t'Hooft claims that all elementary particles must be point particles that they cannot be extended deformable objects.
The identity of all particles of the same type is in the quantum statistics of the permutation group. For example the Pauli exclusion principle for electrons that N-electron wave functions are totally antisymmetric in all quantum numbers - a column in the Young diagram notation for irreducible representations of the permutation group. This is in 3+1 spacetime. Anyons in 2+1 spacetime with fractional quantum statistics and fractional angular momenta and charges are modifications that do not change my objection to t'Hooft's above qualitative "informal language" argument.
My point is especially clear in Bohm's pilot wave-hidden variable interpretation. It is less clear in other interpretations.
The identity of elementary particles is a property of the BIT pilot wave or "quantum potential" Q for particles and "super potential" for fields. The actual hidden variable i.e. Newton's "hard massy ball" perhaps an actual string, or brane, or tiny black hole or tiny wormhole in Salam's strong short-range gravity, need not be a rigid extended object at all. It can support all sorts of modes of vibration like a classical object and still not affect the permutation symmetry of identical particles. Therefore, I say that t'Hooft has made an error in his above qualitative heuristic informal argument.
Truly elementary particles can be extended deformable objects consistent with c as the maximal material signal speed. That will not affect their quantum statistics - certainly not in the Bohm pilot wave interpretation where the hidden variables need not be point particles in space.
Sunday, May 06, 2007
Saturday, April 28, 2007
“Gravity is that field which corresponds to a gauge invariance with
respect to displacement transformations.” Richard Feynman[i]
[i] http:/arXiv.org/abs/gr-qc/9602013 F. Hehl, p. 21
There is a part of F. Hehl's paper 1996 that to me suggests a
connection of the torsion gap, i.e. dislocation density in Kleinert's
world crystal lattice as a kind of poor-man's noncommutative geometry
i.e. 4.3 eqs 51 - 53
More on this - also supersymmetry is the square root of T4 and
Feynman means T4 above - same as me. Same as Hehl. Of course to do it
right we need full 10 parameter Poincare group. T4 enough to get
Einstein 1915 GR with non-dynamical "dummy" spin connections like the
Wheeler-Feynman EM potentials eliminated in terms of the charges &
action both ways in time on the light cones.
Hehl cites a Phys Rev. D Editor high energy theorist Lowell S. Brown who does not
understand Noether's theorem nor what Feynman says above and has
banned torsion papers from Phys. Rev like Stapp's paper on
retrocausality caused a similar ban on related papers!
respect to displacement transformations.” Richard Feynman[i]
[i] http:/arXiv.org/abs/gr-qc/9602013 F. Hehl, p. 21
There is a part of F. Hehl's paper 1996 that to me suggests a
connection of the torsion gap, i.e. dislocation density in Kleinert's
world crystal lattice as a kind of poor-man's noncommutative geometry
i.e. 4.3 eqs 51 - 53
More on this - also supersymmetry is the square root of T4 and
Feynman means T4 above - same as me. Same as Hehl. Of course to do it
right we need full 10 parameter Poincare group. T4 enough to get
Einstein 1915 GR with non-dynamical "dummy" spin connections like the
Wheeler-Feynman EM potentials eliminated in terms of the charges &
action both ways in time on the light cones.
Hehl cites a Phys Rev. D Editor high energy theorist Lowell S. Brown who does not
understand Noether's theorem nor what Feynman says above and has
banned torsion papers from Phys. Rev like Stapp's paper on
retrocausality caused a similar ban on related papers!
Friday, April 27, 2007
Ed Witten & Lenny Susskind lament on absence of an "organizing idea" for M Theory (equivalence principle was the organizing idea for Einstein's 1915 GR). They need lament no more - it's the same organizing idea!
There has been a recent flurry in letters in Physics Today - a bit odd in that Weinberg seems unfamiliar with Hehl's work, yet Hehl gave famous lectures on torsion theory at Institute of Advanced Study in Princeton published in Rev. Mod. Phys. 1976.
Hehl lectures on Einstein's GR as a limiting case of a local Poincare group theory. Utiyama's & Kibble's work on that done in ~ 1961. However, Hehl makes IMHO the incorrect assumption that the torsion field is generated only by the micro-quantum spins hence it does not propagate as a far field wave. Richard Hammond has shown that this assumption is not necessary and indeed there is experimental evidence against it. The coupling should be to the total 4D angular momentum field tensor of all sources including orbital (for 3D part) both real and virtual - the latter includes IMHO both repulsive dark energy and attractive dark matter as negative and positive quantum pressure exotic vacuum phases respectively of a quintessent /\zpf locally variable microscopic -> macroscopic field.
96% of our possibly pocket Hubble bubble universe on the overpopulated cosmic landscape of eternal chaotic inflation (self-created Gott-Li?) is random incoherent off-shell virtual quanta acting as the external "wood" source pump of the "marble" Higgs-Goldstone coherent vacuum condensate field whose Goldstone phase(s) modulation is the smooth c-number emergent warped Einstein-Cartan fabric of spacetime. The Calabi-Yau extra-dimensions are from the 6 "angle parameters" from locally gauging the Lorentz-group whose implied full 4D rotation tensor is the torsion source in the same way that the full 4D translational group's implied "matter" stress-energy tensor is the curvature source. Why only choose the quantum spins of on-shell quanta in the former?
That all non-gravity fields, both real and virtual, participate as sources is part of the equivalence principle.
To be a bit more precise
The 4-parameter translational group's Lie algebra of "observable charges" forms the global total energy-momentum 4-vector of all the source fields. These global integrals are over local stress-energy tensors of the non-gravity fields whose dynamical actions are gauge invariant with respect to the localized Poincare group where curvature and torsion are derived from more fundamental compensating gauge potentials at the square root tetrad + spin connection Cartan 1-form "substratum" level. Supersymmetry is natural in the substratum as is the coupling to spinor field sources. Difficulties in properly defining the integrals at the derived quadratic geometrodynamical level and in trying to include the gravity field itself requiring asymptotic flatness are not relevant to the more fundamental point here. As Penrose et-al point out the pure gravity vacuum field does not have a local self-source stress-energy tensor even though there is total energy-momentum in the vacuum gravity field.
Similarly, the 6-parameter space-time translation group is generated by integrals of the 4D rotational source field tensors of all the non-gravity fields. These 6 parameters are the dimensions of the local Calabi-Yau fiber.
J = L + S
S = quantum spin
L = orbital angular momentum
is only for the 3 space rotations of the Lorentz group's Lie algebra. Hehl, oddly only takes S as the source of the torsion field. This is not even a covariant choice IMHO.
In addition there are the 3 boosts (spacetime rotations) that will contribute to the torsion field.
Gennady Shipov has the germ of this idea in his concept of the "oriented point" needing 2 metrics 4D translation and 6D rotational - the latter years before string theory's construct of the Calabi-Yau fiber space.
http://qedcorp.com/APS/Shipov.jpg
The Calabi-Yau space fiber is compactified in a anisotropic way in general so that the above simple spheres look more like
http://www.futura-sciences.com/comprendre/d/images/510/CalabiYauSpace.jpg
But the idea is clearly similar. Shipov had years before M theory was a glimmer in Witten's eye.
The Kaluza-Klein radii are Ri i = 1 ... 6
Kaluza-Klein charges are ei ~ G*^1/2h/cRi
G* is running gravity coupling constant of the secondary spin-2 geometrodynamic field.
Note that the renormalizable spin-1 vector tetrad fields have dimensionless couplings
(G*h/\zpf/c^3)^1/2 for each vertex in the Feynman diagrams where /\zpf is the quintessent field -> Einstein's cosmological constant in large space scale limit.
The reciprocal of this is the Bekenstein BIT number of deSitter future horizons i.e.
Wheeler's IT FROM BIT
There has been a recent flurry in letters in Physics Today - a bit odd in that Weinberg seems unfamiliar with Hehl's work, yet Hehl gave famous lectures on torsion theory at Institute of Advanced Study in Princeton published in Rev. Mod. Phys. 1976.
Hehl lectures on Einstein's GR as a limiting case of a local Poincare group theory. Utiyama's & Kibble's work on that done in ~ 1961. However, Hehl makes IMHO the incorrect assumption that the torsion field is generated only by the micro-quantum spins hence it does not propagate as a far field wave. Richard Hammond has shown that this assumption is not necessary and indeed there is experimental evidence against it. The coupling should be to the total 4D angular momentum field tensor of all sources including orbital (for 3D part) both real and virtual - the latter includes IMHO both repulsive dark energy and attractive dark matter as negative and positive quantum pressure exotic vacuum phases respectively of a quintessent /\zpf locally variable microscopic -> macroscopic field.
96% of our possibly pocket Hubble bubble universe on the overpopulated cosmic landscape of eternal chaotic inflation (self-created Gott-Li?) is random incoherent off-shell virtual quanta acting as the external "wood" source pump of the "marble" Higgs-Goldstone coherent vacuum condensate field whose Goldstone phase(s) modulation is the smooth c-number emergent warped Einstein-Cartan fabric of spacetime. The Calabi-Yau extra-dimensions are from the 6 "angle parameters" from locally gauging the Lorentz-group whose implied full 4D rotation tensor is the torsion source in the same way that the full 4D translational group's implied "matter" stress-energy tensor is the curvature source. Why only choose the quantum spins of on-shell quanta in the former?
That all non-gravity fields, both real and virtual, participate as sources is part of the equivalence principle.
To be a bit more precise
The 4-parameter translational group's Lie algebra of "observable charges" forms the global total energy-momentum 4-vector of all the source fields. These global integrals are over local stress-energy tensors of the non-gravity fields whose dynamical actions are gauge invariant with respect to the localized Poincare group where curvature and torsion are derived from more fundamental compensating gauge potentials at the square root tetrad + spin connection Cartan 1-form "substratum" level. Supersymmetry is natural in the substratum as is the coupling to spinor field sources. Difficulties in properly defining the integrals at the derived quadratic geometrodynamical level and in trying to include the gravity field itself requiring asymptotic flatness are not relevant to the more fundamental point here. As Penrose et-al point out the pure gravity vacuum field does not have a local self-source stress-energy tensor even though there is total energy-momentum in the vacuum gravity field.
Similarly, the 6-parameter space-time translation group is generated by integrals of the 4D rotational source field tensors of all the non-gravity fields. These 6 parameters are the dimensions of the local Calabi-Yau fiber.
J = L + S
S = quantum spin
L = orbital angular momentum
is only for the 3 space rotations of the Lorentz group's Lie algebra. Hehl, oddly only takes S as the source of the torsion field. This is not even a covariant choice IMHO.
In addition there are the 3 boosts (spacetime rotations) that will contribute to the torsion field.
Gennady Shipov has the germ of this idea in his concept of the "oriented point" needing 2 metrics 4D translation and 6D rotational - the latter years before string theory's construct of the Calabi-Yau fiber space.
http://qedcorp.com/APS/Shipov.jpg
The Calabi-Yau space fiber is compactified in a anisotropic way in general so that the above simple spheres look more like
http://www.futura-sciences.com/comprendre/d/images/510/CalabiYauSpace.jpg
But the idea is clearly similar. Shipov had years before M theory was a glimmer in Witten's eye.
The Kaluza-Klein radii are Ri i = 1 ... 6
Kaluza-Klein charges are ei ~ G*^1/2h/cRi
G* is running gravity coupling constant of the secondary spin-2 geometrodynamic field.
Note that the renormalizable spin-1 vector tetrad fields have dimensionless couplings
(G*h/\zpf/c^3)^1/2 for each vertex in the Feynman diagrams where /\zpf is the quintessent field -> Einstein's cosmological constant in large space scale limit.
The reciprocal of this is the Bekenstein BIT number of deSitter future horizons i.e.
Wheeler's IT FROM BIT
Wednesday, April 18, 2007
For example the classical static Coulomb potential e^2/r when Fourier analyzed is off mass shell i.e. zero frequency virtual photons of all 3D wave vectors K. Indeed the power spectrum of wave vectors is ~ e^2/K^2.
So we need to imagine huge numbers of virtual spacelike photons outside the light cone with longitudinal polarization parallel to each K 3-vector. The relative distribution of the occupation numbers nK of each purely spatial mode (in rest frame of the source charge) ~ 1/K^2. These must be Glauber macroquantum coherent states with ~ 1/K^2.
While all random zero point photons are virtual, not all virtual photons are random zero point. The induction EM near fields inside the walls of our houses and appliances, are non-random macroscopic Bose-Einstein like condensations of jillions and jillions of virtual photons which directly influence phenomena and indeed are a large part of everyday phenomena.
On Apr 18, 2007, at 10:31 PM, Jack Sarfatti wrote:
We need to distinguish the classical limit from the quantum electrodynamics with only a small number of photons.
In quantum electrodynamics the non-propagating EM fields are the off-mass-shell virtual photons. In terms of Feynman's path quantum theory, where second quantized creation and destruction operators are not used, the virtual photons responsible for micro near fields are the contributions that are not at the pole k = 0 of the photon propagator with the common factor ~ 1/k^2 in 4-momentum space for all 4 polarizations. The Lorentz gauge condition k^uAu = 0 is used. Note that k^2 = k^uku The Lorentz gauge condition constrains the longitudinal near field polarization of the 3-vector potential to the timelike polarization of the scalar potential.
Classical near fields only exist when there are a macroscopic number of virtual photons occupying the same wavepacket "mode" with longitudinal polarization of the 3-vector potential. This requires an extension of the Feynman formalism to include ODLRO in the electrodynamic vacuum. One analogy would be trying to do superfluid helium in the language of the Feynman path integrals.
If we use second-quantized canonical formalism of q-number creation and destruction operators then ODLRO formally is
ak = Ak + @k
Ak is a c-number
ak & @k are q numbers
where k here is only the longitudinal & timelike polarizations if we ignore radiation at first.
On Apr 18, 2007, at 4:38 PM, Jack Sarfatti wrote:
According to standard physics
Fuv is the EM field tensor that obeys the Lorentz group
i.e. transforms as an antisymmetric 2nd rank tensor under the transformations of the 6-parameter Lorentz group, specifically the 3 boosts.
This Fuv includes the longitudinal near fields.
This is all a classical physics problem at this stage.
One must think of experiments that can test the transformations of the near fields.
The problem here is to measure from a moving frame S' whose speed v relative to lab frame S
is v ~ c.
On Apr 18, 2007, at 3:23 PM, Jack Sarfatti wrote:
William (et-al)
typo eq 25 should be "-" not "+"
You have already confirmed part of your prediction for microwaves as I recall.
What you say may have practical importance in nanotechnology - especially computer hardware.
These effects have not shown up in the design of high energy accelerators.
They should be there in electrical power systems using near fields.
Clearly a careful analysis is warranted.
Your results do not impact on the experimental tests of either special or general relativity (Cliff Will) because those tests use only far fields for the EM signals. General relativity is a macroscopic theory. However, attempts to model the electron as an extended object, e.g. a kind of tiny Kerr blackhole (or even naked singularity) (A. Burinski) with strong short-range gravity (from extra space dimensions of string theory) and also possible torsion fields as a Bohm hidden variables would seem to be sensitive to the sorts of effects you are suggesting. Indeed an analog for gravity waves as well I would imagine?
Your effects should show up in off-mass-shell virtual quantum propagation in quantum gauge theory calculation of Feynman diagrams perhaps impinging on issues of regularization and renormalization?
On Apr 18, 2007, at 1:02 PM, Jack Sarfatti wrote:
Thanks William
Since your results apply only to the non-radiating near field there is probably no real conflict because the light cone structure basis of relativity only applies to the radiating far-field transverse polarization for on-shell photons, not to the virtual off shell photons in coherent states forming the near induction fields. I will definitely read your paper soon with great interest. :-)
On Apr 18, 2007, at 2:46 AM, William D. Walker wrote:
Hi Jack,
This is William Walker. How are you doing? It has been a long time since we met at the Vigier IV conference in Paris. By the way, do you know of any other similar conferences coming up soon? It would be nice to meet up again.
Not at the moment. With regard to your question deleted here, American theoretical physics is in a depressing state in contrast to experimental physics, which is basically what you do. See the book "Not Even Wrong" by Peter Woit on the dominance of string theory in academic departments. It's controversial and I have not completely given up on certain aspects of string theory as I seem to get what is effectively 6 extra space dimensions in gravity as emergent from a 4D ODLRO "supersolid" version of Hagen Kleinert's "world crystal lattice" in a natural way consistent with the torsion theory of Gennady Shipov. The nodes of the lattice are point defects in the supersolid order parameter that has two Goldstone coherent "world hologram phases" when the theory is projected from 9 + 1 to 3 + 1.
http://qedcorp.com/APS/Shipov.jpg
Since we last met, I have continued my research on superluminal near-field EM and gravitational fields. I have written a new paper which I think you might find interesting:
http://xxx.lanl.gov/pdf/physics/0702166
The paper shows that contrary to the Michelson-Morley results, the speed of light is dependent on the velocity of the source or observer, as well as being faster than c in the nearfield. Because Einstein's relativity theory is based on the assumption that the speed of light is both constant and independent of the source or observer velocity, based on these new findings, I have looked into the possible implications to relativity theory.
So we need to imagine huge numbers of virtual spacelike photons outside the light cone with longitudinal polarization parallel to each K 3-vector. The relative distribution of the occupation numbers nK of each purely spatial mode (in rest frame of the source charge) ~ 1/K^2. These must be Glauber macroquantum coherent states with
While all random zero point photons are virtual, not all virtual photons are random zero point. The induction EM near fields inside the walls of our houses and appliances, are non-random macroscopic Bose-Einstein like condensations of jillions and jillions of virtual photons which directly influence phenomena and indeed are a large part of everyday phenomena.
On Apr 18, 2007, at 10:31 PM, Jack Sarfatti wrote:
We need to distinguish the classical limit from the quantum electrodynamics with only a small number of photons.
In quantum electrodynamics the non-propagating EM fields are the off-mass-shell virtual photons. In terms of Feynman's path quantum theory, where second quantized creation and destruction operators are not used, the virtual photons responsible for micro near fields are the contributions that are not at the pole k = 0 of the photon propagator with the common factor ~ 1/k^2 in 4-momentum space for all 4 polarizations. The Lorentz gauge condition k^uAu = 0 is used. Note that k^2 = k^uku The Lorentz gauge condition constrains the longitudinal near field polarization of the 3-vector potential to the timelike polarization of the scalar potential.
Classical near fields only exist when there are a macroscopic number of virtual photons occupying the same wavepacket "mode" with longitudinal polarization of the 3-vector potential. This requires an extension of the Feynman formalism to include ODLRO in the electrodynamic vacuum. One analogy would be trying to do superfluid helium in the language of the Feynman path integrals.
If we use second-quantized canonical formalism of q-number creation and destruction operators then ODLRO formally is
ak = Ak + @k
Ak is a c-number
ak & @k are q numbers
where k here is only the longitudinal & timelike polarizations if we ignore radiation at first.
On Apr 18, 2007, at 4:38 PM, Jack Sarfatti wrote:
According to standard physics
Fuv is the EM field tensor that obeys the Lorentz group
i.e. transforms as an antisymmetric 2nd rank tensor under the transformations of the 6-parameter Lorentz group, specifically the 3 boosts.
This Fuv includes the longitudinal near fields.
This is all a classical physics problem at this stage.
One must think of experiments that can test the transformations of the near fields.
The problem here is to measure from a moving frame S' whose speed v relative to lab frame S
is v ~ c.
On Apr 18, 2007, at 3:23 PM, Jack Sarfatti wrote:
William (et-al)
typo eq 25 should be "-" not "+"
You have already confirmed part of your prediction for microwaves as I recall.
What you say may have practical importance in nanotechnology - especially computer hardware.
These effects have not shown up in the design of high energy accelerators.
They should be there in electrical power systems using near fields.
Clearly a careful analysis is warranted.
Your results do not impact on the experimental tests of either special or general relativity (Cliff Will) because those tests use only far fields for the EM signals. General relativity is a macroscopic theory. However, attempts to model the electron as an extended object, e.g. a kind of tiny Kerr blackhole (or even naked singularity) (A. Burinski) with strong short-range gravity (from extra space dimensions of string theory) and also possible torsion fields as a Bohm hidden variables would seem to be sensitive to the sorts of effects you are suggesting. Indeed an analog for gravity waves as well I would imagine?
Your effects should show up in off-mass-shell virtual quantum propagation in quantum gauge theory calculation of Feynman diagrams perhaps impinging on issues of regularization and renormalization?
On Apr 18, 2007, at 1:02 PM, Jack Sarfatti wrote:
Thanks William
Since your results apply only to the non-radiating near field there is probably no real conflict because the light cone structure basis of relativity only applies to the radiating far-field transverse polarization for on-shell photons, not to the virtual off shell photons in coherent states forming the near induction fields. I will definitely read your paper soon with great interest. :-)
On Apr 18, 2007, at 2:46 AM, William D. Walker wrote:
Hi Jack,
This is William Walker. How are you doing? It has been a long time since we met at the Vigier IV conference in Paris. By the way, do you know of any other similar conferences coming up soon? It would be nice to meet up again.
Not at the moment. With regard to your question deleted here, American theoretical physics is in a depressing state in contrast to experimental physics, which is basically what you do. See the book "Not Even Wrong" by Peter Woit on the dominance of string theory in academic departments. It's controversial and I have not completely given up on certain aspects of string theory as I seem to get what is effectively 6 extra space dimensions in gravity as emergent from a 4D ODLRO "supersolid" version of Hagen Kleinert's "world crystal lattice" in a natural way consistent with the torsion theory of Gennady Shipov. The nodes of the lattice are point defects in the supersolid order parameter that has two Goldstone coherent "world hologram phases" when the theory is projected from 9 + 1 to 3 + 1.
http://qedcorp.com/APS/Shipov.jpg
Since we last met, I have continued my research on superluminal near-field EM and gravitational fields. I have written a new paper which I think you might find interesting:
http://xxx.lanl.gov/pdf/physics/0702166
The paper shows that contrary to the Michelson-Morley results, the speed of light is dependent on the velocity of the source or observer, as well as being faster than c in the nearfield. Because Einstein's relativity theory is based on the assumption that the speed of light is both constant and independent of the source or observer velocity, based on these new findings, I have looked into the possible implications to relativity theory.
Monday, April 09, 2007
Of course the model below is only a toy model illustrating a set ideas organized in an unfamiliar way in an attempt to shed some light on the greatest mystery in physics today
What is our universe mostly made of?
