(x)) where P(x) and X(x) are canonically
conjugate field momentum and field displacement densities obeying a Poission
Bracket that becomes a quantum commutator.
The quantum wave FUNCTIONAL BASIS (not a simple function like in particle
mechanics) is of the form
<x|i1><x'|i2><x"|i3>.... <i1,i2,i3, ....t|1,2, 3, .....>
This is an infinite product!
The Hilbert space for the quantum wave FUNCTIONAL of the classical field
configuration is the INFINITE TENSOR PRODUCT
h(x)xh(x')x(x") ....
That is a Hilbert space fiber at each x-base point. This is a fiber bundle.
Now, you show me how Mendel Sachs derives this picture to justify using "from"
in his title. Quaternions, shmaturnions, nonlinearities? So what? Where's the
beef? It don't look kosher to The Rabbi Rashi II. Don't look now, here come the
Cossacks! There's a UFO hovering over the roof. :-)
> >
> >We have not yet gotten to entanglement!
> >
> >To review:
> >
> >Start with classical field f(xyzt) whose nonlinearity is as strong as one
> >likes. Quantize that classical field. This gives a field-Hamiltonian H
> >(i.e. a 3D space integral of a quantum field Hamiltonian density) with
> >nonlinear terms i.e. products of the classical field now transformed to
> >a quantum operator. The field theory is "local" if these nonlinear products
> >in the Hamiltonian density are at the same space-time events. A truly
> >nonlocal field theory would have nonlinear field products connecting
> >different events in space-time. Sachs makes no such claim!
>
> I don't see what any of this has to do with Sachs' theory. Quantization
> of the "classical field" is not introduced in this manner.
[Jack]
Maybe not, but it should be.
>
> >
> >Now to get to generic entanglement, without specializing to Paul
> >exclusion principle, form tensor products of the Hilbert space
> >
> >h(2) = h(1)xh(1)
> >
> >h(3) = h(1)xh(1)xh(1)
> >
> >etc.
> >
> >For example, a possible entangled pair state |2> in h(2) is of the
> >form, in the configuration space representation
> >
> ><xyz,x'y'z',t|2> = Sum over k of ck(t) psik(xyz)psik(x'y'z')
> >
> >There is no way to derive this deductively from Sach's model alone
> >IMO.
>
> [Bill Page]
>
> I agree and as far as I see, Sachs make no attempt to do this. What
> he does do is to show that it is possible to put his theory into
> *correspondence* with this part of quantum mechanics.
[Jack]
If you had said that clearly from the beginning there would have been no
argument, but then again, some of this stuff is intrinsically interesting anyway
and clarifies some stuff that I can use in my coming lectures to the "Top Gun"
Space Cadets at United Earth Star Fleet Academy at The Presidio on The Physical
Principles of Reverse Engineering Retrieved Extra-Terrestrial Advanced
Technology. :-)
>
> >>>> [Jack]
> >>>
> >>>>The quantum superposition principle (summing weighted products of
> >>>>single-particle eigenfunctions of relevant observables) is a separate
> >>>>postulate not already demanded by his prior formulation of his theory.
> >>>
> >>> [Bill Page]
> >>>
> >>> I agree. It is also not required in his theory. It is only required in
> >>> the linear approximation to his theory that is quantum mechanics.
> >>
> >
> >[Paul]
> >
> >> By correspondence. Sorry, don't mean to labor this point, but I think
> >> that is the meta-theoretic key to this dispute.
> >
> >[Jack]
> >
> >I have already said as much, but Page persists in disputing this point.
> >
>
> [Bill Page]
>
> No! I completely agree with this point. It is exactly what I have been
> trying to say to you. It is a surprise to me that you think you "have
> already said as much". That is not how I understand any of the points
> you have made over the last few days.
[Jack]
Most peculiar since my perception is that this is what I have been saying to
you. Clearly, this is due to the psychotronic spell of an ill-natured Fairy!
"Mirror, mirror on the wall ..." Sancho, my horse, sword and spear!
>
> >
> >[Page]
> >
> >>> No, this is wrong. The entanglement is introduced by Sachs in the
> >>> initial formulation of his nonlinear field equations. That is can be
> >>> expressed (approximately) as a "coherent superposition of
> >>> products of single particle functions whose domain is configuration
> >>> space and whose range is the tensor product of irreducible
> >>> representations of single particle systems" is what Sachs
> >>> demonstrates in chapter 6.
> >
> >[Jack]
> >
> > Which is to say that Sachs has not done anything really new or
> > parsimonious. He simple sticks in configuration space entanglement ad
> > hoc at the beginning. Where exactly do you say he does that? What
> > exact page and line?
> [Page]
> He does not use configuration space at all except to show the
> correspondence with quantum mechanics.
[Jack]
Alas, poor chap.
>
> > Also, you say "approximately" I say no such qualification is needed.
> > This is a significant difference of principle.
[Page]
>
> The point is: Mendel Sachs' theory only "approximately" corresponds
> to quantum mechanics.
[Jack]
Is that like being "approximately" pregnant?
>
>
> >>>> ...
> >>>>However, the claim in the quantum many-body problem is more than
> >>>>that. First of all, it is never claimed, as Mendel claims, that the
> >>>>energy-momentum transfers between the particles is "weak'.
> >
>
> [Bill Page]
>
> I think you meant to quote some other passage. The above quote is
> your statement. But in response to this perhaps I said that Mendel Sachs
> does not claim that entanglement only occurs in the case of weak
> coupling.
>
> >[Jack]
> >
> >Well you are wrong. I quote Sachs
> >
> >"following as a necessary consequence of its axioms ... a set of coupled,
> >nonlinear spinor field equations, that has an asymptotic limit that
> >corresponds to the many-particle quantum mechanical theory. The
> >limit corresponds to the assumption of sufficiently small energy-momentum
> >transfer among the component elements ..." p. 39
> >Ch 3
> >
> >Now Bill do you mean to quibble that "small" is not the same as "weak"?
> >So it is "never claimed"? I caught you with your pants down and your hand
> >in the cookie jar on this one.
>
> Yes it is "never claimed". Notice that in your above quote Sachs
> repeatedly used the word "corresponds". This is part of the
> *correspondence* that Paul points out. Sachs is stating under
> what circumstances his theory makes the same predictions as
> quantum mechanics.
[Jack]
Makes "some" of the same predictions perhaps. Certainly not all. Also his
foundational ideas are obscure so I see little to recommend it. The Sword still
lies in The Stone.
>
> >
> >[Paul]
> >
> >> So that the empirical content could find expression in terms of an N-body
> >> configuration space and an extended superposition principle, although
> >> such elements are not native to Sach's theory. That would make sense to
> >> me.
> >
> >[Jack]
> >
> >Agreed, but that is not what is being claimed.
> >
>
> [Bill Page]
>
> On the contrary, I think that Paul is right. Sachs is showing that the
> *empirical content* of his theory (in the appropriate linear limit) can
> be (but need not be) expressed in n-body configuration space. He
> does this precisely in order to exhibit the correspondence.
[Jack]
In that case this has been Much Ado About Nothing. Our Great Arguments evaporate
into thin air to justify the way of Sachs to Man.
>
> >
> >[Page]
> >
> >> > These are a consequences of the specific non-linearity of the theory.
> >>
> >> [Paul]
> >>
> >> OK *that* I would really like to see.
> >
> >[Jack]
> >
> >So would I, but there is nothing there. Page is speaking through his hat,
> >blowing hot air. There is no reference to SN in the index, no reference
> >to Young Patterns or parastatistics.
> >
>
> [Bill Page]
>
> Ok. All I am talking about is Sachs detailed derivation of the Pauli
> statistics in section 6.2. This is a case where I was not careful to
> state the limitations along with my general statement. Still, I think
> that the way Sachs' derives the Pauli statistics seems quite general
> and that there is good reason to think that a similar argument can be
> made for the other cases that have been observed.
[Jack]
Perhaps, but I think he avoids the heart of the matter. Bohm's approach is much
clearer and leads to new testable numbers and new relations between cosmology
and consciousness.
