Alleged Advances in Exotic Torsion Field Propulsion in Russia
Akimov in Moscow, and others even more recently connected with Russian Intelligence, has made many claims on the weapons related applications of Gennady Shipov's torsion field theory.
http://www.shipov.com
We were tasked (with plausible denial) at ISSO Science 1999-2000 by USG Intelligence to evaluate the threat potential of these allegations. We had a budget of several million dollars to explore a few different avenues on how the alien ET flying saucers were powered with Shipov's theory as the main contender followed by Jim Corum's. To that end we invited Gennady Shipov from Moscow to San Francisco more than once including such experts as R. Kiehn (Strategic Air Command retired), R. Hammond, Hal Puthoff, Bernie Haisch, J.P. Vigier, Bill Page, Vladimir Poponin, Saul-Paul Sirag, John Brandenburg, John Dering and others under Creon Levit's project management of the Task Force. Creon on leave from NASA Ames.
Our results were inconclusive at the time primarily because we did not understand the key role that dark energy would play. The dark energy was only then beginning to be discovered in 1999 - 2000 and its relevance to Shipov's torsion field theory did not become clear to me until the end of 2002.
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
Now at the beginning of 2007 it is obvious to me that Akimov's claims must be taken seriously in a general way noting that specifics may be disinformation i.e. truth wrapped in a bodyguard of lies.
Shipov's theory has been debunked by unknown Russians using false names. The debunking does not hold up under close analysis and is essentially polemics without substance. The theoretical background for Shipov's theory is respectable starting with T.W.B. Kibble's 1961 paper that derives Einstein's 1915 theory of curvature only plus the Russian torsion field from the battle-tested principle of local gauge invariance on the 10-parameter special relativity Poincare space-time symmetry group that all non-gravity field actions must be invariant under. Kibble showed that the compensating gauge potentials were 16 warped spin 1 tetrad field components for the curvature from locally gauging the 4-parameter translation subgroup alone plus 24 spin connection components for the Russian torsion fields from locally gauging the 6-parameter Lorentz subgroup of the Poincare group. One gets non-dynamical spin connections for the curvature rotations of vectors around shrinking closed loops without torsion gaps to second order from the 16 tetrad components alone. However, there are no independent torsion field in that case from which it follows that the Einstein cosmological constant for the observed cosmic repulsive dark energy must really be constant and uniform in that limit. That would preclude bottling the dark energy for weightless warp drive and star gate wormhole time machines. For the latter metric engineering of Kaku's higher type civilizations whose saucers we see in our skies we need the Russian torsion fields IMHO.
The Shipov theory is a pre-string theory because the 4 coordinates of the center of mass of an extended test particle, which is all that we have in Einstein's 1915 GR of curvature alone, is supplemented by 6 new angular coordinates of 4D orientation like a relativistic rigid body. These 6 new anholonomic degrees of freedom lead to Calabi-Yau space of string theory after the additional step of making the extended test body non-rigid with local vibrations that are essentially the compensating torsion fields.
Shipov postulates an additional constraint of teleparallelism i.e. the total 10D curvature is zero. This gives a relationship between the 6D torsion fields and the 4D curvature. However, I am not yet sure if we need this constraint or even if it is consistent. I simply do not know yet. I see problems with it. More on that later as tonite is New Years Eve and I have to meet some people shortly. It's almost 10 PM in San Francisco.
On Dec 31, 2006, at 8:19 PM, Jack Sarfatti wrote:
To make this clearer.
"curvilinear" means pure 100% local frame-dependent inertial force effect from non-geodesic motion of the local detectors that define the local frames. In this case there is always a non-gravity force pushing the massive on-mass-shell detector off its natural timelike geodesic inside the local light cone.
"warp" means either intrinsic objective local frame invariant curvature or torsion or both.
There are two kinds of curvature "Ricci" + "Weyl conformal"
Ricci contraction & expansion from a local non-gravity source including virtual zero point quanta of non-gravity fields i.e. both dark energy of negative pressure and dark matter of positive pressure. The latter has w = -1 in isotropic distribution but seen from a distance it gravity lenses light rays just like w = 0 CDM.
Weyl conformal stretch-squeeze. Gravity waves are ripples in the Weyl tensor.
ds^2 = guv(curvilinear + warp)dx^udx^v = (I^a(curvilinear) + A^a(warp))((Ia(curvilinear) + Aa(warp))
Note the cross term between inertial force and intrinsic warp effects. Since the geometrodynamic connection field is essentially for the spin 1 renormalizable e^a fields
e^a(d/dx^u)e^b
it's obvious that one cannot eliminate the cross terms between inertial forces and intrinsic warps at the spin 0,1, 2 geometrodynamic level. Therefore, Zielinski's claim that the 1915 GR symmetric zero torsion LC connection splits into
(LC) = (LC|non-tensor inertial force) + (LC|tensor warp force)
with
(LC|tensor warp force) =/= 0
is obviously false. The real situation is
(LC) = (LC|non-tensor inertial force) + (LC|tensor warp force) + (LC|tensor warp-inertial force)
with
(LC|tensor warp force) = 0
because by going to local geodesic coordinates both
(LC|non-tensor inertial force) -> 0
(LC|tensor warp-inertial force) -> 0
separately and independently
and the total (LC) -> 0 from the equivalence principle.
However a tensor = 0 in all components is a local frame-invariant property.
This completes the proof refuting Zielinski's conjecture.
On Dec 31, 2006, at 7:27 PM, Jack Sarfatti wrote:
Zielinski wrote incorrectly crossing out my correct equation:
Fine.
>
> F^aFa torsion field Lagrangian density is local in this Minkowskiab
> space.
>
> Note that the geometrodynamics will still be nonlocal I think.!
Meaning what exactly?
>
> ds^2 = guvdx^udx^v = e^aea = (Minkowski)abe^ae^b
There is no such relationship between the Minkowski and Riemann
metrics. All you can say, even in a completely flat spacetime, is that
at any giv! en space time point both metrics have the same matrix value
*in Lorentz coordinates*.
ds^2 = guv(curvilinear)dx^udx^v = e^aea = (Minkowski) abe^ae^b
is exact and it is local FRAME invariant.
On Dec 31, 2006, at 6:56 PM, Jack Sarfatti wrote:
It is not possible to define it inside of 1915 GR as anything other than zero.
I gave the proof that you cannot follow. It can be non-zero in Shipov's theory
BUT there will still be a NONLOCAL component even then.
i.e.
Weyl curvature part of gravity vacuum energy is nonlocal, i.e. zero local density yet non-zero global integral even when there is a non-zero local torsion field contribution from FaF^a in the Lagrangian density where
F^a = de^a + W^ac/\e^a
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
Sunday, December 31, 2006
Refuting Zielinski's Conjecture
On Dec 31, 2006, at 7:27 PM, Jack Sarfatti wrote:
Zielinski wrote incorrectly crossing out my correct equation:
"Fine."
>
> F^aFa torsion field Lagrangian density is local in this Minkowskiab
> space.
>
> Note that the geometrodynamics will still be nonlocal I think.
"Meaning what exactly?"
>
> ds^2 = guvdx^udx^v = e^aea = (Minkowski)abe^ae^b
"There is no such relationship between the Minkowski and Riemann
metrics. All you can say, even in a completely flat spacetime, is that
at any giv! en space time point both metrics have the same matrix value
*in Lorentz coordinates*."
On the contrary,
ds^2 = guv(curvilinear)dx^udx^v = e^aea = (Minkowski) abe^ae^b
is exact and it is local FRAME invariant.
On Dec 31, 2006, at 6:56 PM, Jack Sarfatti wrote:
It is not possible to define it inside of 1915 GR as anything other than zero.
