bcc

"The Question is: What is The Question?" (John A. Wheeler APS
Philadelphia, 2003)

The issue here is whether the rules of orthodox quantum theory that
apply to a micro-quantum Dirac ket | also apply 100% to the
macro-quantum ODLRO order parameter f(r)?

"and reflect my growing conviction that broken symmetry has a lot to say
about the fundamentals of quantum mechanics and vice versa." P.W. Anderson

My point here is that orthodox quantum measurement theory, i.e. Von
Neumann projection postulate predicated on the Born probability Ansatz
for simple ensembles without ODLRO broken symmetry breaks down
completely for questions in which the macro-quantum coherent order
parameter dominates the phenomenon under study.

The robust "phase rigidity" of the ODLRO order parameter is the new
emergent qualitative phenomenon that prevents the Von Neumann projection
or "collapse". The giant matter wave, whether real in the ground state
of a superfluid, superconductor, high Tc anyon film etc., or virtual
inside the vacuum, is no longer Dirac's simple ket | (even for a large
number of entangled quanta in phase space). The Landau-Ginsburg order
parameter factorization of the micro-quantum N-particle Green's function
propagators is no longer a pure BIT projective ray in which

| --- z| is a physical equivalence class

The relative phase between different parts of the coherent ODLRO field
is a robust physical field in itself. In the case of vacuum ODLRO the
local fabric of Einstein's curved space-time obeying the universal
Equivalence Principle emerges from this coherent relative phase field
according to the equation

B = (hG/c^3)d(Goldstone Phase)

B is the Cartan 1-form in the Einstein-Cartan tetrad

e = 1 + B

B = 0 is globally flat space-time without gravity or inertia comes from
the local gauging of T4 to Diff(4) together with a spontaneous broken
vacuum symmetry.

Einstein's gravity and inertia are inseparable and are a macro-quantum
property. There is no such thing as the "classical world." The
"classical world" is an illusion. If you let h -- 0 and c -- infinity
you lose gravity and inertia completely even if G =/= 0.

The Equivalence Principle relates Einstein's metric field guv as a
bilinear form in the Einstein-Cartan tetrad field e.

d is Cartan's exterior derivative.

The Goldstone phase of the Higgs condensate is a 0-form and, as
explained by John Baez and Hagen Kleinert in different ways, d(Goldstone
Phase) when non-trivial, i.e. not simply an ordinary gauge
transformation leaving the physical observables invariant, is a
"multiple-valued gauge transformation". The "Dirac string" and the
Abrikosov vortex lattice of self-trapped quantized magnetic tubes in
"hard" Type II superconductors and in Ray Chiao's laser filaments in
nonlinear optics, is an example. The Pioneer anomaly is another example.
The SU(2) hypercharge group seems to be the group which gives gravity
and inertia of the finite mass of the weak bosons and the quarks and
leptons. Consistency demands. More on this later.

On Aug 26, 2005, at 7:50 PM, Jack Sarfatti wrote:

See P.W. Anderson "Coherent Matter Field Phenomena in Superfluids" in "A
Career in Theoretical Physics" (World)

"in ... superconductivity and superfluidity, we have been provided with
.... very direct demonstrations which seem to bring the quantum particle
field almost into the ordinary tangible macroscopic realm ... In these
phenomena the quantum particle field plays a role very similar to the
roles, with which we are familiar, of the classical fields, the
electromagnetic and gravitational fields, in our ordinary macroscopic
experience. This has been shown by a series of experiments of various
kinds of coherence in quantum fluids ..."

Enter ODLRO in Galilean relativity " 1951 and 1956 by [Oliver] Penrose
and [Lars] Onsager ... define superfluidity of a Bose system ... as a
state in which the density matrix ... factorized in a certain way [order
parameter f(r)] ... the term which has no dependence on the relative
positions of r and r' is characteristic of superfluidity."

The issue here is whether the rules of orthodox quantum theory that
apply to a micro-quantum Dirac ket | also apply 100% to the
macro-quantum ODLRO order parameter f(r)? I think not. There are
qualitative differences due to "phase rigidity" of f(r) in which the
von-Neumann theory of quantum measurement predicated on the Born
probability interpretation simply breaks down in the regime where the
local order parameter f(r) (a complex function of space & time)
dominates. Of course, orthodox quantum theory still works in the regime
where the normal fluid part of the [first reduced density matrix]
dominates. There will be coupling between the two regimes. A quantum
noise term for the Landau-Ginzburg equation for the single-valued order
parameter and coherent source terms for the normal fluid Schrodinger
equation.

