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Jul
06

I have a hard time wrapping my head around it and other similar papers. It depends on where one starts. What one takes as primitive and what one means by "emergent." I always mean spontaneous symmetry breakdown. Also in the hologram theory, a 2D quantum field theory on our spacetime's future boundary (entropic event horizon) projects the geometrodynamic curved tetrads back from our future. The whole thing is a bootstrap - a Novikov loop in time from Omega to Alpha in the sense of Tamara Davis's Fig 1.1c. - a block universe.

Rest masses m are not fundamental, but are contingent on the Higgs field. Also a clock is a complex mechanism that must include classical scale apparati in sense of Niels Bohr to call h/mc a clock simply replaces one mystery by another since the basic particles have m = 0 and m =/= 0 is a post-inflation after thought.

Most telling is that real particles with m =/= 0 are at most 4% of the universe something Mach did not know. I instinctively reject appeals to Mach' principle as profoundly wrong - my bias. I basically agree with Rovelli's approach in "Quantum Gravity."

In my view God gave us the Poincare group (up to the conformal group) and Minkowski spacetime is its image. Gravity is simply the local gauge (tetrad/spin-connection fields) of the Poincare group. To be more precise - the conformal group extension of the de Sitter group with / =/= 0 and what 15 parameters including the dilaton.

From: Paul Zielinski
To: Jack Sarfatti
Sent: Wed, July 6, 2011 2:34:50 PM

Subject: Re: de Broglie waves as the generator of spacetime

This paper certainly raises a number of interesting questions about emergent geometry, and the physical meaning of

de Broglie waves, even if you don't agree with the content.

On 7/5/2011 7:16 PM, Jack Sarfatti wrote:

Hi Ruth

I am beginning to look at your paper - but have not yet.

I am using Nick Herbert's precognition protocol. ;-)

I am confused as to the basic picture.

How can de Broglie waves exist prior to Minkowski spacetime?

What are they waving in? How can they oscillate before there is time?

OK will look at the paper. :-)

From: Ruth Elinor Kastner
To: Jack Sarfatti ; Paul Zielinski
Sent: Tue, July 5, 2011 3:15:03 PM

Subject: de Broglie waves as the generator of spacetime

The attached is provisionally accepted (pending minor revision) in Foundations of Science (edited by Diederick Aerts). Comments welcome.

Best

Ruth

Jul
06

My prejudices on this sort of investigation:

1) Mach's principle is too vague and is based on naive 17th century ideas of mass.

2) Modern GR is that there is a geometrodynamical field.

3) All boson fields come from local gauging global symmetry groups.

4) The geometry is the symmetry group in the sense of Klein Erlanger Programme.

5) I prefer to start with Minkowski spacetime as an axiom.

6) I then get Einstein's GR simply as the local gauge potential of the translation subgroup of the Poincare group - using the tetrad/spin connection Cartan forms.

Therefore curved spacetime geons exist even in absence of other matter fields. In other words Mach's principle is fundamentally the wrong road.

7) From Penrose we know that the massless spinor fermion fields are simply square roots of the invariant light cone.

8) Rest masses of quarks and leptons from from the Higgs field as in the standard model.

From: Ruth Elinor Kastner

To: Jack Sarfatti <sarfatti@pacbell.net>; Paul Zielinski <iksnileiz@gmail.com>

Sent: Tue, July 5, 2011 7:22:57 PM

Subject: RE: de Broglie waves as the generator of spacetime

Thanks Jack -- maybe think of these questions as similar to those asked about em waves in the early days of relativity-- What are they waving in? there's no 'ether'. It's a wave sans medium.

This is not an oscillation in time as in the usual temporal axis-- perhaps it's similar to Stapp's 'process time'.

Thanks, R.

________________________________________

From: Jack Sarfatti [sarfatti@pacbell.net]

Sent: Tuesday, July 05, 2011 10:16 PM

To: Ruth Elinor Kastner; Paul Zielinski

Subject: Re: de Broglie waves as the generator of spacetime

Hi Ruth

I am beginning to look at your paper - but have not yet.

I am using Nick Herbert's precognition protocol. ;-)

I am confused as to the basic picture.

How can de Broglie waves exist prior to Minkowski spacetime?

What are they waving in? How can they oscillate before there is time?

OK will look at the paper. :-)

________________________________

From: Ruth Elinor Kastner <rkastner@umd.edu>

To: Jack Sarfatti <sarfatti@pacbell.net>; Paul Zielinski <iksnileiz@gmail.com>

Sent: Tue, July 5, 2011 3:15:03 PM

Subject: de Broglie waves as the generator of spacetime

The attached is provisionally accepted (pending minor revision) in Foundations of Science (edited by Diederick Aerts). Comments welcome.

Best

Ruth

1) Mach's principle is too vague and is based on naive 17th century ideas of mass.

2) Modern GR is that there is a geometrodynamical field.

3) All boson fields come from local gauging global symmetry groups.

4) The geometry is the symmetry group in the sense of Klein Erlanger Programme.

5) I prefer to start with Minkowski spacetime as an axiom.

6) I then get Einstein's GR simply as the local gauge potential of the translation subgroup of the Poincare group - using the tetrad/spin connection Cartan forms.

Therefore curved spacetime geons exist even in absence of other matter fields. In other words Mach's principle is fundamentally the wrong road.

7) From Penrose we know that the massless spinor fermion fields are simply square roots of the invariant light cone.

8) Rest masses of quarks and leptons from from the Higgs field as in the standard model.

From: Ruth Elinor Kastner

To: Jack Sarfatti <sarfatti@pacbell.net>; Paul Zielinski <iksnileiz@gmail.com>

Sent: Tue, July 5, 2011 7:22:57 PM

Subject: RE: de Broglie waves as the generator of spacetime

Thanks Jack -- maybe think of these questions as similar to those asked about em waves in the early days of relativity-- What are they waving in? there's no 'ether'. It's a wave sans medium.

This is not an oscillation in time as in the usual temporal axis-- perhaps it's similar to Stapp's 'process time'.

Thanks, R.

________________________________________

From: Jack Sarfatti [sarfatti@pacbell.net]

Sent: Tuesday, July 05, 2011 10:16 PM

To: Ruth Elinor Kastner; Paul Zielinski

Subject: Re: de Broglie waves as the generator of spacetime

Hi Ruth

I am beginning to look at your paper - but have not yet.

I am using Nick Herbert's precognition protocol. ;-)

I am confused as to the basic picture.

How can de Broglie waves exist prior to Minkowski spacetime?

What are they waving in? How can they oscillate before there is time?

OK will look at the paper. :-)

________________________________

From: Ruth Elinor Kastner <rkastner@umd.edu>

To: Jack Sarfatti <sarfatti@pacbell.net>; Paul Zielinski <iksnileiz@gmail.com>

Sent: Tue, July 5, 2011 3:15:03 PM

Subject: de Broglie waves as the generator of spacetime

The attached is provisionally accepted (pending minor revision) in Foundations of Science (edited by Diederick Aerts). Comments welcome.

Best

Ruth

Jul
06

Tagged in:

In a strong measurement, the results are eigenvalues of eigenfunctions. The eigenfunctions describe Bohr's "total experimental arrangement." Therefore, Zielinski's false premise below is that a transformation of basis eigenvectors is a purely formal matter. That is false. Every basis transformation is a physical change of the total experimental arrangement, e.g. changing relative orientations of Stern-Gerlach magnets in testing Bell's inequality in entangled pairs of magnetic spins.

From: Paul Zielinski <iksnileiz@gmail.com>

To: Jack Sarfatti <sarfatti@pacbell.net>

Sent: Tue, July 5, 2011 2:18:24 PM

Subject: Re: Creon Levit's Nano-electronics & The issue of small n - FTL signals via over-complete non-orthogonal coherent states?

On 7/4/2011 5:23 PM, Jack Sarfatti wrote:

From: Paul Zielinski <iksnileiz@gmail.com>

To: Ruth Elinor Kastner <rkastner@umd.edu>

Sent: Mon, July 4, 2011 3:54:52 PM

Subject: Re: Creon's Nano-electronics & The issue of small n - FTL signals via over-complete non-orthogonal coherent states?

PZ: "Orthogonal transformations in ordinary Euclidean 3D space preserve lengths and angles. Non-orthogonal transformations don't. If we apply a non-orthogonal transformation in a Euclidean space, of course we will see formal changes in lengths and angles, but it will have no objective geometric meaning. "

JS: You are wrong. For one thing, you have confused "transformation" with "basis".

PZ: Not at all. The point here is that you have to apply a non-orthogonal transformation to get from an orthogonal basis to a non-orthogonal basis, and the inner product defined by the Euclidean metric is not preserved.

JS: You mean a "non-unitary" transformation. I never denied that. But my argument for entanglement signals never explicitly used a non-unitary transformation. The physical idea is that the non-orthogonal basis is there objectively physically ab-initio for dynamical reasons, e.g. stimulated emission population inversion, some spontaneous symmetry breakdown with a Glauber state condensate of Goldstone bosons etc.