I gave the proof that you cannot follow. It can be non-zero in Shipov's theory BUT there will still be a NONLOCAL component even then.
i.e.
Weyl curvature part of gravity vacuum energy is nonlocal, i.e. zero local density yet non-zero global integral even when there is a non-zero local torsion field contribution from FaF^a in the Lagrangian density where
F^a = de^a + W^ac/\e^aTo make this clearer.
"curvilinear" means pure 100% local frame-dependent inertial force effect from non-geodesic motion of the local detectors that define the local frames. In this case there is always a non-gravity force pushing the massive on-mass-shell detector off its natural timelike geodesic inside the local light cone.
"warp" means either intrinsic objective local frame invariant curvature or torsion or both.
There are two kinds of curvature "Ricci" + "Weyl conformal"
Ricci contraction & expansion from a local non-gravity source including virtual zero point quanta of non-gravity fields i.e. both dark energy of negative pressure and dark matter of positive pressure. The latter has w = -1 in isotropic distribution but seen from a distance it gravity lenses light rays just like w = 0 CDM.
Weyl conformal stretch-squeeze. Gravity waves are ripples in the Weyl tensor.
ds^2 = guv(curvilinear + warp)dx^udx^v = (I^a(curvilinear) + A^a(warp))((Ia(curvilinear) + Aa(warp))
Note the cross term between inertial force and intrinsic warp effects. Since the geometrodynamic connection field is essentially for the spin 1 renormalizable e^a fields
e^a(d/dx^u)e^b
it's obvious that one cannot eliminate the cross terms between inertial forces and intrinsic warps at the spin 0,1, 2 geometrodynamic level. Therefore, Zielinski's claim that the 1915 GR symmetric zero torsion LC connection splits into
(LC) = (LC|non-tensor inertial force) + (LC|tensor warp force)
with
(LC|tensor warp force) =/= 0
is obviously false. The real situation is
(LC) = (LC|non-tensor inertial force) + (LC|tensor warp force) + (LC|tensor warp-inertial force)
with
with
(LC|tensor warp force) = 0
because by going to local geodesic coordinates both
(LC|non-tensor inertial force) -> 0
(LC|tensor warp-inertial force) -> 0
separately and independently
and the total (LC) -> 0 from the equivalence principle.
However a tensor = 0 in all components is a local frame-invariant property.
This completes the proof refuting Zielinski's conjecture.
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 Dec 31, 2006, at 7:27 PM, Jack Sarfatti wrote:
Zielinski wrote incorrectly crossing out my correct equation:
"Fine."
>
> F^aFa torsion field Lagrangian density is local in this Minkowskiab
> space.
>
> Note that the geometrodynamics will still be nonlocal I think.
"Meaning what exactly?"
>
> ds^2 = guvdx^udx^v = e^aea = (Minkowski)abe^ae^b
"There is no such relationship between the Minkowski and Riemann
metrics. All you can say, even in a completely flat spacetime, is that
at any giv! en space time point both metrics have the same matrix value
*in Lorentz coordinates*."
On the contrary,
ds^2 = guv(curvilinear)dx^udx^v = e^aea = (Minkowski) abe^ae^b
is exact and it is local FRAME invariant.
On Dec 31, 2006, at 6:56 PM, Jack Sarfatti wrote:
It is not possible to define it inside of 1915 GR as anything other than zero.
I gave the proof that you cannot follow. It can be non-zero in Shipov's theory BUT there will still be a NONLOCAL component even then.
i.e.
Weyl curvature part of gravity vacuum energy is nonlocal, i.e. zero local density yet non-zero global integral even when there is a non-zero local torsion field contribution from FaF^a in the Lagrangian density where
F^a = de^a + W^ac/\e^aTo make this clearer.
"curvilinear" means pure 100% local frame-dependent inertial force effect from non-geodesic motion of the local detectors that define the local frames. In this case there is always a non-gravity force pushing the massive on-mass-shell detector off its natural timelike geodesic inside the local light cone.
"warp" means either intrinsic objective local frame invariant curvature or torsion or both.
There are two kinds of curvature "Ricci" + "Weyl conformal"
Ricci contraction & expansion from a local non-gravity source including virtual zero point quanta of non-gravity fields i.e. both dark energy of negative pressure and dark matter of positive pressure. The latter has w = -1 in isotropic distribution but seen from a distance it gravity lenses light rays just like w = 0 CDM.
Weyl conformal stretch-squeeze. Gravity waves are ripples in the Weyl tensor.
ds^2 = guv(curvilinear + warp)dx^udx^v = (I^a(curvilinear) + A^a(warp))((Ia(curvilinear) + Aa(warp))
Note the cross term between inertial force and intrinsic warp effects. Since the geometrodynamic connection field is essentially for the spin 1 renormalizable e^a fields
e^a(d/dx^u)e^b
it's obvious that one cannot eliminate the cross terms between inertial forces and intrinsic warps at the spin 0,1, 2 geometrodynamic level. Therefore, Zielinski's claim that the 1915 GR symmetric zero torsion LC connection splits into
(LC) = (LC|non-tensor inertial force) + (LC|tensor warp force)
with
(LC|tensor warp force) =/= 0
is obviously false. The real situation is
(LC) = (LC|non-tensor inertial force) + (LC|tensor warp force) + (LC|tensor warp-inertial force)
with
with
(LC|tensor warp force) = 0
because by going to local geodesic coordinates both
(LC|non-tensor inertial force) -> 0
(LC|tensor warp-inertial force) -> 0
separately and independently
and the total (LC) -> 0 from the equivalence principle.
However a tensor = 0 in all components is a local frame-invariant property.
This completes the proof refuting Zielinski's conjecture.
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
Saturday, December 30, 2006
Nonlocality of the gravity energy in Einstein's 1915 theory
"It's not my model. And as to "cash value", I think you are forgetting
the value of a fully covariant vacuum energy density." Paul Zielinski
There is no value to that in 1915 GR. It contradicts the equivalence principle. That the founding fathers, including Einstein, were confused on this issue is a fact. Whether you can do it in a larger theory is still not settled. Carmelli has a fairly good discussion of this issue. When there is no agreement on something like this for decades, it shows there is something wrong with the formulation of the question. I think ... asked the wrong question. He is not stupid of course.
If one stays at the tetrad level and gets a spin 1 Fuv with Lagrangian ~ F^u^vFuv then that energy density will be local perhaps because the effective metric is Minkowski there! The geometrodynamics is derivative and it's gravity energy is still nonlocal!
That is
e^a = 1^a(flat) + A^a(warped)
F^a = dA^a + W^ac/\A^a = Shipov's TORSION FIELD =/= 0 beyond Einstein's 1915 GR
Note in Einstein's theory this is strictly zero,
F^a = 0 in Einstein's 1915 GR, but not in Shipov's torsion theory.
therefore, the local gravity field energy is strictly zero, but the total gravity energy is not zero. Therefore in Einstein 1915 the non-zero gravity energy is NONLOCAL.
Now this is a rigorous proof as good as anything in Euclid's Elements!
DF^a = 0
D*F^a = *J^a
D*J^a = 0
i.e. essentially a Yang-Mills theory
F^aFa torsion field Lagrangian density is local in this Minkowskiab space.
Note that the geometrodynamics will still be nonlocal I think.
ds^2 = guvdx^udx^v = e^aea = (Minkowski)abe^ae^b
R^a^b(curvature) = dW^a^b + W^ac/\W^c^b
Einstein-Hilbert Lagrangian vacuum density for L(matter) = 0 & /\(dark energy) = 0, i.e. no Ricci local sources is
*R^a^b/\e^c/\e^h
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 Dec 30, 2006, at 2:23 PM, Paul Greenberg wrote:
--- In Sarfatti_Physics_Seminars@yahoogroups.com, Jack Sarfatti
wrote:
>
> Your inertial compensation model is bad physics of no value inside
> the strict domain of Einstein 1915 limiting case.