Jack Sarfatti (sarfatti@pacbell.net) wrote:
Decoding The Cipher of Genesis
Looking at elementary cavity quantum field theory for a scalar field U(x,t) in 1+1 spacetime, e.g. string standing wave oscillations, the mass shell condition f = (signal speed)k for zero dispersion and zero rest mass is enforced by boundary conditions e.g. U(0,t) = U(L,t) so that
f(l) = l(signal speed)/2L
where l is the mode index that in this simple case is an integer 1 to infinity.
group speed = signal speed = phase speed
in this non-dispersive toy model.
The resulting Fock occupation number states |n) are n identical real on shell quanta each of frequency f(l) in the lth mode of wave length 2L/l with l = 1 the fundamental, l =2 the first harmonic and so on. The Fock space vacuum of a given mode with n = 0 has an effective random noise occupation number of 1/2.
In contrast to Fock states that are orthogonal inside a single mode (the modes are, in addition, mutually orthogonal)
(n|n') = 0 when n =/= n'
The macroquantum ODLRO coherent Glauber states |z) are coherent superpositions of different numbers of "real" quanta they are not orthogonal for a given l mode, i.e.
(z|z') =/= 0 ODLRO states when z =/= z'
z is a complex number
z = (n)^1/2e^itheta
theta is the coherent phase
(n) is the mean occupation number
Uncertainty principle
delta(n)delta(theta) ) 1/2
z is a displaced Gaussian in the complex z-plane
|z) = e^(z*a - za*)|0)
|0) is the Fock space vacuum for the single lth standing wave mode of the 1D cavity.
aa* - a*a = 1
a|0) = 0
(0|a* = 0
The single mode Hamiltonian is global over the entire cavity space
H(l) = hf(l)[a*(l)a(l) + 1/2]
I will drop the l for simplicity, understood only a single standing wave mode of sharp wavelength and a definite frequency.
(0|H|0) = hf/2
is the random zero point energy ZPE of that single mode.
This zero point energy in the Fock vacuum |0) directly antigravitates repulsively like an isotropic fluid with w = - 1 in the 3D case - not the present 1D model.
You can think of microquantum |0) as a toy model for the unstable false pre-inflation random incoherent vacuum whose collapse to a more stable less random more coherent macroquantum Glauber state ODLRO "superfluid" vacuum |z).
OK so here is how to do the ODLRO "superfluid" for this single mode.
a = A + @
A is the ODLRO c-number condensate
@ are the random zero point quanta in the coherent vacuum at absolute zero temperature where there are no on-shell elementary excitations "normal fluid" excited states above this Higgs field vacuum where theta is a Goldstone phase.
H(ODLRO) = hf(A* + @*)(A + @) + hf/2
The Glauber states |z) are defined relative to the @ and @* second quantized single-mode destruction and creation operators NOT the original a & a*.
a & a* are the pre-inflation false unstable vacuum operators
@ & @* are the post-inflation dark energy-dark matter metastable vacuum ZPE operators at absolute zero temperature prior to the hot big bang creating ordinary matter and radiation that is only 4% of all the stuff of our accelerating expanding pocket universe in the cosmic landscape of the megaverse of parallel universes including the parallel Virgin Earth's that are part of our Manifest Destiny Matrix - the space migration now professed by Stephen Hawking.
The energy of our false incoherent Fock vacuum without any ODLRO macroquantum condensate is
(0|H|0) = (0|(hf + 1/2)a*a|0) = hf/2
The energy of our more stable coherent vacuum condensate is
(z|H(ODLRO)|z) = hf(|A|^2 + A*z + Az* + |z|^2 + 1/2)
Note if |A| = 0 i.e. no ODLRO
(z|H|z) = ((n) + 1/2)hf ) (0|H|0)
The energy difference of the vacuum phase transition in this single-mode 1D toy model is
(z|H(ODLRO)|z) - (0|H|0) = hf(|A|^2 + A*z + Az* + |z|^2) < 0 stability
|A|^2 = vacuum condensate density
is it real or virtual quanta? (Larry Krauss in "Quintessence")
What does that distinction even mean here?
I opt for virtual since we are at absolute zero.
In superfluid helium at absolute zero the condensate density is 10%, the zero point density is 90% and the total superfluid density is the sum 100% with zero % normal fluid real particles at finite temperature - in thermal equilibrium approximation of course.
|z|^2 = zero point dark energy/matter density
The cross terms are the flow of virtual random quanta into and out of the coherent vacuum condensate reservoir out of which the curved fabric of spacetime emerges as I showed elsewhere.
The energy density per mode released in this first order vacuum phase transition making the hot Big Bang that creates the 4% ordinary matter and radiation we are made out of is determined by the coherent Goldstone phase lag constraint
Vacuum Condensate Density + Dark Energy ZPF Density
+ 2(Vacuum Condensate Density)(Dark Energy ZPF Density)^1/2cos(Goldstone Phase Lag) < 0
Phase lag is between the vacuum condensate phase and the ZPE dark energy phase in this 3 fluid (not 2-fluid macroquantum cosmology toy model with advanced signal retrocausality - discussed elsewhere (pun intended).
These quantum energy densities can go negative.
Either the vacuum condensate energy density or the ZPF energy density can be negative.
Let their ratio be x. The stability inequality is
x + 1/x < 1
therefore x < 0.
positive ZPF energy density is repulsive dark energy
negative ZPF energy density is attractive dark matter
of course the model below is only a toy model illustrating a set ideas organized in an unfamiliar way in an attempt to shed some light on the greatest mystery in physics today
What is our universe mostly made of?
Jack Sarfatti (sarfatti@pacbell.net) wrote:
Sidney Coleman's 1973 Erice Lectures on Hidden Secret Symmetries i.e. spontaneous broken symmetry of ground state comes closest. But Kraus's formulation of the problem may be spurious.
If we have a generally locally variable Higgs field of n real components Psi(x,t) its Fourier integral (assume globally flat spacetime for now) will have components for all frequencies and all wave vectors - hence a mass shell condition makes no sense.
Coleman defines the vacuum condensate for a renormalizable quartic (Mexican Hat) spin 0 scalar quantum field in terms of the connected generating functional W(J) where
e^iW(J) = (0+|0-)
vacuum to vacuum Feynman amplitude
The classical ODLRO vacuum condensate field Psi(x,t) is the functional derivative of W with respect to external source current density J(x)
The effective action is a functional Legendre transform of the generating functional by the global integral of J(x) multiplies by the ODLRO condensate field.
The effective action is also a Taylor series expansion of all nth order IPI Green's functions of the scalar field with nth order product of the ODLRO order parameters. Now I think those IPI Greens functions are all virtual quanta exchanges because "no propagators on the external lines" but I am not sure.
One then gets an effective potential V of the ODLRO vacuum condensate order parameter.
This only scratches the surface of course. Not a solution.
Jack Sarfatti (sarfatti@pacbell.net) wrote:
The problem is not trivial. Appeal to BCS Green's function not good because the condensate there, and in superfluid helium, is on shell real particles in a ground state.
In the case of the actual Higgs field of our universe from inflation out of which curved spacetime emerges, i.e. the tetrad and spin connection 1-forms from the Goldstone phases of the ODLRO coherent vacuum - the issue is are there pole contributions to the vacuum in the Green's functions for elementary excitations of the coherent vacuum, or are the pole terms only in the elementary excitations of the pre-inflation false vacuum prior to the Cosmic Trigger advanced signal from the future deSitter horizon of the emergent pocket universe on the Landscape? The advanced signal lowers the entropy of the early universe explaining how the Arrow of Time of the Second Law of Thermo is "parallel" to the now accelerating expansion of 3D space.
Larry Krauss writes in his book "Quintessence":
"phase transitions in the 'vacuum' (or ground state) of nature can occur. In such cases a finite density of real particles might 'condense' into the new vacuum state." p. 41
If the macro-quantum ODLRO part(s) is from a pole(s) in the appropriate Green's function(s) then Kraus is correct, i.e. if there is a mass shell constraint p^upu = m^2 for the quanta inside the effective BEC(s). There is no microscopic theory of the inflation Higgs field(s) as yet.
For example, in the Glauber state |z) of quantum optics where
a|z) = z|z)
z = (n)^1/2e^i(coherent phase)
f = ck for transverse radiation real photons on mass shell (here mass shell = light cone)
is true physically.
However if one uses a wavelet mode basis this need not be true at all.
A finite spatial wave packet has many k for same frequency f like a virtual photon. This is physically important in a cavity. Of course, such a wavepacket may also have a frequency spread where f = ck.
In the quantum oscillator problem one only uses f and then ad-hoc imposes f = ck in the case of far field transverse photons. However, one can imagine coherent states of virtual photons off mass shell including longitudinal polarization in which a given f has all possible k.
That is, the second-quantized operators a & a* where aa* - a*a = 1 do not refer to plane waves in infinite space but are wave packets inside a cavity.
Note also that the classical static Coulomb potential
V = +- e^2/r
consists of virtual longitudinal photons in a macroquantum coherent f = 0 (DC) state with all possible k momenta i.e.
Vk ~ e^2/k^2
1/k^2 is the almost photon propagator Green's function i.e.
e (1/k^2)e
is essentially a Feynman diagram with charges e at each vertex (dot) and a wiggley virtual photon line connecting the two dots.
To add advanced and retarded boundary conditions
1/(k^2 +- iepsilon)
Jack Sarfatti (sarfatti@pacbell.net) wrote:
Larry Krauss in his 2000 book "Quintessence" says the vacuum condensate is a large number of Bose-Einstein condensed real on shell particles in the same single-particle state. I picture them as virtual off-shell. Who is correct? Must look at Gorkov theory of BCS Green's functions with ODLRO to see what is what here. Real particles are poles in complex energy plane of Green's functions. Pole + off pole parts at T = 0 is 100% L-G superfluid density. Off pole part = locally incoherent nonlocally coherent EPR entangled ZPF if pole part is the ODLRO condensate. I am checking into this.
What is our universe mostly made of?
Jack Sarfatti (sarfatti@pacbell.net) wrote:
Decoding The Cipher of Genesis
Looking at elementary cavity quantum field theory for a scalar field U(x,t) in 1+1 spacetime, e.g. string standing wave oscillations, the mass shell condition f = (signal speed)k for zero dispersion and zero rest mass is enforced by boundary conditions e.g. U(0,t) = U(L,t) so that
f(l) = l(signal speed)/2L
where l is the mode index that in this simple case is an integer 1 to infinity.
group speed = signal speed = phase speed
in this non-dispersive toy model.
The resulting Fock occupation number states |n) are n identical real on shell quanta each of frequency f(l) in the lth mode of wave length 2L/l with l = 1 the fundamental, l =2 the first harmonic and so on. The Fock space vacuum of a given mode with n = 0 has an effective random noise occupation number of 1/2.
In contrast to Fock states that are orthogonal inside a single mode (the modes are, in addition, mutually orthogonal)
(n|n') = 0 when n =/= n'
The macroquantum ODLRO coherent Glauber states |z) are coherent superpositions of different numbers of "real" quanta they are not orthogonal for a given l mode, i.e.
(z|z') =/= 0 ODLRO states when z =/= z'
z is a complex number
z = (n)^1/2e^itheta
theta is the coherent phase
(n) is the mean occupation number
Uncertainty principle
delta(n)delta(theta) ) 1/2
z is a displaced Gaussian in the complex z-plane
|z) = e^(z*a - za*)|0)
|0) is the Fock space vacuum for the single lth standing wave mode of the 1D cavity.
aa* - a*a = 1
a|0) = 0
(0|a* = 0
The single mode Hamiltonian is global over the entire cavity space
H(l) = hf(l)[a*(l)a(l) + 1/2]
I will drop the l for simplicity, understood only a single standing wave mode of sharp wavelength and a definite frequency.
(0|H|0) = hf/2
is the random zero point energy ZPE of that single mode.
This zero point energy in the Fock vacuum |0) directly antigravitates repulsively like an isotropic fluid with w = - 1 in the 3D case - not the present 1D model.
You can think of microquantum |0) as a toy model for the unstable false pre-inflation random incoherent vacuum whose collapse to a more stable less random more coherent macroquantum Glauber state ODLRO "superfluid" vacuum |z).
OK so here is how to do the ODLRO "superfluid" for this single mode.
a = A + @
A is the ODLRO c-number condensate
@ are the random zero point quanta in the coherent vacuum at absolute zero temperature where there are no on-shell elementary excitations "normal fluid" excited states above this Higgs field vacuum where theta is a Goldstone phase.
H(ODLRO) = hf(A* + @*)(A + @) + hf/2
The Glauber states |z) are defined relative to the @ and @* second quantized single-mode destruction and creation operators NOT the original a & a*.
a & a* are the pre-inflation false unstable vacuum operators
@ & @* are the post-inflation dark energy-dark matter metastable vacuum ZPE operators at absolute zero temperature prior to the hot big bang creating ordinary matter and radiation that is only 4% of all the stuff of our accelerating expanding pocket universe in the cosmic landscape of the megaverse of parallel universes including the parallel Virgin Earth's that are part of our Manifest Destiny Matrix - the space migration now professed by Stephen Hawking.
The energy of our false incoherent Fock vacuum without any ODLRO macroquantum condensate is
(0|H|0) = (0|(hf + 1/2)a*a|0) = hf/2
The energy of our more stable coherent vacuum condensate is
(z|H(ODLRO)|z) = hf(|A|^2 + A*z + Az* + |z|^2 + 1/2)
Note if |A| = 0 i.e. no ODLRO
(z|H|z) = ((n) + 1/2)hf ) (0|H|0)
The energy difference of the vacuum phase transition in this single-mode 1D toy model is
(z|H(ODLRO)|z) - (0|H|0) = hf(|A|^2 + A*z + Az* + |z|^2) < 0 stability
|A|^2 = vacuum condensate density
is it real or virtual quanta? (Larry Krauss in "Quintessence")
What does that distinction even mean here?
I opt for virtual since we are at absolute zero.
In superfluid helium at absolute zero the condensate density is 10%, the zero point density is 90% and the total superfluid density is the sum 100% with zero % normal fluid real particles at finite temperature - in thermal equilibrium approximation of course.
|z|^2 = zero point dark energy/matter density
The cross terms are the flow of virtual random quanta into and out of the coherent vacuum condensate reservoir out of which the curved fabric of spacetime emerges as I showed elsewhere.
The energy density per mode released in this first order vacuum phase transition making the hot Big Bang that creates the 4% ordinary matter and radiation we are made out of is determined by the coherent Goldstone phase lag constraint
Vacuum Condensate Density + Dark Energy ZPF Density
+ 2(Vacuum Condensate Density)(Dark Energy ZPF Density)^1/2cos(Goldstone Phase Lag) < 0
Phase lag is between the vacuum condensate phase and the ZPE dark energy phase in this 3 fluid (not 2-fluid macroquantum cosmology toy model with advanced signal retrocausality - discussed elsewhere (pun intended).
These quantum energy densities can go negative.
Either the vacuum condensate energy density or the ZPF energy density can be negative.
Let their ratio be x. The stability inequality is
x + 1/x < 1
therefore x < 0.
positive ZPF energy density is repulsive dark energy
negative ZPF energy density is attractive dark matter
of course the model below is only a toy model illustrating a set ideas organized in an unfamiliar way in an attempt to shed some light on the greatest mystery in physics today
What is our universe mostly made of?
Jack Sarfatti (sarfatti@pacbell.net) wrote:
Sidney Coleman's 1973 Erice Lectures on Hidden Secret Symmetries i.e. spontaneous broken symmetry of ground state comes closest. But Kraus's formulation of the problem may be spurious.
If we have a generally locally variable Higgs field of n real components Psi(x,t) its Fourier integral (assume globally flat spacetime for now) will have components for all frequencies and all wave vectors - hence a mass shell condition makes no sense.
Coleman defines the vacuum condensate for a renormalizable quartic (Mexican Hat) spin 0 scalar quantum field in terms of the connected generating functional W(J) where
e^iW(J) = (0+|0-)
vacuum to vacuum Feynman amplitude
The classical ODLRO vacuum condensate field Psi(x,t) is the functional derivative of W with respect to external source current density J(x)
The effective action is a functional Legendre transform of the generating functional by the global integral of J(x) multiplies by the ODLRO condensate field.
The effective action is also a Taylor series expansion of all nth order IPI Green's functions of the scalar field with nth order product of the ODLRO order parameters. Now I think those IPI Greens functions are all virtual quanta exchanges because "no propagators on the external lines" but I am not sure.
One then gets an effective potential V of the ODLRO vacuum condensate order parameter.
This only scratches the surface of course. Not a solution.
Jack Sarfatti (sarfatti@pacbell.net) wrote:
The problem is not trivial. Appeal to BCS Green's function not good because the condensate there, and in superfluid helium, is on shell real particles in a ground state.
In the case of the actual Higgs field of our universe from inflation out of which curved spacetime emerges, i.e. the tetrad and spin connection 1-forms from the Goldstone phases of the ODLRO coherent vacuum - the issue is are there pole contributions to the vacuum in the Green's functions for elementary excitations of the coherent vacuum, or are the pole terms only in the elementary excitations of the pre-inflation false vacuum prior to the Cosmic Trigger advanced signal from the future deSitter horizon of the emergent pocket universe on the Landscape? The advanced signal lowers the entropy of the early universe explaining how the Arrow of Time of the Second Law of Thermo is "parallel" to the now accelerating expansion of 3D space.
Larry Krauss writes in his book "Quintessence":
"phase transitions in the 'vacuum' (or ground state) of nature can occur. In such cases a finite density of real particles might 'condense' into the new vacuum state." p. 41
If the macro-quantum ODLRO part(s) is from a pole(s) in the appropriate Green's function(s) then Kraus is correct, i.e. if there is a mass shell constraint p^upu = m^2 for the quanta inside the effective BEC(s). There is no microscopic theory of the inflation Higgs field(s) as yet.
For example, in the Glauber state |z) of quantum optics where
a|z) = z|z)
z = (n)^1/2e^i(coherent phase)
f = ck for transverse radiation real photons on mass shell (here mass shell = light cone)
is true physically.
However if one uses a wavelet mode basis this need not be true at all.
A finite spatial wave packet has many k for same frequency f like a virtual photon. This is physically important in a cavity. Of course, such a wavepacket may also have a frequency spread where f = ck.
In the quantum oscillator problem one only uses f and then ad-hoc imposes f = ck in the case of far field transverse photons. However, one can imagine coherent states of virtual photons off mass shell including longitudinal polarization in which a given f has all possible k.
That is, the second-quantized operators a & a* where aa* - a*a = 1 do not refer to plane waves in infinite space but are wave packets inside a cavity.
Note also that the classical static Coulomb potential
V = +- e^2/r
consists of virtual longitudinal photons in a macroquantum coherent f = 0 (DC) state with all possible k momenta i.e.
Vk ~ e^2/k^2
1/k^2 is the almost photon propagator Green's function i.e.
e (1/k^2)e
is essentially a Feynman diagram with charges e at each vertex (dot) and a wiggley virtual photon line connecting the two dots.
To add advanced and retarded boundary conditions
1/(k^2 +- iepsilon)
Jack Sarfatti (sarfatti@pacbell.net) wrote:
Larry Krauss in his 2000 book "Quintessence" says the vacuum condensate is a large number of Bose-Einstein condensed real on shell particles in the same single-particle state. I picture them as virtual off-shell. Who is correct? Must look at Gorkov theory of BCS Green's functions with ODLRO to see what is what here. Real particles are poles in complex energy plane of Green's functions. Pole + off pole parts at T = 0 is 100% L-G superfluid density. Off pole part = locally incoherent nonlocally coherent EPR entangled ZPF if pole part is the ODLRO condensate. I am checking into this.
Thursday, April 05, 2007
Thanks. I have been saying that for at least ten years since reading
his first book.
On Apr 5, 2007, at 11:30 AM, art wagner wrote:
> (um, .... it's a book title) http://www.perseusbookspromos.com/
> docs/PBG-StrangeLoopPostcard.pdf
>
My macro post-quantum theory with signal nonlocality has the strange
loop built in beyond the no-cloning signal locality of micro-quantum
theory. The adaptive self-organizing strange loop is a no-brainer in
the Bohmian ontological interpretation (e.g. A. Valentini's violation
of sub-quantal equilibrium
http://xxx.lanl.gov/abs/quant-ph/0203049),
but is inconceivable in Asher Peres's interpretation. Orthodox
quantum physicists like Satinover (Yale) have cognitive dissonance
over "post-quantum theory" because they implicitly accept the Peres
type interpretation where the wave function is a purely cognitive
tool for making statistical predictions and is not an objective
physical field as it is in the Bohmian picture.
>
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called
research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?
docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
> http://www.flickr.com/photos/lub/sets/72157594439814784
>
his first book.
On Apr 5, 2007, at 11:30 AM, art wagner wrote:
> (um, .... it's a book title) http://www.perseusbookspromos.com/
> docs/PBG-StrangeLoopPostcard.pdf
>
My macro post-quantum theory with signal nonlocality has the strange
loop built in beyond the no-cloning signal locality of micro-quantum
theory. The adaptive self-organizing strange loop is a no-brainer in
the Bohmian ontological interpretation (e.g. A. Valentini's violation
of sub-quantal equilibrium
http://xxx.lanl.gov/abs/quant-ph/0203049),
but is inconceivable in Asher Peres's interpretation. Orthodox
quantum physicists like Satinover (Yale) have cognitive dissonance
over "post-quantum theory" because they implicitly accept the Peres
type interpretation where the wave function is a purely cognitive
tool for making statistical predictions and is not an objective
physical field as it is in the Bohmian picture.
>
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called
research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?
docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
> http://www.flickr.com/photos/lub/sets/72157594439814784
>
Monday, April 02, 2007
"No phenomenon is a phenomenon until it is an observed phenomenon." True?
Hiley shows by explicit calculations that there is no "retrocausality" in Wheeler's delayed choice experiment nor in the variations with a maser cavity in one channel of a Mach-Zehnder interferometer. Even Aharonov & Vaidman made a mistake there! Hiley totally refutes the Asher Peres interpretation of quantum theory, though the late Peres was formidable - a powerful mind. Peter Woit suggest that string theory is pseudoscience, but Hiley shows there has been a lot of bad mystical physics at the foundations of quantum theory - that an ontological reality can be maintained - that Bohr was wrong on that point and Einstein was right, though many of Bohr's insights survive because the opposite of a great truth is another great truth.