>
>
> >[Paul]
> >
> >> It is significant enough that regardless of how it comes out
> >> mathematically, it would be an interesting result. So IMO
> >> it is probably worth the effort to grok his math.
> >
> >[Jack]
> >
> >Page's promise is not kept.
> >
>
> [Bill Page]
>
> What promise are you taking about?
[Jack]
Quantum mechanics FROM General Relativity.
In other words from my Bohmian ontology, General Relativity is an explicate
material mechanical local classical field theory that is form-independent,
intensity-dependent and context-independent. Quantum non-mechanics is an
implicate mental non-mechanical nonlocal form-dependent intensity-independent
context-dependent theory. These terms defined in
http://qedcorp.com/vigier/slides/vigier.htm. So, now you say Sachs pulls the
mental implicate Wabbit out from his material explicate Top Hat. It's a good
trick if you can do it, but he is no Houdini and I wasn't born yesterday. I
didn't buy the Brooklyn Bridge, only Cisco!
>
> >[Paul]
> >
> >>
> >> Again, I think the communication problem here revolves around the
> >> correspondence relationship between the limiting cases of Sachs'
> >> theory and the configuration-space expression of quantum entanglement.
> >
> >[Jack]
> >
> >Correct.
>
> [Bill Page]
>
> How strange. We agree. I think Paul is certainly do a good job
> of mediating this discussion. Thanks, Paul!
>
> >
> > [Jack]
> >
> >Also, I am beginning to think that Sachs has simply garbled the two
> >distinct meanings of "nonlinearity/linearity" and "superposition" in the
> >passage from classical physics to quantum physics. In general classical
> >nonlinearities violating classical superposition map to quantum linear
> >operators with quantum superposition/entanglement. The classical
> >nonlinearites are simply scattering terms in the Hamiltonian that is a
> >linear operator on the Hilbert space.
>
> [Bill Page]
>
> I still do not see what this has to do with Sachs' theory.
>
> >
> > [Jack]
> >
> >In special cases of emergence of phase-coherent order parameters
> >from collective motions, like superconductivity, lasers, and non-
> >equilibrium synergetics (Haken) one has effective nonlinear partial
> >differential equations to solve for these collective many-particle
> >modes.
> >
> [Page]
> If this relates at all to Sachs' theory, then it is the wrong way
> around. In Sachs' theory the nonlinear differential equations
> (field equations) come first. Their correspondence with quantum
> mechanical notion of collective n-body motions is a derived
> concept. Although Mendel Sachs has published numerous
> articles and a book on conventional solid state physics, as far
> as I know, he has not specifically applied his theory of matter
> to such collective states.
>
> >
> >[Jack]
> >
> >What Page says is false. That is, it is not true that "acceptable and
> >sufficiently complete (relative to conventional general relativity and
> >quantum mechanics) theories exist (such as Mendel Sachs' theory)
> >that do not incorporate configuration space as a fundamental concept."
> >
>
> What part of this do you think is false?
>
> 1) that it is not acceptable?
> 2) that it is not sufficiently complete?
> 3) that such theories exist at all?
> 4) that Mendel Sachs' theory does not incorporate configuration
> space?
>
> Regards,
> Bill Page.
[Jack]
1) 2) and 3).
Jack
Paul Zielinski wrote:
> Jack wrote:
>
> > Bill Page wrote:
> >
> > > Jack,
> > >
> > > On Friday, May 19, 2000 1:10 PM you wrote:
> > > >...
> > > >My only point is that there is no mathematical necessity to do what
> > > >Mendel did when he gets to the Pauli exclusion principle. In no sense
> > > >is he forced to do it by the structure of his nonlinear field theory whose
> > > >configurations are limited to 3D space unlike the Bohm quantum
> > > >potential Q.
> > >
> > > You are still missing the main point: The solution to Sachs' nonlinear
> > > field equations is a field defined over space-time. (My present contention
> > > is also that this is the same field defined by what Shipov calls the
> > > structural equations of A4, i.e. we have a 2nd rank spinor = quaternion
> > > field or equivalently an anholonomic tetrad defined over all space-time.)
> > > This is the essential content of Sachs' theory. Everything is ultimately
> > > to be described in terms of this field.
> >
> > So what? It is one thing to say that you have a quaternion classical field over
> > all of spacetime, holonomic or not. It is quite another thing to say that one
> > can deduce, without any additional physical interpretive postulates, the
> > characteristic nonlocal entanglements and special permutation symmetries among
> > spatially separated soliton concentrations of this nonlinear classical field.
>
[Paul]
> The question of entanglement and that of permutational symmetry for identical
> particles, though related, are logically independent and may even arise from distinct
> physical principles in a deeper theory. If Sachs can get entanglement in a
> mathematical clean derivation from his core principles, that would be very significant
> regardless of what happens with permutational symmetry.
[Jack]
Yes, but he does not do that. He never even discusses it to my knowledge, which is limited of
course. I don't think he can pull it off. He only discusses Fermi-Dirac statistics, a special
case of permutational symmetry and, as Page now admits, it's only a compatibility argument,
big deal! So what?
[Paul]
> Jack, you yourself have
> argued that indistinguishability and simple N-particle wavefinction symmetry
> require additional assumptions in conventional QM.
[Jack]
Exactly, and still do. Sachs has not delivered the goods IMO.
> [Paul]
>
> IMO the questions of entanglement and specific permutational symmetry are
> logically spearable in a deeper theory, although admittedly one depends on the
> other in conventional theory.
[Jack]
Agreed.
>
>
> > The key phrase here please note "without any additional physical interpretive
> > postulates" especially "without any". By the way, my objection here also applies
> > to Shipov's A4 theory as well as Sach's. The difference is that Shipov
> > acknowledges the correctness of my point here. My objection is general and
> > applies to any claim that a classical nonlinear local field theory written only
> > as a configuration in 3D space that evolves dynamically, can account for the
> > peculiar entanglements and special permutation symmetries that require a
> > nonclassical central objective role for both configuration space as domain and
> > for tensor products of single-particle Hilbert spaces as range for the
> > many-soliton solutions of the nonlinear field in 3D space. Now if one can show
> > how the subtratum of nonlinearity in 3D creates these nonlocal connections of
> > entanglement and special spin-dependent permutation symmetries for
> > indistinguishable solitons, that would be fine, but I see nothing like that even
> > remotely done mathematically in Sach's book. If I am wrong please point me to
> > the relevant mathematics?
[Paul]
>
> I agree that this is a vast claim and there must be a sold mathematical proof to
> back it up. Jack says it's not in the book. Surely, either it is or it isn't?
>
> Bill, if you say there is a proof, why not lay it out for us as Jack suggests?
> The proof is in the Proof.
>
> > > Sachs' argument is that *if* we make an approximation to these non-
> > > linear field equations as a linear system of differential equations, *then*
> > > they necessarily have the same Hilbert space form (expressed as
> > > wavefunctions over configuration space) as found in quantum mechanics.
> >
> > I know that's what he says. However, I do not see that actually does it in any
> > convincing way beyond the additional postulates he makes, perhaps unconsciously,
> > that are the same in the standard theory.
> >
> > >
> > > Again, this is his deduction: If we start with the full non-linear theory
> > > involving fields over just space-time *and* if we insist on the best
> > > linear approximation to these equations, then the result is quantum
> > > mechanics over configuration space.
> >
> > Again I say this is an unjustified claim that my critical reading of Sach's text
> > does not support. I see no "there" there, no new parsimony or same with less in
> > terms of conceptually independent interpretive postulates needed to get from 3D
> > field theory to configuration space as used in standard quantum theory for
> > several particles whether indistinguishable or not.
> >
> > > In other words: configuration
> > > space in quantum mechanics is just the way that quantum mechanics
> > > uses to cope with the fact that the underlying phenomena is essentially
> > > non-linear.
> >
> > That's a nice idea, but I see no convincing rational proof or even coherent
> > argument why it might be true from Sach's Ch 6. I am not saying it is not true
> > only that I cannot follow Sach's argument that it is true sans additional
> > postulates.