Given that non-orthogonal basis, unitary transformations on it give a new non-orthogonal basis.

OQT does not permit non-unitary dynamics - a weakness of OQT admittedly. It does not apply to open systems. Dissipation introduces non-Hermitian observables for example, e.g. imaginary part of the effective Hamiltonian.

You apply a transformation to a basis.

PZ: Right.

JS: Second, when you move to a uniformly accelerating non-inertial Rindler frame for example, there are cross terms in the metric

gtz =/= 0

PZ: OK...

JS: Also the non-geodesic Rindler guv-detector sees real photons in the form of thermal black body Unruh radiation. In contrast, the geodesic detector nab sees only virtual zero point photons.

PZ: I was making a general mathematical point about inner products and non-orthogonal/non-unitary transformations.

JS: That's not good physics. The job of the theoretical physicist is more physics with less math not the other way round. Any fundamental mathematical process must describe a physical change of some kind. If not, if it's redundant then it is a gauge transformation that must be "gauged away" in some sense. Of course, in GR the gauge transformations have direct physical operational meaning unlike the internal U1, SU2, SU3 gauge transformations.

The tetrad map connecting the two of them is a real physical change i.e. switching a rocket engine on or off for example.

PZ: My point is that any changes in lengths that result purely from the application of non-orthogonal transformations in ordinary 3D Euclidean space, for example, are not actual geometric changes. I am saying that the same applies to non-unitary transformations and inner products in the Hilbert space formalism of QM.

JS: Your remarks are too vague to pin down to my actual toy model. I am saying that stimulated emission with population creates an objectively real Glauber state non-orthogonal basis whose partial traces leaves an entanglement signal when we can entangle two back to back laser beams without orthogonal polarizations destroying the effect. You can in the sense of an analogy compare that to a non-unitary transformation in Hilbert space that indeed does violate OQT in Henry Stapp's sense.

PZ: I think this is a different issue.

JS: No that IS my issue here. You have introduced extraneous side issues.

PZ: Yes one could for example modify the Schrodinger equation such that time evolution of the wave

function is no longer unitary, but that would represent a change in the physics. I suppose one could interpret such non-unitary time evolution in terms of creation/annihilation of particle density (sources and sinks), but that would constitute a change of physical interpretation, which goes well beyond the purely mathematical application of a non-unitary transformation.

JS: That's what happens in a laser where the macro-quantum coherence dynamics is no longer the linear unitary Schrodinger equation entangled in configuration space, but morphs to a nonlinear nonunitary emergent Landau-Ginzburg equation for the order parameter local in physical space! - but with some residual entanglement and still a coupling to micro-quantum noise (Goldstone bosons popping into and out of the Goldstone boson condensate order parameter).

PZ: I'm making a mathematical point about the invariance of lengths and angles (inner products) under a certain class of transformations.

JS: Completely irrelevant to the physics. I am not interested in redundant formal transformations that must be factored out of the actual physics of testable measurements. Please I am not interested side issues of formalism - unless it's an error in my own use of formal symbol strings.

PZ: Non-orthogonal transformations in Euclidean space don't preserve lengths and angles, but in standard Euclidean theory this has no geometric meaning. I'm suggesting that you can make the same argument in a Hilbert space. I'm arguing that changes in the computed inner products that result purely from the mathematical application of a non-unitary transformation do not have any physical meaning in the standard Hilbert space formulation of QM, any more than the analogous changes in lengths and angles resulting from the application of non-orthogonal transformations in Euclidean theory have actual geometric meaning.

JS: Not relevant to the physics I am proposing.

PZ: As you like to say, the map is not the territory.

JS: The quantum unitary transformations are then analogs of the global Lorentz boosts, the global rotations and translations of Special Relativity restricted to the global 10-parameter Poincare group.

PZ: Not in 3D Euclidean space, which is what I was referring to. There we are talking about ordinary orthogonal transformations. Very simple and intuitive. You can construct orthogonal and non-orthogonal bases, and apply orthogonal and non-orthogonal transformations, quite generally in Riemannian geometry.

JS You are losing me. This is a tangent. A distraction.

Adding in the Rindler observers is adding the special conformal transformations I suppose. That is, going to a bigger group.

PZ: Rindler transformations do not change the intrinsic (coordinate invariant) value of the Riemann metric, they only change the representation of the metric. I'm saying an analogous distinction applies in the Hilbert space formalism.

JS: The real measurements of the Rindler observer differ qualitatively from those of the Minkowski observer. True the classical metric structure is the same, but the quantum properties are different. You fail to make the difference that makes a difference. Classical measurements e.g. curvature are the same. On the other hand the Rindler observer feels g-force whilst the Minkowski observer does not. The Rindler observer feels heat, the Minkowski observer does not. Therefore, including quantum measurements, the special conformal boost describes a physical change in the total experimental arrangement in the sense of Bohr. Your mistake Paul is to think too classically. These are new quantum gravity effects.

PZ: The map is not the territory.

JS: Finally GR involves localizing only the 4-parameter translation sub-group of the Poincare group.

Then e.g. cosmology has spontaneous symmetry breakdown of the T1 time translation group i.e. Hubble flow of accelerating expanding universe in which total global energy is not conserved. Thus, in the dS solution we have a constant /\ vacuum energy density so that the total vacuum energy density is not conserved. However it does appear to have a finite upper bound because of the finite distance to our future event horizon.

Our actual universe is not dS at the beginning, so that /\ is not a constant. It is large at inflation and then decreases approaching a small asymptote.

PZ: So how is the situation any different in QM, if we consider the corresponding unitary and non-unitary transformations?

JS: I just showed you. Your analogy is false.

PZ: Well you thought I was confusing non-orthogonal transformations with non-orthogonal basis vectors. Which I wasn't.

JS: Whatever you thought you were doing was not helpful to the real problem at hand which is

1) Do entanglement signals exist in complex biological systems ubiquitously? e.g. Josephson, Bem et-al

2) Do they exist in non-living quantum mechanical systems? - Moddell's problem.

e.g. do they exist whenever LCAO non-orthogonal bases are needed for a correct computation of observables in quantum chemistry for example?

PZ: It seems obvious to me that changes in computed quantities that result purely from the merely mathematical application of a non-unitary transformation to an orthonormal basis spanning a QM Hilbert space in itself has no physical meaning under the standard interpretation of the QM formalism.

JS: Of no relevance to what I am interested in. Different ball park.

PZ: Of course, if the physical interpretation changes, then this may not apply. But that is a different kettle of fish.

JS: It's the kettle I am stirring.

PZ: Surely inner products computed from state vectors subject to non-unitary transformations have a very different meaning in the Hilbert space formalism of QM from those computed under unitary transformations?

JS: Agreed, but that has nothing to do with my original point which is that GIVEN a physically realizable non-orthogonal basis for an entangled system, partially tracing over a part of the system will allow an entangled signal to the other part.

PZ: Why are you so sure that such correlations do not result purely from the non-zero projections of the non-orthogonal basis vectors onto each other? Why are you so sure that such "entanglement" has the same physical meaning as when the observables are represented in an orthonormal basis? Couldn't such "correlations" simply reflect the non-orthogonal character of the basis?

JS: I have no idea what the above string of words means. There is evidence of signal nonlocality in living matter. I am trying to model how that can happen. The basic idea is that the inner products of base states with each other are not formal redundancies, but are objectively real control parameters.

Non-Hermitian Hamiltonians for open systems with dissipation will have non-orthogonal over-complete energy eigenfunctions with complex energy eigenvalues - I think. True they will evolve with a non-unitary dynamics for the emergent order parameter.

PZ: What happens to analogous geometric quantities when we transform to a non-orthogonal vector basis, in plain vanilla Euclidean geometry?

JS: Who cares? Not an interesting question for what I am trying to do.

Your red herring of a non-unitary transformation is nowhere in the actual calculation I gave.

PZ: I feel you are missing the point, which is that in order to get from an orthogonal basis to a non-orthogonal basis you have to apply a non-unitary transformation. I'm not saying that you did that explicitly.

JS: Show how that changes the actual equations in the model I proposed? I don't care in this initial phase what specific physically real non-unitary map may have created the non-orthogonal basis to begin with. I assume it is there as my starting point to get the entanglement signal. The details of the non-unitary physics that forces the non-orthogonal basis is a separate problem of importance obviously.

Now the LCAO basis in the many electron problem may be an example of what I am looking for, but I am not sure.

Well they are definitely using non-orthogonal basis representations of correlated density matrices. There is no

question in my mind at least that technically one can do this.

PZ: My point here is that any change in computed inner products that purely arises from the formal application of a non-unitary transformation to an orthonormal basis cannot have the same meaning as an inner product that is computed in the usual manner.

JS: Irrelevant as I never did that in this case.

PZ: As I said, I think you may be missing the point, which is that in order to get from an orthogonal basis to a

non-orthogonal basis you have apply a non-unitary transformation, which "stretches" the Hilbert space inner products.

