On Aug 8, 2004, at 10:23 AM, Tony ... wrote:
Jack, in your correspondence with Z, you say:
"... Pre-inflation is flat sans gravity.
Post-inflation is curved i.e. gravity
and this is a NONUNITARY process! ...".
How does your process of getting curved spacetime gravity
differ from the process of starting with flat "background"
spacetime and then using an infinite series as done by Deser and
described on pages 424-425 of Gravitation by Misner, Thorne, and Wheeler?
I don't know off-hand since those pages had no influence on what I have done.
I do know that Deser knew nothing about ODLRO nor did he have the idea of vacuum coherence for the emergence of Einstein's field equations as a low energy effective c-number local field theory in anything he was doing back thirty + years ago when MTW was written. Therefore, I suspect there is no connection
Do you think that General Relativity, which is nonlinear,
violates unitarity ?
That's comparing apples with oranges.
General relativity is a classical theory emergent from macro-quantum theory.
Unitarity is a property of micro-quantum theory which has Hermitian operators acting on QUBIT spaces.
Unitarity depends upon the Born probability interpretation, which Bohmians like Valentini have shown is not at all fundamental. Throw out the Born probability intepretation with its signal locality and you no longer have unitarity. Kip Thorne at GR 17 mentioned that the Feynman path integral technique that Hawking uses is general enough to include non-unitary post-quantum theory beyond unitary micro-quantum theory. Penrose's OR also introduces a new level of non-unitarity. Kip Thorne did mention the divide between high energy particle physicists and classical general relativists - the latter do favor NONUNITARITY BTW in the black hole information loss problem. I also note that Feynman and Hibbs in 1965 said they could not do superfluid helium and superconductivity with UNITARY micro-quantum path integrals! On the other hand, Hagen Kleinert years later says he solved the ODLRO problem using Feynman path integral method but I have not seen that detailed paper as yet. PW Anderson also said that Feynman could not solve the superconductivity problem and that Wigner's biggest blunder was his superselection rule on charge and mass that missed the important principle of "More is different."
Now the simple fact is that micro-quantum unitarity does not apply to the ODLRO part in a More is different BEC phase transition because
1. The intensity of the ODLRO parameter has a definite scale and cannot be normalized to 1 as is the case with projective ray micro-quantum waves as explained in beginning of Dirac's text book.
That is |ke> --> z|ket>
z is any complex number, is a projective ray symmetry of micro-quantum theory that is BROKEN in macro-quantum theory where
PSI --> zPSI is not a symmetry any more!
2. The phase rigidity of PSI means it DOES NOT COLLAPSE like the micro-quantum |ket> does in
|ket> = c^k|k>
p(k) = |c^k|^2 = Born probability for |ket> to collapse into the eigenket |k> of the measurement operator K for an esemble.
What does unitarity mean? It means, using summation convention on repeated pairs of sub/superscripts
c*k(t)c^k(t) = 1
for all t.
This whole game does not apply to macro-quantum ODLRO PSI!
There is NO ensemble for one thing. You have a BIG POT of superfluid Helium sitting there not 10^23 pots like the single neutrons in a beam you scatter off a crystal! One must look at the total experimental arrangement before simplistically applying concepts out of their initial physical context. Theoretical physics is in decline because too many formalists with little physical intuition have usurped control of the field with little to show - like M theory and Loop Quantum Gravity. Small bangs for big bucks and major media coverage. On the other hand, experimental physics and astronomy/cosmology are booming leaving the theorists in the dust like when Ed Witten considers the discovery of dark energy in Type 1a supernovae to be the greatest crisis in his career of passing off interesting mathematical conceptual art as if it were physics. Same for John Baez et-al who admitted to me at GR 17 that he could not recover Einstein's c-number field equation from his much hyped quantized area and volume operators and spin-foam formalism. Baez presented a cover theory that does not cover. Penrose showed that the extra space dimensions of M theory and brane theory quickly collapse like the classical electron in a classical hydrogen atom! Such is the sorry state of theory today.
This is the essential meaning of PW Anderson's 1967 insight that "More is different" emergence theory of new orders of complexity in the spontaneous breaking of ground state symmetries. That is, where the symmetry group H of the individual vacua in a space of degenerate vacua is a subgroup of G that is the symmetry group of the dynamical action S. This gives rise to multiplets of complex order parameters whose topological defects studied by Thouless, Berry et-al determine the new emergent properties that are NON-REDUCIBLE to the properties of the initial FALSE VACUUM SUBSTRATUM that is DESTROYED in the PHASE TRANSITION. You have a NEW GAME with NEW RULES i.e. MORE IS DIFFERENT! As Penrose insinuated in his GR 17 talk "Fashion, Faith and Fantasy" Hawking's application of micro-quantum unitarity to 3-Geometry is an act of pious faith with Lenny Susskind as Hawking's "Grand Inquisitor" getting Hawking, like Galileo, to recant to the Mystery of the Holy Unitarity! ;-)
Also, with respect to unitarity,
how do you reconcile your position with the following statement
of Weinberg, in Vol. II of his books The Quantum Theory of Fields
(Cambridge 1996) at page 352:
"... In this appendix we shall show that
in general spontaneously broken gauge theories
it is always possible to adopt a 'unitarity' gauge ...".
Good question. When I understand what he means by that, I will get back to you. You cannot always tell a book by its cover. The Question is: What is The Question? Does Weinberg say that the time-evolution of a macro-quantum wave PSI of a pot of superfluid helium is UNITARY? Where does he say that explicitly? That would mean that
Space integral of |PSI|^2 is a constant of the motion. I can easily disprove that statement and I doubt that Weinberg says that?
What you can prove is that the space-integral of the sum of the superfluid density + normal fluid density is a constant of the motion. That is very different.
In the exotic vacuum application for the emergence of Einstein's smooth c-number vacuum equation
Guv + /\zpfguv = 0
from the Goldstone RIGID phase of the ODLRO vacuum coherence, the "normal fluid density" is precisely the "dark energy density" when its micro-quantum pressure is NEGATIVE with ANTIGRAVITY or is "dark matter density" when its micro-quantum pressure is positive.
I do not need unstable extra space dimensions for any of this. I do need Penrose's massless 4D twistors with 15 parameter conformal group symmetry for the pre-inflationary FALSE VACUUM however!
That appendix immediately follows section 21.6 entitled "Superconductivity",
so it seems to me that Weinberg intends that the statement in that
appendix to apply to superconductivity as well as to electroweak
You have made a too vague unwarranted false inference from one to the other I know that - unless you mean that the Higgs mechanism in electro-weak theory is a small scale version of the inflation field in my theory. That is true, but there is no contradiction here because electro-weak theory is still a MICRO-QUANTUM FIELD THEORY with the U(1)xSU(2) group internal symmetry and a Poincare group space-time symmetry with a vacuum condensate only affecting the SU(2) part. There is no contradiction with what I am saying because there is NO GRAVITY in electro-weak theory. Indeed, that is why it is essentially incomplete if not inconsistent. Hence Penrose's attempt to derive both QFT and Einstein's GR from a common theory. The key is that GR is NOT RENORMALIZABLE and must be BACKGROUND-INDEPENDENT, i.e. a dynamical player on equal footing with all the other fields. That is easy to do using "More is different" and you get both dark energy and dark matter as the bonus as observed! That's the point!
Note that the curvature of Einstein gravity is like the disclination defects of a nematic liquid crystal as shown by Hagen Kleinert - and they can be gotten from the phase singularities of the vacuum condensate.