> >
>
> Right, that makes perfect sense in a programmatic way, but where is the math
> to prove that it actually works?
> Do you really mean that he is *inconsistent*, or that it is just an ad hoc addition
> to his theory? Those are two quite different animals.
[Jack]
He is formally consistent, but informally inconsistent in that his informal claims do not
match his actual formal argument.
>
>
> > > Thus it has the notion of "entangled states" built-in from the
> > > very beginning. If there is only one field, then everything must somehow
> > > be an aspect of this single field.
> >
> > Depends what you mean by "somehow". Lots swept under the rug in that "somehow".
> > If the "somehow" is limited to retarded signals along the forward light cone
> > then it won't work. Sachs does admit advanced solutions along the past light
> > cone and from that he needs to show explicitly how entanglements and permutation
> > symmetries arise. For example, he needs to show how the spin-statistics
> > connection emerges from his theory, and why other parastatistics (Young patterns
> > with mixed permutation symmetries) may arise in lower space dimensions like in
> > quantum wells, wires and dots.
>
> Again, I think the first question to tackle is whether he can get any kind of entanglement
> out of his theory in a suitable limiting case. Then, what additional assumptions if any
> does he need to get quantum statistics? Even if he needs additional hypothesis to
> handle identical particles, that would not kill his program IMO.
[Jack]
Bottom line, in terms of parsimony, there is no advantage to Sach's theory over conventional
theory and his claim that nonlinearity in the classical field as the origin of quantum
nonlocality does not make sense IMO as far as I can understand him.
>
>
> However, I agree with Jack that he needs to show clearly how he can get entanglement
> per se out of his theory.
>
> > > All of these (approximately separate)
> > > aspects are necessarily entangled (contingent on each other) to the
> > > extent required by the fact that the field as a whole is a solution of the
> > > field equations.
> >
> > Handwaving. Not good enough.
> >
> > >
> > >
> > > >The quantum superposition principle (summing weighted products of
> > > >single-particle eigenfunctions of relevant observables) is a separate
> > > >postulate not already demanded by his prior formulation of his theory.
> > >
> > > I agree. It is also not required in his theory. It is only required in the
> > > linear approximation to his theory that is quantum mechanics.
> >
> > There is no evidence whatsoever, that quantum theory is violated in the specific
> > sense of his theory. Correct me if I am wrong.
>
> Yes, obviously his theory would have to deviate empirically from QM outside
> the range of present experiments. But I would assume that there are enough
> adjustable parameters to allow that.
[Jack]
The only evidence for violation of quantum theory is living matter and consciousness, and I
have the handle on that with numbers that agree with experiment (1 sec, 10^18) and others that
are plausible 5 milliwatts per Hertz dissipation to generate a conscious moment with an
electron network all pum,ped by the cosmic Hubble flow - the origin of material order and
consciousness. We are truely connected to the entire universe!
>
>
> > > >> >[Jack]
> > > >> >
> > > >> >Yes, that's what Sachs does at the crucial step. It's the same thing
> > > >> >everyone does.
> > > >> [Bill Page]
> > > >> No. The important steps come before this. It is the fact that the
> > > >> coupled non-linear field equations can be represented in certain
> > > >> cases (approximately) as uncoupled linear equations that is the
> > > >> crucial step.
> > > >
> > > >This is trivial and obvious and in no way impinges on my point.
> > > >To show uncoupled linear equations in a certain limit, is not, by any
> > > >stretch of the imagination, a logical justification for the necessity of
> > > >introducing "entanglement", i.e coherent superposition of products
> > > >of single particle functions whose domain is configuration space
> > > >and whose range is the tensor product of irreducible representations
> > > >of single particle systems as shown in detail, for example, by Hermann
> > > >Weyl in "Theory of Groups in Quantum Mechanics" (Dover).
> > >
> > > No, this is wrong. The entanglement is introduced by Sachs in the initial
> > > formulation of his nonlinear field equations. That is can be expressed
> > > (approximately) as a "coherent superposition of products of single particle
> > > functions whose domain is configuration space and whose range is the
> > > tensor product of irreducible representations of single particle systems"
> > > is what Sachs demonstrates in chapter 6.
> >
> > Well then there is no disagreement. You just admited Sachs postulates it.
>
> No, no -- he is simply saying that the empirical content can be *expressed* --
> in an "approximate" theory -- in terms of a "coherent superposition of products
> of single particle functions whose domain is configuration space and whose
> range is the tensor product of irreducible representations of single particle
> systems", and that a *correspondence relationship* can be set up between that
> approximative framework and his. That is quite different. He is not
> necessarily making configuration space (as an essential physical concept) a
> native element of his theory, as you are suggesting.
[Jack]
I think he actually does when he sets up his interaction functional and conservation of
interaction. He basically makes the standard assumptions there implicitly, perhaps not
consciously.
>
>
> Didn't we have this same ambiguity in the debates with Lawrence Crowell
> and Dr. Evan Harris Walker? Didn't EHW say I was "unwashed" and a "high
> school blowhard" when I tried to point this out?
>
> All this indicates to me a serious defect in the way the typical physicist has
> been educated on these issues.
[Jack]
Yes.
>
>
> > The
> > whole debate here is similar to earlier attempts to derive Euclid's fifth
> > postulate of a unique parallel to a line passing through a point not on the line
> > from his first 4. This could not be done and so non-Euclidean geometries were
> > discovered leading to Riemannian and non-Riemannian geometries. Similarly, you
> > seemed to be claiming that the postulate of configuration space and its
> > entanglements and permutation symmetries (in special cases) were not like
> > Euclid's fifth independent postulates, but were theorems provable from a purely
> > local nonlinear classical field theory with localized particle like soliton
> > solutions from the nonlinearity. This you and Sachs have not done IMO.
>
> But IMO they do not need to do that, any more than you need to make a
> Newtonian independent time a native element of special relativity to get
> satisfactory agreement with ordinary experience. All you need to do in
> that example is show how the independent time coordinate of Newtonian
> theory can be brought into *correspondence* with the time coordinate of
> relativity, aslong as they empirically interpreted numbers agree in the
> limiting case of speeds slow compared to c -- as indeed they do.
[Jack]
Agreed. Page first gave impression that Sachs had proved that configuration space was some
kind of unnecessary illusion - a mere artifact of classical field nonlinearity - a field that
somehow explains inertia as well. Since then, he has back slided to mere "correspondence" with
which I have no objection and never did, but that takes the wind out of the "sales" for this
theory.
>
>
> > > >However, the claim in the quantum many-body problem is more than that.
> > > >First of all, it is never claimed, as Mendel claims, that the energy-
> > > >momentum transfers between the particles is "weak'.
> > >
> > > Mendel Sachs claims that his theory and quantum mechanics make essentially
> > > the same predictions when the energy-momentum transfers between "particles"
> > > is weak. He says the predictions of the two theories will differ in the case
> > > of stronger interactions.
>
> So the strength of the energy-momentum transfer is the "knob" Sach's theory
> uses to achieve consistency with the empirically confirmed content of QM
> and explain its success. That is the correct approach IMO.
[Jack]
That's the claim I think, yes.
>
>
> > Give a specific example that is testable in principle. Even if such an example
> > is given, it really does not prov, without further analysis, that generic
> > entanglements and specialized permutation symmetries are provable from only a
> > local nonlinear classical field, even if it is a quaternion field. That is, it
> > does not prove that 3D is more fundamental than configuration space in more
> > space dimensions.
>
> Again, just because quantum statistics and N-particle superposition are closely
> linked in QM does not mean that they are necessarily liked in a native manner in
> a deeper theory. If Sachs can get any kind of entanglement that is a major
> step.
[Jack]
That he never makes IMO beyond simply implicitly positing it. Entanglement in configuration
space as an independent quantum reality not reducible to classical local realism still stands.
Basically, Page seemed to claim a complete reduction of quantum theory to general relativity.
Sach's title "Quantum Mechanics from General Relativity" suggests as much. It's not true.