That is not a true geometric stretch -- it's a Coney Island fun house optic!

Of course we've already been through all this with objective spacetime warps vs. mere coordinate artifacts in GR. For

example, black hole event horizons are not coordinate-dependent artifacts. Also there is no such thing as a purely formal non-unitary transformation in a real physics theory. Well there is in Euclidean geometry. In Euclidean geometry a non-orthogonal transformation is a fun house mirror. A passive diffeomorphism is a fun house optic.

I'm not saying that one cannot change to physical interpretation of QM such that the effects of non-unitary transformations on inner products can acquire objective physical meaning.

Of course here I'm talking about the standard Hilbert space formulation of orthodox QM.

JS: Any such transformation must describe an objective change - some operation like firing a rocket engine, or adding dissipation to a complex system, pumping it off thermal equilibrium etc.

PZ: Exactly.

PZ: Changes in the computed values of such inner products can only be purely formal in character.

JS: I don't think that is the case.

PZ; I meant to write, "... such changes in the computed values of inner products..."

JS: Sure if, it's only formal you are correct. However, I don't think that is what is happening in the situations Brian Josephson had in mind and in the Daryl Bem data.

PZ: What I'm saying here is not very subtle Jack. Obviously non-orthogonal vectors are "correlated" since they have non-zero projections onto each other. But it has no objective geometric meaning in Euclidean geometry, and I'm saying that something similar applies in QM Hilbert spaces.

I agree that there is a close analogy here with some possible misconceptions in the interpretation of GR. You seem to be implicitly applying a kind of "equivalence principle" to basis-dependent artifacts in QM, rendering them physically indistinguishable from actual changes in physical correlations predicted by QM. Am I wrong?

PZ: Since entanglement correlations for multiparticle systems ultimately have to be computed from such inner products, it is hard to see how such correlations that arise purely from non-unitary transformations of an orthonormal basis to a non-orthonormal basis can have objective physical meaning within the framework of QM.

JS: My idea is that the non-orthogonal basis are actually there in the complex system in a physical sense and are not simply a formal alternative.

PZ: OK.

JS: In other words you will get the wrong answer if you used an orthogonal basis.

PZ: But how do you think can you get a different physical answer simply by changing the basis representation of a QM observable? That's what I don't get.

JS: To make an analogy, you will not measure Unruh temperature unless you switch on your rocket engine - but when you do, your temperature gauge measures a real temperature that drops to zero when you switch off the engine.

PZ: But that is the result of a real physical interaction of the moving detectors with the vacuum. You are confusing a mere coordinate transformation with a physical interaction.

JS: Not at all. Switching on a rocket engine is a real physical process that transforms a Minkowski to a Rindler observer.

PZ: OK then I guess I was right -- you are applying an analog of Einstein's equivalence principle to basis dependent artifacts.

Heuristically speaking this might be OK, and might produce interesting results, but it's kind of crazy from a purely analytical perspective.

There is no such "equivalence principle" in orthodox QM. I think you would have to modify the standard interpretation of the Hilbert space formulation of QM for this even to be relevant.

PZ: Of course one can create non-vanishing non-diagonal matrix elements in any "observable" by going to a non-orthogonal basis, but does this mean that we now have non-vanishing transition probabilities between eigenstates of the observable? It should be obvious that the non-vanishing off-diagonal elements merely reflect the fact that non-orthogonal basis vectors have non-zero projections onto each other.

JS: False. Either the physics gives you an orthogonal basis or not.

PZ: Don't we have to distinguish carefully here between the mathematical choice of basis, on the one hand, and the physical

motivation for the choice of state vectors, on the other? Clearly we want our state vectors to represent the states we actually

prepare, but I think the choice of basis in which to represent Hilbert space operators is another issue.

I say it's a mathematical question. Just as the choice of coordinates in Euclidean space need not have any relationship to the behavior of "observers" -- unless one establishes a convention to that effect.

JS: In OQT you can only use unitary transformations of basis.

PZ: OK.

JS: The inner products are invariant in OQT for a closed system.

PS: OK.

JS: Non-unitary transformations are forbidden in OQT.

Nonunitary transformations require new physics beyond OQT.

PZ: OK.

JS: However, I do agree we need non-unitary transformations in physics. But they are not merely formal crutches.

PZ: Well I would say that mathematically speaking we already have them in any Hilbert space, but they don't have physical meaning in the orthodox interpretation of the QM formalism. Any more than non-orhtogonal transformations have geometric meaning in ordinary Euclidean geometry.

JS: Gerardus 't Hooft does not think so. He thinks the unitary S-Matrix describes black holes for example if you wait long enough. On the other hand, applied physicists do use dissipative non-unitary transformations, but I guess the lip service is that when you include the traced over environment everything is unitary.

PZ: Which raises questions about exactly what the physical chemists think they're doing with those "strongly correlated" density matrices expressed in non-orthogonal bases! I don't think they are offering any modifications of the standard interpretation of the QM formalism.

PZ: So Jack, how is the multiparticle case in essence any different with respect to the entanglement correlations considered in your thought experiment? Of course one can prepare non-orthogonal coherent photon states as you say, but if the effects you predict arise purely from the use of a non-orthogonal basis for the representation of quantum "observables", what makes you think they have any more objective physical meaning than changes in lengths and angles induced in ordinary Euclidean space by non-orthogonal transformations?

JS: Your formal analogy is not correct physically.

Didn't you say or at least imply above that the analogy is good in the standard interpretation of the von Neumann formalism?

PZ: You said non-unitary transformations are not physically admissible in orthodox QM. In order to get from an orthogonal basis to a non-orthogonal basis in QM, you have to apply a non-unitary transformation, which "stretches" the inner products. So any "observable" derived from such quantities will similarly be "stretched". You want to say that an artifact of such a transformation is in certain cases a real physical effect. I'm saying that this would require a fundamental modification of OQT.

JS: Of course it does. However, lasers do that. Spontaneous broken symmetries do it.

Unlike pure mathematics, the transformations in real physics must describe differences that make a physical difference, otherwise the physical theory is ill-posed, wrong or worse not even wrong.

Well exactly. And isn't that my point?

On 7/4/2011 9:45 AM, Ruth Elinor Kastner wrote:

I still think the issue is just that the entanglement is with respect to which-slit (which is an observable whose eigenstates are orthogonal) and not with respect to the nonorthogonal eigenstates of the annihilation operators (coherent states). So I think what needs to be questioned (as you suspected peviously) is your eqn 1-18. Where does this come from? It seems to me that the A1 and A2 have to be just which-slit eigenstates here.

-RK

From: Paul Zielinski <iksnileiz@gmail.com>

To: Jack Sarfatti <sarfatti@pacbell.net>

Sent: Tue, July 5, 2011 2:18:24 PM

Subject: Re: Creon Levit's Nano-electronics & The issue of small n - FTL signals via over-complete non-orthogonal coherent states?

On 7/4/2011 5:23 PM, Jack Sarfatti wrote:

From: Paul Zielinski <iksnileiz@gmail.com>

To: Ruth Elinor Kastner <rkastner@umd.edu>

Sent: Mon, July 4, 2011 3:54:52 PM

Subject: Re: Creon's Nano-electronics & The issue of small n - FTL signals via over-complete non-orthogonal coherent states?

PZ: "Orthogonal transformations in ordinary Euclidean 3D space preserve lengths and angles. Non-orthogonal transformations don't. If we apply a non-orthogonal transformation in a Euclidean space, of course we will see formal changes in lengths and angles, but it will have no objective geometric meaning. "

JS: You are wrong. For one thing, you have confused "transformation" with "basis".

PZ: Not at all. The point here is that you have to apply a non-orthogonal transformation to get from an orthogonal basis to a non-orthogonal basis, and the inner product defined by the Euclidean metric is not preserved.

JS: You mean a "non-unitary" transformation. I never denied that. But my argument for entanglement signals never explicitly used a non-unitary transformation. The physical idea is that the non-orthogonal basis is there objectively physically ab-initio for dynamical reasons, e.g. stimulated emission population inversion, some spontaneous symmetry breakdown with a Glauber state condensate of Goldstone bosons etc.

Given that non-orthogonal basis, unitary transformations on it give a new non-orthogonal basis.

OQT does not permit non-unitary dynamics - a weakness of OQT admittedly. It does not apply to open systems. Dissipation introduces non-Hermitian observables for example, e.g. imaginary part of the effective Hamiltonian.

You apply a transformation to a basis.

PZ: Right.

JS: Second, when you move to a uniformly accelerating non-inertial Rindler frame for example, there are cross terms in the metric

gtz =/= 0

PZ: OK...

JS: Also the non-geodesic Rindler guv-detector sees real photons in the form of thermal black body Unruh radiation. In contrast, the geodesic detector nab sees only virtual zero point photons.

PZ: I was making a general mathematical point about inner products and non-orthogonal/non-unitary transformations.

