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I have suggested that Einstein's gravity/curvature is a post-inflation macro-quantum coherent emergent collective effect in the Higgs-Goldstone vacuum superconductor, an elastic-plastic analog of superflow in liquid helium below the Lambda point ~ gradient of the macro-quantum coherent helium ground state with spontaneous broken non-electromagnetic U1 symmetry.

Here is another interesting approach with the SU2 weak group not the SU3 strong group. It has a kind of twistor nonlocality and non-commutative geometry.

He's got a torsion field there.

I think there is an inconsistency in his math. Can't have d^x^u/ds = constant when the antisymmetric torsion tensor =/= 0.

i.e. the torsion field tensor makes a real force that cannot be eliminated because it is a tensor under the original general coordinate transformations unlike the Christoffel symbol (of Newton's G-force).

GRAVITATIONAL AND ELECTROWEAK UNIFICATION BY REPLACING DIFFEOMORPHISMS WITH LARGER GROUP
DAVE PANDRES, JR.
Abstract. The covariance group for general relativity, the diffeomor-
phisms, is replaced by a group of coordinate transformations which con-
tains the diffeomorphisms as a proper subgroup. The larger group is
defined by the assumption that all observers will agree whether any given
quantity is conserved. Alternatively, and equivalently, it is defined by the
assumption that all observers will agree that the general relativistic wave
equation describes the propagation of light. Thus, the group replacement
is analogous to the replacement of the Lorentz group by the diffeomor-
phisms that led Einstein from special relativity to general relativity, and
is also consistent with the assumption of constant light velocity that led
him to special relativity. The enlarged covariance group leads to a non-
commutative geometry based not on a manifold, but on a nonlocal space
in which paths, rather than points, are the most primitive invariant enti-
ties. This yields a theory which unifies the gravitational and electroweak
interactions. The theory contains no adjustable parameters, such as those
that are chosen arbitrarily in the standard model.

Bohm's Hidden Variables HV in orthodox quantum theory are "test particles" in a similar sense to Einstein's GR test particles. The paths of HV are piloted by the quantum potential Q(nonlocal configuration space for entangled systems) without any direct influence of HV back on Q just like geodesic GR test particles are piloted by the local curvature tensor Ruvwl without being included in Tuv(source).  The lack of direct back reaction in the quantum case corresponds to Valentini's "sub-quantal thermal equilibrium" with Shimony's "passion at a distance" and the no-cloning a quantum theorem.

"Now, in special relativity we can think of an inertial coordinate system, or
`inertial frame', as being dened by a field of clocks, all at rest relative to each
other. In general relativity this makes no sense, since we can only unambiguously
dene the relative velocity of two clocks if they are at the same location. Thus
the concept of inertial frame, so important in special relativity, is banned from
general relativity!"

Baez means Global Inertial Frame (GIF) above. GR replaces GIF with LIF as he points out below.

"If we are willing to put up with limited accuracy, we can still talk about the
relative velocity of two particles in the limit where they are very close, since
curvature eects will then be very small. In this approximate sense, we can talk
about a `local' inertial coordinate system. However, we must remember that
this notion makes perfect sense only in the limit where the region of spacetime
covered by the coordinate system goes to zero in size. ...

Einstein's equation can be expressed as a statement about the relative acceleration
of very close test particles in free fall. Let us clarify these terms a
bit. A `test particle' is an idealized point particle with energy and momentum
so small that its effects on spacetime curvature are negligible." A particle is said
to be in `free fall' when its motion is affected by no forces except gravity. In
general relativity, a test particle in free fall will trace out a `geodesic'. This
means that its velocity vector is parallel transported along the curve it traces
out in spacetime. A geodesic is the closest thing there is to a straight line in
curved spacetime. ...

in general relativity gravity is not really a `force', but just a manifestation
of the curvature of spacetime. ...

To state Einstein's equation in simple English, we need to consider a round ball
of test particles that are all initially at rest relative to each other. As we have
seen, this is a sensible notion only in the limit where the ball is very small. If
we start with such a ball of particles, it will, to second order in time, become
an ellipsoid as time passes. This should not be too surprising, because any
linear transformation applied to a ball gives an ellipsoid, and as the saying goes,
'everything is linear to first order'. Here we get a bit more: the relative velocity
of the particles starts out being zero, so to first order in time the ball does not
change shape at all: the change is a second-order effect.