It's not my model. And as to "cash value", I think you are forgetting
the value of a fully covariant vacuum energy density.
If you think this to be of no value, then you are not in the
mainstream. Just about everyone in gravitational physics acknowledges
the value of a covariant vacuum energy density. The only disagreement
is whether such a quantity can be defined within the formal-empirical
framework of 1915 GR. I say that it can, if Einstein's "strict
equivalence principle" is relaxed.
> It may have some value in Shipov's torsion theory extension of GR,
> but even there I have my doubts if Gennady's interpretation along
> those lines is consistent. I am still thinking about it.
"It's not my model. And as to "cash value", I think you are forgetting
the value of a fully covariant vacuum energy density." Paul Zielinski
There is no value to that in 1915 GR. It contradicts the equivalence principle. That the founding fathers, including Einstein, were confused on this issue is a fact. Whether you can do it in a larger theory is still not settled. Carmelli has a fairly good discussion of this issue. When there is no agreement on something like this for decades, it shows there is something wrong with the formulation of the question. I think ... asked the wrong question. He is not stupid of course.
If one stays at the tetrad level and gets a spin 1 Fuv with Lagrangian ~ F^u^vFuv then that energy density will be local perhaps because the effective metric is Minkowski there! The geometrodynamics is derivative and it's gravity energy is still nonlocal!
That is
e^a = 1^a(flat) + A^a(warped)
F^a = dA^a + W^ac/\A^a = Shipov's TORSION FIELD =/= 0 beyond Einstein's 1915 GR
Note in Einstein's theory this is strictly zero,
F^a = 0 in Einstein's 1915 GR, but not in Shipov's torsion theory.
therefore, the local gravity field energy is strictly zero, but the total gravity energy is not zero. Therefore in Einstein 1915 the non-zero gravity energy is NONLOCAL.
Now this is a rigorous proof as good as anything in Euclid's Elements!
DF^a = 0
D*F^a = *J^a
D*J^a = 0
i.e. essentially a Yang-Mills theory
F^aFa torsion field Lagrangian density is local in this Minkowskiab space.
Note that the geometrodynamics will still be nonlocal I think.
ds^2 = guvdx^udx^v = e^aea = (Minkowski)abe^ae^b
R^a^b(curvature) = dW^a^b + W^ac/\W^c^b
Einstein-Hilbert Lagrangian vacuum density for L(matter) = 0 & /\(dark energy) = 0, i.e. no Ricci local sources is
*R^a^b/\e^c/\e^h
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 Dec 30, 2006, at 2:23 PM, Paul Greenberg wrote:
--- In Sarfatti_Physics_Seminars@yahoogroups.com, Jack Sarfatti
>
> Your inertial compensation model is bad physics of no value inside
> the strict domain of Einstein 1915 limiting case.
It's not my model. And as to "cash value", I think you are forgetting
the value of a fully covariant vacuum energy density.
If you think this to be of no value, then you are not in the
mainstream. Just about everyone in gravitational physics acknowledges
the value of a covariant vacuum energy density. The only disagreement
is whether such a quantity can be defined within the formal-empirical
framework of 1915 GR. I say that it can, if Einstein's "strict
equivalence principle" is relaxed.
> It may have some value in Shipov's torsion theory extension of GR,
> but even there I have my doubts if Gennady's interpretation along
> those lines is consistent. I am still thinking about it.
Thursday, December 28, 2006
Spinor Qubits in Curved Space-Time
The basic spinor qubits here that are square roots of null world vectors are not directly in the quantum Hilbert space of Bohm's pilot waves guiding extended test particles that can be thought of as little wormholes complementary to strings and membranes. Consult R. Wald for the complex details of getting the Hilbert space irreducible representations of the globally flat Poincare group for quantum theory in any interpretation.
The Penrose spinors rely on the fact that the Lie algebra of the globally rigid 10-parameter Poincare group specify 10 Killing vector field isometries - not so simple in general relativity's fields of curvature (Ricci contraction/expansion from matter/ZPF & Weyl vacuum tidal stretch-squeeze) and beyond to torsionic fields where this Poincare group is locally gauged to get 16 non-trivial tetrads and 24 non-trivial spin connections as dynamical compensating gauge potentials.
The spinors in curved base space-time live in the local tangent fibers not in the base space-time. That is, given the 4 Einstein-Cartan 1-forms e^a
e^A^A' = e^a(Sigma)a^A^A' all in the (co)tangent fiber.
The topology of spacetime has profound restrictions on the definition of global spinor field in curved and possibly torsioned spacetime - a non-trivial complicated subject. 13.2 The parallel transport of spinors is defined in terms of its null field flag tensor F. Suppressing these subtle points on topology for now, one can construct the spinor covariant derivative DAA' corresponding to Einstein's 1915 torsion-free theory. Given any Penrose spinor qubit |C>
(DAA'DBB' - DBB'DAA')|C> = ChiAA'BB'C^J|J>
The spinor square root of Einstein's 1915 GR curvature tensor is then the 4-qubit string
RAA'BB'CC'^JJ' = ChiAA'BB'C^JE*C'^J' + Chi*AA'BB'C'^J'EmC^J
Chi splits into 3 pieces (13.2.24) p. 371
Similarly R splits into a Weyl vacuum + Ricci contracted source + Ricci scalar.
The Ricci contraction spinor is independent of the Weyl vacuum spinor.
Newman-Penrose do not use the usual Einstein-Cartan tetrad orthonormal basis with 1 timelike and 3 spacelike tetrads. They use this Penrose spinor basis where
= 0
= = 0
They replace the 24 real spin connections by 12 complex ones. Local gauging of O(1,3) implicit, i.e. Shipov's torsionic field.
They have a special "complex null tetrad" basis
|l^A^A'*> = |A+>|A'+>* retarded future light cone
= 0 null tetrad
similarly for null
|n^A^A*> = |A->|A'->* advanced RETRO-CAUSAL past light cone
with two spacelike tetrads
|m^A^A'> = |A+>|A'-*>
|m^A^A'>* = |A'+*>|A->
|x^A^A'> = (1/2)^1/2[|A'+>*|A-> + |A+>|A'-*>] spin triplet S = 1 Sz = 0 analog
|y^A^A'> = i(1/2)^1/2[|A'+>*|A-> = |A+>|A'-*>] spin singlet S = 0 Sz = 0 analog
The Weyl vacuum stretch-squeeze gravity wave spinor is the symmetrized product of 4 principal null spinors
|A>|B>|C>|J>
|A> can repeat 2,3,4 times.
What about fields with a given rest mass m and spin in globally flat Minkowski spacetime with zero real intrinsic curvature?
The STRICT EQUIVALENCE PRINCIPLE demands MINIMAL COUPLING i.e. use covariant DAA'.
The local spinor currents are no longer conserved - same problem of the stress-energy of the pure gravity field that must be nonlocal. There is no well-posed initial value problem for spin > 1 p. 375. This is why it's better to use renormalizable spin 1 curved tetrad fields and then get spin 2, 1, 0 effects from entangled 1 + 1 = 2,1,0 pairs. For zero rest mass, initial value problem is well posed only for spin 1/2 & spin 1 in curved 3+1 spacetime. This is fine for my theory of gravity emergent from vacuum ODLRO which provides m =/= 0 from ODLRO itself. All basic fields are massless.