JS: That's not good physics. The job of the theoretical physicist is more physics with less math not the other way round. Any fundamental mathematical process must describe a physical change of some kind. If not, if it's redundant then it is a gauge transformation that must be "gauged away" in some sense. Of course, in GR the gauge transformations have direct physical operational meaning unlike the internal U1, SU2, SU3 gauge transformations.

The tetrad map connecting the two of them is a real physical change i.e. switching a rocket engine on or off for example.

PZ: My point is that any changes in lengths that result purely from the application of non-orthogonal transformations in ordinary 3D Euclidean space, for example, are not actual geometric changes. I am saying that the same applies to non-unitary transformations and inner products in the Hilbert space formalism of QM.

JS: Your remarks are too vague to pin down to my actual toy model. I am saying that stimulated emission with population creates an objectively real Glauber state non-orthogonal basis whose partial traces leaves an entanglement signal when we can entangle two back to back laser beams without orthogonal polarizations destroying the effect. You can in the sense of an analogy compare that to a non-unitary transformation in Hilbert space that indeed does violate OQT in Henry Stapp's sense.

PZ: I think this is a different issue.

JS: No that IS my issue here. You have introduced extraneous side issues.

PZ: Yes one could for example modify the Schrodinger equation such that time evolution of the wave

function is no longer unitary, but that would represent a change in the physics. I suppose one could interpret such non-unitary time evolution in terms of creation/annihilation of particle density (sources and sinks), but that would constitute a change of physical interpretation, which goes well beyond the purely mathematical application of a non-unitary transformation.

JS: That's what happens in a laser where the macro-quantum coherence dynamics is no longer the linear unitary Schrodinger equation entangled in configuration space, but morphs to a nonlinear nonunitary emergent Landau-Ginzburg equation for the order parameter local in physical space! - but with some residual entanglement and still a coupling to micro-quantum noise (Goldstone bosons popping into and out of the Goldstone boson condensate order parameter).

PZ: I'm making a mathematical point about the invariance of lengths and angles (inner products) under a certain class of transformations.

JS: Completely irrelevant to the physics. I am not interested in redundant formal transformations that must be factored out of the actual physics of testable measurements. Please I am not interested side issues of formalism - unless it's an error in my own use of formal symbol strings.

PZ: Non-orthogonal transformations in Euclidean space don't preserve lengths and angles, but in standard Euclidean theory this has no geometric meaning. I'm suggesting that you can make the same argument in a Hilbert space. I'm arguing that changes in the computed inner products that result purely from the mathematical application of a non-unitary transformation do not have any physical meaning in the standard Hilbert space formulation of QM, any more than the analogous changes in lengths and angles resulting from the application of non-orthogonal transformations in Euclidean theory have actual geometric meaning.

JS: Not relevant to the physics I am proposing.

PZ: As you like to say, the map is not the territory.

JS: The quantum unitary transformations are then analogs of the global Lorentz boosts, the global rotations and translations of Special Relativity restricted to the global 10-parameter Poincare group.

PZ: Not in 3D Euclidean space, which is what I was referring to. There we are talking about ordinary orthogonal transformations. Very simple and intuitive. You can construct orthogonal and non-orthogonal bases, and apply orthogonal and non-orthogonal transformations, quite generally in Riemannian geometry.

JS You are losing me. This is a tangent. A distraction.

Adding in the Rindler observers is adding the special conformal transformations I suppose. That is, going to a bigger group.

PZ: Rindler transformations do not change the intrinsic (coordinate invariant) value of the Riemann metric, they only change the representation of the metric. I'm saying an analogous distinction applies in the Hilbert space formalism.

JS: The real measurements of the Rindler observer differ qualitatively from those of the Minkowski observer. True the classical metric structure is the same, but the quantum properties are different. You fail to make the difference that makes a difference. Classical measurements e.g. curvature are the same. On the other hand the Rindler observer feels g-force whilst the Minkowski observer does not. The Rindler observer feels heat, the Minkowski observer does not. Therefore, including quantum measurements, the special conformal boost describes a physical change in the total experimental arrangement in the sense of Bohr. Your mistake Paul is to think too classically. These are new quantum gravity effects.

PZ: The map is not the territory.

JS: Finally GR involves localizing only the 4-parameter translation sub-group of the Poincare group.

Then e.g. cosmology has spontaneous symmetry breakdown of the T1 time translation group i.e. Hubble flow of accelerating expanding universe in which total global energy is not conserved. Thus, in the dS solution we have a constant /\ vacuum energy density so that the total vacuum energy density is not conserved. However it does appear to have a finite upper bound because of the finite distance to our future event horizon.

Our actual universe is not dS at the beginning, so that /\ is not a constant. It is large at inflation and then decreases approaching a small asymptote.

PZ: So how is the situation any different in QM, if we consider the corresponding unitary and non-unitary transformations?

JS: I just showed you. Your analogy is false.

PZ: Well you thought I was confusing non-orthogonal transformations with non-orthogonal basis vectors. Which I wasn't.

JS: Whatever you thought you were doing was not helpful to the real problem at hand which is

1) Do entanglement signals exist in complex biological systems ubiquitously? e.g. Josephson, Bem et-al

2) Do they exist in non-living quantum mechanical systems? - Moddell's problem.

e.g. do they exist whenever LCAO non-orthogonal bases are needed for a correct computation of observables in quantum chemistry for example?

PZ: It seems obvious to me that changes in computed quantities that result purely from the merely mathematical application of a non-unitary transformation to an orthonormal basis spanning a QM Hilbert space in itself has no physical meaning under the standard interpretation of the QM formalism.

JS: Of no relevance to what I am interested in. Different ball park.

PZ: Of course, if the physical interpretation changes, then this may not apply. But that is a different kettle of fish.

JS: It's the kettle I am stirring.

PZ: Surely inner products computed from state vectors subject to non-unitary transformations have a very different meaning in the Hilbert space formalism of QM from those computed under unitary transformations?

JS: Agreed, but that has nothing to do with my original point which is that GIVEN a physically realizable non-orthogonal basis for an entangled system, partially tracing over a part of the system will allow an entangled signal to the other part.

PZ: Why are you so sure that such correlations do not result purely from the non-zero projections of the non-orthogonal basis vectors onto each other? Why are you so sure that such "entanglement" has the same physical meaning as when the observables are represented in an orthonormal basis? Couldn't such "correlations" simply reflect the non-orthogonal character of the basis?

JS: I have no idea what the above string of words means. There is evidence of signal nonlocality in living matter. I am trying to model how that can happen. The basic idea is that the inner products of base states with each other are not formal redundancies, but are objectively real control parameters.

Non-Hermitian Hamiltonians for open systems with dissipation will have non-orthogonal over-complete energy eigenfunctions with complex energy eigenvalues - I think. True they will evolve with a non-unitary dynamics for the emergent order parameter.

PZ: What happens to analogous geometric quantities when we transform to a non-orthogonal vector basis, in plain vanilla Euclidean geometry?

JS: Who cares? Not an interesting question for what I am trying to do.

Your red herring of a non-unitary transformation is nowhere in the actual calculation I gave.

PZ: I feel you are missing the point, which is that in order to get from an orthogonal basis to a non-orthogonal basis you have to apply a non-unitary transformation. I'm not saying that you did that explicitly.

JS: Show how that changes the actual equations in the model I proposed? I don't care in this initial phase what specific physically real non-unitary map may have created the non-orthogonal basis to begin with. I assume it is there as my starting point to get the entanglement signal. The details of the non-unitary physics that forces the non-orthogonal basis is a separate problem of importance obviously.

Now the LCAO basis in the many electron problem may be an example of what I am looking for, but I am not sure.

Well they are definitely using non-orthogonal basis representations of correlated density matrices. There is no

question in my mind at least that technically one can do this.

PZ: My point here is that any change in computed inner products that purely arises from the formal application of a non-unitary transformation to an orthonormal basis cannot have the same meaning as an inner product that is computed in the usual manner.

JS: Irrelevant as I never did that in this case.

PZ: As I said, I think you may be missing the point, which is that in order to get from an orthogonal basis to a

non-orthogonal basis you have apply a non-unitary transformation, which "stretches" the Hilbert space inner products.

That is not a true geometric stretch -- it's a Coney Island fun house optic!

Of course we've already been through all this with objective spacetime warps vs. mere coordinate artifacts in GR. For

example, black hole event horizons are not coordinate-dependent artifacts. Also there is no such thing as a purely formal non-unitary transformation in a real physics theory. Well there is in Euclidean geometry. In Euclidean geometry a non-orthogonal transformation is a fun house mirror. A passive diffeomorphism is a fun house optic.

I'm not saying that one cannot change to physical interpretation of QM such that the effects of non-unitary transformations on inner products can acquire objective physical meaning.

Of course here I'm talking about the standard Hilbert space formulation of orthodox QM.