Let V(t) be the volume of the ball after a proper time t has elapsed, as
measured by the particle at the center of the ball. Then Einstein's equation
says:

V^-1d^2V/dt^2 ~ -(1/2)(Ttt + Txx + Tyy + Tzz)

where these flows are measured at the center of the ball at time zero, using local
inertial coordinates. These flows are the diagonal components of a 4x4 matrix
T called the `stress-energy tensor'."

I add here that for random virtual quanta (zero point vacuum fluctuations) in the isotropic case, Lorentz invariance + equivalence principle demand

w = (Pressure per space dimension)/(energy density) = -1

Ttt = - Txx = - Tyy = - Tzz = - P

Therefore the RHS of (2) reduces to - P

If there are anisotropic Casimir effect boundaries this result will change.

Free virtual bosons have P < 0 causing anti-gravity repulsion dark energy

Free closed virtual fermion loops have P > 0 causing gravity attraction dark matter that mimics w = 0 CDM.

Jun 28

Book Review Aharonov's "Quantum Paradoxes" v1

Posted by: JackSarfatti |
Tagged in: Untagged 


Working on Amazon.com book review

From the last chapter (18 The Quantum World)

Physics theories are passive descriptions of certain kinds of controlled procedures "measurements". If the theories do not correctly describe the results of the measurements in a coherent narrative using mathematics as well as ordinary language and if they do not make predictions of future measurements, then they are not good theoretical physics. There is always a subjective element of what is a good elegant coherent narrative in ordinary language. All the work today in quantum theory, with rare exceptions, is axiomatizing quantum theory in its limiting case that excludes what Einstein called "spooky telepathy" - anything paranormal. No one argues that quantum theory does not work for dead matter, however, the Fat Lady has not yet sung on living matter on us, and on exotic forms of matter prepared in the laboratory and possibly in the moment of inflation creation of our observable universe that are pumped off "sub-quantal thermodynamic equilibrium" that results in direct back-reaction of the classical material dynamics (hidden variables) on their "quantum potential" field (Bohm). In other words, quantum theory, as commonly understood, treats the hidden variables as test particles - clearly an approximation.



Measurements do not necessarily disturb the quantum system, e.g. eigenoperator measurements do not. Aharonov introduced new kinds of "weak" and also "protective" measurements.

Are causality and nonlocality sufficient axioms for quantum theory with "passion at a distance" signal locality? Entanglement is used, but not directly as a stand-alone faster-than-light and/or paranormal precognitive retro-causal communication system. This corresponds to Valentini's "sub-quantal thermal equilibrium" or when there is no direct back-reaction of the classical dynamical field hidden variables on their "super" quantum potential (infinite-dimensional configuration space for classical fields). In other words, Wheeler's BIT acts on IT, but IT does not react back directly on its BIT - like a docile horse.

In seeming contradiction to Bohr's principle of complementarity the Aharonov "Tel Aviv" School claims that in a post-selected "weak measurement ... of an expectation value on a PPS ensemble ... it shows through which slit each particle goes and it shows an interference pattern (p. 265)" Would Feynman be shocked? Would Bohr come back from the grave like Hamlet's Ghost? Sir Fred Hoyle in his 1984 "Intelligent Universe" clearly has the key idea implicate in Bohr's turgid prose refined by Wheeler in his delayed choice gedankenexperiment that it is the Omega Point observer at the Conformal End Time that must be taken into account including all other previous measurements in a self-consistent web.


See eq.18.1 p. 266 for the math.

http://stardrive.org (Tamara Davis, 2004 PhD University New South Wales)

"On the one hand, the previous thought experiments confirmed the intuition that 'it is impossible to design an apparatus to determine which hole the electron passes through, that will not at the same time disturb the electrons enough to destroy the interference pattern'. On the other hand, ... a weak measurement on a Pre-Post Selected ensemble tells us about both the pre- and the postselected states - here, about the interference pattern and about the final direction of each electron ..."