On Dec 28, 2006, at 12:23 PM, Jack Sarfatti wrote:
http://www.people.cornell.edu/pages/gnl2/cave.htm
13.1 on Robert Wald's "General Relativity" has a nice discussion of measurement theory in general relativity in terms of "families of observers" that agrees with what I say below on the distinction between local objective invariants (Platonic forms, Jungian Archetypes) and their observer-dependent subjective faithful representations and provides more details.
Diffeomorphisms are not physical, they are too general with tremendous gauge freedom redundancy. We only want their sub Lie group of isometries ("Killing" (man's name) vector fields) so that different observers can meaningfully compare their subjective data, put it into the machine and crank out the same local invariants from the theory. Their goal is each to get the same set of real numbers for observations of equivalent happenings.
"when (and only when) Diff(4) is an isometry, we can use [it] ... to map our original family of physical observers associated with the [tetrads e^a] into a new family of observers associated with [tetrads e^a'] ..." p. 343.
"Here upon we're all agreed all that we two will agree to. To entrust you in The Art, elemental, fundamental ..." W.S. Gilbert, Yeoman of the Guard
Given a set of tetrad 1-forms e^a then as spinors we have
e^AA' = e^a(Newman-Penrose)a^AA'
Each A index = 0,1 is 1 qubit
for this
IT FROM QUBIT
e^BB' = I^BB(flat)' + A(warped)^BB'
Now we come to a strange miracle - the Bell quantum teleportation pair states appear.
Use qubit |A+> of Wald type (0,1;0,0) & qubit |A'->of Wald type (0,0;0,1) (p. 347) each in 2 complex dimensions.
Then, for special relativity, space-time AKA emerges from 2-qubit strings |A> & |A'>.
First take the local diagonal at the same local objective IT coincidence P = P', the space-time operators are entangled 2-qubit strings in 4 complex dimensions, i.e., spinor tensors of type (0,1;0,1) in Wald's notation Ch 13). Thus, we have the pair entangled qubit states
|t^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)+> + |A(P)->|A'(P)->]
Note |t^0^0'>, |t^0^1'>, |t^1^0'> |t^1^1'> span 4 complex dimensions. Similarly for
|x^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)-> + |A(P)->|A'(P)+>]
|y^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)-> - |A(P)->|A'(P)+>]
|z^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)+> - |A(P)->|A'(P)->]
We can generalize the above to the non-local pair states
|t^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')+> + |A(P)->|A'(P')->]
|x^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')-> + |A(P)->|A'(P')+>]
|y^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')-> - |A(P)->|A'(P')+>]
|z^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')+> - |A(P)->|A'(P')->]
We may need to put a path-dependent anholonomic propagator U(P<--->P') here, one for each homotopy equivalence class of paths <---> homotopic to each other from topological obstructions like black hole event horizons and observer dependent horizons in dark energy dominates deSitter space-time.
Below everything is local on the diagonal P = P' for Einstein's "local coincidences" defined by Rovelli in Ch II of his 'Quantum Gravity."
guv ---> gAA'BB' = EABE*A'B" (13.1.15) p. 349 Wald's GR
|EAB> = |A+>|B-> - |A->|B+> = -|EBA>
where = = 1
= = 0 i.e. these qubits have a null inner product that cannot be interpreted as in quantum Hilbert space. That is a differently defined product with complex conjugates. My use of the Dirac bra-ket for e-mail convenience may not be the best here because it can lead to that confusion.
Choose the following canonical basis with components (A), (B) etc. The 2x2 "basis" matrices are
E(A)(B)11 = 0
E(A)(B)12 = 1
E(A)(B)21 = -1
E(A)(B)22 = 0
t^(A)^(A') = Pauli Spin Matrix(t) (with added factor -1/2^1/2)
x^(A)^(A') = Pauli Spin Matrix(x)
y^(A)^(A') = Pauli Spin Matrix(y)
z^(A)^(A') = Pauli Spin Matrix(z)
These 2x2 matrices do not commute, so we have a non-commutative geometry in spinor tensor space. They have the same formal Lie algebra of internal SU(2) of the weak force fiber even though they represent Minkowski spacetime base space.
Any globally flat Minkowski world vector first rank tensor can be represented as the second rank spinor (mod - 1/2^1/2) in a 2x2 matrix representation
V^A^A' = V^t Pauli Spin Matrix(t) + Vx Pauli Spin Matrix(t) + (13.1.29) p. 351 Wald
Lorentz transformations are SL(2C) similarity transformations in this notation.
These single qubit "potential" spinors map to null vectors on the light cone in globally flat Minkowski spacetime. The qubit is the square root of a null world vector V^^a^a', i.e.
|V^A^A'*> = |A+>|A'+>*
= 0
One can also make 2nd rank antisymmetric null world field tensors (AKA null bivectors).
F^A^A'^B^B' = |A>||B>E*^A'^B' + |A'>*||B'>*E^A^B
F^2 = 0
FV = 0
(indices understood) p. 352 Wald.
This null F defines the Penrose "null flag".
To include T4 translations we must extend SL(2,C) to ISL(2,C) covering the 10-parameter Poincare group whose local gauging in all non-gravity field actions i.e. equivalence principle gives curvature + torsion i.e. independent 16 non-trivial tetrad components and 24 antisymmetric spin connection components packaged into 4 tetrad 1-forms e^a and 6 spin-connection 1-forms W^a^b in tangent vector/cotangent form fibers.
Lie derivatives of spinor fields are only definable for Killing isometries. You cannot do it for a general Diff(4) p. 353 Wald.
Newman-Penrose components are using the 16 tetrad components
(Sigma)^aAA' = e^a0tAA' - e^a1xAA' - e^a2yAA' - e^a3zAA'
so this shows how to generalize to curved and torsioned spacetime!
to be continued.
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://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 Dec 26, 2006, at 1:00 PM, Jack Sarfatti wrote:
"The Question is: What is The Question?" John Archibald Wheeler
<12essa.1.jpg>
http://cecelia.physics.indiana.edu/p453/essays/quantum/wheeler.html
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_12_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_51_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_46_jpg.htm
The total energy of the universe is obviously not conserved in the standard model that fits observations to ~ 1% precision.
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_08_jpg.htm
The total w = -1 dark energy repulsive cosmic antigravity field accelerating the 3D space expansion of the universe is obviously not conserved. The total w = -1 dark energy content of our universe from Rocky Kolb's first slide above scales as a(t)^3.
The total w = 0 on-mass shell finite rest mass matter-energy is conserved scaling as a(t)^0 = 1.
The total zero rest mass w = +1/3 on light cone radiation energy is not conserved, it scales as a(t)^-1 -> zero from the cosmic redshift. Note that the chemical potential of radiation is zero, therefore there is no general global conservation law for radiation.
The general point here is that global space-time conservation laws are not fundamental unlike the local versions, which are satisfied e.g.
Tuv(matter)^;v = 0
locally in 1915 GR with the (LC) connection covariant partial derivative ;v.
Global conservation laws require
[Tuv(Matter) + tuv(Matter-Gravity)]^,v = 0
where ,v is the ordinary partial derivative.
This cannot be done in general in curved space-time with tuv(Matter-Gravity) as a kosher localized T4 tensor. tuv(Matter-Gravity) is a pseudo-tensor because in LNIF's the energy-momentum of the non-geodesic detectors powered by non-gravity forces makes a contribution to the vacuum gravity field that, by the equivalence principle, cannot be locally distinguished from the "real gravity field." Garbage in -> garbage out. Ask a stupid question, get a stupid answer. Trying to globally conserve total energy, trying to conserve total linear and angular momentum in a generally curved and torsioned spacetime is a stupid thing to try to do. We already know this from Noether's theorem. This is simply because the global Poincare group is locally gauged and all we can hope for is to locally conserve the total stress-energy current densities, which in fact is the case.