JS: Any such transformation must describe an objective change - some operation like firing a rocket engine, or adding dissipation to a complex system, pumping it off thermal equilibrium etc.

PZ: Exactly.

PZ: Changes in the computed values of such inner products can only be purely formal in character.

JS: I don't think that is the case.

PZ; I meant to write, "... such changes in the computed values of inner products..."

JS: Sure if, it's only formal you are correct. However, I don't think that is what is happening in the situations Brian Josephson had in mind and in the Daryl Bem data.

PZ: What I'm saying here is not very subtle Jack. Obviously non-orthogonal vectors are "correlated" since they have non-zero projections onto each other. But it has no objective geometric meaning in Euclidean geometry, and I'm saying that something similar applies in QM Hilbert spaces.

I agree that there is a close analogy here with some possible misconceptions in the interpretation of GR. You seem to be implicitly applying a kind of "equivalence principle" to basis-dependent artifacts in QM, rendering them physically indistinguishable from actual changes in physical correlations predicted by QM. Am I wrong?

PZ: Since entanglement correlations for multiparticle systems ultimately have to be computed from such inner products, it is hard to see how such correlations that arise purely from non-unitary transformations of an orthonormal basis to a non-orthonormal basis can have objective physical meaning within the framework of QM.

JS: My idea is that the non-orthogonal basis are actually there in the complex system in a physical sense and are not simply a formal alternative.

PZ: OK.

JS: In other words you will get the wrong answer if you used an orthogonal basis.

PZ: But how do you think can you get a different physical answer simply by changing the basis representation of a QM observable? That's what I don't get.

JS: To make an analogy, you will not measure Unruh temperature unless you switch on your rocket engine - but when you do, your temperature gauge measures a real temperature that drops to zero when you switch off the engine.

PZ: But that is the result of a real physical interaction of the moving detectors with the vacuum. You are confusing a mere coordinate transformation with a physical interaction.

JS: Not at all. Switching on a rocket engine is a real physical process that transforms a Minkowski to a Rindler observer.

PZ: OK then I guess I was right -- you are applying an analog of Einstein's equivalence principle to basis dependent artifacts.

Heuristically speaking this might be OK, and might produce interesting results, but it's kind of crazy from a purely analytical perspective.

There is no such "equivalence principle" in orthodox QM. I think you would have to modify the standard interpretation of the Hilbert space formulation of QM for this even to be relevant.

PZ: Of course one can create non-vanishing non-diagonal matrix elements in any "observable" by going to a non-orthogonal basis, but does this mean that we now have non-vanishing transition probabilities between eigenstates of the observable? It should be obvious that the non-vanishing off-diagonal elements merely reflect the fact that non-orthogonal basis vectors have non-zero projections onto each other.

JS: False. Either the physics gives you an orthogonal basis or not.

PZ: Don't we have to distinguish carefully here between the mathematical choice of basis, on the one hand, and the physical

motivation for the choice of state vectors, on the other? Clearly we want our state vectors to represent the states we actually

prepare, but I think the choice of basis in which to represent Hilbert space operators is another issue.

I say it's a mathematical question. Just as the choice of coordinates in Euclidean space need not have any relationship to the behavior of "observers" -- unless one establishes a convention to that effect.

JS: In OQT you can only use unitary transformations of basis.

PZ: OK.

JS: The inner products are invariant in OQT for a closed system.

PS: OK.

JS: Non-unitary transformations are forbidden in OQT.

Nonunitary transformations require new physics beyond OQT.

PZ: OK.

JS: However, I do agree we need non-unitary transformations in physics. But they are not merely formal crutches.

PZ: Well I would say that mathematically speaking we already have them in any Hilbert space, but they don't have physical meaning in the orthodox interpretation of the QM formalism. Any more than non-orhtogonal transformations have geometric meaning in ordinary Euclidean geometry.

JS: Gerardus 't Hooft does not think so. He thinks the unitary S-Matrix describes black holes for example if you wait long enough. On the other hand, applied physicists do use dissipative non-unitary transformations, but I guess the lip service is that when you include the traced over environment everything is unitary.

PZ: Which raises questions about exactly what the physical chemists think they're doing with those "strongly correlated" density matrices expressed in non-orthogonal bases! I don't think they are offering any modifications of the standard interpretation of the QM formalism.

PZ: So Jack, how is the multiparticle case in essence any different with respect to the entanglement correlations considered in your thought experiment? Of course one can prepare non-orthogonal coherent photon states as you say, but if the effects you predict arise purely from the use of a non-orthogonal basis for the representation of quantum "observables", what makes you think they have any more objective physical meaning than changes in lengths and angles induced in ordinary Euclidean space by non-orthogonal transformations?

JS: Your formal analogy is not correct physically.

Didn't you say or at least imply above that the analogy is good in the standard interpretation of the von Neumann formalism?

PZ: You said non-unitary transformations are not physically admissible in orthodox QM. In order to get from an orthogonal basis to a non-orthogonal basis in QM, you have to apply a non-unitary transformation, which "stretches" the inner products. So any "observable" derived from such quantities will similarly be "stretched". You want to say that an artifact of such a transformation is in certain cases a real physical effect. I'm saying that this would require a fundamental modification of OQT.

JS: Of course it does. However, lasers do that. Spontaneous broken symmetries do it.

Unlike pure mathematics, the transformations in real physics must describe differences that make a physical difference, otherwise the physical theory is ill-posed, wrong or worse not even wrong.

Well exactly. And isn't that my point?

On 7/4/2011 9:45 AM, Ruth Elinor Kastner wrote:

I still think the issue is just that the entanglement is with respect to which-slit (which is an observable whose eigenstates are orthogonal) and not with respect to the nonorthogonal eigenstates of the annihilation operators (coherent states). So I think what needs to be questioned (as you suspected peviously) is your eqn 1-18. Where does this come from? It seems to me that the A1 and A2 have to be just which-slit eigenstates here.

-RK

Jul
05

Tagged in:

However, when one writes them in second-quantization, we regain linearity in the sharp number orthogonal basis Fock space.

In first quantization

http://vergil.chemistry.gatech.edu/notes/hf-intro/img63.png

note the 3rd term on the LHS that couples the different base eigenfunctions in the integral.

http://vergil.chemistry.gatech.edu/notes/hf-intro/node7.html

compare to the emergent SSB Landau-Ginzburg L-G equation e.g.

http://upload.wikimedia.org/math/9/4/5/945a3f42246130d5daba8e3c6417aec4.png

http://en.wikipedia.org/wiki/Ginzburg–Landau_theory

But the L-G equation is fundamentally zero-quantization i.e. a c-number emergent nonlinear local equation that trivially solves the emergence of classicality problem of quantum reality explaining why no big Schrodinger Tigers.

For example, crystal lattices come from spontaneous broken T3 symmetry in the ground states of systems of atoms in thermal equilibrium at low enough temperature - the lattice positions are a set of emergent "phonon" Goldstone boson condensate macro-quantum coherent order parameters. See Hagen Kleinert's books for the details.

http://users.physik.fu-berlin.de/~kleinert/kleinert/?p=booklist&details=9

In first quantization

http://vergil.chemistry.gatech.edu/notes/hf-intro/img63.png

note the 3rd term on the LHS that couples the different base eigenfunctions in the integral.

http://vergil.chemistry.gatech.edu/notes/hf-intro/node7.html

compare to the emergent SSB Landau-Ginzburg L-G equation e.g.

http://upload.wikimedia.org/math/9/4/5/945a3f42246130d5daba8e3c6417aec4.png

http://en.wikipedia.org/wiki/Ginzburg–Landau_theory

But the L-G equation is fundamentally zero-quantization i.e. a c-number emergent nonlinear local equation that trivially solves the emergence of classicality problem of quantum reality explaining why no big Schrodinger Tigers.

For example, crystal lattices come from spontaneous broken T3 symmetry in the ground states of systems of atoms in thermal equilibrium at low enough temperature - the lattice positions are a set of emergent "phonon" Goldstone boson condensate macro-quantum coherent order parameters. See Hagen Kleinert's books for the details.

http://users.physik.fu-berlin.de/~kleinert/kleinert/?p=booklist&details=9

Jul
05

Tagged in:

From: Paul Zielinski
To: Ruth Elinor Kastner
Sent: Mon, July 4, 2011 3:54:52 PM

Subject: Re: Creon's Nano-electronics & The issue of small n - FTL signals via over-complete non-orthogonal coherent states?

PZ: "Orthogonal transformations in ordinary Euclidean 3D space preserve lengths and angles. Non-orthogonal transformations don't. If we apply a non-orthogonal transformation in a Euclidean space, of course we will see formal changes in lengths and angles, but it will have no objective geometric meaning. "

JS: You are wrong. For one thing, you have confused "transformation" with "basis". You apply a transformation to a basis.

Second, when you move to a uniformly accelerating non-inertial Rindler frame for example, there are cross terms in the metric

gtz =/= 0

Also the non-geodesic Rindler guv-detector sees real photons in the form of thermal black body Unruh radiation. In contrast, the geodesic detector nab sees only virtual zero point photons.