Aharonov invokes a Rube Goldbergian excess axiom of "stable collapse" without which the Born probability rule is violated opening Pandora's Box to controllable  spooky paranormal actions at a distance across spacelike separated senders and receivers and, worse, even precognitive remote viewing as reported by Russell Targ at the June 2006 AAAS "Retrocausality Workshop" at USD in San Diego that I attended. The game here is to see what kinds of shackles must bind Dame Nature to avoid the unavoidable occurrence of Aleister Crowley's "Magick without Magic" sought by Jack Parsons and L. Ron Hubbard in the California desert as reported in the book "Strange Angel" on the creation of NASA's JPL and DOD contractor Aerojet General. Remember Newton's passion for Alchemy did not detract from his mechanical equations for gravity.

to be continued

From: JACK SARFATTI Date: June 27, 2010 2:39:21 PM PDT

Scientists see evidence that rules of particle physics may need a rewrite
www.physorg.com
(PhysOrg.com) -- Two separate collaborations involving Indiana University scientists have reported new results suggesting unexpected differences between neutrinos and their antiparticle brethren. These results could set the stage for what one IU physicist calls a 'radical modification of our understanding...


One sunrise ago at 1:01 in the evenin' · Weigh in  · Blabber t' yer mates
Michael Eugene Patton, Nicole Tedesco, Daniel Piersee an' 4 other mateys be likin' this ere' scroll.

Jack Sarfatti
The particle-antiparticle symmetry is built into the Dirac square root equation from the Klein-Gordon equation. Anti-particles are the negative energy solutions basically from the mass-shell condition

E =+- [(pc)^2 + (mc^2)^2]^1/2

same "m" a negative energy particle moving backward in time is same as a positive energy anti-particle moving forward in time. Also need the discrete CPT symmetry - it get's tricky why the "m" of the anti-particle is not the "m" of the particle - the "m" for leptons and quarks comes from the Higgs-Goldstone post-inflation vacuum superconductor (see Frank Wilzcek's "Lightness of Being")

Gareth Lee Meredith
Is this because in the Hamiltonian, the best way to describe a particle under E=Mc^2. is better described as E= +- Mc^2 in a Dirac Sea Model?

Jack Sarfatti
Since P, C, T need not be conserved conserved individually in the weak force, I suppose that is relevant to the difference in the "m"s (there are radiative corrections to the bare masses - very messy).

Jack Sarfatti
Special relativity demands E = +-Mc^2 - need both roots.

Gareth Lee Meredith
They have just as much REAL effects in the world - i know this.

Jack Sarfatti
Virtual particles are inside the vacuum. Real particles are outside the vacuum (analogous to excited states of a ground state). Jack Sarfatti
Real particles correspond to poles of the Feynman propagator in the complex energy plane - they are on mass-shell i.e.


E^2 = (pc)^2 + (mc^2)^2

the product of their conjugate uncertainties is greater than the quantum of action (neglecting dimensionless factor like 1/2 - matter of definition of "quantum of action") Virtual particles are off-mass-shell and the product of their conjugate uncertainties is less than the quantum of action.
Jack Sarfatti
PS of course virtual particles have observable effects


1) Casimir force


2) Lamb shift, anomalous magnetic moment of electron - all radiative corrections in quantum field theory

Jack Sarfatti
The vacuum is a coherent superfluid with geodesic motion analogous to superflow without viscosity

Jack Sarfatti
The geodesic equation for non-accelerating test particles is analogous to v = (h/m)Grad(coherent phase) of superflow.

Jack Sarfatti
Technically the Einstein gravity tetrad fields are functions of gradients of 8 coherent Higgs-Goldstone phases that emerge in the moment of inflation and are essentially the 8 strong force massless gluon phases, i.e. a unification of the compact internal SU3 gauge force with the non-compact T4 curved spacetime universal gravity coupling to all non-gravity fields.