Thus Hiley's Bohmian analysis is consistent with the no cloning theorem in which the denial of signal nonlocality imposes strict limits on imperfect optimal cloning of an unknown quantum bit - something like 5/6 for maximal fidelity of the cloning beyond which one gets signal nonlocality and true retrocausality as in the remote viewing and presponse experiments on living matter. This is consistent with David Deutsch's and Wigner's view that consciousness is a violation of microscopic quantum theory. Note there is no measurement problem and no "collapse" in the Bohmian view of micro-quantum theory although in many experiments it's as if collapse. True retrocausality with signal nonlocality is a fundamental breakdown microscopic quantum theory's "sub-quantal equilibrium" (A. Valentini) in which macroquantum spontaneous symmetry breaking leading to emergent phenomena like conscious brains and our accelerating expanding pocket deSitter horizoned universe on the cosmic landscape of the megaverse are prime examples. There is no Hawking wave function of the universe in the macro-world, although it is there in the initial cosmic trigger from the future that retro-causally creates the primordial inflation bubble evolving to the hot Big Bang whose remnant we see in the COBE & WMAP NASA probes. The Hawking wave function of the universe is replaced by the Landau-Ginzburg order parameter that in 3D + 1 is local, which is why there are no giant Schrodinger Cats. Note however that 2D + 1 boundaries with "anyons" have nonlocal order parameters which have a hologram nature.
On Apr 2, 2007, at 8:01 PM, Jack Sarfatti wrote:
Demystifies a lot of quantum
nonsense not only in pop books, but also in standard text books. Even the great Wheeler may be wrong about the quantum?
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
Hiley shows by explicit calculations that there is no "retrocausality" in Wheeler's delayed choice experiment nor in the variations with a maser cavity in one channel of a Mach-Zehnder interferometer. Even Aharonov & Vaidman made a mistake there! Hiley totally refutes the Asher Peres interpretation of quantum theory, though the late Peres was formidable - a powerful mind. Peter Woit suggest that string theory is pseudoscience, but Hiley shows there has been a lot of bad mystical physics at the foundations of quantum theory - that an ontological reality can be maintained - that Bohr was wrong on that point and Einstein was right, though many of Bohr's insights survive because the opposite of a great truth is another great truth.
Thus Hiley's Bohmian analysis is consistent with the no cloning theorem in which the denial of signal nonlocality imposes strict limits on imperfect optimal cloning of an unknown quantum bit - something like 5/6 for maximal fidelity of the cloning beyond which one gets signal nonlocality and true retrocausality as in the remote viewing and presponse experiments on living matter. This is consistent with David Deutsch's and Wigner's view that consciousness is a violation of microscopic quantum theory. Note there is no measurement problem and no "collapse" in the Bohmian view of micro-quantum theory although in many experiments it's as if collapse. True retrocausality with signal nonlocality is a fundamental breakdown microscopic quantum theory's "sub-quantal equilibrium" (A. Valentini) in which macroquantum spontaneous symmetry breaking leading to emergent phenomena like conscious brains and our accelerating expanding pocket deSitter horizoned universe on the cosmic landscape of the megaverse are prime examples. There is no Hawking wave function of the universe in the macro-world, although it is there in the initial cosmic trigger from the future that retro-causally creates the primordial inflation bubble evolving to the hot Big Bang whose remnant we see in the COBE & WMAP NASA probes. The Hawking wave function of the universe is replaced by the Landau-Ginzburg order parameter that in 3D + 1 is local, which is why there are no giant Schrodinger Cats. Note however that 2D + 1 boundaries with "anyons" have nonlocal order parameters which have a hologram nature.
On Apr 2, 2007, at 8:01 PM, Jack Sarfatti wrote:
Demystifies a lot of quantum
nonsense not only in pop books, but also in standard text books. Even the great Wheeler may be wrong about the quantum?
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
Thursday, March 22, 2007
The GCT invariant M Matrix is
M^a^b = (Theta)^a/\(dPhi)^b - (dTheta)^a/\(Phi)^b
dM^a^b = 2(dTheta)^a/\(dPhi)^b
d^2M^a^b = 0 World Hologram, Bekenstein area bits
(Theta)^a and (Phi)^b are Lorentz 4-vectors of 0-form Goldstone phases with 9 real Higgs field components
The Einstein-Cartan tetrad co-frame field 1-forms are
e^a = I^a + (Lp^2/\zpf)^1/2M^a^a
Lp^2 = hG/c^3
Spin connection 1-forms are
S^a^b = - S^b^a ~ M^[a,b]
Four M^aa from locally gauging T(1,3) 4-parameter translation group
Six S^a^b from locally gauging SO(1,3) 6-parameter Lorentz group
M^a^b = (Theta)^a/\(dPhi)^b - (dTheta)^a/\(Phi)^b
dM^a^b = 2(dTheta)^a/\(dPhi)^b
d^2M^a^b = 0 World Hologram, Bekenstein area bits
(Theta)^a and (Phi)^b are Lorentz 4-vectors of 0-form Goldstone phases with 9 real Higgs field components
The Einstein-Cartan tetrad co-frame field 1-forms are
e^a = I^a + (Lp^2/\zpf)^1/2M^a^a
Lp^2 = hG/c^3
Spin connection 1-forms are
S^a^b = - S^b^a ~ M^[a,b]
Four M^aa from locally gauging T(1,3) 4-parameter translation group
Six S^a^b from locally gauging SO(1,3) 6-parameter Lorentz group
How to visualize the spacelike curvature singularity of a non-rotating black hole
http://universe-review.ca/I15-61-interior.jpg
Here we have the absolute light cone field of the black hole (a static spherically symmetric vacuum solution of Ruv = 0).
Note that the above solution in terms of local objective absolute invariant light cones is independent of the choice of local coordinate frames and patches. This is a picture like Egyptian hieroglyphs with the Cartan form "co-frame" tetrads and spin connections as the invariant algebra.
In special relativity without gravity the vertical axis is "time" in a given global frame as is actually depicted in the upper & lower left of the picture. The frame is global because all the invariant light cones are parallel to each other. Now the light cone's origins are "events", i.e. local coincidences like the collisions of two particles. The event is not a raw manifold point. You can get away with that in special relativity but not in general relativity (Einstein Hole Paradox of 1917). The infinitesimal world line segment forming the axis of symmetry of the local light cone, now tilted by curvature relative to its close neighbors, is timelike. We see at the lightlike event horizon that outward bound light rays are trapped on it and the inward bound light rays hit the vertical line at the center. However, that vertical line inside the horizon is not timelike, but has switched over to a spacelike line. Inside the horizon both outward and inward light rays hit the singularity.
We need to look at the math, in what would be static coordinates outside the horizon at r = 2M
ds^2 = -(1 - 2M/r)dt^2 + (1 - 2M/r)^-1dr^2 + transverse metric
for 2M/r < 1
but inside the horizon 2M/r > 1, therefore there is a signature switch of sign to
ds'^2 = -(2M/r - 1)^-1dr^2 + (2M/r - 1)dt^2 + transverse metric
where (2M/r - 1) is a positive
Therefore inside the horizon r is a timelike coordinate, the singularity at r = 0 is not located at a tiny point in 3D space, but is rather a "moment" over the entire 3D spacelike surface with spacelike coordinates t,theta, phi.
Note that
transverse metric = r^2(dtheta^2 + sin^2theta dphi^2)
so at the singularity r = 0 the transverse metric disappears.
Actually if the diagram was drawn more accurately the local light cones at the r = 0 spacelike singularity should be tipped over all the way to the horizontal on the vertical line. It then becomes intuitively obvious that r = 0 is not a locally timelike line inside the local light cone, but is a spacelike line outside that local light cone, which means that r = 0 is the FINITE moment of ultimate destruction of any observer who has fallen through the horizon.
Of course George Chapline has a new idea with Robert Laughlin that there is a dark zero point energy core of negative pressure inside the horizon.
Note that finite electron shells of charge have positive pressure zero point energy inside them. They appear as point particles in large momentum transfer probes because of the enormous space curvature induced by the positive pressure "dark matter" zero point energy cores.
That is, for a simple non-rotating shell of charge toy model "electron", the effective surface area of the spinless "electron" in a scattering with momentum transfer p from probe to target is
Effective area of "electron" Bohm hidden variable ~ (h/mc)^2(1 - p/mc) -> 0 at the Compton radius.
http://universe-review.ca/I15-61-interior.jpg
Here we have the absolute light cone field of the black hole (a static spherically symmetric vacuum solution of Ruv = 0).
Note that the above solution in terms of local objective absolute invariant light cones is independent of the choice of local coordinate frames and patches. This is a picture like Egyptian hieroglyphs with the Cartan form "co-frame" tetrads and spin connections as the invariant algebra.
In special relativity without gravity the vertical axis is "time" in a given global frame as is actually depicted in the upper & lower left of the picture. The frame is global because all the invariant light cones are parallel to each other. Now the light cone's origins are "events", i.e. local coincidences like the collisions of two particles. The event is not a raw manifold point. You can get away with that in special relativity but not in general relativity (Einstein Hole Paradox of 1917). The infinitesimal world line segment forming the axis of symmetry of the local light cone, now tilted by curvature relative to its close neighbors, is timelike. We see at the lightlike event horizon that outward bound light rays are trapped on it and the inward bound light rays hit the vertical line at the center. However, that vertical line inside the horizon is not timelike, but has switched over to a spacelike line. Inside the horizon both outward and inward light rays hit the singularity.
We need to look at the math, in what would be static coordinates outside the horizon at r = 2M
ds^2 = -(1 - 2M/r)dt^2 + (1 - 2M/r)^-1dr^2 + transverse metric
for 2M/r < 1
but inside the horizon 2M/r > 1, therefore there is a signature switch of sign to
ds'^2 = -(2M/r - 1)^-1dr^2 + (2M/r - 1)dt^2 + transverse metric
where (2M/r - 1) is a positive
Therefore inside the horizon r is a timelike coordinate, the singularity at r = 0 is not located at a tiny point in 3D space, but is rather a "moment" over the entire 3D spacelike surface with spacelike coordinates t,theta, phi.
Note that
transverse metric = r^2(dtheta^2 + sin^2theta dphi^2)
so at the singularity r = 0 the transverse metric disappears.
Actually if the diagram was drawn more accurately the local light cones at the r = 0 spacelike singularity should be tipped over all the way to the horizontal on the vertical line. It then becomes intuitively obvious that r = 0 is not a locally timelike line inside the local light cone, but is a spacelike line outside that local light cone, which means that r = 0 is the FINITE moment of ultimate destruction of any observer who has fallen through the horizon.
Of course George Chapline has a new idea with Robert Laughlin that there is a dark zero point energy core of negative pressure inside the horizon.
Note that finite electron shells of charge have positive pressure zero point energy inside them. They appear as point particles in large momentum transfer probes because of the enormous space curvature induced by the positive pressure "dark matter" zero point energy cores.
That is, for a simple non-rotating shell of charge toy model "electron", the effective surface area of the spinless "electron" in a scattering with momentum transfer p from probe to target is
Effective area of "electron" Bohm hidden variable ~ (h/mc)^2(1 - p/mc) -> 0 at the Compton radius.
Sunday, March 11, 2007
Are those Lockheed-Martin guys using some kind of inteferometric method in their "patent."? So far I cannot tell from the patent but have not read very far. It's obvious they confounded wave vector with wave length. They say wavelength of entangled multiphoton scales as N which would be no good at all for increasing resolution. The wavelength of the entangled multiphoton is the same as the initial pump photon that splits into N components in parametric down conversion (as far as I know N = 2 only? But larger N conceivable.) So the write up is are garbled at the beginning causing me to lose interest in reading beyond that colossal screw up. What Creon is talking about below is independent of the L-M Skunkworks patent.
On Mar 10, 2007, at 2:33 PM, Creon Levit (NASA) wrote:
Jack:
Those references are interesting. I suggest taking a look at http://arxiv.org/abs/quant-ph/0202133
Two key sentences:
"For optical interferometers operating at several milliwatts, the quantum sensitivity improvement corresponds to an enhanced signal to noise ratio of eight orders of magnitude."
"In classical optical lithography the minimum feature size is determined by the Rayleigh diffraction limit of λ/4,where λ is the wavelength of the light.... Using the same entangled-photons technique, it is possible to image the features substantially smaller... yielding a resolution of λ/(4N)"
Note that N above is the number of photons!
I had missed this. Eight orders of magnitude improvement in atom/laser gyros! That could detect frame dragging easily & maybe torsion. Similar improvements in optical microscopy and lithography cold make a practical nanoelectronics industry, and perhaps other nanotechnology as well. How about LISA with entangled/squeezed states? It could boost the sensitivity dramatically and perhaps detect local fluctuations in dark matter & dark energy content of the vacuum? There could be similar improvements for atomic clocks, rangefinders (GPS), prospecting, low power communication (deep space?), eavesdropping, tomography, spectroscopy, holography... on and on.....
>6 order-of-magnitude improvements come along once per technological revolution. The only examples I can think of are: 1) nuclear energy vs. chemical energy, 2) electronic information processing (computation & communication) vs. mechanical information processing, and perhaps 3) molecular biology & biotechnology vs. pre-molecular biology.
This sounds too good to be true, but these are smart guys. Can you please have a look and tell me what you think of http://arxiv.org/abs/quant-ph/0202133 ?
Jack Sarfatti wrote:
Thanks, but I got stuck on their 0009 p.3 where they seem to confound wave vector with wavelength. :-)
On Mar 10, 2007, at 12:31 PM, Srikanth R wrote:
Dear Prof. Jack,
I haven't read the patent application fully, but if the applicants have got the physics right, they are probably talking about ideas in quantum metrology/quantum lithography, where path-entangled photons of the type
|0,N> + |N,0>
are used for imaging, which allows one to go beyond the Rayleigh-limited single-photon diffraction pattern, to have resolution improved N-fold.
Do you mean "vacuum" by "0" in above notation? Thanks for references. They look interesting even if the patent is not even wrong. :-)
Two references that might be of relevance:
[1] "Quantum-enhanced measurements: beating the standard quantum limit"
Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo
Science 306 1330 (2004); quant-ph/0412078
[2] "A Quantum Rosetta Stone for Interferometry"
Lee, Hwang; Kok, Pieter; Dowling, Jonathan P.
Journal of Modern Optics 49 2325 (2002); quant-ph/0202133.
With best regards,
Srik.
On Mar 11, 2007, at 9:19 AM, Jack Sarfatti wrote:
On Mar 11, 2007, at 7:04 AM, Srikanth R wrote:
Dear Prof. Jack,
On Sat, 10 Mar 2007, Jack Sarfatti wrote:
Thanks, but I got stuck on their 0009 p.3 where they seem to confound wave vector with wavelength. :-)
Indeed!
On Mar 10, 2007, at 12:31 PM, Srikanth R wrote:
I haven't read the patent application fully, but if the applicants have got the physics right, they are probably talking about ideas in quantum metrology/quantum lithography, where path-entangled photons of the type
|0,N> + |N,0>
are used for imaging, which allows one to go beyond the Rayleigh-limited single-photon diffraction pattern, to have resolution improved N-fold.
Do you mean "vacuum" by "0" in above notation? Thanks for references. They look interesting even if the patent is not even wrong. :-)
Actually, path entangled states of the following type are meant:
|00000..> + |11111..>
where {|0>,|1>} are a basis for single photons. (The earlier notation is due to ref. [2]!)
With best regards,
Srik.
So that's a coherent state superposing the vacuum |0>i for the i-th mode with the single particle state |1>i with i = 1 to N modes entangled.
Barring superselection rules (the one on charge violated in superconductor) it should also work for fermions because it does not violate the exclusion principle.
On Fri, 9 Mar 2007, Jack Sarfatti wrote:
If anyone has any details on what the key idea here is mathematically I am interested. Thanks.
They obviously have a collinear pulse of entangled photon pairs from parametric down conversion
http://www.ien.it/~castelle/fig1.jpg
The entangled double pulse is reflected back.
Entangled beams allow the absorption spectrum and the resolution limit of quantum radar systems to be selected independently of one another. Thus, while classical radar systems must compromise between range and resolution, quantum radar systems can simultaneously achieve the low attenuation/high range associated with a long wave length and the high resolution associated with a short wave length.
So obviously they do two incompatible measurements of "range" and "resolution" one on each component of the entangled double beam, but, off-hand, I do not as yet see the advantage of entanglement here? "Range" is simply timing of the return pulse relative to the sent pulse. So you want the pulse width as short as possible. Short wave is a momentum measurement. The higher the momentum the shorter the wavelength. So?
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
On Mar 10, 2007, at 2:33 PM, Creon Levit (NASA) wrote:
Jack:
Those references are interesting. I suggest taking a look at http://arxiv.org/abs/quant-ph/0202133
Two key sentences:
"For optical interferometers operating at several milliwatts, the quantum sensitivity improvement corresponds to an enhanced signal to noise ratio of eight orders of magnitude."
"In classical optical lithography the minimum feature size is determined by the Rayleigh diffraction limit of λ/4,where λ is the wavelength of the light.... Using the same entangled-photons technique, it is possible to image the features substantially smaller... yielding a resolution of λ/(4N)"
Note that N above is the number of photons!
I had missed this. Eight orders of magnitude improvement in atom/laser gyros! That could detect frame dragging easily & maybe torsion. Similar improvements in optical microscopy and lithography cold make a practical nanoelectronics industry, and perhaps other nanotechnology as well. How about LISA with entangled/squeezed states? It could boost the sensitivity dramatically and perhaps detect local fluctuations in dark matter & dark energy content of the vacuum? There could be similar improvements for atomic clocks, rangefinders (GPS), prospecting, low power communication (deep space?), eavesdropping, tomography, spectroscopy, holography... on and on.....
>6 order-of-magnitude improvements come along once per technological revolution. The only examples I can think of are: 1) nuclear energy vs. chemical energy, 2) electronic information processing (computation & communication) vs. mechanical information processing, and perhaps 3) molecular biology & biotechnology vs. pre-molecular biology.
This sounds too good to be true, but these are smart guys. Can you please have a look and tell me what you think of http://arxiv.org/abs/quant-ph/0202133 ?
Jack Sarfatti wrote:
Thanks, but I got stuck on their 0009 p.3 where they seem to confound wave vector with wavelength. :-)
On Mar 10, 2007, at 12:31 PM, Srikanth R wrote:
Dear Prof. Jack,
I haven't read the patent application fully, but if the applicants have got the physics right, they are probably talking about ideas in quantum metrology/quantum lithography, where path-entangled photons of the type
|0,N> + |N,0>
are used for imaging, which allows one to go beyond the Rayleigh-limited single-photon diffraction pattern, to have resolution improved N-fold.
Do you mean "vacuum" by "0" in above notation? Thanks for references. They look interesting even if the patent is not even wrong. :-)
Two references that might be of relevance:
[1] "Quantum-enhanced measurements: beating the standard quantum limit"
Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo
Science 306 1330 (2004); quant-ph/0412078
[2] "A Quantum Rosetta Stone for Interferometry"
Lee, Hwang; Kok, Pieter; Dowling, Jonathan P.
Journal of Modern Optics 49 2325 (2002); quant-ph/0202133.
With best regards,
Srik.
On Mar 11, 2007, at 9:19 AM, Jack Sarfatti wrote:
On Mar 11, 2007, at 7:04 AM, Srikanth R wrote:
Dear Prof. Jack,
On Sat, 10 Mar 2007, Jack Sarfatti wrote:
Thanks, but I got stuck on their 0009 p.3 where they seem to confound wave vector with wavelength. :-)
Indeed!
On Mar 10, 2007, at 12:31 PM, Srikanth R wrote:
I haven't read the patent application fully, but if the applicants have got the physics right, they are probably talking about ideas in quantum metrology/quantum lithography, where path-entangled photons of the type
|0,N> + |N,0>
are used for imaging, which allows one to go beyond the Rayleigh-limited single-photon diffraction pattern, to have resolution improved N-fold.
Do you mean "vacuum" by "0" in above notation? Thanks for references. They look interesting even if the patent is not even wrong. :-)
Actually, path entangled states of the following type are meant:
|00000..> + |11111..>
where {|0>,|1>} are a basis for single photons. (The earlier notation is due to ref. [2]!)
With best regards,
Srik.
So that's a coherent state superposing the vacuum |0>i for the i-th mode with the single particle state |1>i with i = 1 to N modes entangled.
Barring superselection rules (the one on charge violated in superconductor) it should also work for fermions because it does not violate the exclusion principle.
On Fri, 9 Mar 2007, Jack Sarfatti wrote:
If anyone has any details on what the key idea here is mathematically I am interested. Thanks.
They obviously have a collinear pulse of entangled photon pairs from parametric down conversion
http://www.ien.it/~castelle/fig1.jpg
The entangled double pulse is reflected back.
Entangled beams allow the absorption spectrum and the resolution limit of quantum radar systems to be selected independently of one another. Thus, while classical radar systems must compromise between range and resolution, quantum radar systems can simultaneously achieve the low attenuation/high range associated with a long wave length and the high resolution associated with a short wave length.
So obviously they do two incompatible measurements of "range" and "resolution" one on each component of the entangled double beam, but, off-hand, I do not as yet see the advantage of entanglement here? "Range" is simply timing of the return pulse relative to the sent pulse. So you want the pulse width as short as possible. Short wave is a momentum measurement. The higher the momentum the shorter the wavelength. So?
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
Thursday, March 08, 2007
What is spin in a curved torsioned spacetime?
PS
1. We want to directly couple the torsion field not only to spin S of matter but to J = L + S of matter. Most important is orbital angular momentum L-torsion field coupling and I know papers exist on this topic.
2. The association of the 4 intrinsically warped tetrad fields A(4)^a is to a kind of Yang-Mills field not the EM potential.
Note the EM potential is A(EM) = Au(EM)dx^u
no "internal Yang-Mills index" ^a which in our case transforms under space-time SO(1,3) rather than internal SU(2)weak or SU(3)strong with chiral breaking of mirror symmetry in the fundamental lepton-quark multiplets etc.
The 4 tetrad 1-forms A(4)^a transform as a SO(1,3) 4-vector and they are separately GCT scalar invariants, i.e.
A(4)^a = A(4)^audx^u
u-indices are GCT tensor indices.