((-detguv)^1/2Tuv(matter))^,v + (-detguv)^1/2(LC(observer))u^v^wTvw(matter) = 0
Actual observations given above show that the total energy of the universe is not conserved. It's time to slay that Sacred Cow.
What the pure mathematicians, who lack physical understanding do not get, is that any representation of curved space-time guv is observer dependent i.e. relative to any conceivable network of ideal local observers on arbitrary worldlines inside the local light cone field. For example, in the non-rotating black hole outside the event horizon rs/r < 1
g00 = -1/g11 = 1 - rs/r
is only for that special class of static LNIF "shell" (J.A. Wheeler's term) observers at fixed r without orbital angular momentum. They need to fire rockets to stay in place. Note that warp drive "UFO" observers see a different metric field representation. What "Diff(4)" (local T4) frame shifts do is to connect different networks of local observers. That's the physical meaning of the abstract math missed by many of the formalists in the field. The local relation between objective reality and the observer's experience is
ds^2(objective observer invariant) = guv(observer dependent)dx^udx^v
= (Tetrad)^a(Tetrad)a
Space-time physics is local only because curved space-time is emergent from a local vacuum ODLRO world hologram Higgsian field with several coherent Goldstone phases that encode the 10^122 bits of our universe retrocausally from far future Omega to past Alpha at The Creation in our deSitter Universe.
http://qedcorp.com/APS/Adam.jpg
http://qedcorp.com/APS/desitter.jpg
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://lifeboat.com/ex/bios.jack.sarfatti
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
The basic spinor qubits here that are square roots of null world vectors are not directly in the quantum Hilbert space of Bohm's pilot waves guiding extended test particles that can be thought of as little wormholes complementary to strings and membranes. Consult R. Wald for the complex details of getting the Hilbert space irreducible representations of the globally flat Poincare group for quantum theory in any interpretation.
The Penrose spinors rely on the fact that the Lie algebra of the globally rigid 10-parameter Poincare group specify 10 Killing vector field isometries - not so simple in general relativity's fields of curvature (Ricci contraction/expansion from matter/ZPF & Weyl vacuum tidal stretch-squeeze) and beyond to torsionic fields where this Poincare group is locally gauged to get 16 non-trivial tetrads and 24 non-trivial spin connections as dynamical compensating gauge potentials.
The spinors in curved base space-time live in the local tangent fibers not in the base space-time. That is, given the 4 Einstein-Cartan 1-forms e^a
e^A^A' = e^a(Sigma)a^A^A' all in the (co)tangent fiber.
The topology of spacetime has profound restrictions on the definition of global spinor field in curved and possibly torsioned spacetime - a non-trivial complicated subject. 13.2 The parallel transport of spinors is defined in terms of its null field flag tensor F. Suppressing these subtle points on topology for now, one can construct the spinor covariant derivative DAA' corresponding to Einstein's 1915 torsion-free theory. Given any Penrose spinor qubit |C>
(DAA'DBB' - DBB'DAA')|C> = ChiAA'BB'C^J|J>
The spinor square root of Einstein's 1915 GR curvature tensor is then the 4-qubit string
RAA'BB'CC'^JJ' = ChiAA'BB'C^JE*C'^J' + Chi*AA'BB'C'^J'EmC^J
Chi splits into 3 pieces (13.2.24) p. 371
Similarly R splits into a Weyl vacuum + Ricci contracted source + Ricci scalar.
The Ricci contraction spinor is independent of the Weyl vacuum spinor.
Newman-Penrose do not use the usual Einstein-Cartan tetrad orthonormal basis with 1 timelike and 3 spacelike tetrads. They use this Penrose spinor basis where
They replace the 24 real spin connections by 12 complex ones. Local gauging of O(1,3) implicit, i.e. Shipov's torsionic field.
They have a special "complex null tetrad" basis
|l^A^A'*> = |A+>|A'+>* retarded future light cone
similarly for null
|n^A^A*> = |A->|A'->* advanced RETRO-CAUSAL past light cone
with two spacelike tetrads
|m^A^A'> = |A+>|A'-*>
|m^A^A'>* = |A'+*>|A->
|x^A^A'> = (1/2)^1/2[|A'+>*|A-> + |A+>|A'-*>] spin triplet S = 1 Sz = 0 analog
|y^A^A'> = i(1/2)^1/2[|A'+>*|A-> = |A+>|A'-*>] spin singlet S = 0 Sz = 0 analog
The Weyl vacuum stretch-squeeze gravity wave spinor is the symmetrized product of 4 principal null spinors
|A>|B>|C>|J>
|A> can repeat 2,3,4 times.
What about fields with a given rest mass m and spin in globally flat Minkowski spacetime with zero real intrinsic curvature?
The STRICT EQUIVALENCE PRINCIPLE demands MINIMAL COUPLING i.e. use covariant DAA'.
The local spinor currents are no longer conserved - same problem of the stress-energy of the pure gravity field that must be nonlocal. There is no well-posed initial value problem for spin > 1 p. 375. This is why it's better to use renormalizable spin 1 curved tetrad fields and then get spin 2, 1, 0 effects from entangled 1 + 1 = 2,1,0 pairs. For zero rest mass, initial value problem is well posed only for spin 1/2 & spin 1 in curved 3+1 spacetime. This is fine for my theory of gravity emergent from vacuum ODLRO which provides m =/= 0 from ODLRO itself. All basic fields are massless.
On Dec 28, 2006, at 12:23 PM, Jack Sarfatti wrote:
http://www.people.cornell.edu/pages/gnl2/cave.htm
13.1 on Robert Wald's "General Relativity" has a nice discussion of measurement theory in general relativity in terms of "families of observers" that agrees with what I say below on the distinction between local objective invariants (Platonic forms, Jungian Archetypes) and their observer-dependent subjective faithful representations and provides more details.
Diffeomorphisms are not physical, they are too general with tremendous gauge freedom redundancy. We only want their sub Lie group of isometries ("Killing" (man's name) vector fields) so that different observers can meaningfully compare their subjective data, put it into the machine and crank out the same local invariants from the theory. Their goal is each to get the same set of real numbers for observations of equivalent happenings.
"when (and only when) Diff(4) is an isometry, we can use [it] ... to map our original family of physical observers associated with the [tetrads e^a] into a new family of observers associated with [tetrads e^a'] ..." p. 343.
"Here upon we're all agreed all that we two will agree to. To entrust you in The Art, elemental, fundamental ..." W.S. Gilbert, Yeoman of the Guard
Given a set of tetrad 1-forms e^a then as spinors we have
e^AA' = e^a(Newman-Penrose)a^AA'
Each A index = 0,1 is 1 qubit
for this
IT FROM QUBIT
e^BB' = I^BB(flat)' + A(warped)^BB'
Now we come to a strange miracle - the Bell quantum teleportation pair states appear.
Use qubit |A+> of Wald type (0,1;0,0) & qubit |A'->of Wald type (0,0;0,1) (p. 347) each in 2 complex dimensions.
Then, for special relativity, space-time AKA emerges from 2-qubit strings |A> & |A'>.