> To get quantum statistics he could then play around with all kinds of
> auxillary hypotheses, and we would be no worse off than we are in conventional
> theory.
>
> > > >It is never claimed that there are separate uncoupled equations one for
> > > >each particle. Indeed, that defeats the very idea of the many-body problem
> > > >in orthodox quantum physics as shown in any standard text book on the
> > > >subject.
> > >
> > > Sachs makes no such claim.
> >
> > Then what is his claim? I think we are spinning our wheels on this. His claim is
> > very vague and carries no logical necessity to my mind.
>
> The way I understand Bill's remarks, Sachs' claim is that he can explain the success
> of N-particle QM with its extended superposition principle by bringing it into
> correspondence with limiting cases of his own fundamentally non-linear theory in
> 4-space -- within the domain of "weak" momentum-energy exchange between the
> particles.
>
> That makes perfect sense to me. My only question is, does it actually work
> mathematically?
[Jack]
I strongly doubt it. I could be wrong. His text did not convince me. Indeed it seemed
irrelevant to the purpose. You should read it. Sach's basic ideas "conservation of
interaction" and "interaction functional" are not clearly explained and are so vague that he
is able to slip in standard ideas through the back door.
>
>
> > > >The quantum superposition principle in the Galilean relativity many-body
> > > >problem is
> > > >
> > > >
> > > >PSI(x1,x2,x3, ... xN, t) = Sum i1.... iN C(i1.... iN)
> > > >fi1(x1,t)fi2(x2,t)fi3(x3,t).... fiN(xN,t)
> > > >
> > > >
> > > >This is obviously a physically independent new postulate not at all
> > > >dependent on any approximation of uncoupled equations.
> > >
> > > This is not a postulate of Sachs theory.
> >
> > So you claim it is a theorem? Where is the proof?
>
> I Bill is saying that Sachs doesn't *need* to do this.
>
> > > >This is general. In addition, if you want the Pauli exclusion principle you
> > > > need to add still more postulates!
> > >
> > > Sachs shows in chapter 6 is mathematical detail that this is not true.
>
> What? He recovers Pauli without additional assumptions? This I gotta see.
[Jack]
You will be dissapointed I think.
>
>
> > No he did not. All he did there is some vague handwaving. There is no rigorous
> > proof there to my mind. Only a kind of shell game that pretends to be different
> > from the standard intepretive postulates but in fact is not different according
> > to my standards of rigor.
>
> Now *this* sounds like a decidable issue. Except that his book costs $165.:-)
>
> > > >You need to add the notion of nonlocal permutation symmetry from the
> > > >irreducible representations of the finite symmetric group SN for which
> > > >there are many Young Patterns of parastatistics.
> > >
> > > These are a consequences of the specific non-linearity of the theory.
> >
> > Show me in special cases. Show me parastatistics in spaces of lower space
> > dimensions as are now done routinely experimentally in solid state physics
> > "anyons". That is show, in Sach's theory, how the dimensionality of space
> > affects the permutation symmetry.
>
> Since parastatistics are not empirically validated, Sachs does not need to recover
> them. In fact, ironically, it might be a plus for his theory if he *doesn't* get them.
> The fact that QM accomodates them might then be viewed as a weakness of N-
> body QM, since it might predict *too much*.
[Jack]
It is my impression that anyons in quantum wells are an example of parastatistics. I mean
intermediate Young diagrams with mixed symmetry and antisymmetry. I have to check that. I
could be wrong. I thought parastatistics was suggested as part of the mechanism for high Tc
superconductivity.
>
>
> Sachs need not recover all of the theoretical predictions of QM -- only the
> well-confirmed empirical content.
>
> > Also, prior to that, show why the basic spin 1/2 solitons of the nonlinear 3D
> > field must have complete antisymmetry rather than complete symmetry? Show that
> > without adding new postulates to the theory. I say it cannot be done.
>
> But that is also true in the conventional theory, isn't it? Although do we have the
> Pauli spin-statistics theorem, for what that's worth.
[Jack]
Of course, but Sachs seemed to claim he had something better than conventional theory.
>
>
> > > >Then you need to specialize. You need to impose complete antisymmetry
> > > >(a particular Young Pattern of a single row of boxes in the usual notation)
> > > >for identical fermions.
> > >
> > > You are correct that this is an additional postulate in conventional
> > > quantum mechanics.
> >
> > And in Sach's theory as well. All he did was to handwave on this point.
>
> That doesn't surprise me.
>
> > > >None of this is in Mendel's theory in 3D space. Its role is not even
> > > >recognized by him at least as far as I read to Ch 6 in his book. For
> > > >this reason his claim and yours is completely naive mathematically
> > > >as a look at Weyl's classic book on the subject clearly shows.
> > > >
> > >
> > > You need to study the rest of chapter 6 more carefully.
> > >
> > > >> ...
> > > >> >Bill Page oversold the reality when he said that Mendel Sachs proved
> > > >> >that configuration space is not a fundamental quantum concept but can
> > > >> >be derived from classical theory in ordinary space.
> > > >>
> > > >> When did I say that configuration space can be derived from classical
> > > >> theory? I don't believe that I did.
> > > >
> > > >Oh, I thought you did. I thought that was the whole point. If that's not
> > > >what you claimed, then I do not know what the dispute was about?
> > >
> > > You do not seem to be willing to consider Mendel Sachs' theory
> > > as a viable alternative to quantum mechanics.
> >
> > I am willing to consider it, but, so far, I see no convincing rational argument
> > that it is so. All I see is handwaving and unconscious adoption of postulates.
>
> Bill, I agree with Jack that the burden of mathematical proof is on you and Sachs.
>
> > > > It is clearly what Mendel is claiming I think.
> > >
> > > I don't think so.
> > >
> > > >
> > > >> Also, I never argued whether not configuration space was "a fundamental
> > > >> quantum concept". Certainly it plays a fundamental role in quantum
> > > >> theory. What I said was (more or less) that it apparently wasn't a
> > > >> fundamental *physical* concept, i.e. that acceptable and sufficiently
> > > >> complete (relative to conventional general relativity and quantum
> > > >> mechanics) theories exist (such as Mendel Sachs' theory) that do not
> > > >> incorporate configuration space as a fundamental concept.
> > > >
> > > >A delicate distinction! (Gilbert and Sullivan)
> > > >
> > >
> > > Not so subtle, I think. You only need to have less of an intellectual
> > > commitment to only one theory. Physics is a complex subject. All
> > > answers are provisional.
> > >
> > >
> >
> > Indeed, including Mendel's. :-)
>
> Yes, let's all keep a reasonably open mind.
>
> Paul Zielinski
Jack
can get someone to retrieve them. However, can you explain the key math
ideas Sachs uses to achieve these miracles? I mean how do they differ
substantially from standard mathematical methods? How does one use
nonlinearity in a local classical field theory to get to many-particle wave
functions over configuration space different from the usual orthodox method
i.e. local classical field is second quantized to a linear operator acting
on the occupation number basis spanning Fock space for the quanta of the
field. The spin-statistics connection is imposed so that spin 1/2 fields
anticommute in the usual way, spin 1 fields commute etc. The classical
field's nonlinearity shows itself in the structure of the Hamiltonian. For
example, suppose the classical partial differential equation for the
classical field f(xyzt) has a local cubic nonlinearity proportional to
f^3(xyzt). This is a local nonlinearity. A nonlocal nonlinearity might be
be a term in the now differential integral equation with something like
|dx'd"f(x)f(x')f(x")g(x,x',x") that no one knows how to solve. Returning to
the local classical nonlinearity gives a quartic term in the Hamiltonian
(still a linear operator in the Fock space) corresponding to collisions of
2 field quanta. A cubic term in the Hamiltonian, corresponding to a
quadratic classical nonlinearity is two field quanta fusing to one field
quantum etc. Now this is standard procedure. What is the Sachs advantage
over this? How does it work qualitatively? What is the idea behind the
math? Where is Sachs coming from? What is his physical idea, his
motivation? Why should we bother with Sachs? We can't get off home plate
until you or Page provide some incentive since the stuff in Sachs's book is
obscure on the physical motivational level, why should his early papers be
any better. Einstein was able to explain his vision without requiring the
general reader to become a mathematical expert. All great physicists can do
that when they make an important fundamental breakthrough. Why can't any of
you do that for Sachs?