The 6 torsion field spin-connection 1-forms S(1,3)^a^b = - S(1,3)^a^b are anti-symmetric second rank SO(1,3) tensors analogous to the spin 1 EM field tensor 2-form F(EM) = dA(EM).
Note that each individual S(1,3)^a^b component is a GCT scalar invariant.
So what spin should we associate with the spin connection? I suppose it is spin 2 since it is a second-rank SO(1,3) tensor?
Note in the globally flat EM case we do not have this problem since
F(EM) = F(EM)uvdx^u/\dx^v
and here the u,v indices are globally flat Poincare group tensor indices so no ambiguity in how to define spin in that limiting simple case.
On Mar 8, 2007, at 11:16 AM, Jack Sarfatti wrote:
Show the details please Ark. Cannot evaluate your too-short cryptic verbal-only remarks.
One equation is worth a jillion words. ;-)
Also "tensor" is defined relative to a group. In context they mean
GCT, i.e. localized T4.
Also, as I show in detail in last message to Becker
the relation of torsion & curvature to the local gauging of which group is
a bit subtle & counter-intuitive though the formal math is clear enough, i.e. Robert Becker wrote:
"Hehl brings out another important point: the relation of Torsion to translation. It is customary in physics to associate Torsion with spin one way or another. I believe both you and Shipov follow this interpretation. However, Vargas and others, like Pommaret, reject the association of Torsion spin or rotation because it is mathematically closely related to translation as Hehl highlights in his Letter. Vargas finds a geometrodynamical association of Torsion with the EM field, rather than spin."
I pointed out this is a tricky point that Rovelli and Kibble clarify.
The GCT gauge freedom of 1915 GR comes from localizing only the 4-parameter translation subgroup T(4) of the 10-parameter Poincare group P[T(4),SO(1,3)]. Clearly the local GCT's
x^u = x^u(x^u') are localized infinitesimal translations a^u(x^u'), i.e. 4-parameter
x^u -> x^u + a^u(x^u')
In global 1905 special relativity the infinitesimal "elastic deformation" a^u(x^u') of Hagen Kleinert's 4D world crystal Planck lattice is a global constant over the entire infinity of Minkowski spacetime. This is global action at a distance that violates local objective light cone limited causality, hence localization is absolutely necessary to maintain orthodox causality. Global special relativity without gravity is a half-way house first-approximation that is not internally consistent from this POV.
On the other hand there is no question that dislocation defects in the Kleinert world crystal lattice (Burger's vectors et-al) form the torsion field gaps and that the disclination defects for parallel transport around closed loops of the lattice where
V^u(finish) - V^u(start) ~ SO(1,3)^uu'V^u'(start) ~ R^uvwlA^v^wV^l(start)
A^v^w = - A^w^v is the sectional area element of the small loop
form the curvature.
Therefore there are two dual POV
on the one hand
1915 GR with curvature only and zero torsion emerges from the local gauging of 4-parameter T(4)
on the other hand
1915 GR with curvature only and zero torsion is associated with a local Lorentz transformation LLT of the 4-vector around the closed loop (no torsion gap).
Of course when one does the actual Cartan form algebra there is no problem. The problem is only one of the informal language (Bohm) not of the mathematics.
Thus the 4 GCT invariant tetrad 1-forms are the LLT 4-vector components
e(4)^a = I^a + A(4)^a
I^a is the trivial globally flat 1905 SR tetrad
A(4)^a is the intrinsically warped "gauge connection potential" from localizing 4-parameter T(4).
Einstein's 1915 fundamental local GCT & LLT scalar invariant is
ds^2 = e^aea = (Minkowski metric)abe^ae^b = guvdx^udx^v
Einstein's 1915 constraint of zero torsion is the vanishing 2-form
T(4)^a = de(4)^a + S(4)^ac/\e(4)^c = 0
This with metricity, see Rovelli's explicit formula Ch 2 of his online "Quantum Gravity" gives the 6 zero torsion field effective spin-connnection 1-forms
S(4)^a^b = - S(4)^b^a
only from localizing T(4) to get the spin 1 Yang-Mills potential A(4)^a
A(4)^a spin 1 because it's a Lorentz group 4-vector in the a-index.
This warped localized tetrad resembles the EM 4-potential with "internal index" "a" i.e. "Yang-Mills".
The pure disclination curvature defects without torsion gaps then come from the curvature 2-form
R(4)^a^b = dS(4)^a^b + S(4)^ac/\S^cb
And no TP of course at this stage as you say.
Next step is to locally gauge SO(1,3) giving the additional independent torsion gap field spin connection 1-forms
S(1,3)^a^b
The full connection is then S(4)^a^b + S(1,3)^a^b
Where now
T^a(1,3) = S(1,3)^ac/\e^c =/= 0
R(10)^a^b = d[S(4)^a^b + S(1,3)^a^b] + [S(4)^ac + S(1,3)^ac]/\[S(4)^c^b + S(1,3)^c^b]
Where the TP Ansatz is obviously in my transparent notation using only local objective GCT invariants (coordinate independent)
R(10)^a^b = 0
where
R(10)^a^b = R(4)^a^b + R(1,3)^a^b + S(4)^ac/\S(1,3)^cb + S(1,3)^ac/\S(4)^cb
Hence two "diagonal" curvature 2-forms. Utiyama in 1960 computed R(1,3)^a^b in effect without R(4)^a^b.
This settles the above informal language confusion you mention!
Note also the two T(4) x SO(1,3) cross-coupling terms.
*I am going to completely rewrite my emergent gravity archive paper with these new results of course.
On Mar 8, 2007, at 1:54 AM, Arkadiusz Jadczyk wrote:
On 7 Mar 2007 at 16:40, Jack Sarfatti wrote:
>
> On Mar 7, 2007, at 4:16 PM, Dr. Eric Davis wrote:
>
> > Jack:
> >
> > Attached is a letter to the editor of Physics Today (March 2007)
> > written by F. W. Hehl. In answering a previously published
> > complaint about the relevancy of the torsion tensor by Steven
> > Weinberg (UT-Austin), Hehl explains the physical nature and
> > relevance of the torsion tensor in GR.
Both Hehl and Weinberg are right and wrong. Weinberg is right
because in the standard presentation torsion is just a tensor. Weinberg
is wrong because there are other presentations possible where torsion is
NOT just a tensor. Hehl is right with the fact that torsion may be an important
factor when it comes from gauging of the translation group. Hehl is wrong when
he writes that torsion is "just not a tensor, but very specific tensor". Even
very specific
tensor is just a tensor.
When one is VERY careful (I mean "mathematically careful" - which is not what
is being advocated among the readers of Sarfatti Physics seminars), one can
find that torsion
is NOT a tensor at at all and that the fact that it does not have to be a
tensor may have physical implications. Explaining this would take us into
"knowing what we do", while
here "not knowing what we do" is being considered as the superior way :)
ark
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
PS
1. We want to directly couple the torsion field not only to spin S of matter but to J = L + S of matter. Most important is orbital angular momentum L-torsion field coupling and I know papers exist on this topic.
2. The association of the 4 intrinsically warped tetrad fields A(4)^a is to a kind of Yang-Mills field not the EM potential.
Note the EM potential is A(EM) = Au(EM)dx^u
no "internal Yang-Mills index" ^a which in our case transforms under space-time SO(1,3) rather than internal SU(2)weak or SU(3)strong with chiral breaking of mirror symmetry in the fundamental lepton-quark multiplets etc.
The 4 tetrad 1-forms A(4)^a transform as a SO(1,3) 4-vector and they are separately GCT scalar invariants, i.e.
A(4)^a = A(4)^audx^u
u-indices are GCT tensor indices.
The 6 torsion field spin-connection 1-forms S(1,3)^a^b = - S(1,3)^a^b are anti-symmetric second rank SO(1,3) tensors analogous to the spin 1 EM field tensor 2-form F(EM) = dA(EM).
Note that each individual S(1,3)^a^b component is a GCT scalar invariant.
So what spin should we associate with the spin connection? I suppose it is spin 2 since it is a second-rank SO(1,3) tensor?
Note in the globally flat EM case we do not have this problem since
F(EM) = F(EM)uvdx^u/\dx^v
and here the u,v indices are globally flat Poincare group tensor indices so no ambiguity in how to define spin in that limiting simple case.
On Mar 8, 2007, at 11:16 AM, Jack Sarfatti wrote:
Show the details please Ark. Cannot evaluate your too-short cryptic verbal-only remarks.
One equation is worth a jillion words. ;-)
Also "tensor" is defined relative to a group. In context they mean
GCT, i.e. localized T4.
Also, as I show in detail in last message to Becker
the relation of torsion & curvature to the local gauging of which group is
a bit subtle & counter-intuitive though the formal math is clear enough, i.e. Robert Becker wrote:
"Hehl brings out another important point: the relation of Torsion to translation. It is customary in physics to associate Torsion with spin one way or another. I believe both you and Shipov follow this interpretation. However, Vargas and others, like Pommaret, reject the association of Torsion spin or rotation because it is mathematically closely related to translation as Hehl highlights in his Letter. Vargas finds a geometrodynamical association of Torsion with the EM field, rather than spin."
I pointed out this is a tricky point that Rovelli and Kibble clarify.
The GCT gauge freedom of 1915 GR comes from localizing only the 4-parameter translation subgroup T(4) of the 10-parameter Poincare group P[T(4),SO(1,3)]. Clearly the local GCT's
x^u = x^u(x^u') are localized infinitesimal translations a^u(x^u'), i.e. 4-parameter
x^u -> x^u + a^u(x^u')
In global 1905 special relativity the infinitesimal "elastic deformation" a^u(x^u') of Hagen Kleinert's 4D world crystal Planck lattice is a global constant over the entire infinity of Minkowski spacetime. This is global action at a distance that violates local objective light cone limited causality, hence localization is absolutely necessary to maintain orthodox causality. Global special relativity without gravity is a half-way house first-approximation that is not internally consistent from this POV.
On the other hand there is no question that dislocation defects in the Kleinert world crystal lattice (Burger's vectors et-al) form the torsion field gaps and that the disclination defects for parallel transport around closed loops of the lattice where
V^u(finish) - V^u(start) ~ SO(1,3)^uu'V^u'(start) ~ R^uvwlA^v^wV^l(start)
A^v^w = - A^w^v is the sectional area element of the small loop
form the curvature.
Therefore there are two dual POV
on the one hand
1915 GR with curvature only and zero torsion emerges from the local gauging of 4-parameter T(4)
on the other hand
1915 GR with curvature only and zero torsion is associated with a local Lorentz transformation LLT of the 4-vector around the closed loop (no torsion gap).
Of course when one does the actual Cartan form algebra there is no problem. The problem is only one of the informal language (Bohm) not of the mathematics.
Thus the 4 GCT invariant tetrad 1-forms are the LLT 4-vector components
e(4)^a = I^a + A(4)^a
I^a is the trivial globally flat 1905 SR tetrad
A(4)^a is the intrinsically warped "gauge connection potential" from localizing 4-parameter T(4).
Einstein's 1915 fundamental local GCT & LLT scalar invariant is
ds^2 = e^aea = (Minkowski metric)abe^ae^b = guvdx^udx^v
Einstein's 1915 constraint of zero torsion is the vanishing 2-form
T(4)^a = de(4)^a + S(4)^ac/\e(4)^c = 0
This with metricity, see Rovelli's explicit formula Ch 2 of his online "Quantum Gravity" gives the 6 zero torsion field effective spin-connnection 1-forms
S(4)^a^b = - S(4)^b^a
only from localizing T(4) to get the spin 1 Yang-Mills potential A(4)^a
A(4)^a spin 1 because it's a Lorentz group 4-vector in the a-index.
This warped localized tetrad resembles the EM 4-potential with "internal index" "a" i.e. "Yang-Mills".
The pure disclination curvature defects without torsion gaps then come from the curvature 2-form
R(4)^a^b = dS(4)^a^b + S(4)^ac/\S^cb
And no TP of course at this stage as you say.
Next step is to locally gauge SO(1,3) giving the additional independent torsion gap field spin connection 1-forms
S(1,3)^a^b
The full connection is then S(4)^a^b + S(1,3)^a^b
Where now
T^a(1,3) = S(1,3)^ac/\e^c =/= 0
R(10)^a^b = d[S(4)^a^b + S(1,3)^a^b] + [S(4)^ac + S(1,3)^ac]/\[S(4)^c^b + S(1,3)^c^b]
Where the TP Ansatz is obviously in my transparent notation using only local objective GCT invariants (coordinate independent)
R(10)^a^b = 0
where
R(10)^a^b = R(4)^a^b + R(1,3)^a^b + S(4)^ac/\S(1,3)^cb + S(1,3)^ac/\S(4)^cb
Hence two "diagonal" curvature 2-forms. Utiyama in 1960 computed R(1,3)^a^b in effect without R(4)^a^b.
This settles the above informal language confusion you mention!
Note also the two T(4) x SO(1,3) cross-coupling terms.
*I am going to completely rewrite my emergent gravity archive paper with these new results of course.
On Mar 8, 2007, at 1:54 AM, Arkadiusz Jadczyk wrote:
On 7 Mar 2007 at 16:40, Jack Sarfatti wrote:
>
> On Mar 7, 2007, at 4:16 PM, Dr. Eric Davis wrote:
>
> > Jack:
> >
> > Attached is a letter to the editor of Physics Today (March 2007)
> > written by F. W. Hehl. In answering a previously published
> > complaint about the relevancy of the torsion tensor by Steven
> > Weinberg (UT-Austin), Hehl explains the physical nature and
> > relevance of the torsion tensor in GR.
Both Hehl and Weinberg are right and wrong. Weinberg is right
because in the standard presentation torsion is just a tensor. Weinberg
is wrong because there are other presentations possible where torsion is
NOT just a tensor. Hehl is right with the fact that torsion may be an important
factor when it comes from gauging of the translation group. Hehl is wrong when
he writes that torsion is "just not a tensor, but very specific tensor". Even
very specific
tensor is just a tensor.
When one is VERY careful (I mean "mathematically careful" - which is not what
is being advocated among the readers of Sarfatti Physics seminars), one can
find that torsion
is NOT a tensor at at all and that the fact that it does not have to be a
tensor may have physical implications. Explaining this would take us into
"knowing what we do", while
here "not knowing what we do" is being considered as the superior way :)
ark
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
Steven Weinberg says he doesn't get it on torsion in Physics Today March 2007
Aha! Thanks. :-)
On Mar 8, 2007, at 3:06 AM, ROBERT BECKER (RB) wrote:
Jack,
"The reason that Weinberg says in the excerpt you quote below on Torsion, 'Sorry, I still don't get it.' rather than just 'I don't get it.', is because Weinberg had already said "I don't get it" in response to my Letter published in the 4/06 Physics Today referenced by Hehl in his 3/07 Letter. One cannot conduct an extended tit-for-tat debate in the Letters section of Physics Today, so I could not respond further to Weinberg, but it looks like Hehl took up the mantle. Hehl cites some other authors on torsion; I had cited Vargas's papers and also Shipov. Vargas was left rather aghast to say the least when he saw the apparent obtuseness of Weinberg's response." - RB
It is amazing. The great professor is but a shadow of his former self it appears. Weinberg's 3 books on quantum field theory have all the basic ideas needed to understand torsion brilliantly presented. Old age I guess.
"Apart from any other consideration, Weinberg chose to overlook the potential utilitarian advantage to gravitation physics of what I said in my Letter regarding Teleparallelism (TP). To formally integrate objects such as energy-momentum densities that are used in conservation laws for gravitation and in the question of the definition and locality of energy-momentum in gravitation physics, one needs to "add together" objects belonging to tangent spaces of different, neighboring points. But this can not be done in a path independent manner, if at all, unless the affine curvature vanishes. The affine curvature, which is what is actually obtained from the Cartan moving frame method (or equivalently from the tetrads) in the types derivations you have provided many times in this forum, is not the same object in general as the familiar GR Riemannian curvature." - RB
The tetrad/spin connection substratum field equations are essentially spin 1 Yang-Mills type, but for the 10-parameter localized spacetime universal Poincare symmetry group for all non-gravity source field dynamical global actions. Therefore, according to t'Hooft, if you quantize them they are renormalizable in the local gauge invariant "square root" substratum of the spin 2 non-renormalizable composite geometrodynamical field of Einstein 1915.
"In particular, the vanishing affine curvature requires non-vanishing Torsion. This is the TP postulate, which Einstein tried to utilize in his reworkings of GR in the late 20s-early 30s. Since GR, as you correctly point out, has vanishing Torsion, it does not postulate TP. As Vargas has discussed in many Papers, this GR non-assumption, in turn, may have a profound effect on the issue of conservation laws and the definition of energy-momentum in GR and gravitation physics." - RB
Indeed, that may be the origin of the fact that 1915 GR with zero torsion (i.e. not all of the 10-parameter Poincare group is localized) has nonrenormalizable spin 2 nonlocality in the gravity vacuum stress-energy. I am not sure of that of course.
"Hehl brings out another important point: the relation of Torsion to translation. It is customary in physics to associate Torsion with spin one way or another. I believe both you and Shipov follow this interpretation. However, Vargas and others, like Pommaret, reject the association of Torsion spin or rotation because it is mathematically closely related to translation as Hehl highlights in his Letter. Vargas finds a geometrodynamical association of Torsion with the EM field, rather than spin." - RB
I pointed out this is a tricky point that Rovelli and Kibble clarify.
The GCT gauge freedom of 1915 GR comes from localizing only the 4-parameter translation subgroup T(4) of the 10-parameter Poincare group P[T(4),SO(1,3)]. Clearly the local GCT's
x^u = x^u(x^u') are localized infinitesimal translations a^u(x^u'), i.e. 4-parameter
x^u -> x^u + a^u(x^u')
In global 1905 special relativity the infinitesimal "elastic deformation" a^u(x^u') of Hagen Kleinert's 4D world crystal Planck lattice is a global constant over the entire infinity of Minkowski spacetime. This is global action at a distance that violates local objective light cone limited causality, hence localization is absolutely necessary to maintain orthodox causality. Global special relativity without gravity is a half-way house first-approximation that is not internally consistent from this POV.
On the other hand there is no question that dislocation defects in the Kleinert world crystal lattice (Burger's vectors et-al) form the torsion field gaps and that the disclination defects for parallel transport around closed loops of the lattice where
V^u(finish) - V^u(start) ~ SO(1,3)^uu'V^u'(start) ~ R^uvwlA^v^wV^l(start)
A^v^w = - A^w^v is the sectional area element of the small loop
form the curvature.
Therefore there are two dual POV
on the one hand
1915 GR with curvature only and zero torsion emerges from the local gauging of 4-parameter T(4)
on the other hand
1915 GR with curvature only and zero torsion is associated with a local Lorentz transformation LLT of the 4-vector around the closed loop (no torsion gap).
Of course when one does the actual Cartan form algebra there is no problem. The problem is only one of the informal language (Bohm) not of the mathematics.
Thus the 4 GCT invariant tetrad 1-forms are the LLT 4-vector components
e(4)^a = I^a + A(4)^a
I^a is the trivial globally flat 1905 SR tetrad
A(4)^a is the intrinsically warped "gauge connection potential" from localizing 4-parameter T(4).
Einstein's 1915 fundamental local GCT & LLT scalar invariant is
ds^2 = e^aea = (Minkowski metric)abe^ae^b = guvdx^udx^v
Einstein's 1915 constraint of zero torsion is the vanishing 2-form
T(4)^a = de(4)^a + S(4)^ac/\e(4)^c = 0
This with metricity, see Rovelli's explicit formula Ch 2 of his online "Quantum Gravity" gives the 6 zero torsion field effective spin-connnection 1-forms
S(4)^a^b = - S(4)^b^a
only from localizing T(4) to get the spin 1 Yang-Mills potential A(4)^a
A(4)^a spin 1 because it's a Lorentz group 4-vector in the a-index.
This warped localized tetrad resembles the EM 4-potential with "internal index" "a" i.e. "Yang-Mills".
The pure disclination curvature defects without torsion gaps then come from the curvature 2-form
R(4)^a^b = dS(4)^a^b + S(4)^ac/\S^cb
And no TP of course at this stage as you say.
Next step is to locally gauge SO(1,3) giving the additional independent torsion gap field spin connection 1-forms
S(1,3)^a^b
The full connection is then S(4)^a^b + S(1,3)^a^b
Where now
T^a(1,3) = S(1,3)^ac/\e^c =/= 0
R(10)^a^b = d[S(4)^a^b + S(1,3)^a^b] + [S(4)^ac + S(1,3)^ac]/\[S(4)^c^b + S(1,3)^c^b]
Where the TP Ansatz is obviously in my transparent notation using only local objective GCT invariants (coordinate independent)
R(10)^a^b = 0
where
R(10)^a^b = R(4)^a^b + R(1,3)^a^b + S(4)^ac/\S(1,3)^cb + S(1,3)^ac/\S(4)^cb
Hence two "diagonal" curvature 2-forms. Utiyama in 1960 computed R(1,3)^a^b in effect without R(4)^a^b.
This settles the above informal language confusion you mention!
Note also the two T(4) x SO(1,3) cross-coupling terms.
*I am going to completely rewrite my emergent gravity archive paper with these new results of course.
Jack Sarfatti wrote to Mark Pesses:
Yes, thanks I know. :-)
BTW my theory for emergent gravity with torsion needs exactly 8 Higgs
bosons one for each Goldstone boson.
I have N = 8 to get Einstein's tetrads and spin connections emergent.
from my CIT talk under construction (outline sans math type equations)
M Theory for Idiots
Emergence of tetrads and spin connections from the spontaneous
breakdown of localized Poincare group symmetry in the post-inflation
physical vacuum.
Jack Sarfatti
Missing Organizing Idea
Witten and Green say they are missing the key idea denoted as â€Å“?â€
No Rigid Symmetries
Locally gauging a nondynamical rigid symmetry group of the action
(either internal or spacetime) of a given source field introduces a
gauge force coupled to the source as the compensating connection
field needed to maintain gauge invariance for the now dynamical non-
rigid symmetry group.
Weinberg doesn̢۪t get it?
How is that possible?
â€Å“Sorry I still don’t get it. Is there any physical principle, such
as a principle of invariance that would require the Christoffel
symbol to be accompanied by some specific additional tensor? …â€
Steven Weinberg to Fred Hehl on the role of the torsion field in
spacetime physics in March, 2007 Physics Today.