The tetrad map connecting the two of them is a real physical change, i.e. switching a rocket engine on or off for example.

Now you can in the sense of an analogy compare that to a non-unitary transformation in Hilbert space that indeed does violate OQT in Henry Stapp's sense.

The quantum unitary transformations are then analogs of the global Lorentz boosts, the global rotations and translations of Special Relativity restricted to the global 10-parameter Poincare group.

Adding in the Rindler observers is adding the special conformal transformations I suppose. That is, going to a bigger group.

Finally GR involves localizing only the 4-parameter translation sub-group of the Poincare group.

Then e.g. cosmology has spontaneous symmetry breakdown of the T1 time translation group i.e. Hubble flow of accelerating expanding universe in which total global energy is not conserved. Thus, in the dS solution we have a constant / vacuum energy density so that the total vacuum energy density is not conserved. However it does appear to have a finite upper bound because of the finite distance to our future event horizon.

Our actual universe is not dS at the beginning, so that / is not a constant. It is large at inflation and then decreases approaching a small asymptote.

PZ: So how is the situation any different in QM, if we consider the corresponding unitary and non-unitary transformations?

JS: I just showed you. Your analogy is false.

PZ: Surely inner products computed from state vectors subject to non-unitary transformations have a very different meaning in the Hilbert space formalism of QM from those computed under unitary transformations?

JS: Agreed, but that has nothing to do with my original point which is that GIVEN a physically realizable non-orthogonal basis for an entangled system, partially tracing over a part of the system will allow an entangled signal to the other part. You red herring of a non-unitary transformation is nowhere in the actual calculation I gave. Now the LCAO basis in the many electron problem may be an example of what I am looking for, but I am not sure.

PZ: My point here is that any change in computed inner products that purely arises from the formal application of a non-unitary transformation to an orthonormal basis cannot have the same meaning as an inner product that is computed in the usual manner.

JS: Irrelevant as I never did that in this case. Also there is no such thing as a purely formal non-unitary transformation in a real physics theory. Any such transformation must describe an objective change - some operation like firing a rocket engine, or adding dissipation to a complex system, pumping it off thermal equilibrium etc.

PZ: Changes in the computed values of such inner products can only be purely formal in character.

JS: I don't think that is the case. Sure if, it's only formal you are correct. However, I don't think that is what is happening in the situations Brian Josephson had in mind and in the Daryl Bem data.

PZ: Since entanglement correlations for multiparticle systems ultimately have to be computed from such inner products, it is hard to see how such correlations that arise purely from non-unitary transformations of an orthonormal basis to a non-orthonormal basis can have objective physical meaning within the framework of QM.

JS: My idea is that the non-orthogonal basis are actually there in the complex system in a physical sense and are not simply a formal alternative. In other words you will get the wrong answer if you used an orthogonal basis. To make an analogy, you will not measure Unruh temperature unless you switch on your rocket engine - but when you do, your temperature gauge measures a real temperature that drops to zero when you switch off the engine.

PZ: Of course one can create non-vanishing non-diagonal matrix elements in any "observable" by going to a non-orthogonal basis, but does this mean that we now have non-vanishing transition probabilities between eigenstates of the observable? It should be obvious that the non-vanishing off-diagonal elements merely reflect the fact that non-orthogonal basis vectors have non-zero projections onto each other.

JS: False. Either the physics gives you an orthogonal basis or not. In OQT you can only use unitary transformations of basis. The inner products are invariant in OQT for a closed system. Non-unitary transformations are forbidden in OQT. Nonunitary transformations require new physics beyond OQT. However, I do agree we need non-unitary transformations in physics. But they are not merely formal crutches. Gerardus 't Hooft does not think so. He thinks the unitary S-Matrix describes black holes for example if you wait long enough. On the other hand, applied physicists do use dissipative non-unitary transformations, but I guess the lip service is that when you include the traced over environment everything is unitary.

PZ: So Jack, how is the multiparticle case in essence any different with respect to the entanglement correlations considered in your thought experiment? Of course one can prepare non-orthogonal coherent photon states as you say, but if the effects you predict arise purely from the use of a non-orthogonal basis for the representation of quantum "observables", what makes you think they have any more objective physical meaning than changes in lengths and angles induced in ordinary Euclidean space by non-orthogonal transformations?

JS: Your formal analogy is not correct physically. Unlike pure mathematics, the transformations in real physics must describe differences that make a physical difference, otherwise the physical theory is ill-posed, wrong or worse not even wrong.

On 7/4/2011 9:45 AM, Ruth Elinor Kastner wrote:

I still think the issue is just that the entanglement is with respect to which-slit (which is an observable whose eigenstates are orthogonal) and not with respect to the nonorthogonal eigenstates of the annihilation operators (coherent states). So I think what needs to be questioned (as you suspected peviously) is your eqn 1-18. Where does this come from? It seems to me that the A1 and A2 have to be just which-slit eigenstates here.

JS: Maybe so, but I am using the Feynman path history picture.

represent the complete complex number Feynman amplitudes for a Glauber state in the entangled pair to be emitted at the source, take all possible paths passing through slits 1' and 2' and be detected on the screen at x' (from the central peak in Young's set up).

= exp{-[1 - cos@(x')]}

is an intuitive Ansatz I inferred from Glauber's work - but it extends it admittedly and may be wrong.

Remember Feynman played with his intuitive pictures before he really had much of the formal algebra.

@(x') is the net relative phase weighted by all possible paths with the same emission at the laser source landing at same x' through both A1' and A2'.

The RHS is an interesting function as ---> infinity basically it's a comb of Dirac delta functions at @ = integer x 2pi

The physical observable of interest is then the integral over x' of

e^i@(x') = Integral over x' of exp{i@(x') - (1 - cos@(x')}

This is sort of pretty.

However, even if this particular model is wrong, it does not change the general fact that a non-orthogonal partial trace gives an entanglement signal. The use of LCAO non-orthogonal base functions is certainly an alarm bell.

Also, my above model may be correct in the end. It must be tested with entangled laser beams.

Nick's attitude of don't even look in that part of the room is not wise in my opinion.

As I said at the beginning I am Devil's Advocate - no telling where these attempts will lead. The prize is great if in fact there is entanglement signaling ubiquitous in nature especially in biological systems as Brian Josephson was the first to suggest.

That's why I am not content with Henry Stapp's general philosophical arguments though he may be correct in the end - there is also some ambiguity in the boundary of "Orthodox Quantum Theory" - does it include spontaneous symmetry breakdown with the emergence of non-unitary local Landau-Ginzberg dynamics for macro-quantum coherent order parameters?

Jul
04

Tagged in:

The non-orthogonal LCAO orbitals may play a role there.*Scientists have further realized that the Kondo effect results from a relationship between electrons known as "entanglement" in which the quantum state of one electron is tied to those of neighboring electrons, even if the particles are later separated by considerable distances. In the case of Kondo effect, a trapped electron is entangled in a complex manner with a cloud of surrounding electrons.
Researchers have been intrigued by the Kondo effect in part because understanding how a trapped electron becomes entangled with its environment could help overcome barriers to quantum computing, which could lead to far more powerful computers than currently exist.*

http://www.sciencedaily.com/releases/2011/06/110629132544.htm

When I was at UCSD with the Benford brothers in the late 60's Walter Kohn and Harry Suhl were very interested in the Kondo effect. Too bad the connection to entanglement was not understood back then. Also in photosynthesis and no doubt many biological processes.

On Jul 3, 2011, at 9:56 PM, JACK SARFATTI wrote:

this one looks most relevant

A. O. Mitrushenkov, Guido Fano, Roberto Linguerri, Paolo Palmieri

(Submitted on 3 Jun 2003)

The generalization of Density Matrix Renormalization Group (DMRG) approach as implemented in quantum chemistry, to the case of non-orthogonal orbitals is carefully analyzed. This generalization is attractive from the physical point of view since it allows a better localization of the orbitals. The possible implementation difficulties and drawbacks are estimated. General formulae for hamiltonian matrix elements useful in DMRG calculations are given.

Comments: 14 pages

Subjects: Strongly Correlated Electrons (cond-mat.str-el)

Cite as: arXiv:cond-mat/0306058v1 [cond-mat.str-el]

Submission history

From: Roberto Linguerri [view email]

[v1] Tue, 3 Jun 2003 10:02:27 GMT (15kb)

However, none of them directly address our problem of entanglement signals. However, if these non-orthogonal LCAO orbitals are physically significant it might explain the nonlocal effects in photosynthesis and I bet in many complex systems not in thermodynamic equilibrium as entanglement signaling? Also Hameroff's microtubules etc.

On Jul 3, 2011, at 4:34 PM, Paul Zielinski wrote:

However, naively speaking it seems to me that if the trace of a density matrix, or of the product of a density matrix and an "observable", is only invariant under unitary transformations, then applying a non-unitary transformation to get from an orthogonal basis to a non- orthogonal basis representation necessarily changes the physical meaning of the trace.

