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
Thursday, March 22, 2007
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
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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€
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 doesn’t get it?
How is that possible?
“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 “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 “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 “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 “monopole†defects in
3D space.
A single Goldstone phase has two real Higgs fields with stable
quantized (winding integers) line “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.
Stoke’s Theorem
The deRahm integral of a p-form on a p-cycle (without boundary)
equals the p-form’s 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 “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 “holes†where the 3 real Higgs fields
all vanish so that the 2 compacted Goldstone phases are undefined, is
quantized.
Volume without volume
Although Stoke’s 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 “oriented
point†(suggesting “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.
Shipov’s 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 “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 “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.
>
> “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 doesn’t
> address.
>
> “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. “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. “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.
>
> “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 NMSSM’s 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.
>
> “The LHC and ILC have the capability of finding the charginos
> predicted by supersymmetric theories, depending on the chargino
> masses,†Tandean said. “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. “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€
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 doesn’t get it?
How is that possible?
“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 “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 “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 “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 “monopole†defects in
3D space.
A single Goldstone phase has two real Higgs fields with stable
quantized (winding integers) line “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.
Stoke’s Theorem
The deRahm integral of a p-form on a p-cycle (without boundary)
equals the p-form’s 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 “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 “holes†where the 3 real Higgs fields
all vanish so that the 2 compacted Goldstone phases are undefined, is
quantized.
Volume without volume
Although Stoke’s 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 “oriented
point†(suggesting “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.
Shipov’s 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 “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 “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.
>
> “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 doesn’t
> address.
>
> “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. “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. “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.
>
> “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 NMSSM’s 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.
>
> “The LHC and ILC have the capability of finding the charginos
> predicted by supersymmetric theories, depending on the chargino
> masses,†Tandean said. “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. “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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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."
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