Spontaneous Symmetry Breaking
Spontaneously breaking a vacuum symmetry means macroscopic occupation
of a single-particle mode by a large number of virtual off-mass-shell
particles.
In a vacuum the ODLRO condensate is composed of virtual quanta in
contrast to the ground state of superfluid helium where the
condensate is made from real helium atoms on mass shell.
Local & Broken
The broken symmetry need not be the same as the locally gauged
symmetry, but can be. In gravity theory rigid translational symmetry
is spontaneously broken in order to have localized variable spacetime
curvature. The action still obeys the symmetry, only the vacuum does
not obey it.
Higgs Vacuum Manifold
N independent Goldstone phases require N+1 real Higgs scalar fields.
The degenerate vacua lie on the unit SN spherical hypersurface:
Higgs Vacuum Potential
The â€Å“More is different†emergent macro-quantum coherent vacuum
order parameter has the effective potential
Dynamical L-G Eq.
Covariant dynamical Landau-Ginzburg equation for the macro-quantum
coherent hologram â€Å“Volume without volume†vacuum order parameter is
Local Gauge Invariance
Localizing the 10-parameter globally rigid Poincare group of 1905 SR
universally for all non-gravity source field actions gives the 4
Einstein-Cartan tetrads and the 6 spin connections as compensating
gauge potentials.
This is similar to localizing the internal symmetry groups in Yang-
Mills theory of the electroweak-strong forces.
M = My Mystery Matrix
Start with two Lorentz 4-vectors of 0-forms
Compactification
Each Minkowski 4-vector has magnitude
Michael Faraday
I use Faraday’s â€Å“lines of force†in a metaphorical way for the
geometrodynamic field compacted down from 9 + 1 to 3 + 1.
Two Goldstone phases have three single-valued real Higgs fields with
stable quantized (wrapping integers) point â€Å“monopole†defects in
3D space.
A single Goldstone phase has two real Higgs fields with stable
quantized (winding integers) line â€Å“vortex core†stringy defects.
Line Density Operator
The geometrodynamic line density operator is the non-closed 1-form
Area Density Operator
The geometrodynamic area density 2-form is closed. This is the world
hologram idea in action.
Stoke̢۪s Theorem
The deRahm integral of a p-form on a p-cycle (without boundary)
equals the p-form̢۪s exterior derivative on a p+1 co-form whose
boundary is the p-cycle.
Closed Forms
A p-form is closed if its exterior derivative vanishes. When the
interior of the p-cycle is simply connected without â€Å“holes†the
integral of the closed p-form vanishes.
Otherwise the integral is proportional to an integer analogous to
Bohr-Sommerfeld quantization in the old quantum theory and quantized
circulation in superfluid helium vortices.
World Holography
The geometrodynamic volume density operator 3-form should be
proportional to the exterior derivative of the area density operator
2-form. However, the area operator is closed. Therefore, the volume
operator is locally zero.
Volume is a holographic projection of the area density operator
integrated on a nonbounding 2-cycle enclosing point defects in the
single-valued 3-real Higgs component field projection on 3+1 from 9
+ 1 spacetime.
Bekenstein BITS
The integral of the geometrodynamic area density operator 2-form,
over a non-bounding closed 2-surface (cycle) surrounding a multiply-
connected 3D interior with â€Å“holes†where the 3 real Higgs fields
all vanish so that the 2 compacted Goldstone phases are undefined, is
quantized.
Volume without volume
Although Stoke̢۪s theorem rigorously does not apply to closed non-
bounding 2D surfaces S2 , whose 3D interior M3 is multiply connected,
physical intuition demands the as-if holographic imaging
Calabi-Yau
These 2 constraints leave 6 angular Kaluza-Klein Goldstone phases
whose radii determine coupling constants like the moduli of Calabi-
Yau space.
Gennady Shipov gets this structure in his version of torsion field
theory calling the extra 6 degrees of freedom an â€Å“oriented
point†(suggesting â€Å“branesâ€)
Higgs Potential
The 8 Goldstone phases require 9 real Higgs scalar fields.
One degenerate vacuum manifold is S8. There are other topologies.
From the POV of nontrivial homotopy groups for stable topological
defects they fit most naturally in the 9D + 1 spacetime of
superstring theory.
Shipov̢۪s Brane Worlds
Thus
Einstein-Cartan Tetrads
The four GCT invariant 1-forms are
Analogy to Superfluid
The fabric of spacetime is an elastic 4D GCT covariant supersolid,
compare
Macro-Quantum Gravity
There is no curvature gravity field in my emergent â€Å“More is
different†(P.W. Anderson) theory if
G = 0
h = 0
1/c = 0
Cartan 1-Forms
In terms of GCT tensor scalar invariant products, the 4 tetrads and 6
antisymmetric spin connection 1-forms are
Tetrad Decomposition
The GCT invariant globally flat tetrads and locally curved tetrads
are respectively
Spin Connections
The six GCT invariant connection 1-forms are
GCT Covariant D
The curved Cartan exterior derivative is
Torsion Field 2-Form
In 1915 GR this is zero
Curvature 2-Form
Take the covariant exterior derivative of the 1-form spin connection
to get the curvature 2-form
Einstein-Hilbert Action
The GCT & LLT field Lagrangian density is
On Mar 7, 2007, at 8:48 PM, MPOGO@aol.com wrote:
> Particle X in rare decay could belong to a new physics model
>
> By Lisa Zyga
> A particle that may mediate the rare decay of a Sigma-plus hyperon
> appears to have close affiliations with a light Higgs boson found
> in one supersymmetric model—an interpretation suggesting
> unambiguous evidence for physics beyond the standard model (SM),
> scientists say.
>
>
> Xiao-Gang He of the National Taiwan University, Jusak Tandean of
> the University of La Verne, and German Valencia of Iowa State have
> investigated the so-called HyperCP result observed at Fermilab a
> little over two years ago. While the HyperCP Collaboration began as
> a search for CP symmetry violation, the rare decay of the Sigma-
> plus hyperon (made of a strange quark and two up quarks) opens the
> possibility for the existence of a new particle with unusual
> characteristics.
>
>
> This unverified particle, which He and colleagues call particle X,
> would act as the intermediate state when the Sigma-plus decays to
> its final state, of a proton, muon-plus and muon-minus. With its
> extremely light mass (214.3 MeV), low energy, and smallest-ever
> branching ratio for a baryon decay, particle X would have less than
> a 1% chance of being accounted for within the SM.
>
> Although He and colleagues showed in an earlier paper that the
> HyperCP result may be explained by the SM if there is no new
> particle, the implications of a new particle are considerable. If
> scientists find that particle X is indeed a new particle belonging
> to a different model, the breakdown of the SM would open up new
> doors for future investigations in many areas, and possibly answer
> many questions unanswered by the SM.
>
> In their recent paper published in Physical Review Letters, He et
> al. turned their attention to a model called the â€Å“next-to-minimal
> sypersymmetric standard model†(NMSSM) that contains seven Higgs
> bosons. The scientists showed that the lightest one is the main
> component of a particle called A01, and that A01 satisfies all the
> constraints of particle X.
>
> â€Å“If the existence of a very light A01 is confirmed, other models
> such as the SM, which do not have any light Higgs bosons, will be
> ruled out,†Tandean told PhysOrg.com.
>
> Tandean also explained how, although the SM has withstood many
> experimental tests, there are some issues that the model doesn̢۪t
> address.
>
> â€Å“One issue is the so-called hierarchy problem: why the electroweak
> scale (represented by the W and Z boson masses, of order 100 GeV)
> is so much smaller than the Planck scale (1019 GeV), at which
> gravity becomes important for elementary particle interactions,â€
> he said. â€Å“One aspect of this issue is that quantum corrections to
> the Higgs mass make its value arbitrarily large, up to the Planck
> scale. This clearly contradicts the requirement that the Higgs be
> lighter than a few hundred GeV.â€
>
> However, as Tandean explained, supersymmetric models (where every
> SM particle has a corresponding superpartner) can provide a natural
> solution to this problem.
>
> â€The presence of the superpartners results in the cancellation of
> the large quantum corrections, leading to a Higgs mass at the
> desired level,†he said. â€Å“The minimal version of such models is
> called the Minimal Supersymmetric Standard Model (MSSM). The MSSM
> is a very attractive model in many ways, but it does not address
> the question of why the electroweak scale is much smaller than the
> Planck scale to begin with—this is the so-called mu problem.
>
> â€Å“Interestingly, the Next-to-Minimal Supersymmetric Standard Model
> (NMSSM) solves this problem by adding a set of two particles to the
> MSSM in such a way that the electroweak scale can be naturally
> small. The NMSSM has been extensively studied in the literature and
> has many other interesting features. It is therefore a well-
> motivated model.â€
> Among the constraints that the NMSSM̢۪s A01 can satisfy include
> explaining why X is very light: the mass of A01 can be as low as
> 100 MeV, and when the mass is 214.3 MeV, the decay into a muon-anti-
> muon dominates over other possible modes. Secondly, the
> interactions of A01 can produce the same rate found in the HyperCP
> observation.
>
> Thirdly, A01 explains why previous experiments with kaons and B-
> mesons that thoroughly explored the same regions where X exists
> never saw X. For these reasons, kaon and B-meson decays impose
> severe constraints on the properties of X, specifically regarding
> two-quark couplings. This means that, even though A01 could explain
> the new particle over a wide range of parameters, there are only
> narrow ranges for which the kaon constraints are also satisfied.
> However, the scientists also suggest that revisiting these
> constraints might reveal some overlooked data.
>
> In the future, two new particle accelerators—the Large Hadron
> Collider (LHC) and International Linear Collider (ILC)—might shed
> more light on the Higgs hypothesis. Supersymmetry may determine
> some parameters of particle X, where investigations of squark and
> chargino intermediate states in the NMSSM might provide more evidence.
>
> â€Å“The LHC and ILC have the capability of finding the charginos
> predicted by supersymmetric theories, depending on the chargino
> masses,†Tandean said. â€Å“In our study, we find that in order to
> explain the HyperCP results, the lighter chargino mass has to be
> around 100 GeV, which is within the range to be probed by the LHC
> and ILC. At the LHC and ILC, it is also possible to study the usual
> Higgs boson, h, in detail (or the one playing the role of h in
> NMSSM). If the A01 is the X particle, the process h --> XX can
> occur and may become the dominant decay mode if the h mass is
> relatively small (120 to 130 GeV). By studying the properties of h
> in detail, one may verify that X is the A01.â€
>
> Citation: He, Xiao-Gang, Tandean, Jusak, Valencia, G. â€Å“Does the
> HyperCP Evidence for the Decay ‘Sigma-plus to a proton, muon-plus
> and muon-minus’ Indicate a Light Pseudoscalar Higgs Boson?â€
> Physical Review Letters 98, 081802 (2007).
>
> By Lisa Zyga, Copyright 2007 PhysOrg.com.
> All rights reserved. This material may not be published, broadcast,
> rewritten or redistributed in whole or part without the express
> written permission of PhysOrg.com.
>
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
Aha! Thanks. :-)
On Mar 8, 2007, at 3:06 AM, ROBERT BECKER (RB) wrote:
Jack,
"The reason that Weinberg says in the excerpt you quote below on Torsion, 'Sorry, I still don't get it.' rather than just 'I don't get it.', is because Weinberg had already said "I don't get it" in response to my Letter published in the 4/06 Physics Today referenced by Hehl in his 3/07 Letter. One cannot conduct an extended tit-for-tat debate in the Letters section of Physics Today, so I could not respond further to Weinberg, but it looks like Hehl took up the mantle. Hehl cites some other authors on torsion; I had cited Vargas's papers and also Shipov. Vargas was left rather aghast to say the least when he saw the apparent obtuseness of Weinberg's response." - RB
It is amazing. The great professor is but a shadow of his former self it appears. Weinberg's 3 books on quantum field theory have all the basic ideas needed to understand torsion brilliantly presented. Old age I guess.
"Apart from any other consideration, Weinberg chose to overlook the potential utilitarian advantage to gravitation physics of what I said in my Letter regarding Teleparallelism (TP). To formally integrate objects such as energy-momentum densities that are used in conservation laws for gravitation and in the question of the definition and locality of energy-momentum in gravitation physics, one needs to "add together" objects belonging to tangent spaces of different, neighboring points. But this can not be done in a path independent manner, if at all, unless the affine curvature vanishes. The affine curvature, which is what is actually obtained from the Cartan moving frame method (or equivalently from the tetrads) in the types derivations you have provided many times in this forum, is not the same object in general as the familiar GR Riemannian curvature." - RB
The tetrad/spin connection substratum field equations are essentially spin 1 Yang-Mills type, but for the 10-parameter localized spacetime universal Poincare symmetry group for all non-gravity source field dynamical global actions. Therefore, according to t'Hooft, if you quantize them they are renormalizable in the local gauge invariant "square root" substratum of the spin 2 non-renormalizable composite geometrodynamical field of Einstein 1915.
"In particular, the vanishing affine curvature requires non-vanishing Torsion. This is the TP postulate, which Einstein tried to utilize in his reworkings of GR in the late 20s-early 30s. Since GR, as you correctly point out, has vanishing Torsion, it does not postulate TP. As Vargas has discussed in many Papers, this GR non-assumption, in turn, may have a profound effect on the issue of conservation laws and the definition of energy-momentum in GR and gravitation physics." - RB
Indeed, that may be the origin of the fact that 1915 GR with zero torsion (i.e. not all of the 10-parameter Poincare group is localized) has nonrenormalizable spin 2 nonlocality in the gravity vacuum stress-energy. I am not sure of that of course.
"Hehl brings out another important point: the relation of Torsion to translation. It is customary in physics to associate Torsion with spin one way or another. I believe both you and Shipov follow this interpretation. However, Vargas and others, like Pommaret, reject the association of Torsion spin or rotation because it is mathematically closely related to translation as Hehl highlights in his Letter. Vargas finds a geometrodynamical association of Torsion with the EM field, rather than spin." - RB
I pointed out this is a tricky point that Rovelli and Kibble clarify.
The GCT gauge freedom of 1915 GR comes from localizing only the 4-parameter translation subgroup T(4) of the 10-parameter Poincare group P[T(4),SO(1,3)]. Clearly the local GCT's
x^u = x^u(x^u') are localized infinitesimal translations a^u(x^u'), i.e. 4-parameter
x^u -> x^u + a^u(x^u')
In global 1905 special relativity the infinitesimal "elastic deformation" a^u(x^u') of Hagen Kleinert's 4D world crystal Planck lattice is a global constant over the entire infinity of Minkowski spacetime. This is global action at a distance that violates local objective light cone limited causality, hence localization is absolutely necessary to maintain orthodox causality. Global special relativity without gravity is a half-way house first-approximation that is not internally consistent from this POV.
On the other hand there is no question that dislocation defects in the Kleinert world crystal lattice (Burger's vectors et-al) form the torsion field gaps and that the disclination defects for parallel transport around closed loops of the lattice where
V^u(finish) - V^u(start) ~ SO(1,3)^uu'V^u'(start) ~ R^uvwlA^v^wV^l(start)
A^v^w = - A^w^v is the sectional area element of the small loop
form the curvature.
Therefore there are two dual POV
on the one hand
1915 GR with curvature only and zero torsion emerges from the local gauging of 4-parameter T(4)
on the other hand
1915 GR with curvature only and zero torsion is associated with a local Lorentz transformation LLT of the 4-vector around the closed loop (no torsion gap).
Of course when one does the actual Cartan form algebra there is no problem. The problem is only one of the informal language (Bohm) not of the mathematics.
Thus the 4 GCT invariant tetrad 1-forms are the LLT 4-vector components
e(4)^a = I^a + A(4)^a
I^a is the trivial globally flat 1905 SR tetrad
A(4)^a is the intrinsically warped "gauge connection potential" from localizing 4-parameter T(4).
Einstein's 1915 fundamental local GCT & LLT scalar invariant is
ds^2 = e^aea = (Minkowski metric)abe^ae^b = guvdx^udx^v
Einstein's 1915 constraint of zero torsion is the vanishing 2-form
T(4)^a = de(4)^a + S(4)^ac/\e(4)^c = 0
This with metricity, see Rovelli's explicit formula Ch 2 of his online "Quantum Gravity" gives the 6 zero torsion field effective spin-connnection 1-forms
S(4)^a^b = - S(4)^b^a
only from localizing T(4) to get the spin 1 Yang-Mills potential A(4)^a
A(4)^a spin 1 because it's a Lorentz group 4-vector in the a-index.
This warped localized tetrad resembles the EM 4-potential with "internal index" "a" i.e. "Yang-Mills".
The pure disclination curvature defects without torsion gaps then come from the curvature 2-form
R(4)^a^b = dS(4)^a^b + S(4)^ac/\S^cb
And no TP of course at this stage as you say.
Next step is to locally gauge SO(1,3) giving the additional independent torsion gap field spin connection 1-forms
S(1,3)^a^b
The full connection is then S(4)^a^b + S(1,3)^a^b
Where now
T^a(1,3) = S(1,3)^ac/\e^c =/= 0
R(10)^a^b = d[S(4)^a^b + S(1,3)^a^b] + [S(4)^ac + S(1,3)^ac]/\[S(4)^c^b + S(1,3)^c^b]
Where the TP Ansatz is obviously in my transparent notation using only local objective GCT invariants (coordinate independent)
R(10)^a^b = 0
where
R(10)^a^b = R(4)^a^b + R(1,3)^a^b + S(4)^ac/\S(1,3)^cb + S(1,3)^ac/\S(4)^cb
Hence two "diagonal" curvature 2-forms. Utiyama in 1960 computed R(1,3)^a^b in effect without R(4)^a^b.
This settles the above informal language confusion you mention!
Note also the two T(4) x SO(1,3) cross-coupling terms.
*I am going to completely rewrite my emergent gravity archive paper with these new results of course.
Jack Sarfatti
Yes, thanks I know. :-)
BTW my theory for emergent gravity with torsion needs exactly 8 Higgs
bosons one for each Goldstone boson.
I have N = 8 to get Einstein's tetrads and spin connections emergent.
from my CIT talk under construction (outline sans math type equations)
M Theory for Idiots
Emergence of tetrads and spin connections from the spontaneous
breakdown of localized Poincare group symmetry in the post-inflation
physical vacuum.
Jack Sarfatti
Missing Organizing Idea
Witten and Green say they are missing the key idea denoted as â€Å“?â€
No Rigid Symmetries
Locally gauging a nondynamical rigid symmetry group of the action
(either internal or spacetime) of a given source field introduces a
gauge force coupled to the source as the compensating connection
field needed to maintain gauge invariance for the now dynamical non-
rigid symmetry group.
Weinberg doesn̢۪t get it?
How is that possible?
â€Å“Sorry I still don’t get it. Is there any physical principle, such
as a principle of invariance that would require the Christoffel
symbol to be accompanied by some specific additional tensor? …â€
Steven Weinberg to Fred Hehl on the role of the torsion field in
spacetime physics in March, 2007 Physics Today.
Spontaneous Symmetry Breaking
Spontaneously breaking a vacuum symmetry means macroscopic occupation
of a single-particle mode by a large number of virtual off-mass-shell
particles.
In a vacuum the ODLRO condensate is composed of virtual quanta in
contrast to the ground state of superfluid helium where the
condensate is made from real helium atoms on mass shell.
Local & Broken
The broken symmetry need not be the same as the locally gauged
symmetry, but can be. In gravity theory rigid translational symmetry
is spontaneously broken in order to have localized variable spacetime
curvature. The action still obeys the symmetry, only the vacuum does
not obey it.
Higgs Vacuum Manifold
N independent Goldstone phases require N+1 real Higgs scalar fields.
The degenerate vacua lie on the unit SN spherical hypersurface:
Higgs Vacuum Potential
The â€Å“More is different†emergent macro-quantum coherent vacuum
order parameter has the effective potential
Dynamical L-G Eq.
Covariant dynamical Landau-Ginzburg equation for the macro-quantum
coherent hologram â€Å“Volume without volume†vacuum order parameter is
Local Gauge Invariance
Localizing the 10-parameter globally rigid Poincare group of 1905 SR
universally for all non-gravity source field actions gives the 4
Einstein-Cartan tetrads and the 6 spin connections as compensating
gauge potentials.
This is similar to localizing the internal symmetry groups in Yang-
Mills theory of the electroweak-strong forces.
M = My Mystery Matrix
Start with two Lorentz 4-vectors of 0-forms
Compactification
Each Minkowski 4-vector has magnitude
Michael Faraday
I use Faraday’s â€Å“lines of force†in a metaphorical way for the
geometrodynamic field compacted down from 9 + 1 to 3 + 1.
Two Goldstone phases have three single-valued real Higgs fields with
stable quantized (wrapping integers) point â€Å“monopole†defects in
3D space.
A single Goldstone phase has two real Higgs fields with stable
quantized (winding integers) line â€Å“vortex core†stringy defects.
Line Density Operator
The geometrodynamic line density operator is the non-closed 1-form
Area Density Operator
The geometrodynamic area density 2-form is closed. This is the world
hologram idea in action.
Stoke̢۪s Theorem
The deRahm integral of a p-form on a p-cycle (without boundary)
equals the p-form̢۪s exterior derivative on a p+1 co-form whose
boundary is the p-cycle.
Closed Forms
A p-form is closed if its exterior derivative vanishes. When the
interior of the p-cycle is simply connected without â€Å“holes†the
integral of the closed p-form vanishes.
Otherwise the integral is proportional to an integer analogous to
Bohr-Sommerfeld quantization in the old quantum theory and quantized
circulation in superfluid helium vortices.
World Holography
The geometrodynamic volume density operator 3-form should be
proportional to the exterior derivative of the area density operator
2-form. However, the area operator is closed. Therefore, the volume
operator is locally zero.
Volume is a holographic projection of the area density operator
integrated on a nonbounding 2-cycle enclosing point defects in the
single-valued 3-real Higgs component field projection on 3+1 from 9
+ 1 spacetime.
Bekenstein BITS
The integral of the geometrodynamic area density operator 2-form,
over a non-bounding closed 2-surface (cycle) surrounding a multiply-
connected 3D interior with â€Å“holes†where the 3 real Higgs fields
all vanish so that the 2 compacted Goldstone phases are undefined, is
quantized.
Volume without volume
Although Stoke̢۪s theorem rigorously does not apply to closed non-
bounding 2D surfaces S2 , whose 3D interior M3 is multiply connected,
physical intuition demands the as-if holographic imaging
Calabi-Yau
These 2 constraints leave 6 angular Kaluza-Klein Goldstone phases
whose radii determine coupling constants like the moduli of Calabi-
Yau space.