Isn't that what Kastner is saying here? How do you answer that?

Simple, I only claimed that the initial choice of a non-orthogonal basis is preserved under unitary transformations. I never invoked a non-unitary transformation from an orthogonal to a non-orthogonal basis, though that is also of interest. It is another story.

On 7/3/2011 4:13 PM, Jack Sarfatti wrote:

No I don't think it's that simple. Sure, if you use spins then the eigenstates are orthogonal and no FTL signal. We all agree on that. Simply because we maybe cannot do it with polarization entanglements does not mean we can't do it with other degrees of freedom.

The Glauber states are a different story. Suppose mean n i.e. is small order of 1 or 2

z = ^1/2e^i@

the point is that there is coherence between the vacuum |0>, and all states |1>, |2> ....

but the peak is at with a Poisson distribution. The coherence properties are qualitatively different from that of a sharp n Fock state - though not so different when is small agreed.

Even when >> 1 it is a mistake to think of it as a classical EM wave in the sense of Maxwell theory prior to laser beams.

I think Roy Glauber's original papers explain why. I need to refresh my memory on this from the 1960's.

Coherent microwaves are close to Glauber states, but not ordinary optical sources that are not lasers.

Glauber states and their squeezed variations have properties above and beyond their non-laser cousins e.g. from an incandescent lamp etc.

From: Ruth Elinor Kastner To: Jack Sarfatti Sent: Sun, July 3, 2011 12:38:36 PM

Subject: RE: The issue of small n

RK:

where we're pretty sure it can't be done.

JS: All you sort of showed was that there was allegedly no way to prepare an over-complete basis of spin states of sharp n. Lasers show how to prepare many-photon states as Glauber states all with same polarization. The issue is then how they can entangle. Can we entangle laser beams with opposite momenta Fourier components as in the original EPR all with same polarizations? That's what I assumed in the toy model.

________________________________________

From: Jack Sarfatti [sarfatti@pacbell.net]

Sent: Sunday, July 03, 2011 3:00 PM

To: Ruth Elinor Kastner

Cc: nick herbert; david kaiser; Saul-Paul Sirag

Subject: The issue of small n

Assuming I did not make an error:

Large is not needed

Even small works in principle, though perhaps with a much smaller signal to noise ratio?

If there is large n then only the constructive peaks contribute to the non-orthogonality

If n is small then more relative phases @ contribute

= e^-(1-cos@(x'))

this formula of mine may be wrong, I am not sure. It has nice properties however as a comb of Dirac delta functions when ---> infinity at @ = integer multiples of 2pi (constructive interference of the Young double slit fringes).

where

= x' integral over the screen of we also need

= x' integral over the screen of e^i@(x)

On Jul 3, 2011, at 9:03 AM, Ruth Elinor Kastner wrote:

RK:

JS: Exactly. For some reason Nick Herbert took umbrage at that.

RK:

JS: It's too simple to say large means classical waves. That's like saying the superfluid is a giant classical wave. In other words there is a distinction between macro-quantum coherent waves and classical waves of the same that shows up in the coherence correlation functions e.g. see modern books on quantum optics (or even Wikipedia).

In any case we agree this is a valid question that deserves careful investigation. I am not aware if any such work has been done?

Begin forwarded message:

From: Jack Sarfatti <sarfatti@pacbell.net>

Date: July 3, 2011 4:13:33 PM PDT

To: Ruth Elinor Kastner <rkastner@umd.edu>

Subject: Re: The issue of small n - FTL signals via over-complete non-orthogonal coherent states?

No I don't think it's that simple.

Sure, if you use spins then the eigenstates are orthogonal and no FTL signal. We all agree on that.

Simply because we maybe cannot do it with polarization entanglements does not mean we can't do it with other degrees of freedom.

The Glauber states are a different story. Suppose mean n i.e. <n> is small order of 1 or 2

z = <n>^1/2e^i@

the point is that there is coherence between the vacuum |0>, and all states |1>, |2> ....

but the peak is at <n> with a Poisson distribution. The coherence properties are qualitatively different from that of a sharp n Fock state - though not so different when <n> is small agreed.

Even when <n> >> 1 it is a mistake to think of it as a classical EM wave in the sense of Maxwell theory prior to laser beams.

I think Roy Glauber's original papers explain why. I need to refresh my memory on this from the 1960's.

Coherent microwaves are close to Glauber states, but not ordinary optical sources that are not lasers.

Glauber states and their squeezed variations have properties above and beyond their non-laser cousins e.g. from an incandescent lamp etc.

From: Ruth Elinor Kastner <rkastner@umd.edu>

To: Jack Sarfatti <sarfatti@pacbell.net>

Sent: Sun, July 3, 2011 12:38:36 PM

Subject: RE: The issue of small n

RK: OK then the issue is just the non-orthogonality itself ; this yields apparent FTL signalling trivially in cases
where we're pretty sure it can't be done. R.

JS: All you sort of showed was that there was allegedly no way to prepare an over-complete basis of spin states of sharp n. Lasers show how to prepare many-photon states as Glauber states all with same polarization. The issue is then how they can entangle. Can we entangle laser beams with opposite momenta Fourier components as in the original EPR all with same polarizations? That's what I assumed in the toy model.

________________________________________

From: Jack Sarfatti [sarfatti@pacbell.net]

Sent: Sunday, July 03, 2011 3:00 PM

To: Ruth Elinor Kastner

Cc: nick herbert; david kaiser; Saul-Paul Sirag

Subject: The issue of small n

Assuming I did not make an error

Large <n> is not needed

Even small <n> works in principle, though perhaps with a much smaller signal to noise ratio?

If there is large n then only the constructive peaks contribute to the non-orthogonality

If n is small then more relative phases @ contribute

<A1'|x'><x'|A2> = e^-<n>(1-cos@(x'))

this formula of mine may be wrong, I am not sure. It has nice properties however as a comb of Dirac delta functions when <n> ---> infinity at @ = integer multiples of 2pi (constructive interference of the Young double slit fringes).

where

<A1'|A2'> = x' integral over the screen of <A1'|x'><x'|A2>

we also need

<A1'|e^i@|A2'> = x' integral over the screen of <A1'|x'><x'|A2>e^i@(x)

On Jul 3, 2011, at 9:03 AM, Ruth Elinor Kastner <rkastner@umd.edu> wrote:

RK: Hi all, I was just addressing the point stressed by Jack about using a non-orthonormal basis to compute the partial trace, since that's crucial to Jack's goal of obtaining a nonlocal signal. This is independent of whether or not there's a detailed picture of the experimental apparatus. I just take it as a conceptual thought experiment.

JS: Exactly. For some reason Nick Herbert took umbrage at that.

RK: The point is that if you allow partial trace to be done in a non-orthonormal basis you can get trivial nonlocal signalling in an ordinary EPR -spin experiment. So the question is whether using a nonorthonormal basis has any genuine physical application -- which seems doubtful, but the point is that IF you could use such states for your experiment, and maintain the entanglement you apparently get nonlocal signalling. It appears to me from at least one of the refs Jack sent on entangled coherent states that the entanglement depends on having a very small avg photon number (< or = 2) so that the partial trace does not depart from the standard def., and that one cannot use those for nonlocal signalling (which in Jack's analysis requires large avg photon mumber). Again I think the crucial point is that large n coherent states approximate classical waves which can't be entangled at the individual photon level. I would love to try to work this out quantitatively but too busy right now...

JS: It's too simple to say large <n> means classical waves. That's like saying the superfluid is a giant classical wave. In other words there is a distinction between macro-quantum coherent waves and classical waves of the same <n> that shows up in the coherence correlation functions e.g. see modern books on quantum optics (or even Wikipedia).

In any case we agree this is a valid question that deserves careful investigation. I am not aware if any such work has been done?

Whoops, sorry Ruth I had your last name spelled incorrectly on last letter when I entered it in my Iphone hit t rather than r.

The real issue is whether physical observables must be Hermitian operators. I think the answer is no because laser beams are essentially eigenstates of the non-Hermitian destruction operators a in second quantization. These generally arise in spontaneous symmetry breakdown SSB relative to some group in ground states of real on-mass-shell particles and in vacuum states of virtual off -mass-shell particles. Indeed these emergent order parameters no longer obey the Schrodinger equation in configuration space, so you are right to question whether we can still entangle them without some limit.

However consider, for example, the entangled non-Hermitian operator

a1b2 + a2b1

Does it have a physically realizable eigenstate

(a1b2 + a2b1)|z1w2 + z2w1> = (z1w2 + z2w1)|z1w2 + z2w1>

where z1, z2, w1, w2 are points on the complex plane?

PS crystals emerge from SSB of T3 in systems of atoms and molecules

ferromagnets emerge from SSB of O(3) in systems of magnetic spins

superfluids emerge from SSB of two kinds of U1 in helium and electron-phonon systems respectively

The Higgs field emerges from SSB of SU2 in the physical vacuum in the standard model.