 

Chapter 6 has several seemingly paranormal orthodox quantum effects that seem magical to the strictly classical Newtonian mind such as the average member of the Committee to Investigate Claims of the Paranormal. This is even before we put in post-quantum signal nonlocality, the real OTO  Crowleyan Magick without Magic that L. Ron Hubbard and Jack Parsons were looking for in the desert according to Robert Anton Wilson's "Illuminatus Trilogy "and other weird writings. See also the book "Strange Angel."

"What matters is that the ball has changed the energy of the particle in the cylinder even when the particle is far from the piston. Thus a change in the energy of the ball immediately shows that there is a particle in the cylinder even if the particle is nowhere near the piston! Now that is action at a distance." p. 79 Aharonov & Rohrlich

This is most easily understood as the action of the entangled Bohm quantum potential Q separate from the matter hidden variables "ball" and particle. However, all of Chapter 6 assumes Abner Shimony's "passion at a distance", there is always a Catch 22 even with the "modular observables" in which the spooky action-at-a-distance is uncontrollably random outside the future light cones of the entangled subsystems and there is no faster-than-light and retro-causal precognition in any of the effects Aharonov dares to tackle. In Valentini's terms Aharonov restricts his book to the limiting case of thermodynamic equilibrium of the matter classical dynamical degrees of freedom (aka "hidden variables). So Aharonov does not ask the really important question in my opinion.

I agree with his 6.4 on the analogy between quantum theory and Einstein's 1905 Special Relativity (SR), indeed, just as 1905 SR is the limiting case of Einstein's 1916 General Relativity (GR) in the limit of zero global curvature, so, too, is quantum theory the limiting case of post-quantum theory in the limit of zero direct back-action of the material hidden variables on the qubit Bohm quantum potential Q. One can use Antony Valentini's sub-quantal non-equilibrium of the hidden variables as equivalent to back-action. Therefore, pumped dissipative structures should generally allow signal-nonlocality outside the local light cones if this line of argument is correct - a testable Popper falsifiable proposition.

Note on Aharonov's 6.4: local signal quantum theory uniquely derives from two axioms

i) All physical interactions respect causality.

ii) Some physical interactions are nonlocal ("modular observables" have nonlocal dynamics)

analogous to Einstein's 1905 SR that derives uniquely from

i') The laws of physics are the same in all inertial reference frames.

ii') The speed of light in vacuum is invariant c.

Note that 1916 GR replaces i) by

i") The laws of physics are the same in all locally coincident frames of reference whether inertial or non-inertial. (general covariance)

ii") The laws of 1905 SR work inside zero g-force local inertial frames (Einstein's Equivalence Principle)

Similarly, in post-quantum theory

iii") Some physical interactions do not respect restrictions to the local forward light cones of the detectors. "Causality" is violated.

ii''') same as ii).

 

 

Aharonov's post-selection need not be done literally in the future and does not necessarily imply the kind of real retro-causality that is in the Wheeler-Feynman idea. Thus, Aharonov's use of "destiny" for post-selection and "history" for pre-selection" is misleading. All Aharonov seems to be saying is to use a protocol set in advance in which only conditional probabilities in which a subset of the set of distinguishable final outputs is considered. The more interesting issue is a real retro-causation closely allied to real signal nonlocality in which entanglement is used as a real communication channel outside the light cones in the sense John S. Bell explained. This would be a gross violation of quantum theory of course, and it is my conjecture that such gross violation is necessary for living matter.

"The uncertainty principle implies a loss of quantum interference whenever we can detect through which slit a particle passes ... applied the uncertainty principle to the detector to explain the loss of interference, but applying the uncertainty principle to the particle tells us nothing about loss of interference ... " Quantum Paradoxes p. 61

It needs to be understood that Aharonov's new book with Rohrlich only deals with the paradoxical thinking of orthodox quantum theory that has Shimony's "passion at a distance" where the classical matter dynamical "hidden variables" are in "sub-quantal thermodynamic equilibrium" in which the Bohm quantum pilot wave "potential Q" acts on these hidden variables without any direct back-reaction of them on their Q to close the loop of action and reaction. This is essentially what in general relativity we recognize as the "test particle approximation" i.e. the hidden variables are test objects not sources of the quantum potential Q (or super-potential in classical field theory). Everything in Aharonov's book breaks down fundamentally in the post-quantum theory where the hidden variables of the classical matter fields are not only not in thermal equilibrium but are prevented from relaxing to thermal equilibrium by an external pump of some kind. All living matter is post-quantum in this sense with direct back-reaction of the hidden variables on their Q forming a "more is different" self-organizing emergen creative loop controllably nonlocal in both space and time. Our inner consciousness is the key emergent property of sustained thermal non-equilibrium of the hidden variables.