First take the local diagonal at the same local objective IT coincidence P = P', the space-time operators are entangled 2-qubit strings in 4 complex dimensions, i.e., spinor tensors of type (0,1;0,1) in Wald's notation Ch 13). Thus, we have the pair entangled qubit states
|t^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)+> + |A(P)->|A'(P)->]
Note |t^0^0'>, |t^0^1'>, |t^1^0'> |t^1^1'> span 4 complex dimensions. Similarly for
|x^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)-> + |A(P)->|A'(P)+>]
|y^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)-> - |A(P)->|A'(P)+>]
|z^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)+> - |A(P)->|A'(P)->]
We can generalize the above to the non-local pair states
|t^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')+> + |A(P)->|A'(P')->]
|x^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')-> + |A(P)->|A'(P')+>]
|y^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')-> - |A(P)->|A'(P')+>]
|z^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')+> - |A(P)->|A'(P')->]
We may need to put a path-dependent anholonomic propagator U(P<--->P') here, one for each homotopy equivalence class of paths <---> homotopic to each other from topological obstructions like black hole event horizons and observer dependent horizons in dark energy dominates deSitter space-time.
Below everything is local on the diagonal P = P' for Einstein's "local coincidences" defined by Rovelli in Ch II of his 'Quantum Gravity."
guv ---> gAA'BB' = EABE*A'B" (13.1.15) p. 349 Wald's GR
|EAB> = |A+>|B-> - |A->|B+> = -|EBA>
where
Choose the following canonical basis with components (A), (B) etc. The 2x2 "basis" matrices are
E(A)(B)11 = 0
E(A)(B)12 = 1
E(A)(B)21 = -1
E(A)(B)22 = 0
t^(A)^(A') = Pauli Spin Matrix(t) (with added factor -1/2^1/2)
x^(A)^(A') = Pauli Spin Matrix(x)
y^(A)^(A') = Pauli Spin Matrix(y)
z^(A)^(A') = Pauli Spin Matrix(z)
These 2x2 matrices do not commute, so we have a non-commutative geometry in spinor tensor space. They have the same formal Lie algebra of internal SU(2) of the weak force fiber even though they represent Minkowski spacetime base space.
Any globally flat Minkowski world vector first rank tensor can be represented as the second rank spinor (mod - 1/2^1/2) in a 2x2 matrix representation
V^A^A' = V^t Pauli Spin Matrix(t) + Vx Pauli Spin Matrix(t) + (13.1.29) p. 351 Wald
Lorentz transformations are SL(2C) similarity transformations in this notation.
These single qubit "potential" spinors map to null vectors on the light cone in globally flat Minkowski spacetime. The qubit is the square root of a null world vector V^^a^a', i.e.
|V^A^A'*> = |A+>|A'+>*
One can also make 2nd rank antisymmetric null world field tensors (AKA null bivectors).
F^A^A'^B^B' = |A>||B>E*^A'^B' + |A'>*||B'>*E^A^B
F^2 = 0
FV = 0
(indices understood) p. 352 Wald.
This null F defines the Penrose "null flag".
To include T4 translations we must extend SL(2,C) to ISL(2,C) covering the 10-parameter Poincare group whose local gauging in all non-gravity field actions i.e. equivalence principle gives curvature + torsion i.e. independent 16 non-trivial tetrad components and 24 antisymmetric spin connection components packaged into 4 tetrad 1-forms e^a and 6 spin-connection 1-forms W^a^b in tangent vector/cotangent form fibers.
Lie derivatives of spinor fields are only definable for Killing isometries. You cannot do it for a general Diff(4) p. 353 Wald.
Newman-Penrose components are using the 16 tetrad components
(Sigma)^aAA' = e^a0tAA' - e^a1xAA' - e^a2yAA' - e^a3zAA'
so this shows how to generalize to curved and torsioned spacetime!
to be continued.
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://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 Dec 26, 2006, at 1:00 PM, Jack Sarfatti wrote:
"The Question is: What is The Question?" John Archibald Wheeler
<12essa.1.jpg>
http://cecelia.physics.indiana.edu/p453/essays/quantum/wheeler.html
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_12_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_51_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_46_jpg.htm
The total energy of the universe is obviously not conserved in the standard model that fits observations to ~ 1% precision.
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_08_jpg.htm
The total w = -1 dark energy repulsive cosmic antigravity field accelerating the 3D space expansion of the universe is obviously not conserved. The total w = -1 dark energy content of our universe from Rocky Kolb's first slide above scales as a(t)^3.
The total w = 0 on-mass shell finite rest mass matter-energy is conserved scaling as a(t)^0 = 1.
The total zero rest mass w = +1/3 on light cone radiation energy is not conserved, it scales as a(t)^-1 -> zero from the cosmic redshift. Note that the chemical potential of radiation is zero, therefore there is no general global conservation law for radiation.
The general point here is that global space-time conservation laws are not fundamental unlike the local versions, which are satisfied e.g.
Tuv(matter)^;v = 0
locally in 1915 GR with the (LC) connection covariant partial derivative ;v.
Global conservation laws require
[Tuv(Matter) + tuv(Matter-Gravity)]^,v = 0
where ,v is the ordinary partial derivative.
This cannot be done in general in curved space-time with tuv(Matter-Gravity) as a kosher localized T4 tensor. tuv(Matter-Gravity) is a pseudo-tensor because in LNIF's the energy-momentum of the non-geodesic detectors powered by non-gravity forces makes a contribution to the vacuum gravity field that, by the equivalence principle, cannot be locally distinguished from the "real gravity field." Garbage in -> garbage out. Ask a stupid question, get a stupid answer. Trying to globally conserve total energy, trying to conserve total linear and angular momentum in a generally curved and torsioned spacetime is a stupid thing to try to do. We already know this from Noether's theorem. This is simply because the global Poincare group is locally gauged and all we can hope for is to locally conserve the total stress-energy current densities, which in fact is the case.
((-detguv)^1/2Tuv(matter))^,v + (-detguv)^1/2(LC(observer))u^v^wTvw(matter) = 0
Actual observations given above show that the total energy of the universe is not conserved. It's time to slay that Sacred Cow.
What the pure mathematicians, who lack physical understanding do not get, is that any representation of curved space-time guv is observer dependent i.e. relative to any conceivable network of ideal local observers on arbitrary worldlines inside the local light cone field. For example, in the non-rotating black hole outside the event horizon rs/r < 1
g00 = -1/g11 = 1 - rs/r
is only for that special class of static LNIF "shell" (J.A. Wheeler's term) observers at fixed r without orbital angular momentum. They need to fire rockets to stay in place. Note that warp drive "UFO" observers see a different metric field representation. What "Diff(4)" (local T4) frame shifts do is to connect different networks of local observers. That's the physical meaning of the abstract math missed by many of the formalists in the field. The local relation between objective reality and the observer's experience is
ds^2(objective observer invariant) = guv(observer dependent)dx^udx^v
= (Tetrad)^a(Tetrad)a
Space-time physics is local only because curved space-time is emergent from a local vacuum ODLRO world hologram Higgsian field with several coherent Goldstone phases that encode the 10^122 bits of our universe retrocausally from far future Omega to past Alpha at The Creation in our deSitter Universe.
http://qedcorp.com/APS/Adam.jpg
http://qedcorp.com/APS/desitter.jpg
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://lifeboat.com/ex/bios.jack.sarfatti
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
Roger Penrose's qubit spinor pre-geometry
http://www.people.cornell.edu/pages/gnl2/cave.htm
13.1 on Robert Wald's "General Relativity" has a nice discussion of measurement theory in general relativity in terms of "families of observers" that agrees with what I say below on the distinction between local objective invariants (Platonic forms, Jungian Archetypes) and their observer-dependent subjective faithful representations and provides more details.
Diffeomorphisms are not physical, they are too general with tremendous gauge freedom redundancy. We only want their sub Lie group of isometries ("Killing" (man's name) vector fields) so that different observers can meaningfully compare their subjective data, put it into the machine and crank out the same local invariants from the theory. Their goal is each to get the same set of real numbers for observations of equivalent happenings.