David Cyganski wrote:
> Jack, et al.,
>
> I've been keeping silent during this exchange up until now
> as I've have lot's of interesting projects to finish before
> I start a new one such as engaging in this discussion. But,
> I have been reading the exchanges as time permits and felt
> that it was time I interjected some information that might
> might get the discussion back onto mathematics and off of
> aimless speculation. The current state of the discussion seems
> to have degenerated from lack of access to Sachs' works. But,
> the high priced books need not scare you if you have a library
> to access. I will recommend here some of the papers that Sachs
> has written that may serve even better than one or both of his
> monographs of his field theory.
>
> "A Self-Consistent Field Theory of Quantum Electrodynamics,"
> by M. Sachs and S.L. Schwebel, Supplemento Al Volume XXI, Serie X
> Del Nuovo Cimento, No. 2, 1961, pp. 197-229.
>
> This is a very long and detailed introduction to his field theory
> development beginning with a derivation of Maxwell's equations
> in spinor form, development of the Pauli exclusion principle
> from his c-number based non-linear field equations and working
> through positronium and pair annihilation-creation process. It
> finishes with a computation of the hydrogen spectrum by linearization of
> the field equations (recovering the Dirac/Pauli representation) and
> derivation of the Lamb shift.
>
> "The Pauli Exclusion Principle from a Self-Consistent Field-Theory of
> Quantum Electrodynamics," M. Sachs, Il Nuovo Cimento, Serie X, Vol. 27,
> 1962, 138-1150.
>
> This expounds further than the first paper regarding the comparison of
> the way in which the exclusion principle was forced into the usual
> conception of QM and how it arises in his own work.
>
> While you are at the library, you might also want to pick up:
>
> "Bell's Inequalities from the Field Concept in General Relativity,"
> M. Sachs, Il Nuovo Cimento, Vol. 58 A, no. 1, 1980, pp. 1-10.
>
> Since the question arose in this exchange regarding Bell's
> Inequality and entanglement relative to Sachs' theory, here
> we find some explanation. In a nutshell, for spin 1/2 matter
> fields this theory obtains Bell's Ineq. violation, i.e. QM
> non-locality, for time-like separated particles while Bell's
> Ineq. are not violated for space-like separation.
[Jack]
Good. This is an interesting and important prediction that can be tested. I
wonder if it has not already been done for electron-positron pairs? If not
it should be attempted. If I was given millions to spend I would have such
an experiment done. My bet is that Sach's theory will fail this test. That
is, quantum nonlocality from phase entanglement over spacelike separations
is universal and not dependent either on the spin, the charges or the rest
mass of the entangled particles.
[David]
> Sachs carefully
> indicates that he had not treated photons yet and hence these
> results for fermions did not necessarily apply. Perhaps Mendel
> could update me with respect to further work encompassing the
> case of photons that he may have executed as I have located
> none in the literature.
>
> As a side note: during his long career, Sachs has made many
> predictions like that above which were untested at the time.
> Many of those predictions ran counter to convention wisdom at the time.
> In every case, and there have been many, in which tests followed,
> his predictions have been correct. I wish I had that kind of record.
[Jack]
Well this is important news. Please be specific with all the details. What
predictions? What tests?
>
>
> I hope this helps the discussion.
>
> David
Jack
Paul Zielinski wrote:
> Creon Levit wrote:
>
> > At 1:32 PM -0700 5/22/00, Jack wrote:
> >
> > >Paul Zielinski wrote:
> > >
> > > >
> > >> At the same time, it is hard to see how Bohmians can claim that
> > >>the symmetrization
> > >> postulate (including the Pauli principle) "drops out" of their theory.
> > >
> > >[Jack]
> > >
> > >I am not aware that they make such a claim? My understanding is that
> > >the spin-statistics
> > >connection is simply assumed as an independent postulate in the Bohm ontology.
> > >
> > >Paul Zielinski wrote:
> > >
> > >> As far as I
> > >> am aware this was never satisfactorily explained in Bohmian terms
> > >>-- although of
> > > > course Bohmian theory is no worse off in that respect than is
> > >conventional QM.
> >
> > Hammond's book has a good section on this. The Bohmians do not claim
> > that symetrization drops out, but they do show that exclusion (via
> > particle trajectories) does drop out once one imposes
> > [anti]symetrization.
> >
> > At least that is what I remember.
>
> Well, that is mathematically trivial in view of the way Bohm works backwards
> from the psi function and the Schrodinger equation to arrive at the quantum
> potential, as in TUU.
>
> I didn't really mean to say that contemporary Bohmians had actually made this
> claim. I guess what I meant was that Bohmian theory does not appear to have the
> heuristic muscle to get the Pauli principle without imposing *ad hoc* formal
> restrictions on permutational symmetry, just as in conventional QM -- contrary to
> what one might have hoped for in a realist theory like Bohm's. So I think we are
> all in agreement on this.
Yes, with the understanding that Bohmians do not make the kind of claim for the
primacy of 3-space or 4-space-time that Sachs makes. Vigier may be the exception
here, but I have not seen any paper where he really proves it mathematically. The
quantum potential for entangled particles acts directly in their configuration space.
Note, that the superposition of classical forces assumes classical pair potentials
V(r,r'). A many-body potential V(r,r'.r") violates classical force superposition. The
quantum potential is in this sense a many-body potential with other nonclassical
properties of course.
> [Paul]
>
> The point is that Bohmian mechanics and conventional QM are at least as impotent
> in this regard as Jack says Sachs' theory is.
[Jack]
Yes. The issue is does Sachs have something better? Now if he really makes
predictions confirmed by experiments as David claims, the issue gets much more
important and pressing.
Jack
Paul Zielinski wrote:
> > > The essential physical meaning of entanglement is the ability to alter correlations
> > > between the results of measurement on well-separated components of a quantum
> > > system where there can be no question of a physical disturbance in the conventional
> > > sense. It is not clear that this effect can *only* be accounted for by reference to
> > > N-body configuration space, which is what you seem to claim.
> >
> > [Jack]
> >
> > There is no formal alternative to configuration space as the domain of entangled states for
> > N separated particles. Show me a mathematical counter example to what I just said.
>
[Paul]
> But I thought we were talking about configuration space in a stronger than purely formal
> sense. Of course, if we want to analyze correlations between the measured values of
> particle variables, we need to refer to the variables at least for mathematical purposes.
> This is always true for multivariate analysis, even where the random variables have no
> real connection.
[Jack]
The physical idea behind the ontological necessity of configuration space in the Bohmian ontology is
that the quantum potential exerts real influences across spacelike intervals separating particles.
In this way the original EPR argument of 1935 is solved, the Heisenberg uncertainty principle is
saved by "spooky telepathic" faster-than-light action at a distance between the nonlocally connected
parts of the non-mechanical "organic" whole. Given a quantum potential of N entangled particles one,
in principle, can make a computer simulation of the pattern of these FTL influences, if N is not too
large, and indeed one can suppose that there is a local field theory providing these influences
perhaps. But would it work universally? Or would it be ugly and unwieldy requiring a different
classical field law for each case? The point is that there are no-preassigned mechanical couplings
so it is hard to see how to make a universal mechanical field theory that can universally simulate
quantum mechanics. It's like asking if one can design a classical computer to simulate a quantum
computer? Indeed, since quantum mechanics is equivalent to a quantum computer, it might be possible
to adapt Godel-Turing machine ideas to show a general theorem that the sort of thing Sachs suggests
is not possible - a more powerful version of Bell's locality inequality. Indeed, one might argue, as
you began to suggest, that Sach's theory is a local hidden variable theory?