Gennady Shipov gets this structure in his version of torsion field
theory calling the extra 6 degrees of freedom an â€Å“oriented
point†(suggesting â€Å“branesâ€)
Higgs Potential
The 8 Goldstone phases require 9 real Higgs scalar fields.
One degenerate vacuum manifold is S8. There are other topologies.
From the POV of nontrivial homotopy groups for stable topological
defects they fit most naturally in the 9D + 1 spacetime of
superstring theory.
Shipov̢۪s Brane Worlds
Thus
Einstein-Cartan Tetrads
The four GCT invariant 1-forms are
Analogy to Superfluid
The fabric of spacetime is an elastic 4D GCT covariant supersolid,
compare
Macro-Quantum Gravity
There is no curvature gravity field in my emergent â€Å“More is
different†(P.W. Anderson) theory if
G = 0
h = 0
1/c = 0
Cartan 1-Forms
In terms of GCT tensor scalar invariant products, the 4 tetrads and 6
antisymmetric spin connection 1-forms are
Tetrad Decomposition
The GCT invariant globally flat tetrads and locally curved tetrads
are respectively
Spin Connections
The six GCT invariant connection 1-forms are
GCT Covariant D
The curved Cartan exterior derivative is
Torsion Field 2-Form
In 1915 GR this is zero
Curvature 2-Form
Take the covariant exterior derivative of the 1-form spin connection
to get the curvature 2-form
Einstein-Hilbert Action
The GCT & LLT field Lagrangian density is
On Mar 7, 2007, at 8:48 PM, MPOGO@aol.com wrote:
> Particle X in rare decay could belong to a new physics model
>
> By Lisa Zyga
> A particle that may mediate the rare decay of a Sigma-plus hyperon
> appears to have close affiliations with a light Higgs boson found
> in one supersymmetric model—an interpretation suggesting
> unambiguous evidence for physics beyond the standard model (SM),
> scientists say.
>
>
> Xiao-Gang He of the National Taiwan University, Jusak Tandean of
> the University of La Verne, and German Valencia of Iowa State have
> investigated the so-called HyperCP result observed at Fermilab a
> little over two years ago. While the HyperCP Collaboration began as
> a search for CP symmetry violation, the rare decay of the Sigma-
> plus hyperon (made of a strange quark and two up quarks) opens the
> possibility for the existence of a new particle with unusual
> characteristics.
>
>
> This unverified particle, which He and colleagues call particle X,
> would act as the intermediate state when the Sigma-plus decays to
> its final state, of a proton, muon-plus and muon-minus. With its
> extremely light mass (214.3 MeV), low energy, and smallest-ever
> branching ratio for a baryon decay, particle X would have less than
> a 1% chance of being accounted for within the SM.
>
> Although He and colleagues showed in an earlier paper that the
> HyperCP result may be explained by the SM if there is no new
> particle, the implications of a new particle are considerable. If
> scientists find that particle X is indeed a new particle belonging
> to a different model, the breakdown of the SM would open up new
> doors for future investigations in many areas, and possibly answer
> many questions unanswered by the SM.
>
> In their recent paper published in Physical Review Letters, He et
> al. turned their attention to a model called the â€Å“next-to-minimal
> sypersymmetric standard model†(NMSSM) that contains seven Higgs
> bosons. The scientists showed that the lightest one is the main
> component of a particle called A01, and that A01 satisfies all the
> constraints of particle X.
>
> â€Å“If the existence of a very light A01 is confirmed, other models
> such as the SM, which do not have any light Higgs bosons, will be
> ruled out,†Tandean told PhysOrg.com.
>
> Tandean also explained how, although the SM has withstood many
> experimental tests, there are some issues that the model doesn̢۪t
> address.
>
> â€Å“One issue is the so-called hierarchy problem: why the electroweak
> scale (represented by the W and Z boson masses, of order 100 GeV)
> is so much smaller than the Planck scale (1019 GeV), at which
> gravity becomes important for elementary particle interactions,â€
> he said. â€Å“One aspect of this issue is that quantum corrections to
> the Higgs mass make its value arbitrarily large, up to the Planck
> scale. This clearly contradicts the requirement that the Higgs be
> lighter than a few hundred GeV.â€
>
> However, as Tandean explained, supersymmetric models (where every
> SM particle has a corresponding superpartner) can provide a natural
> solution to this problem.
>
> â€The presence of the superpartners results in the cancellation of
> the large quantum corrections, leading to a Higgs mass at the
> desired level,†he said. â€Å“The minimal version of such models is
> called the Minimal Supersymmetric Standard Model (MSSM). The MSSM
> is a very attractive model in many ways, but it does not address
> the question of why the electroweak scale is much smaller than the
> Planck scale to begin with—this is the so-called mu problem.
>
> â€Å“Interestingly, the Next-to-Minimal Supersymmetric Standard Model
> (NMSSM) solves this problem by adding a set of two particles to the
> MSSM in such a way that the electroweak scale can be naturally
> small. The NMSSM has been extensively studied in the literature and
> has many other interesting features. It is therefore a well-
> motivated model.â€
> Among the constraints that the NMSSM̢۪s A01 can satisfy include
> explaining why X is very light: the mass of A01 can be as low as
> 100 MeV, and when the mass is 214.3 MeV, the decay into a muon-anti-
> muon dominates over other possible modes. Secondly, the
> interactions of A01 can produce the same rate found in the HyperCP
> observation.
>
> Thirdly, A01 explains why previous experiments with kaons and B-
> mesons that thoroughly explored the same regions where X exists
> never saw X. For these reasons, kaon and B-meson decays impose
> severe constraints on the properties of X, specifically regarding
> two-quark couplings. This means that, even though A01 could explain
> the new particle over a wide range of parameters, there are only
> narrow ranges for which the kaon constraints are also satisfied.
> However, the scientists also suggest that revisiting these
> constraints might reveal some overlooked data.
>
> In the future, two new particle accelerators—the Large Hadron
> Collider (LHC) and International Linear Collider (ILC)—might shed
> more light on the Higgs hypothesis. Supersymmetry may determine
> some parameters of particle X, where investigations of squark and
> chargino intermediate states in the NMSSM might provide more evidence.
>
> â€Å“The LHC and ILC have the capability of finding the charginos
> predicted by supersymmetric theories, depending on the chargino
> masses,†Tandean said. â€Å“In our study, we find that in order to
> explain the HyperCP results, the lighter chargino mass has to be
> around 100 GeV, which is within the range to be probed by the LHC
> and ILC. At the LHC and ILC, it is also possible to study the usual
> Higgs boson, h, in detail (or the one playing the role of h in
> NMSSM). If the A01 is the X particle, the process h --> XX can
> occur and may become the dominant decay mode if the h mass is
> relatively small (120 to 130 GeV). By studying the properties of h
> in detail, one may verify that X is the A01.â€
>
> Citation: He, Xiao-Gang, Tandean, Jusak, Valencia, G. â€Å“Does the
> HyperCP Evidence for the Decay ‘Sigma-plus to a proton, muon-plus
> and muon-minus’ Indicate a Light Pseudoscalar Higgs Boson?â€
> Physical Review Letters 98, 081802 (2007).
>
> By Lisa Zyga, Copyright 2007 PhysOrg.com.
> All rights reserved. This material may not be published, broadcast,
> rewritten or redistributed in whole or part without the express
> written permission of PhysOrg.com.
>
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
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http://www.flickr.com/photos/lub/sets/72157594439814784
Sunday, March 04, 2007
From: sarfatti@pacbell.net
Subject: Re: My Cal Tech M Theory Talk - Draft 3 March 16-17 2007
Date: March 5, 2007 3:12:09 PM PST
To: Sarfatti_Physics_Seminars@yahoogroups.com
This is a more popular version. CIT version will be edited down.
On Mar 4, 2007, at 5:13 PM, Jack Sarfatti wrote:
I challenge Witten's M Theory with the Destiny M Theory! ;-)
On Mar 3, 2007, at 6:36 PM, Jack Sarfatti wrote:
Actually I will not have all this intro-discussion in the Cal Tech talk, which I think is 10 minutes and all those guys know about local gauge invariance and something about spontaneous symmetry breaking from inflation cosmology.
1. The principle of local gauge invariance together with spontaneous breakdown of vacuum/ground state symmetry is the most successful battle-tested technique in physics today.
Localizing a rigid global symmetry of the initial action of some source field (e.g. lepton and quark spinors) is a deep expression of the generalized relativity principle of no action without direct reaction,i.e., no absolute arenas in the sense of Rovelli's discussion of Leibniz vs Newton in his "Quantum Gravity" on-line book.
2. What is local gauge invariance?
Start with the nonlocal Lagrange method used by Feynman in his path integral amplitude formulation of micro-quantum theory in contrast to the fixed time Hamiltonian wave function method. All physical systems are controlled by their "classical dynamical action S." S is an integral over a finite region of space-time, indeed in some cases it can include the entire history of the universe from Alpha Point inflation to hot big bang to us to the dark energy deSitter "thermal future horizon" Omega Point worth 10^122 Bekenstein BITS of "entropy." Indeed, it may be that this future world hologram screen sends advanced waves back from the future to the initial Planck area scaled seeds that inflated to our own "pocket universe" in the megaverse on the populated cosmic landscape (Lenny Susskind) of eternal chaotic inflation.

http://qedcorp.com/APS/ureye.gif
Self-Creating Pocket Universe
The colored dashes are advanced waves from the future dark energy deSitter horizon of huge area to the tiny area seeds of inflation in the false vacuum of the Higgs potential.
Tiny area early seed universe (white ball on top of the hill) in unstable false vacuum pre-inflation.
http://ha2.seikyou.ne.jp/home/Kiyoshi.Shiraishi/jpeg/Hsymtoy.jpg
The white golf ball is the inflation seed proto-universe poised unstably in the false vacuum. A random quantum fluctuation sends it rolling down the viscous molasses slope causing the tiny proto-universe to inflate by at least 10^60.

http://stardrive.org/logo.gif

http://ha2.seikyou.ne.jp/home/Kiyoshi.Shiraishi/jpeg/Hasymtoy.jpg
Much larger area-entropy by 10^60 early universe post-inflation.
Damping of ball's Higgs motion up and down slope provides heat for hot Big Bang.
Random motion around the rim is Goldstone phase noise.
The jiggling Higgs motion up and down the slope is, via A. Linde's viscosity, transformed into the tremendous heat of the big bang. What happens next is described vividly by Steven Weinberg in "The First Three Minutes."

http://www.theoryandpractice.org/kyle/Photography/Math/phitothe4.jpg
The actual potential may have a rim that is not S1 as pictured, but S8 that we cannot visualize directly. S8 gives curvature + torsion with the 6D Gennady Shipov "oriented point" as the proto Calabi-Yau space giving different positions on Susskind's cosmic landscape. With signal nonlocality violating the no-cloning-a-quantum theorem we can detect the entire cosmic landscape of parallel pocket universes in principle here-now because linearity, unitarity & Born probability all break down in the "More is different" emergence of the smooth c-number geometrodynamic macro-quantum field. The local nonlinear non-unitary Landau-Ginburg equation (for emergent complexity inherent in the post-inflation vacuum order parameters) replaces the nonlocal linear unitary Schrodinger equation for the large-scale structure of the string theory megaverse made Popper testable through signal nonlocality as in telepathic remote viewing used allegedly succesfully by the US military intelligence.
Facts come from unexpected corners. The true skeptic ignores facts like unexplained UFOS and alleged floating stargate portals at the Bigelow Utah Ranch at his peril. Note that multi-millionaire Robert Bigelow has a personal satellite orbiting Earth and he has funded serious UFO research using retired military intelligence personnel and PhD physicists.
http://www.mpe.mpg.de/~amueller/images/intermed/HiggsPot.jpg
This in a nutshell is the Stanford Duet, lyric of A. Linde & L. Susskind.
You can also wear the wire mesh on your head to gather orgone energy! :-)
Symmetry is a core concept of physics.
Symmetry is the stillness in the movement.
The fixed point.
The Center of the Cyclone.
Symmetry is the set of invariants that do not change relative to a "group" of transformations of frames of reference, i.e. observers looking at the same objective reality processes from different perspectives.
Global symmetry is "rigid" "absolute" it means that exactly the same changes are made over the entire universe. Localizing the symmetry is the Triumph of Our Freedom of The Will. Note I am listening to Maestro Furioso, Arturo Toscanni, overture Tristan & Isolde (1865).
All local observers are free to do as they wilt! This induces the compensating gauge potentials also called the connection fields for parallel transport of tensor and spinor structures along the paths of the destiny matrix (world lines or "timelines" if you like).
Examples of the technique.
Standard model of leptons, quarks, gauge force bosons of electro-weak (beta-radioactive) and strong sub-nuclear forces of the solar inferno.
We have three globally rigid internal symmetry groups of extra dimensions.
The single-parameter group U(1) is generated by the electric charge operating rigidly, the same phase shift over the entire universe of the lepton and quark spinor fields. Spinors are a special kind of "qubit" of the world quantum computer having to do with invariant properties of light in Einstein's 1905 special theory of relativity. Localizing this rigid U(1) "unitary symmetry group" gives the compensating gauge potential called the "vector potential" 1-form. Its Cartan exterior differential is
F(EM) = dA(EM)
is the Maxwell field 2-form that is the curvature of the connection 1-form in the internal space. You can think of it as a tiny unit circle at each point of space and time. Indeed, as a tiny clock with only one hand.
http://www.zamazing.org/imaj/zabun/one-handed-clock.jpg
Above is global rigid gauge or phase invariance of the source fields, i.e., same clock hand position shift everywhere-when.
The effect of local gauging. ;-)
http://www.gadgetshop.com/pws/images/catalogue/full/247825-B.jpg (Salvador Dali)
The Triumph of Freedom of the Will, is that you can locally set the hand of the clock anyway you like on your transient timeline from birth to death. Get the picture? The quantum of the A(EM) 1-form compensating field is the photon.
We now have a larger dynamical global action than we started with. It is invariant under this large group of localized U(1) transformations in which all of you Angels, Humans & Demons in the The Great Chain of Being and Becoming are free to move the one hand on your local clocks willy nilly as the spirit moves you. ;-)
The next group is SU(2) with 3 weak charges generating it operating on both quarks and leptons, corresponding to three angles of rotation in internal space. You might try to think of this in analogy with U(1) as a tiny unit 3-D spherical surface embedded in a 4 real dimensional space explicated out of 2 complex dimensions. (However, see below.) There are now 3 Yang-Mills connection field 1-forms A^a(Weak), a = 1,2,3 whose quanta when combined with A(EM) give the photon, two charged weak currents and one neutral weak current.
But now
F(Weak)^a = dA^a(Weak) + Cbc^aA^b/\A^c
The weak bosons are charged and self-interact. This is unlike the photon that does not carry electric charge but connects electric charges.
Cbc^a are structure constants of the closed Lie algebra of commutators of the charges of the internal symmetry Yang-Mills Lie group.
The general rule for SU(N) is N^2 - 1 "charge" generators of the continuous Lie group that form a Lie algebra whose "products" are "commutators."
This is not the whole story. We also have "chirality". The universe is not mirror symmetric. Left-handed leptons and quark spinors behave very differently from right-handed leptons and quarks.
http://en.wikipedia.org/wiki/Particle_physics_standard_model
Furthermore here we need spontaneous breakdown of symmetry, i.e. Higgs mechanism to give the weak gauge bosons a mass ~ 100 Gev. The nucleon (proton & neutron mass ~ 1 Gev, electron mass ~ 1/2000 of that roughly).
Spontaneous symmetry breaking is the emergence of new orders of complexity of matter, what P.W. Anderson calls "More is different." It's important in the condensed matter physics of metals, ferromagnets, lasers, superfluids, superconductors, 2D anyon physics of the fraction quantum Hall effect, and all sorts of nano-tech phenomena and applications like LCD & plasma screens for HDTV.
In fact the theory of the origin of inertia (rest masses) of Haisch and Puthoff et-al is wrong in the view of ALL elementary particle physicists who believe in this standard model Higgs-Goldstone mechanism that is battle-tested though it does have a lot of fudge factors - nevertheless, it explains very accurately and makes correct precise predictions that the Haisch-Puthoff theory cannot even formulate. Note that looking for the actual Higgs quanta on-mass-shell is not directly relevant to the Higgs vacuum condensate which is a macro-quantum coherent Glauber (possibly squeezed) state of virtual off-mass-shell Higgs intensity and Goldstone phase quanta.
Next we have SU(3) in three complex dimensions. N^2 - 1 = 9 - 1 = 8 strong charges that operate on the quarks, but not the leptons. You can think of an abstract 8D unit spherical surface embedded in a 9 real-D internal space. How that maps to space of 3 complex dimensions is not obvious until you think of matrices.
SU(3) consists of 3x3 matrices with complex matrix elements and one constraint (unit determinant). So you have 8 independent complex matrix elements (each one like a little U(1) S1 unit circle). Similarly, SU(2) consists of 2x2 complex matrices hence 3 little unit U(1) circles. You can also try to think of these as "tori"
S1xS1xS1 3-torus, also S2xS1 as well as S3.
In any case we now have 8 connection 1-forms for the strong sub-nuclear force
A(Strong)^a
a = 1,2,3, ... 8
The scheme is similar to the above weak fields.
Now finally we come to gravity and torsion fields!
All of the above symmetries are internal symmetries. Also they are not universal. Leptons do not have strong charges for example.
Einstein's special relativity is universal - all fields "carry" special relativity charges of total energy, total linear momentum, total rotational (angular momentum) and Boosts between inertial observers moving uniformly relative to each other.
The number of 4D space-time charges is
1 + 3 + 3 + 3 = 10
This is the RIGID 10-parameter Poincare group of 1905 special relativity.
Einstein did not think this way in 1905 nor in 1915 because Emmy Nother did her famous theorem about all this in 1915 the same time of Einstein's "Kampf" to get general relativity. We are looking backward from the modern POV.
Take the 1 + 3 of energy and linear momentum, that's the 4-parameter translation group T4. Localize it for all non-gravity field actions. The compensating gauge potentials are the curved pieces A^a of the Einstein-Cartan tetrad 1-forms e^a
e^a = I^a + A^a
a = 1,2,3,4
A^a is the intrinsic objective WARP "gravity field" (Rovelli's book on Quantum Gravity).
I^a is the curvilinear (accelerated frame) tetrad of globally flat special relativity.
In this 1915 limit, the torsion field is zero, there is only curvature.
This means
T^a = de^a + W(T4)^ab/\e^b = 0 = vanishing torsion field 2-form
W(T4)^a^b is the non-dynamical curvature-only piece of the spin connection to parallel transport spinors. Einstein's Levi-Civita connection is related to it in a complex way that is too much detail for now.
The curvature field of gravity is the 2-form
R^a^b = dW^a^b + W^ac/\W^cb
Note the analogy to the Yang-Mills fields
F^a = dA^a + C^abcA^b/\A^c
A^a is not the direct potential in Einstein's 1915 theory, it determines W^a^b with the constraints of zero torsion and something called metricity.
Einstein's key local invariant is the differential squared line element
ds^2 = e^aea = (Flat Metric)abe^ae^b
= (Curvilinear Metric)uvdx^udx^v
The next step is to locallize the 3 + 3 Lorentz group to get the torsion field spin connection 1-form S^a^b
Then we derive A^a and S^a^b
Where the non-vanishing torsion field 2-form is
T^a = S^ab/\e^b
Finally we get A^a & S^a^b from the coherent vacuum Goldstone phases of the post-inflation Higgs field controlling both dark energy and dark matter.
That's the idea that A^a & S^a^b emerge like the superflow 1-form field in liquid helium 4 at low temperature.
Imagine two sets of 4 Cartan scalar 0-forms that I will call "Goldstone phases."
Theta^a & Phi^a
a = 0,1,2,3
I define the GCT scalar local invariant non-closed 1-form M matrix
M^a^b = (Theta)^a/\d(Phi)^b - d(Theta)^a/\(Phi)^b
I define the localized 4-parameter translation subgroup T4 intrinsic curvature piece of the Einstein-Cartan tetrads as the diagonal
A(T4)^a = M^a^a = (Theta)^a/\d(Phi)^a - d(Theta)^a/\(Phi)^a
e^a = I^a + A(T4)^a
I^a is the globally flat set of tetrad 1-form fields when T4 is globally rigid.
My M-Theory equation
A(T4)^a = M^a^a = (Theta)^a/\d(Phi)^a - d(Theta)^a/\(Phi)^a
was motivated by the much simpler superfluid helium velocity field equation
v = (h/m)dTheta
v is the velocity 1-from in Galilean relativity 3D space.
(h/m) is the quantum of circulation-vorticity.
Theta is the single Goldstone phase of the helium 4 ground state order parameter.
The non-trivial first order homotopy gives vortex core string stable topological defects.
I need a dimensionless order parameter. The obvious choice is the number of Bekenstein BITs (or rather its inverse square root). That is
e^a = I^a + (Lp*^2/\zpf)^1/2A^a
Where /\zpf is the scale-dependent local dark energy/matter density.
Lp*^2 = hG*/c^3
G* is the renormalization group flowing scale-dependent gravity coupling.
Note there is no gravity when
/\zpf = 0
h = 0
c -> infinity
(Lp*^2/\zpf)^1/2 is the 4D SUPERSOLID analog to SUPERFLUID HELIUM h/m
The curved A^a(T4) with the non-vanishing 2-form
F(T4)^a = dA(T4)^a = 2d(Theta)^a/\d(Phi)^a
With vanishing 3-form
dF(T4)^a = d^2A(T4)^a = 0
Note the Dirac substratum Maxwellian field structure
d*F(T4)^a = d*dA(T4)^a = J(T4)^a source current density
dJ(T4)^a = 0
local conservation of substratum current density.
The above is the substratum for 1915 GR i.e. curvature without torsion
T(T4)^a) = de^a + S(T4)^ac/\e^a = 0
S(T4)^ac are the curvature-only zero torsion non-dynamical spin connection 1-forms determined by metricity plus zero torsion from keeping the 6-parameter Lorentz subgroup SO(1,3) globally rigid.
The Riemann-Christoffel curvature 2-form is
R(T4)^a^b = dS(T4)^a^b + S(T4)^ac/\S(T4)^c^b
The Einstein-Hilbert action density with cosmological constant /\zpf is the 0-form local frame-invariant scalar under GCTs and LLTs.