Jun 19

"De Broglie-Bohm theory is a 'hidden variables' formulation of quantum
 mechanics initially developed by de Broglie from 1923-1927 and clarified and
extended by Bohm beginning in 1952. In non-relativistic quantum theory it
differs from the orthodox viewpoint in that the notion of 'probability' refers to the
probability that a particle is at some position, rather than to its probability of
being found there in a suitable measurement. From this seemingly subtle
difference it is easy to show that - contrary to popular belief - QM can be
interpreted as a dynamical theory of particle trajectories rather than as a
statistical theory of observation. In such a formalism the standard paradoxes
related to measurement, observation and wave function collapse (Schroedinger's
cat, and so on) largely evaporate. The classical limit does not have to be
presupposed and emerges from the theory in a relatively clear way. All the 'talk'
is replaced by sharply-defined mathematics, it becomes possible to 'visualize' the
reality of most quantum events, and - most importantly - the theory is completely
consistent with the full range of QM predictive-observational data. While some
believe the study of interpretational questions to be mere semantics or 'just
philosophy', it is often forgotten that the location of the boundary between
philosophy and physics is unknown, and that one's philosophical perspective can
guide mathematical developments. For many people it is clear that de Broglie-
Bohm theory should be studied, not only because it is beginning to make
apparently testable predictions, but also because it has the potential to suggest
possible directions towards the next generation of ideas in theoretical physics.

...

Quantum non-equilibrium and 'signal non-locality'.

Dynamical relaxation to quantum equilibrium.

Potential instabilities in the Bohm dynamics.

Possible deeper interpretations of de Broglie-Bohm theory (such as Basil
Hiley's new quantum algebra work).

Pilot-wave field theories and relativistic generalizations

De Broglie-Bohm quantum cosmology

Deconstructing' the wave function. Can the theory be reduced to 3-space
waves? Norsen's 'theory of exclusively local beables'.

Proposed experimental tests (Valentini, Riggs, etc..)

The ontological status of the theory. First or Second order?

Energy.

Empty waves.

The arguments for and against psi-epistemic hidden-variables theories.

Alternative formulations of deterministic hidden-variables theories.

Non-Markovian trajectory theories.


Comparison with the consistent histories formulation


Use of trajectories for efficient numerical simulations in quantum chemistry.

Spin, antisymmetry, the exclusion principle and the 'quantum force.'

Responses to common objections (it's not possible for particles to exist; particles going round corners ought to radiate etc.)."

-- Michael Towler, Canbridge University, Web page

 

Jun 18

BP Spill - A Perfect Storm?

Posted by: JackSarfatti |
Tagged in: Untagged 

Martin Rees

 

Added June 18, 2010

"The system will collapse or fail substantially before we reach the finish line ahead of the well and the worst is yet to come. Sorry to bring you that news, I know it is grim, but that is the way I see it....I sincerely hope I am wrong. We need to prepare for the possibility of this blow out sending more oil into the gulf per week then what we already have now, because that is what a collapse of the system will cause. All the collection efforts that have captured oil will be erased in short order. The magnitude of this disaster will increase exponentially by the time we can do anything to halt it and our odds of actually even being able to halt it will go down. The magnitude and impact of this disaster will eclipse anything we have known in our life times if the worst or even near worst happens..."

 http://www.theoildrum.com/node/6593/648967

 

Hi L

Now, why didn't I think of that? Too freaked out by the whole thing. Very elegant, obvious in hindsight, but I suppose the issue is how many barrels escape before mechanical quasi-hydrostatic equilibrium sets in? What about chemical potential gradient - diffusion of oil molecules into the lower concentration of the outside water - what is characteristic time for that? In other words, the boundary between the oil and the water is porous

On Jun 17, 2010, at 10:09 PM, L S PhD wrote:

"The reservoir only has so much oil. I mean even if they can't stop the flow mechanically it will stop pretty soon on its own ... as the pressure in the reservoir equalizes with the external


I meant "stop eventually" ... I understand why there is a moratorium on the drilling now but ..actually if there was more drilling out there now the spill would come to a natural stop sooner because the combined production would lower the reservoir pressure faster."