>
> > [Jack]
> >
> > He is claiming that and he needs to claim that. The title of his book is "Quantum Mechanics
> > FROM General Relativity". (CAPS not in original). The "FROM" is key.
>
> I agree he is advertising a reductionist program, and you are right to ask "where's the beef".
>
> Paul Z.
Jack
Paul Zielinski wrote:
>
> > [Jack]
> >
> > Yes, but he does not do that. He never even discusses it to my knowledge, which is limited of
> > course. I don't think he can pull it off. He only discusses Fermi-Dirac statistics, a special
> > case of permutational symmetry and, as Page now admits, it's only a compatibility argument,
> > big deal! So what?
>
> If he can get entanglement without N-body configuration space "taken seriously," that would be
> a radical achievement in and of itself. If he can get Fermions without defining N-body
> permutations,
> it would be icing on the cake.
>
> We get fermions in QFT by setting up anti-commutation rules for the field operators. No
> permutations.
> So formally, it can be done. Although there is no deep physical reason to explain why Fermi field
> operators should obey anti-commutation rules.
>
> My guess is that fermions would be tougher than bosons for a field theory.
>
> Again, the only real question here is, can he? If he can, he should get a Nobel.
[Jack]
You need to read the book. I don't think he pulls it off. But I could be wrong. I do have other things
to do. I don't see how it is possible in principle to pull this White Wabbit out of the Top Hat.
>
> > [Paul]
> >
> > > Jack, you yourself have
> > > argued that indistinguishability and simple N-particle wavefinction symmetry
> > > require additional assumptions in conventional QM.
> >
> > [Jack]
> >
> > Exactly, and still do. Sachs has not delivered the goods IMO.
>
> Well, you've seen his book.
[Jack]
Come on over. Saul-Paul is here until Sunday. I am going to Cal Tech next week.
>
>
> > > [Paul]
> > >
> > > IMO the questions of entanglement and specific permutational symmetry are
> > > logically spearable in a deeper theory, although admittedly one depends on the
> > > other in conventional theory.
> >
> > [Jack]
> >
> > Agreed.
>
> OK, no need to beat this particular dead horse. :-)
>
>
> > [Jack]
> >
> > He is formally consistent, but informally inconsistent in that his informal claims do not
> > match his actual formal argument.
>
[Paul]
> So your view is that his "proof", by relying on tacit additional assumptions that are
> the equivalent of positing configuration space (in the strong sense), directly undermine
> his claim to have reduced QM to 4D field theory?
[Jack]
Yes, that's my present understanding of the reality here. Of course, I bought Cisco at 80! :-)
>
> > [Jack]
> >
> > The only evidence for violation of quantum theory is living matter and consciousness, and I
> > have the handle on that with numbers that agree with experiment (1 sec, 10^18) and others that
> > are plausible 5 milliwatts per Hertz dissipation to generate a conscious moment with an
> > electron network all pumped by the cosmic Hubble flow - the origin of material order and
> > consciousness. We are truely connected to the entire universe!
>
[Paul]
>
> The only known evidence. That follows trivially from "outside the range of present experiments".
>
> No question that QM is extremely accurate and any deviations would have to be within the
> range of present experimental error. So this empirical accuracy would have to be explained
> by any deeper theory which claims to reduce QM.
>
>
> > [Jack]
> >
> > I think he actually does when he sets up his interaction functional and conservation of
> > interaction. He basically makes the standard assumptions there implicitly, perhaps not
> > consciously.
>
> We are making a distinction between configuration space as a mathematical artifice
> ("weak" CS), and configuration space as supporting a physical process in an essential
> way ("strong CS"). Obvious Sachs has to deal with particle coordinates to draw
> a correspondence with conventional theory. That does not necessarily mean he is
> making "strong" CS a native element of his non-linear field theory.
>
> You seem to be saying that he is forced to import "strong" CS into his theory *as a native
> element* in order to get entanglement.
[Jack]
Yes.
>
> > [Jack]
> >
> > Agreed. Page first gave impression that Sachs had proved that configuration space was some
> > kind of unnecessary illusion - a mere artifact of classical field nonlinearity - a field that
> > somehow explains inertia as well. Since then, he has back slided to mere "correspondence" with
> > which I have no objection and never did, but that takes the wind out of the "sales" for this
> > theory.
>
[Paul]
> I don't understand this. Correspondence allows for reduction. In fact, that's what correspondence
> is all about. That's how we reduce thermodynamics to statistical mechanics, special relativity to
> Newtonian mechanics, chemistry to physics, etc. etc. We get the empirically interpreted numbers
> to converge in a limited domain, while the theoretical meaning of the quantities changes
> incommensurably when we go to the deeper reducing framework. That *is* the "structure of
> scientific revolutions". That's why we need correspondence rules, conceived as a mapping of
> semantically incommensurable theoretic terms.
[Jack]
If you mean "correspondence" in sense of a limiting case when a control parameter vanishes, like h -> 0
is the classical limit of quantum, v/c -> 0 is the Galilean limit of special relativity, curvature -> 0
is the special relativistic limit of general relativity, torsion -> 0 takes Einstein's "unified field
connection theory" UFT to his "metric gravity theory" GR, quantum action barrier height << post-quantum
reaction barrier height is the quantum limit of the post-quantum theory, etc. then I do not think that
is what Sachs did. All Sach's did IMHO was to show no contradiction not correspondence in your sense.
That is, "correspondence" in the sense of no-contradiction or compatibility. When v/c -> 0 you have no
choice in where you arrive. Sachs has no comparable necessity in his argument as I presently understand
it. Now, you may show me the error of my ways perhaps, or David, or Bill? What about the experiments
David alleged? That's the important thing now.
>
> [Bill]
> > > > > >However, the claim in the quantum many-body problem is more than that.
> > > > > >First of all, it is never claimed, as Mendel claims, that the energy-
> > > > > >momentum transfers between the particles is "weak'.
> > > > >
[Jack]
> > > > > Mendel Sachs claims that his theory and quantum mechanics make essentially
> > > > > the same predictions when the energy-momentum transfers between "particles"
> > > > > is weak. He says the predictions of the two theories will differ in the case
> > > > > of stronger interactions.
> > >
> > > So the strength of the energy-momentum transfer is the "knob" Sach's theory
> > > uses to achieve consistency with the empirically confirmed content of QM
> > > and explain its success. That is the correct approach IMO.
> >
> > [Jack]
> >
> > That's the claim I think, yes.
>
[Paul]
> What I meant was that he has to adjust his theory so that any deviations fall outside the
> range of existing experimental technique. A pretty obvious point.
>
> > > > Give a specific example that is testable in principle. Even if such an example
> > > > is given, it really does not prove, without further analysis, that generic
> > > > entanglements and specialized permutation symmetries are provable from only a
> > > > local nonlinear classical field, even if it is a quaternion field. That is, it
> > > > does not prove that 3D is more fundamental than configuration space in more
> > > > space dimensions.
> > >
> > > Again, just because quantum statistics and N-particle superposition are closely
> > > linked in QM does not mean that they are necessarily liked in a native manner in
> > > a deeper theory. If Sachs can get any kind of entanglement that is a major
> > > step.
> >
> > [Jack]
> >
> > That he never makes IMO beyond simply implicitly positing it. Entanglement in configuration
> > space as an independent quantum reality not reducible to classical local realism still stands.
> >
> > Basically, Page seemed to claim a complete reduction of quantum theory to general relativity.
> > Sach's title "Quantum Mechanics from General Relativity" suggests as much.
>
> Yes.
>
> > It's not true.
>
> That wouldn't be very surprising. However, if you are right and a deep thinker like Sachs -- who
> is no dummy -- has made a career out of this project and has failed, that would tell us something
> interesting.
[Jack]
I could be wrong. I am no expert on Sach's theory and I have not spent a lot of time on it. I hope I am
wrong and he is right. I am just saying where I am placing my marker right know on which horse. But so
far, neither Bill nor David, and not Sachs, have been able to come up with a vivid compelling clear
statement of what his basic idea really is and how he does it. They just point to turgid tomes of
incomprehensible mathematics when we are very busy with great affairs of state ...