&S(E-H)/&x^4 = *[R(T4)^a^b/\e^c/\e^d + /\zpfe^a/\e^b/\e^c/\e^d]
* is the Hodge dual i.e. contract with completely antisymmetric tensor in 4D
* = {abcd}
Next to get the dynamically independent torsion field localize SO(1,3).
T^a(1,3) ~ S^(1,3)/\e^a =/= 0
The new spin connection 1-form to define the extended curvature 2-form is therefore
S^a^b(10) = S(T4)^a^b + S^(1,3)^a^b
where, in terms of the 8 0-form Goldstone phases, we take the antisymmetrized part of the matrix M^a^b
S^a^b(1,3) = M^[a,b] = - S^b^a
The additional 6 angular degrees of freedom of Gennady Shipov's "oriented point" lumped parameter description of the extended M-matrix object is a proto Calabi-Yau space

http://qedcorp.com/APS/Shipov.jpg
Subject: Re: My Cal Tech M Theory Talk - Draft 3 March 16-17 2007
Date: March 5, 2007 3:12:09 PM PST
To: Sarfatti_Physics_Seminars@yahoogroups.com
This is a more popular version. CIT version will be edited down.
On Mar 4, 2007, at 5:13 PM, Jack Sarfatti wrote:
I challenge Witten's M Theory with the Destiny M Theory! ;-)
On Mar 3, 2007, at 6:36 PM, Jack Sarfatti wrote:
Actually I will not have all this intro-discussion in the Cal Tech talk, which I think is 10 minutes and all those guys know about local gauge invariance and something about spontaneous symmetry breaking from inflation cosmology.
1. The principle of local gauge invariance together with spontaneous breakdown of vacuum/ground state symmetry is the most successful battle-tested technique in physics today.
Localizing a rigid global symmetry of the initial action of some source field (e.g. lepton and quark spinors) is a deep expression of the generalized relativity principle of no action without direct reaction,i.e., no absolute arenas in the sense of Rovelli's discussion of Leibniz vs Newton in his "Quantum Gravity" on-line book.
2. What is local gauge invariance?
Start with the nonlocal Lagrange method used by Feynman in his path integral amplitude formulation of micro-quantum theory in contrast to the fixed time Hamiltonian wave function method. All physical systems are controlled by their "classical dynamical action S." S is an integral over a finite region of space-time, indeed in some cases it can include the entire history of the universe from Alpha Point inflation to hot big bang to us to the dark energy deSitter "thermal future horizon" Omega Point worth 10^122 Bekenstein BITS of "entropy." Indeed, it may be that this future world hologram screen sends advanced waves back from the future to the initial Planck area scaled seeds that inflated to our own "pocket universe" in the megaverse on the populated cosmic landscape (Lenny Susskind) of eternal chaotic inflation.

http://qedcorp.com/APS/ureye.gif
Self-Creating Pocket Universe
The colored dashes are advanced waves from the future dark energy deSitter horizon of huge area to the tiny area seeds of inflation in the false vacuum of the Higgs potential.
Tiny area early seed universe (white ball on top of the hill) in unstable false vacuum pre-inflation.
http://ha2.seikyou.ne.jp/home/Kiyoshi.Shiraishi/jpeg/Hsymtoy.jpg
The white golf ball is the inflation seed proto-universe poised unstably in the false vacuum. A random quantum fluctuation sends it rolling down the viscous molasses slope causing the tiny proto-universe to inflate by at least 10^60.

http://stardrive.org/logo.gif

http://ha2.seikyou.ne.jp/home/Kiyoshi.Shiraishi/jpeg/Hasymtoy.jpg
Much larger area-entropy by 10^60 early universe post-inflation.
Damping of ball's Higgs motion up and down slope provides heat for hot Big Bang.
Random motion around the rim is Goldstone phase noise.
The jiggling Higgs motion up and down the slope is, via A. Linde's viscosity, transformed into the tremendous heat of the big bang. What happens next is described vividly by Steven Weinberg in "The First Three Minutes."

http://www.theoryandpractice.org/kyle/Photography/Math/phitothe4.jpg
The actual potential may have a rim that is not S1 as pictured, but S8 that we cannot visualize directly. S8 gives curvature + torsion with the 6D Gennady Shipov "oriented point" as the proto Calabi-Yau space giving different positions on Susskind's cosmic landscape. With signal nonlocality violating the no-cloning-a-quantum theorem we can detect the entire cosmic landscape of parallel pocket universes in principle here-now because linearity, unitarity & Born probability all break down in the "More is different" emergence of the smooth c-number geometrodynamic macro-quantum field. The local nonlinear non-unitary Landau-Ginburg equation (for emergent complexity inherent in the post-inflation vacuum order parameters) replaces the nonlocal linear unitary Schrodinger equation for the large-scale structure of the string theory megaverse made Popper testable through signal nonlocality as in telepathic remote viewing used allegedly succesfully by the US military intelligence.
Facts come from unexpected corners. The true skeptic ignores facts like unexplained UFOS and alleged floating stargate portals at the Bigelow Utah Ranch at his peril. Note that multi-millionaire Robert Bigelow has a personal satellite orbiting Earth and he has funded serious UFO research using retired military intelligence personnel and PhD physicists.
http://www.mpe.mpg.de/~amueller/images/intermed/HiggsPot.jpg
This in a nutshell is the Stanford Duet, lyric of A. Linde & L. Susskind.
You can also wear the wire mesh on your head to gather orgone energy! :-)
Symmetry is a core concept of physics.
Symmetry is the stillness in the movement.
The fixed point.
The Center of the Cyclone.
Symmetry is the set of invariants that do not change relative to a "group" of transformations of frames of reference, i.e. observers looking at the same objective reality processes from different perspectives.
Global symmetry is "rigid" "absolute" it means that exactly the same changes are made over the entire universe. Localizing the symmetry is the Triumph of Our Freedom of The Will. Note I am listening to Maestro Furioso, Arturo Toscanni, overture Tristan & Isolde (1865).
All local observers are free to do as they wilt! This induces the compensating gauge potentials also called the connection fields for parallel transport of tensor and spinor structures along the paths of the destiny matrix (world lines or "timelines" if you like).
Examples of the technique.
Standard model of leptons, quarks, gauge force bosons of electro-weak (beta-radioactive) and strong sub-nuclear forces of the solar inferno.
We have three globally rigid internal symmetry groups of extra dimensions.
The single-parameter group U(1) is generated by the electric charge operating rigidly, the same phase shift over the entire universe of the lepton and quark spinor fields. Spinors are a special kind of "qubit" of the world quantum computer having to do with invariant properties of light in Einstein's 1905 special theory of relativity. Localizing this rigid U(1) "unitary symmetry group" gives the compensating gauge potential called the "vector potential" 1-form. Its Cartan exterior differential is
F(EM) = dA(EM)
is the Maxwell field 2-form that is the curvature of the connection 1-form in the internal space. You can think of it as a tiny unit circle at each point of space and time. Indeed, as a tiny clock with only one hand.
http://www.zamazing.org/imaj/zabun/one-handed-clock.jpg
Above is global rigid gauge or phase invariance of the source fields, i.e., same clock hand position shift everywhere-when.
The effect of local gauging. ;-)
http://www.gadgetshop.com/pws/images/catalogue/full/247825-B.jpg (Salvador Dali)
The Triumph of Freedom of the Will, is that you can locally set the hand of the clock anyway you like on your transient timeline from birth to death. Get the picture? The quantum of the A(EM) 1-form compensating field is the photon.
We now have a larger dynamical global action than we started with. It is invariant under this large group of localized U(1) transformations in which all of you Angels, Humans & Demons in the The Great Chain of Being and Becoming are free to move the one hand on your local clocks willy nilly as the spirit moves you. ;-)
The next group is SU(2) with 3 weak charges generating it operating on both quarks and leptons, corresponding to three angles of rotation in internal space. You might try to think of this in analogy with U(1) as a tiny unit 3-D spherical surface embedded in a 4 real dimensional space explicated out of 2 complex dimensions. (However, see below.) There are now 3 Yang-Mills connection field 1-forms A^a(Weak), a = 1,2,3 whose quanta when combined with A(EM) give the photon, two charged weak currents and one neutral weak current.
But now
F(Weak)^a = dA^a(Weak) + Cbc^aA^b/\A^c
The weak bosons are charged and self-interact. This is unlike the photon that does not carry electric charge but connects electric charges.
Cbc^a are structure constants of the closed Lie algebra of commutators of the charges of the internal symmetry Yang-Mills Lie group.
The general rule for SU(N) is N^2 - 1 "charge" generators of the continuous Lie group that form a Lie algebra whose "products" are "commutators."
This is not the whole story. We also have "chirality". The universe is not mirror symmetric. Left-handed leptons and quark spinors behave very differently from right-handed leptons and quarks.
http://en.wikipedia.org/wiki/Particle_physics_standard_model
Furthermore here we need spontaneous breakdown of symmetry, i.e. Higgs mechanism to give the weak gauge bosons a mass ~ 100 Gev. The nucleon (proton & neutron mass ~ 1 Gev, electron mass ~ 1/2000 of that roughly).
Spontaneous symmetry breaking is the emergence of new orders of complexity of matter, what P.W. Anderson calls "More is different." It's important in the condensed matter physics of metals, ferromagnets, lasers, superfluids, superconductors, 2D anyon physics of the fraction quantum Hall effect, and all sorts of nano-tech phenomena and applications like LCD & plasma screens for HDTV.
In fact the theory of the origin of inertia (rest masses) of Haisch and Puthoff et-al is wrong in the view of ALL elementary particle physicists who believe in this standard model Higgs-Goldstone mechanism that is battle-tested though it does have a lot of fudge factors - nevertheless, it explains very accurately and makes correct precise predictions that the Haisch-Puthoff theory cannot even formulate. Note that looking for the actual Higgs quanta on-mass-shell is not directly relevant to the Higgs vacuum condensate which is a macro-quantum coherent Glauber (possibly squeezed) state of virtual off-mass-shell Higgs intensity and Goldstone phase quanta.
Next we have SU(3) in three complex dimensions. N^2 - 1 = 9 - 1 = 8 strong charges that operate on the quarks, but not the leptons. You can think of an abstract 8D unit spherical surface embedded in a 9 real-D internal space. How that maps to space of 3 complex dimensions is not obvious until you think of matrices.
SU(3) consists of 3x3 matrices with complex matrix elements and one constraint (unit determinant). So you have 8 independent complex matrix elements (each one like a little U(1) S1 unit circle). Similarly, SU(2) consists of 2x2 complex matrices hence 3 little unit U(1) circles. You can also try to think of these as "tori"
S1xS1xS1 3-torus, also S2xS1 as well as S3.
In any case we now have 8 connection 1-forms for the strong sub-nuclear force
A(Strong)^a
a = 1,2,3, ... 8
The scheme is similar to the above weak fields.
Now finally we come to gravity and torsion fields!
All of the above symmetries are internal symmetries. Also they are not universal. Leptons do not have strong charges for example.
Einstein's special relativity is universal - all fields "carry" special relativity charges of total energy, total linear momentum, total rotational (angular momentum) and Boosts between inertial observers moving uniformly relative to each other.
The number of 4D space-time charges is
1 + 3 + 3 + 3 = 10
This is the RIGID 10-parameter Poincare group of 1905 special relativity.
Einstein did not think this way in 1905 nor in 1915 because Emmy Nother did her famous theorem about all this in 1915 the same time of Einstein's "Kampf" to get general relativity. We are looking backward from the modern POV.
Take the 1 + 3 of energy and linear momentum, that's the 4-parameter translation group T4. Localize it for all non-gravity field actions. The compensating gauge potentials are the curved pieces A^a of the Einstein-Cartan tetrad 1-forms e^a
e^a = I^a + A^a
a = 1,2,3,4
A^a is the intrinsic objective WARP "gravity field" (Rovelli's book on Quantum Gravity).
I^a is the curvilinear (accelerated frame) tetrad of globally flat special relativity.
In this 1915 limit, the torsion field is zero, there is only curvature.
This means
T^a = de^a + W(T4)^ab/\e^b = 0 = vanishing torsion field 2-form
W(T4)^a^b is the non-dynamical curvature-only piece of the spin connection to parallel transport spinors. Einstein's Levi-Civita connection is related to it in a complex way that is too much detail for now.
The curvature field of gravity is the 2-form
R^a^b = dW^a^b + W^ac/\W^cb
Note the analogy to the Yang-Mills fields
F^a = dA^a + C^abcA^b/\A^c
A^a is not the direct potential in Einstein's 1915 theory, it determines W^a^b with the constraints of zero torsion and something called metricity.
Einstein's key local invariant is the differential squared line element
ds^2 = e^aea = (Flat Metric)abe^ae^b
= (Curvilinear Metric)uvdx^udx^v
The next step is to locallize the 3 + 3 Lorentz group to get the torsion field spin connection 1-form S^a^b
Then we derive A^a and S^a^b
Where the non-vanishing torsion field 2-form is
T^a = S^ab/\e^b
Finally we get A^a & S^a^b from the coherent vacuum Goldstone phases of the post-inflation Higgs field controlling both dark energy and dark matter.
That's the idea that A^a & S^a^b emerge like the superflow 1-form field in liquid helium 4 at low temperature.
Imagine two sets of 4 Cartan scalar 0-forms that I will call "Goldstone phases."
Theta^a & Phi^a
a = 0,1,2,3
I define the GCT scalar local invariant non-closed 1-form M matrix
M^a^b = (Theta)^a/\d(Phi)^b - d(Theta)^a/\(Phi)^b
I define the localized 4-parameter translation subgroup T4 intrinsic curvature piece of the Einstein-Cartan tetrads as the diagonal
A(T4)^a = M^a^a = (Theta)^a/\d(Phi)^a - d(Theta)^a/\(Phi)^a
e^a = I^a + A(T4)^a
I^a is the globally flat set of tetrad 1-form fields when T4 is globally rigid.
My M-Theory equation
A(T4)^a = M^a^a = (Theta)^a/\d(Phi)^a - d(Theta)^a/\(Phi)^a
was motivated by the much simpler superfluid helium velocity field equation
v = (h/m)dTheta
v is the velocity 1-from in Galilean relativity 3D space.
(h/m) is the quantum of circulation-vorticity.
Theta is the single Goldstone phase of the helium 4 ground state order parameter.
The non-trivial first order homotopy gives vortex core string stable topological defects.
I need a dimensionless order parameter. The obvious choice is the number of Bekenstein BITs (or rather its inverse square root). That is
e^a = I^a + (Lp*^2/\zpf)^1/2A^a
Where /\zpf is the scale-dependent local dark energy/matter density.
Lp*^2 = hG*/c^3
G* is the renormalization group flowing scale-dependent gravity coupling.
Note there is no gravity when
/\zpf = 0
h = 0
c -> infinity
(Lp*^2/\zpf)^1/2 is the 4D SUPERSOLID analog to SUPERFLUID HELIUM h/m
The curved A^a(T4) with the non-vanishing 2-form
F(T4)^a = dA(T4)^a = 2d(Theta)^a/\d(Phi)^a
With vanishing 3-form
dF(T4)^a = d^2A(T4)^a = 0
Note the Dirac substratum Maxwellian field structure
d*F(T4)^a = d*dA(T4)^a = J(T4)^a source current density
dJ(T4)^a = 0
local conservation of substratum current density.
The above is the substratum for 1915 GR i.e. curvature without torsion
T(T4)^a) = de^a + S(T4)^ac/\e^a = 0
S(T4)^ac are the curvature-only zero torsion non-dynamical spin connection 1-forms determined by metricity plus zero torsion from keeping the 6-parameter Lorentz subgroup SO(1,3) globally rigid.
The Riemann-Christoffel curvature 2-form is
R(T4)^a^b = dS(T4)^a^b + S(T4)^ac/\S(T4)^c^b
The Einstein-Hilbert action density with cosmological constant /\zpf is the 0-form local frame-invariant scalar under GCTs and LLTs.
&S(E-H)/&x^4 = *[R(T4)^a^b/\e^c/\e^d + /\zpfe^a/\e^b/\e^c/\e^d]
* is the Hodge dual i.e. contract with completely antisymmetric tensor in 4D
* = {abcd}
Next to get the dynamically independent torsion field localize SO(1,3).
T^a(1,3) ~ S^(1,3)/\e^a =/= 0
The new spin connection 1-form to define the extended curvature 2-form is therefore
S^a^b(10) = S(T4)^a^b + S^(1,3)^a^b
where, in terms of the 8 0-form Goldstone phases, we take the antisymmetrized part of the matrix M^a^b
S^a^b(1,3) = M^[a,b] = - S^b^a
The additional 6 angular degrees of freedom of Gennady Shipov's "oriented point" lumped parameter description of the extended M-matrix object is a proto Calabi-Yau space

http://qedcorp.com/APS/Shipov.jpg
Paul Zielinski AKA Z has for almost a decade been fighting a hopeless rear-guard action to restore the Lorentzian physical length contraction "aether" interpretation not only for global special relativity without gravity but for general relativity. Similar attempts are seen in Hal Puthoff's PV model based on outmoded ideas of Dicke (1961) and Yilmaz. None of these models are consistent with Einstein's local equivalence principle with general covariance. I think James Woodward's Mach Principle model for propellantless propulsion is also subject to this same defect because his theory is based on a globally flat scalar wave equation that is not generally covariant if I am not mistaken?
Z tries to restore Newtonian "inertial compensation." Let's review how that works. In Newton's 17th Century classical mechanics if we look at a cannon ball shot out of a cannon
http://www.martinirepublic.com/wp-content/images/munchausen02.jpg
The Earth bound observer is approximated to be in a global inertial (non-accelerating) frame of reference in which there is a conservative gravity potential per unit test mass
V(Newton) = -GM/r
M = source mass
m = test particle mass
Newton's second law for the path-independent holonomic potential in the inertial frame
F/m = - dV(Newton)/dr = -GM/r^2
The result is a parabolic path, details depend on initial position, velocity etc.
This curved parabolic path is not a "geodesic" (AKA straightest path) in the flat Galilean spacetime.
Therefore, in Newton's physics there is a gravity force just like an electric force, no essential conceptual difference.
But Baron Munchausen is weightless (no g-force on him). No problem, the Baron is in an accelerating frame and the "fictitious inertial translational force" on the Baron exactly cancels, compensates, the gravity force on the Baron so that the net force on the Baron is zero. Another way to understand this is that the cannonball is not pushing back up on the Baron's rear end because they are both falling with the same acceleration. This later way of looking at it is simpler and more in line with Einstein's thinking based on the equivalence principle.
Now here is how Einstein explains the same above problem.
First of all the observer Bob on Earth feels "weight," i.e. g-force. Therefore, the Earth-bound observer is in the non-inertial accelerating non-geodesic frame relative to curved space-time. Two observers on Earth anti-podally placed on opposite sides on a line through the Earth's center are accelerating relative each other, but their separation does not change because this back-to-back mutual acceleration is in curved spacetime. Of course if the spacetime were flat the distance between them would change. See Hawking's "The Universe in a Nutshell" for a nice picture of this. Therefore, the weightless Baron Munchausen is on a geodesic non-accelerating local inertial frame. It's the Earth-bound observer Bob who is really accelerating. Bob feels weight because the electrical forces of the ground are pushing him off his natural weightless curved spacetime geodesic path. This g-force on Bob is created by the non-gravity electrical force of the ground (with quantum exchange effects of Pauli exclusion et-al).
In fact, in the math of Einstein's theory the curved spacetime non-geodesic Earth-bound observer has a non-vanishing covariant scalar invariant magnitude 4-acceleration "a" caused by the non-gravity force in the covariant generalization of Newton's second law F = ma. The Baron's geodesic invariant acceleration is zero.
Now, with that as background, to Creon Levit's gedankenexperiment. Creon and I met at Caffe Trieste last Fri nite and I have added some detail to his thought that night.
Alice is in a rocket ship stationary at fixed r a safe distance from a small rapidly evaporating black hole of mass M(t).
Her arrival in position is at t = 0. Her protocol is to fire her rocket at t = 0 at a thrust directed to the center of the black hole corresponding to
g = GM(0)/r^2 ~ c^2(Local Curvature at t = 0)r
She closes her ports and agrees not to look outside.
M(t) decreases rapidly to zero from the Hawking radiation.
What does Alice experience? She feels no local change. Her artificial gravity g is same because her rocket engine thrust is kept constant. However, Eve looking at the whole thing from the outside sees Alice's radial position r(t) relative to the shrinking black hole increasing. The local curvature field at Alice's position is evaporating away. But it makes no difference to Alice's local measurements of first-order g-force. Of course if she measured geodesic deviation of freely falling test particles inside her ship she could detect the evaporating curvature field, but that measurement is orthogonal to her g-force measurement. The corresponding operators commute, they are compatible measurements in the quantum sense.
Now Z says that the local g-force = tensor curvature piece + inertial force piece
Z then argues that
g = GM/r^2 is the tensor piece
However he never proves that this term is actually a GCT tensor. I am pretty sure it's not.
So in Z's view at t = 0 the complete g-force is a tensor with no inertial part, and at t -> infinity the complete g-force is inertial with no tensor part.
This is simply word play of course and there is no formal proof that
g = GM(0)/r^2
is a GCT tensor. What it really is, is an arbitrary choice of convenience. i.e. choosing a "static" constant r observer (assuming no evaporation of the source mass of course). If Alice looked outside she would have to lower her thrust to stay at fixed r.
PS. Z's appeal to the arcane math of Alex Poltorak and Waldyr Rodrigues, Jr on ineffable connections and non-metricities are clearly excess formal baggage muddying clear waters, red herrings designed to dazzle and snow experimental physicists. Fancy math is used when the write lacks a good physical idea. Most papers in theory on archive today are of that character. I would rather have "mathematical nonsense" like Feynman's diagrams than rigor mortis math that is "physical nonsense."
Z tries to restore Newtonian "inertial compensation." Let's review how that works. In Newton's 17th Century classical mechanics if we look at a cannon ball shot out of a cannon
http://www.martinirepublic.com/wp-content/images/munchausen02.jpg
The Earth bound observer is approximated to be in a global inertial (non-accelerating) frame of reference in which there is a conservative gravity potential per unit test mass
V(Newton) = -GM/r
M = source mass
m = test particle mass
Newton's second law for the path-independent holonomic potential in the inertial frame
F/m = - dV(Newton)/dr = -GM/r^2
The result is a parabolic path, details depend on initial position, velocity etc.