Did a 'sleeper' field awake to expand the universe?
    •    11 June 2010 by Anil Ananthaswamy

To overcome this daunting discrepancy, physicists have resorted to other explanations for the recent cosmic acceleration. One explanation is the idea that space-time is suffused with a field called quintessence. This field is scalar, meaning that at any given point in space-time it has a value, but no direction. Einstein's equations show that in the presence of a scalar field that changes very slowly, space-time will expand at an ever-increasing rate...

Thank ye,
Th' Admiralty

Cap'n Jack Sarfatti http://stardrive.org/index.php?option=com_content&view=article&id=1378:physics-vs-metaphysics-knowledge-vs-wisdom&catid=43:science&Itemid=82

Physics vs. metaphysics, knowledge vs. wisdom

One sunrise ago at 6:41 in the evenin' · Weigh in ·  · Gareth Lee Meredith an Denise Dallas find this pleasin' to the eye.

Sam Arnold
Answer: VALIS ;)
One sunrise ago at 7:04 in the evenin' · Jeff Adams
Good post, Jack. I think we all want the answer to Hawking's question. I am not personally worried about it because I know the answer for me and I am very content with it.
One sunrise ago at 7:30 in the evenin' · Jack Sarfatti
VALIS is our future event horizon hologram screen that computes us as images back from the future in my crazy theory. Is it crazy enough to be true or just crazy? This nutty notion started with Gerardus 't Hooft and Lenny Susskind. I grabbed their ball and am running with it to score a basket. ;-)
One sunrise ago at 7:31 in the evenin' · Sam Arnold
Well it can't be any crazier than "the universe exists, why there is something greater than nothing"- hold off on putting Sarfatti in that strait jacket gentlemen...perhaps the world would do well to listen to him ;)
One sunrise ago at 7:37 in the evenin' · Gareth Lee Meredith
I applaud you Jack for taking on Gerard, t'Hoofts holographic principle, and soon that ball will become large enough so that perhaps its not too crazy after all.
'bout one turn o' yer hourglass ago · Jack Sarfatti
The surface of the ball is our future event horizon hologram screen and we are always inside it at its exact center according to Einstein's gravity field equations when combined with dark energy data. This has been proved in Tamara Davis's 2004 Ph.D. dissertation on-line in her Fig 1.1 computer simulation.
'bout one turn o' yer hourglass ago · Jack Sarfatti
See the picture here.

It's a metaphoric representation of the hologram universe - we are always at the center of the holographic universe, i.e. observer-dependent future de Sitter cosmological horizon. This turns Copernicus on his head and is a return to the Medieval View in a way. Actually it's more complex than that and we need to invoke Bohr's Principle of Complementarity.
'bout one turn o' yer hourglass ago · Donald McLean

Gareth Lee Meredith
So, i've learned a little of the Holographic Principle, but what do you mean ''we are always inside it at its exact center'' - is it something obvious? :)
12 shots o' rum ago · Jack Sarfatti
Yes, most theorists do not have a good idea in their heads. They are good math technicians who cannot think well physically. They come up with silly Rube Goldberg mechanisms that are more complicated than the actual facts demand. There is a very simple explanation for both the dark energy and the dark matter using only basic quantum theory and Einstein's general relativity that I have been professing since 2002 or so. My theory makes predictions and is Popper falsifiable. So far, so good - all the observations to date are in my favor. Let's see what the LHC gives.

On the exact center - Google "observer-dependent horizons" "de Sitter space". What we measure depends on light signals. Gravity bends light. Dark energy bends light in a peculiar way.