SONG--GIUSEPPE with CHORUS.
Rising early in the morning,
We proceed to light the fire, Then our Majesty adorning
In its workaday attire,
We embark without delay
On the duties of the day.
First, we polish off some batches
Of political despatches,
And foreign politicians circumvent;
Then, if business isn't heavy,
We may hold a Royal levee,
Or ratify some Acts of Parliament.
Then we probably review the household troops--
With the usual "Shalloo humps!" and "Shalloo hoops!"
Or receive with ceremonial and state
An interesting Eastern potentate.
After that we generally
Go and dress our private valet--
(It's a rather nervous duty--he's a touchy little man)--
Write some letters literary
For our private secretary--
He is shaky in his spelling, so we help him if we can.
Then, in view of cravings inner,
We go down and order dinner;
Then we polish the Regalia and the Coronation Plate--
Spend an hour in titivating
All our Gentlemen-in-Waiting;
Or we run on little errands for the Ministers of State.
Oh, philosophers may sing
Of the troubles of a King;
Yet the duties are delightful, and the privileges great;
But the privilege and pleasure
That we treasure beyond measure
Is to run on little errands for the Ministers of State.
CHORUS
Oh, philosophers may sing, etc.
After luncheon (making merry
On a bun and glass of sherry),
If we've nothing in particular to do,
We may make a Proclamation,
Or receive a deputation--
Then we possibly create a Peer or two.
Then we help a fellow-creature on his path
With the Garter or the Thistle or the Bath,
Or we dress and toddle off in semi-state
To a festival, a function, or a fete.
Then we go and stand as sentry
At the Palace (private entry),
Marching hither, marching thither, up and down and to and fro,
While the warrior on duty
Goes in search of beer and beauty
(And it generally happens that he hasn't far to go).
He relieves us, if he's able,
Just in time to lay the table,
Then we dine and serve the coffee, and at half-past twelve or one,
With a pleasure that's emphatic,
We retire to our attic
With the gratifying feeling that our duty has been done!
Oh, philosophers may sing
Of the troubles of a King,
But of pleasures there are many and of worries there are none;
And the culminating pleasure
That we treasure beyond measure
Is the gratifying feeling that our duty has been done!
CHORUS
Oh, philosophers may sing, etc.
Exeunt all but Marco and Giuseppe.
>
> [Paul]
> Many smart theoreticians broke their teeth on the anomalous orbit of Mercury, and that told us
> something interesting about classical mechanics and special relativity...
>
> [Paul]
> > >
> > > That makes perfect sense to me. My only question is, does it actually work
> > > mathematically?
> >
> > [Jack]
> >
> > I strongly doubt it. I could be wrong. His text did not convince me. Indeed it seemed
> > irrelevant to the purpose. You should read it.
>
> OK.
>
> > Sach's basic ideas "conservation of
> > interaction" and "interaction functional" are not clearly explained and are so vague that he
> > is able to slip in standard ideas through the back door.
>
[Paul]
> OK, so there's the critical step. Of course, Sachs may not even be aware of exactly what
> he has done.
>
> The wonders of peer review.
March. Enter Procession of Peers.
CHORUS
Loudly let the trumpet bray!
Tantantara!
Proudly bang the sounding
brasses!
Tzing! Boom!
As upon its lordly way
This unique procession passes,
Tantantara! Tzing! Boom!
Bow, bow, ye lower middle classes!
Bow, bow, ye tradesmen, bow, ye
masses!
Blow the trumpets, bang the brasses!
Tantantara! Tzing! Boom!
We are peers of highest station,
Paragons of legislation,
Pillars of the British nation!
Tantantara! Tzing! Boom!
Enter the Lord Chancellor, followed by his train-bearer.
>
> [Paul]
> > >
> > > What? He recovers Pauli without additional assumptions? This I gotta see.
> >
> > [Jack]
> >
> > You will be disappointed I think.
>
[Paul]
> Probably.
>
>
> >
> > [Jack]
> >
> > It is my impression that anyons in quantum wells are an example of parastatistics. I mean
> > intermediate Young diagrams with mixed symmetry and antisymmetry. I have to check that. I
> > could be wrong. I thought parastatistics was suggested as part of the mechanism for high Tc
> > superconductivity.
>
[Paul]
> Because they can. Since parastatistics are formally admissible, they have been entertained as
> a technical solution to various anomalies, but I have never seen anything that seems convincing.
> My point is that we cannot assert at this stage that paraparticles or parafields actually exist, and
> therefore we should not demand *a priori* that a candidate theory like Sachs' reproduce all formally
> admissible symmetry types, which may well be mere artifacts of a relatively superficial formalism.
> Indeed, this *might* be be an unsatisfactory feature of conventional QM, and a clue to the
> fictitious character of the N-body approach, when viewed through an alternative optic such as Sachs'.
>
> In other words, I do not think we can include parastatistics within the "empirically well-confirmed
> content" of conventional QM.
>
> Technically, N-body QM also allows -- and even predicts -- "mixons" (say, Bose *and* Fermi
> electrons), but these are simply not observed in nature.
[Jack]
There is supposed to be a super-selection rule forbidding that - there is also supposed to be
supersymmetry at very high energy.
>
> [Paul]
> If N-body QM and its configuration space are "real", why not?
>
>
> > [Jack]
> >
> > Of course, but Sachs seemed to claim he had something better than conventional theory.
>
[Paul]
> As suggested by the title of his book.
Jack
Paul Zielinski wrote:
> Jack wrote:
>
> > Paul Zielinski wrote:
> >
> > > > [Jack]
> > > >
> > > > Agreed. Page first gave impression that Sachs had proved that configuration space was some
> > > > kind of unnecessary illusion - a mere artifact of classical field nonlinearity - a field that
> > > > somehow explains inertia as well. Since then, he has back slided to mere "correspondence" with
> > > > which I have no objection and never did, but that takes the wind out of the "sales" for this
> > > > theory.
> > >
> >
> > [Paul]
> >
> > > I don't understand this. Correspondence allows for reduction. In fact, that's what correspondence
> > > is all about. That's how we reduce thermodynamics to statistical mechanics, special relativity to
> > > Newtonian mechanics, chemistry to physics, etc. etc. We get the empirically interpreted numbers
> > > to converge in a limited domain, while the theoretical meaning of the quantities changes
> > > incommensurably when we go to the deeper reducing framework. That *is* the "structure of
> > > scientific revolutions". That's why we need correspondence rules, conceived as a mapping of
> > > semantically incommensurable theoretic terms.
> >
> > [Jack]
> >
> > If you mean "correspondence" in sense of a limiting case when a control parameter vanishes, like h -> 0
> > is the classical limit of quantum, v/c -> 0 is the Galilean limit of special relativity, curvature -> 0
> > is the special relativistic limit of general relativity, torsion -> 0 takes Einstein's "unified field
> > connection theory" UFT to his "metric gravity theory" GR, quantum action barrier height << post-quantum
> > reaction barrier height is the quantum limit of the post-quantum theory, etc.
>
[Paul]
> By "correspondence" I mean more than convergence of the empirically interpreted numerical output. I
> mean, in addition, a mapping of the theoretic terms of two (incommensurate) frameworks, where one is
> "reduced" to the other.
[Jack]
No he does not do that to my mind. I am still at a loss thinking "huh?". I do not see how he crossed the
conceptual gap from explicate 3D to implicate 3ND spacelike entanglements in a smooth continuous logical way
different from the discontinuity of postulating the duality of the explicate material 4D spacetime order and the
implicate mental beyond spacetime order the way I do. Indeed, David tells us Sachs has NOT done that. That is
David says that Sachs's theory FORBIDS implicate spacelike entanglement for massive spin 1/2 particles!
> [Paul]
> Empirical interpretation of the numerical predictions is relatively theory-independent, while the
> theoretical
> meaning of those predictions can change radically and incommensurably as we jump from one theoretic
> "gestalt" to another.