This curved parabolic path is not a "geodesic" (AKA straightest path) in the flat Galilean spacetime.
Therefore, in Newton's physics there is a gravity force just like an electric force, no essential conceptual difference.
But Baron Munchausen is weightless (no g-force on him). No problem, the Baron is in an accelerating frame and the "fictitious inertial translational force" on the Baron exactly cancels, compensates, the gravity force on the Baron so that the net force on the Baron is zero. Another way to understand this is that the cannonball is not pushing back up on the Baron's rear end because they are both falling with the same acceleration. This later way of looking at it is simpler and more in line with Einstein's thinking based on the equivalence principle.
Now here is how Einstein explains the same above problem.
First of all the observer Bob on Earth feels "weight," i.e. g-force. Therefore, the Earth-bound observer is in the non-inertial accelerating non-geodesic frame relative to curved space-time. Two observers on Earth anti-podally placed on opposite sides on a line through the Earth's center are accelerating relative each other, but their separation does not change because this back-to-back mutual acceleration is in curved spacetime. Of course if the spacetime were flat the distance between them would change. See Hawking's "The Universe in a Nutshell" for a nice picture of this. Therefore, the weightless Baron Munchausen is on a geodesic non-accelerating local inertial frame. It's the Earth-bound observer Bob who is really accelerating. Bob feels weight because the electrical forces of the ground are pushing him off his natural weightless curved spacetime geodesic path. This g-force on Bob is created by the non-gravity electrical force of the ground (with quantum exchange effects of Pauli exclusion et-al).
In fact, in the math of Einstein's theory the curved spacetime non-geodesic Earth-bound observer has a non-vanishing covariant scalar invariant magnitude 4-acceleration "a" caused by the non-gravity force in the covariant generalization of Newton's second law F = ma. The Baron's geodesic invariant acceleration is zero.
Now, with that as background, to Creon Levit's gedankenexperiment. Creon and I met at Caffe Trieste last Fri nite and I have added some detail to his thought that night.
Alice is in a rocket ship stationary at fixed r a safe distance from a small rapidly evaporating black hole of mass M(t).
Her arrival in position is at t = 0. Her protocol is to fire her rocket at t = 0 at a thrust directed to the center of the black hole corresponding to
g = GM(0)/r^2 ~ c^2(Local Curvature at t = 0)r
She closes her ports and agrees not to look outside.
M(t) decreases rapidly to zero from the Hawking radiation.
What does Alice experience? She feels no local change. Her artificial gravity g is same because her rocket engine thrust is kept constant. However, Eve looking at the whole thing from the outside sees Alice's radial position r(t) relative to the shrinking black hole increasing. The local curvature field at Alice's position is evaporating away. But it makes no difference to Alice's local measurements of first-order g-force. Of course if she measured geodesic deviation of freely falling test particles inside her ship she could detect the evaporating curvature field, but that measurement is orthogonal to her g-force measurement. The corresponding operators commute, they are compatible measurements in the quantum sense.
Now Z says that the local g-force = tensor curvature piece + inertial force piece
Z then argues that
g = GM/r^2 is the tensor piece
However he never proves that this term is actually a GCT tensor. I am pretty sure it's not.
So in Z's view at t = 0 the complete g-force is a tensor with no inertial part, and at t -> infinity the complete g-force is inertial with no tensor part.
This is simply word play of course and there is no formal proof that
g = GM(0)/r^2
is a GCT tensor. What it really is, is an arbitrary choice of convenience. i.e. choosing a "static" constant r observer (assuming no evaporation of the source mass of course). If Alice looked outside she would have to lower her thrust to stay at fixed r.
PS. Z's appeal to the arcane math of Alex Poltorak and Waldyr Rodrigues, Jr on ineffable connections and non-metricities are clearly excess formal baggage muddying clear waters, red herrings designed to dazzle and snow experimental physicists. Fancy math is used when the write lacks a good physical idea. Most papers in theory on archive today are of that character. I would rather have "mathematical nonsense" like Feynman's diagrams than rigor mortis math that is "physical nonsense."
Wednesday, February 28, 2007
Emergence of Gravity from Vacuum Coherence
There are TWO GCT tensor pieces to AFFINE non-metricity and torsion, both are ZERO in GR, but torsion is not zero in the extended theory e.g. Shipov's.
You get the 4 Einstein-Cartan tetrad 1-forms e^a from locally gauging T4 in all actions. The warped part C^a^a of e^a are the spin 1 compensating gauge potentials where the gauge transformations are simply Einstein's GCTs that define the multi-linear "tensors."
The spin 2 affine connection in general is something like
A^wuv = e^wa(d/dx^u)e^av
Its quadratic in the fundamental spin 1 Yang-Mills fields from locally gauging the 4-parameter translation group T4 in all physical actions of special relativistic fields. That, BTW is a deep formulation of the equivalence principle.
In QM 1 + 1 = 2 + 1 + 0
so, in general, there are spin 2 tensor + spin 1 vector + spin 0 scalar quanta if you quantize this smooth c-number vacuum ODLRO "supersolid" emergent gravity theory.
The torsion connection tensor is
S^wuv = A^w[u,v]
S^wuv =/= 0 when we also locally gauge the 6-parameter Lorentz group SO(1,3) and this corresponds to the 6 1-forms C^[a,b] below in terms of the 8 0-form Goldstone phases of the 9 real component Higgs post-inflation scalar fields.
This is a generalization of the Jahn-Teller effect in a crystal I suppose? My paper with Marshall Stoneham 1967 at Harwell AERE + my 1969 PhD thesis on gauge fields and ODLRO in superfluids + my 1969 paper predicting the supersolid phase of Helium 4 that David Goodstein and Richard Feynman helped me with. I would drive up to Cal Tech from San Diego. Also my 1966 Landau-Ginzburg Mexican Hat potential model of self-trapped laser filaments paper that Ray Chiao said he read when he was doing his famous experiments on them at Berkeley.
The 6 dynamical torsion field spin connection 1-forms (not in 1915 GR) correspond to Gennady Shipov's 10-D oriented point test particle. Einstein's 1915 GR only has a 4D point test particle.
http://qedcorp.com/APS/Shipov.jpg
This picture from Shipov shows a primitive 6D Calabi-Yau "fiber" of string theory.
My 9 real Higgs fields fit most naturally into 9D spacelike slices with brane worlds corresponding to stable topological defects from non-trivial homotopy groups with quantized deRham integrals from single-valued Higgs fields as shown in general in the David Thouless book on topological methods in quantum theory.
Therefore, vacuum coherent ODLRO Higgs-Goldstone fields + local gauging of spacetime symmetries (AKA equivalence principle) seems to be the missing organizing idea of string theory. It's been there all the time right under their noses.
On Feb 28, 2007, at 2:16 AM, Paul Zielinski wrote:
"It looks like you are still thinking that the tensor part of LC is supposed to be the "non-metricity tensor of the Levi-Civita connection". Of course, the non-metricity of the LC connection is exactly zero.
The tensor part of LC is not this quantity. It is a tensor X = -Q_A that is equal to the negative of the non-metricity tensor of a different (i.e., non-metric) torsion-free affine connection A =/= LC, where
A = LC + Q_A, and Q_A =/= 0."
There is no physics to this. There is no way to measure Q_A independently. It's not GR. You cannot say you have a new way to reinterpret GR with this formal shell game.
"There is no question that the non-metricity tensor Q_LC of the LC connection is zero. However, it does not follow from this that the LC connection doesn't contain the tensor X = -Q_A."
1. Take the Schwarzschild metric
1. Compute X.
2. Show how to measure X independently.
Meantime all the cool stuff I showed you re: C^a^b went over your head.
Jack Sarfatti wrote:
On Feb 27, 2007, at 10:56 PM, Paul Zielinski wrote:
"OK Jack, fire away. Give me your best shot.
Here is a direct quote from Carroll:
'...any set of connections can be expressed as some fiducial connection plus a tensorial correction.' (Notes on General Relativity, p 59).
Now explain to us why this doesn't apply to the LC connection?"
I told you a jillion times. Read the rest of what he says!
"Clearly, a zero "correction" is no correction at all. For Carroll's statement to be non-trivial, the tensorial correction must be non-vanishing.
Yet you are saying, in effect, that in the case of the LC connection the tensorial correction is always exactly zero. I think you have to prove
this mathematically, in the abstract, without any appeal to any particular physical theory."
Irrelevant.
"So you are saying that this doesn't apply to the LC connection? Why not?"
Sean Carroll like many others points out that most generally
Affine = LC + Torsion + Nonmetricity
Affine = LC + Torsion + Nonmetricity of Affine
Torsion and non-metricity are GCT 3rd rank tensors.
"Right."
LC is not a tensor.
"Right."
GR is precisely that theory in the set of theories with different connections such that
Affine = LC
End of trivial story.
"No. It is a theory such that the metric-compatible affine connection LC, defined on a 4D spacetime manifold, is taken to represent the Einstein field. But this is also true in the alternative model.
None of this has anything to do with the purely mathematical question of whether the LC connection contains a tensor -Q_A for some torsion-free non-metric affine connection A."
Physically LC parallel transports vectors along worldlines. While maintaining the inner products of vectors constant during the parallel transport process. Going around a closed worldline the difference of orientation of the vector with itself is a measure of the average curvature over the area of the loop - shrunk to zero - i.e. crystal disclination defect.
"Right."
Limit of the ratio of angle deficit to area of shrinking loop is the sectional curvature dimensions 1/Area.
"OK."
If there is non-metricity the length of the vector will also change in the parallel transport and in a loop you will get a discrepancy in lengths of the vector unless you impose a kind of Bohr-Sommerfeld quantization on the closed loop.
"Exactly. But this has nothing to do with coordinate curvilinearity or with Riemann curvature."
If there is torsion starting with two sides of an infinitesimal parallelogram and parallel transporting one against the other both ways the loop does not close to second order - there is a torsion gap, i.e. crystal dislocation defect.
"Right. If the connection is torsion-free this doesn't happen."
In my theory you have a set of 0-forms the Goldstone phases of the vacuum coherence ODLRO Higgs field.
From the 0-forms comes a set of 1-forms.
There are 10 1-forms.
4 tetrad 1-forms & 6 spin connection 1-forms.
Then you have GR + torsion trivially.
i.e. a theory with
A = LC + Torsion Tensor
beyond 1915 GR of course.
dO-form = 1-form
d^2)-form = 0
However that 1-form need not be exact if the 0-form has a singularity, i.e.
Integral of the 1-form over a non-bounding 1-cycle without boundary = winding number integer
Bohr-Sommerfeld condition from non-trivial 1-homotopy.
Then you can pretend Stoke's theorem works, i.e. flux without flux beyond Wheeler's "charge without charge" - these are 1D string vortex defects.
The integral of the 1-form around the loop is the surface integral of a ghostly 2-form flux through the area of the loop. This is related to the Bohm-Aharonov effect.
Similarly given 2 0-forms A & B, I define the non-closed 1-form as
C = dA/\B - A/\dB 1-form
dC = 2dA/\dB =/= 0 2-form
I can now play the same game one dimension higher! These are 0D point monopole stable defects.
Now we have star gate wormholes!
The mouth of the wormhole is the non-bounding 2-cycle without boundary - the portal like they see on the Skinwalker Ranch!
The deRham integral of 2-form C over the closed 2-surface is now an integer wrapping number ~ Bekenstein BITS for the entropy of black hole event horizons, de Sitter dark energy future observer horizons, Unruh effect, Hawking radiation, you name it. I got it all topologically pre-metrically.
There is again the world hologram ghostly volume 3-form without volume from the actual hologram area 2-form dC.
OK everything I need comes from C as the template.
C^a^b = dA^a/\B^b - A^a/\dB^b
The 4 Einstein curvature tetrad 1-forms are the diagonal matrix elements
C^a^a
The 6 torsion field spin connection 1-forms are the anti-symmetrized off-diagonal matrix elements
C^[a,b] = - C^[b,a]
Einstein's 1915 GR is the limit
C^[a,b] = 0
D = d + W^ac/\
e^a = I^a + C^a^a
The torsion 1-form is
T^a = De^a = 0
This determines the non-dynamical zero torsion spin connections W^ac from
de^a + W^ac/\e^c = 0
The curvature 2-form is
R^a^b = DW^a^b
The Einstein-Hilbert action density is
{a,b,c,d}R^a^b/\e^c/\e^d
and the rest is history.
See Rovelli Ch II for the details.
Plus it's obvious how to generalize for torsion.
So I have 8 0-form Goldstone phases from 9 real Higgs fields with vacuum manifold S^8.
This fits most naturally in terms of stable defects into a 9+1 D spacetime. Hey that's interesting. Where have we seen that before?
I want to compactify to 3 large space dimensions so I can use
A^2 = A^aAa
B^2 = B^aBa
take square roots.
And I am back to the Bekenstein world holography bits with point defects in the world crystal's spacelike slices. They are the "lattice points"!
"All very interesting, but I still don't see a mathematical proof of your contention that the LC connection defined on an arbitrary Riemannian manifold does not contain a tensor X_A = -Q_A for each torsion-free non-metric connection A."
Even if it did, who cares? Where's the new physics to that? Where's the beef?
The Question is: What should be The Question?
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
There are TWO GCT tensor pieces to AFFINE non-metricity and torsion, both are ZERO in GR, but torsion is not zero in the extended theory e.g. Shipov's.
You get the 4 Einstein-Cartan tetrad 1-forms e^a from locally gauging T4 in all actions. The warped part C^a^a of e^a are the spin 1 compensating gauge potentials where the gauge transformations are simply Einstein's GCTs that define the multi-linear "tensors."
The spin 2 affine connection in general is something like
A^wuv = e^wa(d/dx^u)e^av
Its quadratic in the fundamental spin 1 Yang-Mills fields from locally gauging the 4-parameter translation group T4 in all physical actions of special relativistic fields. That, BTW is a deep formulation of the equivalence principle.
In QM 1 + 1 = 2 + 1 + 0
so, in general, there are spin 2 tensor + spin 1 vector + spin 0 scalar quanta if you quantize this smooth c-number vacuum ODLRO "supersolid" emergent gravity theory.
The torsion connection tensor is
S^wuv = A^w[u,v]
S^wuv =/= 0 when we also locally gauge the 6-parameter Lorentz group SO(1,3) and this corresponds to the 6 1-forms C^[a,b] below in terms of the 8 0-form Goldstone phases of the 9 real component Higgs post-inflation scalar fields.
This is a generalization of the Jahn-Teller effect in a crystal I suppose? My paper with Marshall Stoneham 1967 at Harwell AERE + my 1969 PhD thesis on gauge fields and ODLRO in superfluids + my 1969 paper predicting the supersolid phase of Helium 4 that David Goodstein and Richard Feynman helped me with. I would drive up to Cal Tech from San Diego. Also my 1966 Landau-Ginzburg Mexican Hat potential model of self-trapped laser filaments paper that Ray Chiao said he read when he was doing his famous experiments on them at Berkeley.
The 6 dynamical torsion field spin connection 1-forms (not in 1915 GR) correspond to Gennady Shipov's 10-D oriented point test particle. Einstein's 1915 GR only has a 4D point test particle.
http://qedcorp.com/APS/Shipov.jpg
This picture from Shipov shows a primitive 6D Calabi-Yau "fiber" of string theory.
My 9 real Higgs fields fit most naturally into 9D spacelike slices with brane worlds corresponding to stable topological defects from non-trivial homotopy groups with quantized deRham integrals from single-valued Higgs fields as shown in general in the David Thouless book on topological methods in quantum theory.
Therefore, vacuum coherent ODLRO Higgs-Goldstone fields + local gauging of spacetime symmetries (AKA equivalence principle) seems to be the missing organizing idea of string theory. It's been there all the time right under their noses.
On Feb 28, 2007, at 2:16 AM, Paul Zielinski wrote:
"It looks like you are still thinking that the tensor part of LC is supposed to be the "non-metricity tensor of the Levi-Civita connection". Of course, the non-metricity of the LC connection is exactly zero.
The tensor part of LC is not this quantity. It is a tensor X = -Q_A that is equal to the negative of the non-metricity tensor of a different (i.e., non-metric) torsion-free affine connection A =/= LC, where
A = LC + Q_A, and Q_A =/= 0."
There is no physics to this. There is no way to measure Q_A independently. It's not GR. You cannot say you have a new way to reinterpret GR with this formal shell game.
"There is no question that the non-metricity tensor Q_LC of the LC connection is zero. However, it does not follow from this that the LC connection doesn't contain the tensor X = -Q_A."
1. Take the Schwarzschild metric
1. Compute X.
2. Show how to measure X independently.
Meantime all the cool stuff I showed you re: C^a^b went over your head.
Jack Sarfatti wrote:
On Feb 27, 2007, at 10:56 PM, Paul Zielinski wrote:
"OK Jack, fire away. Give me your best shot.
Here is a direct quote from Carroll:
'...any set of connections can be expressed as some fiducial connection plus a tensorial correction.' (Notes on General Relativity, p 59).
Now explain to us why this doesn't apply to the LC connection?"
I told you a jillion times. Read the rest of what he says!
"Clearly, a zero "correction" is no correction at all. For Carroll's statement to be non-trivial, the tensorial correction must be non-vanishing.
Yet you are saying, in effect, that in the case of the LC connection the tensorial correction is always exactly zero. I think you have to prove
this mathematically, in the abstract, without any appeal to any particular physical theory."
Irrelevant.
"So you are saying that this doesn't apply to the LC connection? Why not?"
Sean Carroll like many others points out that most generally
Affine = LC + Torsion + Nonmetricity
Affine = LC + Torsion + Nonmetricity of Affine
Torsion and non-metricity are GCT 3rd rank tensors.
"Right."
LC is not a tensor.
"Right."
GR is precisely that theory in the set of theories with different connections such that
Affine = LC
End of trivial story.
"No. It is a theory such that the metric-compatible affine connection LC, defined on a 4D spacetime manifold, is taken to represent the Einstein field. But this is also true in the alternative model.
None of this has anything to do with the purely mathematical question of whether the LC connection contains a tensor -Q_A for some torsion-free non-metric affine connection A."
Physically LC parallel transports vectors along worldlines. While maintaining the inner products of vectors constant during the parallel transport process. Going around a closed worldline the difference of orientation of the vector with itself is a measure of the average curvature over the area of the loop - shrunk to zero - i.e. crystal disclination defect.
"Right."
Limit of the ratio of angle deficit to area of shrinking loop is the sectional curvature dimensions 1/Area.
"OK."
If there is non-metricity the length of the vector will also change in the parallel transport and in a loop you will get a discrepancy in lengths of the vector unless you impose a kind of Bohr-Sommerfeld quantization on the closed loop.
"Exactly. But this has nothing to do with coordinate curvilinearity or with Riemann curvature."
If there is torsion starting with two sides of an infinitesimal parallelogram and parallel transporting one against the other both ways the loop does not close to second order - there is a torsion gap, i.e. crystal dislocation defect.
"Right. If the connection is torsion-free this doesn't happen."
In my theory you have a set of 0-forms the Goldstone phases of the vacuum coherence ODLRO Higgs field.
From the 0-forms comes a set of 1-forms.
There are 10 1-forms.
4 tetrad 1-forms & 6 spin connection 1-forms.
Then you have GR + torsion trivially.
i.e. a theory with
A = LC + Torsion Tensor
beyond 1915 GR of course.
dO-form = 1-form
d^2)-form = 0
However that 1-form need not be exact if the 0-form has a singularity, i.e.
Integral of the 1-form over a non-bounding 1-cycle without boundary = winding number integer
Bohr-Sommerfeld condition from non-trivial 1-homotopy.
Then you can pretend Stoke's theorem works, i.e. flux without flux beyond Wheeler's "charge without charge" - these are 1D string vortex defects.
The integral of the 1-form around the loop is the surface integral of a ghostly 2-form flux through the area of the loop. This is related to the Bohm-Aharonov effect.
Similarly given 2 0-forms A & B, I define the non-closed 1-form as
C = dA/\B - A/\dB 1-form
dC = 2dA/\dB =/= 0 2-form
I can now play the same game one dimension higher! These are 0D point monopole stable defects.
Now we have star gate wormholes!
The mouth of the wormhole is the non-bounding 2-cycle without boundary - the portal like they see on the Skinwalker Ranch!
The deRham integral of 2-form C over the closed 2-surface is now an integer wrapping number ~ Bekenstein BITS for the entropy of black hole event horizons, de Sitter dark energy future observer horizons, Unruh effect, Hawking radiation, you name it. I got it all topologically pre-metrically.
There is again the world hologram ghostly volume 3-form without volume from the actual hologram area 2-form dC.
OK everything I need comes from C as the template.
C^a^b = dA^a/\B^b - A^a/\dB^b
The 4 Einstein curvature tetrad 1-forms are the diagonal matrix elements
C^a^a
The 6 torsion field spin connection 1-forms are the anti-symmetrized off-diagonal matrix elements
C^[a,b] = - C^[b,a]
Einstein's 1915 GR is the limit
C^[a,b] = 0
D = d + W^ac/\
e^a = I^a + C^a^a
The torsion 1-form is
T^a = De^a = 0
This determines the non-dynamical zero torsion spin connections W^ac from
de^a + W^ac/\e^c = 0
The curvature 2-form is
R^a^b = DW^a^b
The Einstein-Hilbert action density is
{a,b,c,d}R^a^b/\e^c/\e^d
and the rest is history.
See Rovelli Ch II for the details.
Plus it's obvious how to generalize for torsion.
So I have 8 0-form Goldstone phases from 9 real Higgs fields with vacuum manifold S^8.
This fits most naturally in terms of stable defects into a 9+1 D spacetime. Hey that's interesting. Where have we seen that before?
I want to compactify to 3 large space dimensions so I can use
A^2 = A^aAa
B^2 = B^aBa
take square roots.
And I am back to the Bekenstein world holography bits with point defects in the world crystal's spacelike slices. They are the "lattice points"!
"All very interesting, but I still don't see a mathematical proof of your contention that the LC connection defined on an arbitrary Riemannian manifold does not contain a tensor X_A = -Q_A for each torsion-free non-metric connection A."
Even if it did, who cares? Where's the new physics to that? Where's the beef?
The Question is: What should be The Question?
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
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