Actually dark energy defocuses light like passing a collimated beam through a concave lens. In contrast, dark matter like, ordinary matter, focuses light like a convex lens. The dark energy accelerating the rate of expansion of  space defocuses light into a future horizon that is literally a spherical shell of "null geodesics" - possible paths of actual light rays we emit here and now. Our future horizon is always a finite distance from us. We keep getting closer to it, but it would take an infinite amount of clock time to reach it at the Omega Point (not in Frank Tipler's sense of the word). Similarly, we keep getting further away from our past particle horizon that is the shell of light expanding away from the Alpha Point of inflation creating our observable piece of the multiverse.




Jun 11

The Wheeler-Feynman Gravity Spinor QuBITS

Posted by: JackSarfatti |
Tagged in: Untagged 

The Local Inertial Frame orthogonal transformation from rectangular Cartesian triads to spherical polar triads.

Using the equivalence principle the domain of validity of the LIF is a 4D spacetime volume small compared to the locally variable curvature radii.

The origin of the spherical polar triads is the idealized point emission event origin of the local light cones. So this is a fiber bundle of triads.

Let @ stand for the polar angle "theta" i.e. latitude on the (anti) celestial sphere aka (future) past light cone spacelike slices. Let & stand for the longitudinal azimuthal angle.

 

For the orthonormal base triads of Cartan's mobile frames.

eR  = isin@cos& + jsin@sin& + kcos@

~ (1/2)^1/2[sin@cos& (|A+>|A'-> + |A->|A'+>) + sin@sin&(|A+>|A'-> - |A->|A'+>) + cos@(|A+>|A'+> - |A->|A'->)]


e@ = icos@cos& + jcos@sin& - ksin@

~ (1/2)^1/2[cos@cos& (|A+>|A'-> + |A->|A'+>) + cos@sin&(|A+>|A'-> - |A->|A'+>) + sin@(|A+>|A'+> - |A->|A'->)]


e& = -isin& + jcos&

~ (1/2)^1/2[-sin& (|A+>|A'-> + |A->|A'+>) + cos&(|A+>|A'-> - |A->|A'+>) These are spacelike vectors outside the light cone.

et is a timelike vector inside the light cone. ~ (1/2)^1/2(|A+>|A'+> + |A->|A'->)]


The real Wheeler-Feynman null tetrads are

lwf = (1/2)^1/2(et + eR)  the advanced destiny real null tetrad

nwf = (1/2)^1/2(et - eR)  the retarded history real null tetrad

mwf =  (1/2)^1/2(e@ - ie&) Limiting cases, along the arbitrary Cartesian z-axis, @ = 0 et is a timelike vector inside the light cone. ~ (1/2)^1/2(|A+>|A'+> + |A->|A'->) independent of @ and &

eR  ---> k

~ (1/2)^1/2(|A+>|A'+> - |A->|A'->)

lwf = (1/2)^1/2(et + eR)  the advanced destiny real null tetrad ---> |A+>|A'+>

Therefore, "+" means "advanced" or "destiny" or retro-causal back-from-the-future pointing rather than an abstract "up" spin projection state, in this new geometrodynamical context. Similarly,

nwf = (1/2)^1/2(et - eR)  the retarded history real null tetrad ---> |A->|A'->

Therefore, "-" means "retarded" or "history" or causal past-to-future pointing rather than an abstract "down" spin projection state, in this new geometrodynamical context. These geometrodynamical light cone spinors are different from, independent of the ordinary magnetic moment lepton-quark spinor degrees of freedom.


We can also use the Paul spin matrices (quaternion hyper-complex numbers) where the tetrad basis et,i,j,k set are the 2x2 matrices.

The infinitesimal quaternion (c = 1)

ds = dtet  + dxi + dyj + dzk

ds^2 = dt^2 - dx^2 - dy^2 - dz^2

taking the complex conjugate

dsds* = Euclidean metric (Wick rotation to imaginary time of temperature statistical Green's functions).

Note in spherical coordinates where the local light cone origin R = 0 is at each point emission event

ds = dtet  + dReR + Rd@e@ + Rsin@d&e&

i.e. a fiber bundle field of light cones, where curvature is the relative tipping of neighboring light cones.