"when (and only when) Diff(4) is an isometry, we can use [it] ... to map our original family of physical observers associated with the [tetrads e^a] into a new family of observers associated with [tetrads e^a'] ..." p. 343.
"Here upon we're all agreed all that we two will agree to. To entrust you in The Art, elemental, fundamental ..." W.S. Gilbert, Yeoman of the Guard
Given a set of tetrad 1-forms e^a then as spinors we have
e^AA' = e^a(Newman-Penrose)a^AA'
Each A index = 0,1 is 1 qubit
for this
IT FROM QUBIT
e^BB' = I^BB(flat)' + A(warped)^BB'
Now we come to a strange miracle - the Bell quantum teleportation pair states appear.
Use qubit |A+> of Wald type (0,1;0,0) & qubit |A'->of Wald type (0,0;0,1) (p. 347) each in 2 complex dimensions.
Then, for special relativity, space-time AKA emerges from 2-qubit strings |A> & |A'>.
First take the local diagonal at the same local objective IT coincidence P = P', the space-time operators are entangled 2-qubit strings in 4 complex dimensions, i.e., spinor tensors of type (0,1;0,1) in Wald's notation Ch 13). Thus, we have the pair entangled qubit states
|t^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)+> + |A(P)->|A'(P)->]
Note |t^0^0'>, |t^0^1'>, |t^1^0'> |t^1^1'> span 4 complex dimensions. Similarly for
|x^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)-> + |A(P)->|A'(P)+>]
|y^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)-> - |A(P)->|A'(P)+>]
|z^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)+> - |A(P)->|A'(P)->]
We can generalize the above to the non-local pair states
|t^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')+> + |A(P)->|A'(P')->]
|x^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')-> + |A(P)->|A'(P')+>]
|y^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')-> - |A(P)->|A'(P')+>]
|z^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')+> - |A(P)->|A'(P')->]
We may need to put a path-dependent anholonomic propagator U(P<--->P') here, one for each homotopy equivalence class of paths <---> homotopic to each other from topological obstructions like black hole event horizons and observer dependent horizons in dark energy dominates deSitter space-time.
Below everything is local on the diagonal P = P' for Einstein's "local coincidences" defined by Rovelli in Ch II of his 'Quantum Gravity."
guv ---> gAA'BB' = EABE*A'B" (13.1.15) p. 349 Wald's GR
|EAB> = |A+>|B-> - |A->|B+> = -|EBA>
where = = 1
= = 0 i.e. these qubits have a null inner product that cannot be interpreted as in quantum Hilbert space. That is a differently defined product with complex conjugates. My use of the Dirac bra-ket for e-mail convenience may not be the best here because it can lead to that confusion.
Choose the following canonical basis with components (A), (B) etc. The 2x2 "basis" matrices are
E(A)(B)11 = 0
E(A)(B)12 = 1
E(A)(B)21 = -1
E(A)(B)22 = 0
t^(A)^(A') = Pauli Spin Matrix(t) (with added factor -1/2^1/2)
x^(A)^(A') = Pauli Spin Matrix(x)
y^(A)^(A') = Pauli Spin Matrix(y)
z^(A)^(A') = Pauli Spin Matrix(z)
These 2x2 matrices do not commute, so we have a non-commutative geometry in spinor tensor space. They have the same formal Lie algebra of internal SU(2) of the weak force fiber even though they represent Minkowski spacetime base space.
Any globally flat Minkowski world vector first rank tensor can be represented as the second rank spinor (mod - 1/2^1/2) in a 2x2 matrix representation
V^A^A' = V^t Pauli Spin Matrix(t) + Vx Pauli Spin Matrix(t) + (13.1.29) p. 351 Wald
Lorentz transformations are SL(2C) similarity transformations in this notation.
These single qubit "potential" spinors map to null vectors on the light cone in globally flat Minkowski spacetime. The qubit is the square root of a null world vector V^^a^a', i.e.
|V^A^A'*> = |A+>|A'+>*
= 0
One can also make 2nd rank antisymmetric null world field tensors (AKA null bivectors).
F^A^A'^B^B' = |A>||B>E*^A'^B' + |A'>*||B'>*E^A^B
F^2 = 0
FV = 0
(indices understood) p. 352 Wald.
This null F defines the Penrose "null flag".
To include T4 translations we must extend SL(2,C) to ISL(2,C) covering the 10-parameter Poincare group whose local gauging in all non-gravity field actions i.e. equivalence principle gives curvature + torsion i.e. independent 16 non-trivial tetrad components and 24 antisymmetric spin connection components packaged into 4 tetrad 1-forms e^a and 6 spin-connection 1-forms W^a^b in tangent vector/cotangent form fibers.
Lie derivatives of spinor fields are only definable for Killing isometries. You cannot do it for a general Diff(4) p. 353 Wald.
Newman-Penrose components are using the 16 tetrad components
(Sigma)^aAA' = e^a0tAA' - e^a1xAA' - e^a2yAA' - e^a3zAA'
so this shows how to generalize to curved and torsioned spacetime!
"The Question is: What is The Question?" John Archibald Wheeler
http://cecelia.physics.indiana.edu/p453/essays/quantum/wheeler.html
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_12_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_51_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_46_jpg.htm
The total energy of the universe is obviously not conserved in the standard model that fits observations to ~ 1% precision.
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_08_jpg.htm
The total w = -1 dark energy repulsive cosmic antigravity field accelerating the 3D space expansion of the universe is obviously not conserved. The total w = -1 dark energy content of our universe from Rocky Kolb's first slide above scales as a(t)^3.
The total w = 0 on-mass shell finite rest mass matter-energy is conserved scaling as a(t)^0 = 1.
The total zero rest mass w = +1/3 on light cone radiation energy is not conserved, it scales as a(t)^-1 -> zero from the cosmic redshift. Note that the chemical potential of radiation is zero, therefore there is no general global conservation law for radiation.
The general point here is that global space-time conservation laws are not fundamental unlike the local versions, which are satisfied e.g.
Tuv(matter)^;v = 0
locally in 1915 GR with the (LC) connection covariant partial derivative ;v.
Global conservation laws require
[Tuv(Matter) + tuv(Matter-Gravity)]^,v = 0
where ,v is the ordinary partial derivative.
This cannot be done in general in curved space-time with tuv(Matter-Gravity) as a kosher localized T4 tensor. tuv(Matter-Gravity) is a pseudo-tensor because in LNIF's the energy-momentum of the non-geodesic detectors powered by non-gravity forces makes a contribution to the vacuum gravity field that, by the equivalence principle, cannot be locally distinguished from the "real gravity field." Garbage in -> garbage out. Ask a stupid question, get a stupid answer. Trying to globally conserve total energy, trying to conserve total linear and angular momentum in a generally curved and torsioned spacetime is a stupid thing to try to do. We already know this from Noether's theorem. This is simply because the global Poincare group is locally gauged and all we can hope for is to locally conserve the total stress-energy current densities, which in fact is the case.
((-detguv)^1/2Tuv(matter))^,v + (-detguv)^1/2(LC(observer))u^v^wTvw(matter) = 0
Actual observations given above show that the total energy of the universe is not conserved. It's time to slay that Sacred Cow.