Perhaps the mental field in our brains emerges from SSB of some group for some subsystem e.g. Hameroff, Vitiello?

We have Dean Radin's "Entangled Minds" for example.

The real issue is whether physical observables must be Hermitian operators. I think the answer is no because laser beams are essentially eigenstates of the non-Hermitian destruction operators a in second quantization. These generally arise in spontaneous symmetry breakdown SSB relative to some group in ground states of real on-mass-shell particles and in vacuum states of virtual off -mass-shell particles. Indeed these emergent order parameters no longer obey the Schrodinger equation in configuration space, so you are right to question whether we can still entangle them without some limit.

However consider, for example, the entangled non-Hermitian operator

a1b2 + a2b1

Does it have a physically realizable eigenstate

(a1b2 + a2b1)|z1w2 + z2w1> = (z1w2 + z2w1)|z1w2 + z2w1>

where z1, z2, w1, w2 are points on the complex plane?

PS crystals emerge from SSB of T3 in systems of atoms and molecules

ferromagnets emerge from SSB of O(3) in systems of magnetic spins

superfluids emerge from SSB of two kinds of U1 in helium and electron-phonon systems respectively

The Higgs field emerges from SSB of SU2 in the physical vacuum in the standard model.

Perhaps the mental field in our brains emerges from SSB of some group for some subsystem e.g. Hameroff, Vitiello?

We have Dean Radin's "Entangled Minds" for example.

From: Ruth Elinor Kastner
To: JACK SARFATTI
Sent: Sat, July 2, 2011 4:45:54 PM

Subject: RE: Devil's Advocate Refutation of Stapp's Proof forbidding entanglement signals in OQT v2 corrected

Ruth: In contrast to Nick I think your calculation presents something concrete to consider.

Jack: Indeed Nick responded inappropriately with polemics. He has always felt competitive with me. If Fig. 9.1 has no value, then why did David Kaiser even include it and spend several pages in Chapter 9 describing it?

Ruth: However I would note that the Trace is defined strictly in terms of an orthonormal basis.

Jack: News to me, but perhaps you are correct. Or, rather, perhaps that should be added as an "axiom" to what is meant by "Orthodox Quantum Theory"?

Ruth: If you want to generalize the trace to something summed over an overcomplete, non-orthogonal basis, you can get apparent nonlocal signalling

even for the usual spin-EPR experiment -- I just did a quick calculation for a singlet state with a rudimentary overcomplete 'basis' consisting of {1/rt2 |z up + x up>, |z down>} and got cross terms also. Does this represent anything physical meaningful? It seems doubtful.

Jack: If I recall from the USD AAAS Retrocausation Meeting that kind of over-complete basis makes sense in Aharonov's "weak measurement"? But perhaps I am mistaken? Remember they get rare weak values arbitrarily far outside the strong measurement eigenvalue spectral range.

Ruth: Again I think the overcompleteness of the coherent states is related to their indefinite photon number and that you have to have a definite

photon number (or close to it) to get entanglement-- which is why they can get entangled laser beams for small average photon #.

Jack: I am not aware that one cannot have entangled laser beams above a critical laser intensity. Reference? Also we must not confuse laser light with ordinary light of the same intensity. They have very different coherence properties. The laser beam is analogous to the giant wave function of superfluid helium while ordinary light sources of the same intensity is analogous to normal liquid helium. The indefiniteness of photon number is needed for a more definite phase, so I would be surprised if you could not entangle waves that were sharp in phase and unsharp in intensity? Any good reference on these issues?

I am now somewhat suspicious of my eq. 1.18 perhaps it is mistaken?

In any case, even if this model fails, the issue of over-complete non-orthogonal base states as a loop hole for entanglement signaling inside OQT needs to be more carefully considered. Perhaps it has? References?

Ruth: One can 'predict' trivial nonlocal signalling by calculating a 'trace' wrt an overcomplete basis, and I think that's what going on here. I think the mistake is assuming that you get valid statistical predictions by trying to calculate a 'trace' with a nonorthonormal basis.

Jack: Well at least we agree on this formal point. The issue now is what does Nature say? Experiments would be in order on this issue. As I recall, the actual experiments with entangled double slit systems do not use laser beams?

Ruth

Agreed

From: Saul-Paul and Mary-Minn Sirag
To: nick herbert
Cc: JACK SARFATTI ; Fred Wolf
Sent: Sat, July 2, 2011 5:48:12 PM

Subject: Re: How The Hippies Saved Physics

On Jul 2, 2011, at 5:44 PM, Saul-Paul and Mary-Minn Sirag wrote:

Hi Nick,

I am reminded that I should have CCd you and Jack and Fred in this email to David Kaiser on his book.

I liked this "Hippie" book very much!

Saul-Paul

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

Begin forwarded message:

From: Saul-Paul and Mary-Minn Sirag
Date: June 29, 2011 7:05:42 PM PDT

To: David Kaiser
Subject: How The Hippies Saved Physics

Hi David,

Thank you for sending a copy of your book!

I have finished reading it, and it is a splendid achievement.

There are a few errors that I have noticed. I could send you a list if you like.

The relationship of the "Hippie" books and Bell's theorem is curious. For example in 1975 two "Hippie" books were published.

(1) "Space-Time and Beyond" by Bob Toben, Jack Sarfatti, and Fred Wolf (Dutton). On page 134 Sarfatti wrote:

"Bell's criterion for quantum interconnectedness was experimentally tested in the 1973 Harvard doctoral dissertation of A. Holt. H

Holt's result is that the quantum potential (hidden variable interpretation of quantum theory due to de Broglie and Bohm agrees more closely wiith experiment than does the conventional interpretation, which denies the existence of hidden variables."

This experiment by Holt (advised by Pipkin) at Harvard was consistent with Bell's inequality -- and thus, if verified, would falsify the statistical predictions of quantum mechanics. In fact, John Clauser, for his second Bell's theorem experiment redid Holt's version of the experiment (using mercury atoms). This was the version of Clauser's experiment that Elizabeth Rauscher, Nick Herbert, and I saw running in 1974. Jack and Fred and the rest of the FFG saw Clauser's experimental setup after the experiment was completed in 1975.

This was when Clauser had placed a sign over his experimental apparatus which read: "We have met the hidden variables, and they is us!--Pogo." Clauser was also amused that Holt had received his Ph.D. under Pipkin for falsifying Quantum Theory. I happen to have a "samizdat" copy of the paper by R.A. Holt and F.M. Pipkin "Quantum Mechanics vs. Hidden Variables: Polarization Correlation Measurement on an Atomic Mercury Cascade." (This paper was never published.)

There is a good description of this early experimental work in the 1978 paper, by Clauser and Shimony, which you reference.

(2) "The Tao of Physics" by Fritjov Capra" (Shambhala, Berkeley, 1975).

It is notable that there is no mention of Bell's Theorem in this book. Capra has a brief (but inadequate) description of Bell's theorem in his second book, "The Turning Point: Science, Society and the Rising Culture" (Simon and Schuster, 1982).

Of course by this time "The Dancing Wu Li Masters" by Gary Zukov (Morrow, 1979)

He spells it Zukav.

had been out for three years, with a much more adequate description of Bell's theorem and the experimental results.

Yes, because you Saul-Paul and me and a few others worked closely with Gary on his book and by that time Gary had attended many of the Berkeley Seminars. I wrote the above quote on Holt in 1974 before we had the Berkeley Seminars with Clauser.

Also Bernard d'Espagnat's article, "The quantum theory and Reality" (Scientific American, Nov. 1979) was very influential at that time. I had the amusing experience of asking a Berkeley physics professor (who taught a course on quantum mechanics) if he had read d'Espagnat's article. He said that he had but couldn't understand it!

It is perhaps noteworthy that the first (popular level) book describing Bell's theorem and the experimental results was Robert Anton Wilson's "Cosmic Trigger" (And/Or press, Berkeley, 1977).

Which you especially and I and I suppose Nick helped him with.

All for now;-)

Saul-Paul

Jul
02

Tagged in:

Einstein's relativity both special and general is only concerned with the limitations on measurements with real light and real massive particles used as signals. Entanglement signals do not need real light or real particles in their direct communication link channel. The real particles only play a role locally in the detection physics.

Entanglement signals are non-metrical linking arbitrarily possibly widely separated irreversibly recorded detection events. In the case of special relativity there is a unique global spacetime separation between them. That is not really useful because spacetime is curved and there is no path-independent measure of global separation.

Suppose Alice and Bob have entanglement signaling capability. The obvious protocol should be for each to note their CMB temperature from the Big Bang as well as their peculiar velocity relative to the Hubble flow as shown by departures from isotropy of the CMB. They can also note what star system they are in.

Other than that, there is no conceptual clash with relativity. Entanglement signaling is a global topological effect independent of metrical constraints and consistent with them.

Alice and Bob can communicate across time, both forwards and backwards.