[Jack]
Yes, well by your definitions, Sachs has not done that IMO. I completely agree with you. Indeed my post quantum
theory PQT is a good example of what you say. In the old physics the Hubble flow parameter H is purely
explicate-mechanical
speed of receding galaxy = H distance of galaxy to Earth
giving the empirical cosmological red shift
In PQT it is as above, but in addition:
H = universal rate of consciousness generation per qubit
HN = universal rate of consciousness generation of a coherent qubit computing network of N nodes. This comes
from my modification of Bohm & Hiley's Gaussian back-action derivation of the GRW phenomenological model
replacing the Schrodinger equation. It's not "objective reduction" OR as commonly thought, but, rather,
spontaneous self-organization from the "two-way relation" between the coherent pilot field of thought
(collective nonequilibrium pumped Frohlich mode of the billion billion caged electrons in the brain forming the
Bohm-Pribram "hologram" phase-locked or "enslaved" (Haken) by the Francis Crick 40 Hz brain clock near electric
field oscillation) and the actual momentary spatial configuration of the caged electrons in either of two minima
in their double well potentials which nonlocally control the protein switch configurations, the neural firings
and even cell replication apparently.
Add to that the 1/N^2 coherence lowering of the height of the reaction barrier relative to that of the action
barrier and we are in business. This is an additional postulate of PQT. It says that the two-way relation
between mind and matter requires equal heights (in units of h) of the barrier for mind to move matter and for
matter to change mind. The change in mind by matter is consciousness. Ordinary quantum theory is precisely that
limit in which incoherent random unconscious mind moves matter with high probability with a very low probability
for any compensating reaction of matter back on mind. This is Bohm's theorem for "passion at a distance" based
on the "fragility" of the quantum potential.
http://qedcorp.com/pcr/vigier/slides/vigier.htm
When 1/N2 is small enough the probability of matter changing its mind pilot field increases and then from the
"strange loop" of two-way co-evolution of the mind field and its attached material caged electron configuration,
the mind field undergoes a catastrophic synergetic critical phase transition from unconscious random incoherence
to conscious nonrandom large scale coherence! This is the post-quantum awakening out of the darkness of the
quantum night. And God said, let there be consciousness, and there was consciousness. All of this information
was, of course, in the much rumored Third Tablet that SPECTRA gave to Moses on The Magick Mountain that he
brokeon his way back, tired by his long ordeal of "abduction". I have been authorized by "THE NINE" to reveal it
now. :-)
No. 9. I've jibe and joke The Yeomen of the Guard (G&S)
(SONG)
Jack Point
JACK POINT I've jibe and joke
And quip and crank
For lowly folk
And men of rank.
I ply my craft
And know no fear.
But aim my shaft
At prince or peer.
At peer or prince-- at prince or peer,
I aim my shaft and know no fear!
I've wisdom from the East and from the West,
That's subject to no academic rule;
You may find it in the jeering of a jest,
Or distil it from the folly of a fool.
I can teach you with a quip, if I've a mind;
I can trick you into learning with a laugh;
Oh, winnow all my folly, folly, folly, and
you'll find
A grain or two of truth among the chaff!
Oh, winnow all my folly, folly, folly, and
you'll find
A grain or two of truth among the chaff!
I can set a braggart quailing with a quip,
The upstart I can wither with a whim;
He may wear a merry laugh upon his lip,
But his laughter has an echo that is grim.
When they're offered to the world in merry
guise,
Unpleasant truths are swallowed with a will,
For he who'd make his fellow,
fellow, fellow creatures wise
Should always gild the philosophic pill!
For he who'd make his fellow,
fellow, fellow creatures wise
Should always gild the philosophic pill!
> [Paul]
>
> That's why I have objected to the common usage of the term "approximation" in this context, since it
> studiously ignores the second layer and is thus a misnomer IMO. For example, in special relativity time
> does not suddenly become physically separate from the three spacial coordinates as we go v/c -> 0.
> Rather, in this limited domain we can *pretend* that it does, thus reverting to a (relative to the deeper
> theory) "fictitious" Newtonian interpretation. Obviously, from the standpoint of special relativity, the
> world does not suddenly become Newtonian, and Minkowski 4-space does not suddenly evaporate, just
> because we are moving (relatively) slowly.
>
> It is in this sense that "correspondence" is an essentially meta-theoretic concept with a strong semantical
> component.
[Jack Point]
No. 15. Hereupon we're both agreed
(DUET)
Point and Wilfred
BOTH Hereupon we're both agreed,
All that we two
Do agree to
We'll secure by solemn deed,
To prevent all
Error fundamental.
> [Jack - prev]
>
> > then I do not think that
> > is what Sachs did. All Sach's did IMHO was to show no contradiction not correspondence in your sense.
> > That is, "correspondence" in the sense of no-contradiction or compatibility.
>
[Paul]
> This is very closely related. I would suggest that as long as there is compatibility, we can usually set up a
> correspondence relationship according to my definition. However, you may be right that Sachs has not
> explicitly done this. That in itself would not necessarily mean that he *cannot*.
>
> I agree with Cyganski that there is little point hacking away at this any further until we all have access
> to
> Sachs' book and earlier papers on the subject.
>
> > When v/c -> 0 you have no
> > choice in where you arrive.
>
> Numerically at least.
>
> > Sachs has no comparable necessity in his argument as I presently understand
> > it. Now, you may show me the error of my ways perhaps, or David, or Bill? What about the experiments
> > David alleged? That's the important thing now.
>
> It's all important IMO.
>
> Paul Z.
Jack
"Gary S. Bekkum" wrote:
> Jack wrote:
>
> > Yes, well by your definitions, Sachs has not done that IMO. I completely agree with you. Indeed my post quantum
> > theory PQT is a good example of what you say. In the old physics the Hubble flow parameter H is purely
> > explicate-mechanical
> >
> > speed of receding galaxy = H distance of galaxy to Earth
> >
> > giving the empirical cosmological red shift
> >
> > In PQT it is as above, but in addition:
> >
> > H = universal rate of consciousness generation per qubit
>
> [From Mendel Sachs' "Dialogues"]
>
> "According to Einstein's theory of relativity, space, per se, CANNOT
> EXPAND by itself. It is only there to provide a language for the
> purpose of facilitating an expression for the laws of matter...the
> time...(since the Big Bang)...is only a measure from our reference frame
> of the universe, where we sit on Earth in our solar system, which is an
> infinitesimal part of our particular galaxy...according to the theory of
> relativity, there is no absolute time measure...observations of other
> observers who may live in different parts of the universe, in the
> reference frames of different galaxies...may determine that the last
> 'big bang', in translating their time to ours, was 300 billion years
> ago, some other observers may determine that it was only 2 billion years
> ago, and so on. That is, the time measure is strictly subjective...what
> is truly objective, i.e. what every observer in the universe would agree
> upon, is the oscillatory behavior of the universe as a whole...'big
> bang' cosmology claims there was an absolute beginning of time...this is
> not compatible with the relativity of time measure..."
This is wrong. The absolute temperature of the cosmic blackbody radiation is an objective measure of cosmological
time. I can quote both Stapp and Bohm on this where they agree even though on opposite sides of the Bohr-Einstein
divide.
Stapp says nonobjective nonlocality, Bohm says objective nonlocality. Note, Einstein had hoped for objective locality
demolished by the experimental test of Bell's locality inequality for spin correlated particle pairs.
Sach's says no spacelike correlations for massive pairs - contradicts quantum theory.
In general any attempt, like Sach's, to derive quantum theory from classical general relativity is an attempt to
return to the mechanical clockwork universe in which determinism prevents morally responsible free will.
The implicate quantum nonmechanical nonlocal objective order beyond 4D spacetime is a physical immaterial thoughtlike
order of reality not reducible to the explicate classical mechanical material local objective order trapped in the
prison of the 4D spacetime "block universe" like Merlin encased in the Ice under the Lake by Morgana La Fey.
http://qedcorp.com/pcr/vigier/slides/vigier.htm
http://stardrive.org/Lilly/
http://stardrive.org/Jack/Synergy.pdf