"Beliaev extended this concept of factorization to the time-dependent
Green's functions [for superfluid helium] ... Gorkov observed that the
same kind of theory could be generalized to apply to the electrons of
superconductivity ... if one substituted the two-particle Green's
function ... So Gorkov introduced a [order parameter] F*(X1,X2) ... and
factorized his two-particle Green's function

G(X1,X2,X3,X4) = F*(X1,X2)F(X3,X4) + small terms

One thinks of F*(X1,X2) as a kind of two-particle wavefunction."

Note the qualification "as a kind of".

"And the two bound electrons in such a wave function should remain close
together."

Note in my theory of the emergence of gravity from the vacuum, instead
of the above two bound electrons, each on mass shell, I imagine a
virtual electron-positron pair off-mass-shell yet bound by the exchange
of a virtual photon - as the dominant Feynman history into which
jillions of virtual pairs Bose-Einstein condense.

"Gorkov showed that this theory, if one took F to be homogeneous in
space, was completely equivalent to the then just developed ... BCS
theory of superconductivity ... In superconductivity, there already
existed a theory of Ginsburg and Landau, which seems to describe
superconductivity from a phenomenological point of view very
satisfactorily. This theory describes the ... superconductor in terms of
.... the order parameter ... but the basic equations of the theory were
remarkably similar to the equations for the ordinary one-particle
quantum mechanics in terms of a single-particle wave function PSI(r)."

Do not confound this FORMAL SIMILARITY with the INFORMAL LANGUAGE
PHYSICAL INTERPRETATION. There is a qualitative difference in the
INFORMAL LANGUAGE in the two regimes when it comes to operational
procedures for observables and measurements. For example, it's easy to
make a diffraction grating for a beam of neutrons in a single-particle
wave function ensemble described by the Born probability rules, or the
Feynman rules for adding amplitudes for indistinguishable/alternatives
alternatives. But those rules break down entirely for the macro-quantum
order parameters. Thus, how can we make a diffraction grating for the
FLOW of superfluid helium without destroying the superfluidity?

To be continued.

On Aug 26, 2005, at 6:27 PM, Jack Sarfatti wrote:



On Aug 26, 2005, at 5:10 PM, George Chapline wrote:



On Aug 26, 2005, at 3:41 PM, George Chapline wrote:


"hi Jack,

Atomic clocks are nice because, in contrast with sundials, the time they
produce is directly related to quantum mechanics. Their use also
highlights the folly of doing quantum field theory inside an event
horizon, because according to GR atomic clocks no longer measure time
inside an event horizon. The celebrated treatments of QFT in curved
space-time ... claiming consistency with event horizons are just baloney.
Actually it is quite clear that the vacuum inside dark energy stars is
qualitatively the same as the ordinary vacuum (in the sense for example
a liquid and gas are the same). In particular, the vacuum energy in both
cases scales as 1/GR^2; it is just implausible that this is a
coincidence. The QFT in curved space-time gurus and string quacks
("theorists") missed this by a mile. I am astonished at the number of
people who question whether quantum mechanics works for macroscopic
length scales. I thought this question was settled by extant quantum
communication systems, but apparently there are many people who think
these systems are actually "microscopic". Also I don't understand at all
your assertion that the non-linear mean field equations for a superfluid
are inconsistent with QM. There isn't the slightest chance that QM
fails for any condensed matter system."


I mean that the "mean field" local nonunitary semi-phenomenological
Landau-Ginzburg equation for the order parameter replaces the
Schrodinger equation to some extent when dealing with the condensate. Of
course the "normal excitations" still obey the ordinary quantum rules.


"The non-linear Schrodinger equation satisfies the same probability
conservation equation as the ordinary Schrodinger equation!"



Yes, I know that. However, it is not clear that |order parameter|^2 is a
quantum probability. For example, how do you do a Stern-Gerlach
filtering, or a momentum filtering with a giant quantum field?

If you read Dirac for example, the quantum state is really a projective
ray, however the macro-quantum field does not have that property. P.W.
Anderson goes into this. I will collect his remarks later to make a
clearer more rigorous argument. The linear superposition principle
breaks down if we are talking only of the order parameter. Of course the
normal fluid excitations above the ODLRO ground state do obey the
ordinary quantum rules.

Look at NR second quantization (roughly off top of my head)

The field operator is now

total field = c-number order parameter macro-quantum part + normal
excitation micro-quantum part (let | mean integral)

H ~ |d^3x(total field)*Del^2(total field) + |d^3x'(total fieldx')*(total
fieldx')V(x - x')(total fieldx)*(total fieldx) + exchange part etc.

ih(order parameter + normal quantum operator),t = [H,(order parameter +
normal quantum operator)]

[ ] = commutator

This effectively splits into two equations one for the condensate and
one for the normal fluid with coupling between the condensate and the
normal excitations. We need to use the c-number Poisson bracket for the
condensate part to get a Landau-Ginzburg type c-number equation.

I have to look at Gorkov - did it correctly with Green's functions with
ODLRO. Will do it correctly later.