What the pure mathematicians, who lack physical understanding do not get, is that any representation of curved space-time guv is observer dependent i.e. relative to any conceivable network of ideal local observers on arbitrary worldlines inside the local light cone field. For example, in the non-rotating black hole outside the event horizon rs/r < 1
g00 = -1/g11 = 1 - rs/r
is only for that special class of static LNIF "shell" (J.A. Wheeler's term) observers at fixed r without orbital angular momentum. They need to fire rockets to stay in place. Note that warp drive "UFO" observers see a different metric field representation. What "Diff(4)" (local T4) frame shifts do is to connect different networks of local observers. That's the physical meaning of the abstract math missed by many of the formalists in the field. The local relation between objective reality and the observer's experience is
ds^2(objective observer invariant) = guv(observer dependent)dx^udx^v
= (Tetrad)^a(Tetrad)a
Space-time physics is local only because curved space-time is emergent from a local vacuum ODLRO world hologram Higgsian field with several coherent Goldstone phases that encode the 10^122 bits of our universe retrocausally from far future Omega to past Alpha at The Creation in our deSitter Universe.
http://qedcorp.com/APS/Adam.jpg
http://qedcorp.com/APS/desitter.jpg
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://lifeboat.com/ex/bios.jack.sarfatti
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.people.cornell.edu/pages/gnl2/cave.htm
13.1 on Robert Wald's "General Relativity" has a nice discussion of measurement theory in general relativity in terms of "families of observers" that agrees with what I say below on the distinction between local objective invariants (Platonic forms, Jungian Archetypes) and their observer-dependent subjective faithful representations and provides more details.
Diffeomorphisms are not physical, they are too general with tremendous gauge freedom redundancy. We only want their sub Lie group of isometries ("Killing" (man's name) vector fields) so that different observers can meaningfully compare their subjective data, put it into the machine and crank out the same local invariants from the theory. Their goal is each to get the same set of real numbers for observations of equivalent happenings.
"when (and only when) Diff(4) is an isometry, we can use [it] ... to map our original family of physical observers associated with the [tetrads e^a] into a new family of observers associated with [tetrads e^a'] ..." p. 343.
"Here upon we're all agreed all that we two will agree to. To entrust you in The Art, elemental, fundamental ..." W.S. Gilbert, Yeoman of the Guard
Given a set of tetrad 1-forms e^a then as spinors we have
e^AA' = e^a(Newman-Penrose)a^AA'
Each A index = 0,1 is 1 qubit
for this
IT FROM QUBIT
e^BB' = I^BB(flat)' + A(warped)^BB'
Now we come to a strange miracle - the Bell quantum teleportation pair states appear.
Use qubit |A+> of Wald type (0,1;0,0) & qubit |A'->of Wald type (0,0;0,1) (p. 347) each in 2 complex dimensions.
Then, for special relativity, space-time AKA emerges from 2-qubit strings |A> & |A'>.
First take the local diagonal at the same local objective IT coincidence P = P', the space-time operators are entangled 2-qubit strings in 4 complex dimensions, i.e., spinor tensors of type (0,1;0,1) in Wald's notation Ch 13). Thus, we have the pair entangled qubit states
|t^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)+> + |A(P)->|A'(P)->]
Note |t^0^0'>, |t^0^1'>, |t^1^0'> |t^1^1'> span 4 complex dimensions. Similarly for
|x^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)-> + |A(P)->|A'(P)+>]
|y^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)-> - |A(P)->|A'(P)+>]
|z^AA'(P)> = (2)^-1/2[|A(P)+>|A'(P)+> - |A(P)->|A'(P)->]
We can generalize the above to the non-local pair states
|t^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')+> + |A(P)->|A'(P')->]
|x^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')-> + |A(P)->|A'(P')+>]
|y^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')-> - |A(P)->|A'(P')+>]
|z^AA'(P,P')> = (2)^-1/2[|A(P)+>|A'(P')+> - |A(P)->|A'(P')->]
We may need to put a path-dependent anholonomic propagator U(P<--->P') here, one for each homotopy equivalence class of paths <---> homotopic to each other from topological obstructions like black hole event horizons and observer dependent horizons in dark energy dominates deSitter space-time.
Below everything is local on the diagonal P = P' for Einstein's "local coincidences" defined by Rovelli in Ch II of his 'Quantum Gravity."
guv ---> gAA'BB' = EABE*A'B" (13.1.15) p. 349 Wald's GR
|EAB> = |A+>|B-> - |A->|B+> = -|EBA>
where
Choose the following canonical basis with components (A), (B) etc. The 2x2 "basis" matrices are
E(A)(B)11 = 0
E(A)(B)12 = 1
E(A)(B)21 = -1
E(A)(B)22 = 0
t^(A)^(A') = Pauli Spin Matrix(t) (with added factor -1/2^1/2)
x^(A)^(A') = Pauli Spin Matrix(x)
y^(A)^(A') = Pauli Spin Matrix(y)
z^(A)^(A') = Pauli Spin Matrix(z)
These 2x2 matrices do not commute, so we have a non-commutative geometry in spinor tensor space. They have the same formal Lie algebra of internal SU(2) of the weak force fiber even though they represent Minkowski spacetime base space.
Any globally flat Minkowski world vector first rank tensor can be represented as the second rank spinor (mod - 1/2^1/2) in a 2x2 matrix representation
V^A^A' = V^t Pauli Spin Matrix(t) + Vx Pauli Spin Matrix(t) + (13.1.29) p. 351 Wald
Lorentz transformations are SL(2C) similarity transformations in this notation.
These single qubit "potential" spinors map to null vectors on the light cone in globally flat Minkowski spacetime. The qubit is the square root of a null world vector V^^a^a', i.e.
|V^A^A'*> = |A+>|A'+>*
One can also make 2nd rank antisymmetric null world field tensors (AKA null bivectors).
F^A^A'^B^B' = |A>||B>E*^A'^B' + |A'>*||B'>*E^A^B
F^2 = 0
FV = 0
(indices understood) p. 352 Wald.
This null F defines the Penrose "null flag".
To include T4 translations we must extend SL(2,C) to ISL(2,C) covering the 10-parameter Poincare group whose local gauging in all non-gravity field actions i.e. equivalence principle gives curvature + torsion i.e. independent 16 non-trivial tetrad components and 24 antisymmetric spin connection components packaged into 4 tetrad 1-forms e^a and 6 spin-connection 1-forms W^a^b in tangent vector/cotangent form fibers.
Lie derivatives of spinor fields are only definable for Killing isometries. You cannot do it for a general Diff(4) p. 353 Wald.
Newman-Penrose components are using the 16 tetrad components
(Sigma)^aAA' = e^a0tAA' - e^a1xAA' - e^a2yAA' - e^a3zAA'
so this shows how to generalize to curved and torsioned spacetime!
"The Question is: What is The Question?" John Archibald Wheeler
http://cecelia.physics.indiana.edu/p453/essays/quantum/wheeler.html
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_12_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_51_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_46_jpg.htm
The total energy of the universe is obviously not conserved in the standard model that fits observations to ~ 1% precision.
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_08_jpg.htm
The total w = -1 dark energy repulsive cosmic antigravity field accelerating the 3D space expansion of the universe is obviously not conserved. The total w = -1 dark energy content of our universe from Rocky Kolb's first slide above scales as a(t)^3.
The total w = 0 on-mass shell finite rest mass matter-energy is conserved scaling as a(t)^0 = 1.
The total zero rest mass w = +1/3 on light cone radiation energy is not conserved, it scales as a(t)^-1 -> zero from the cosmic redshift. Note that the chemical potential of radiation is zero, therefore there is no general global conservation law for radiation.
The general point here is that global space-time conservation laws are not fundamental unlike the local versions, which are satisfied e.g.
Tuv(matter)^;v = 0
locally in 1915 GR with the (LC) connection covariant partial derivative ;v.
Global conservation laws require
[Tuv(Matter) + tuv(Matter-Gravity)]^,v = 0
where ,v is the ordinary partial derivative.
This cannot be done in general in curved space-time with tuv(Matter-Gravity) as a kosher localized T4 tensor. tuv(Matter-Gravity) is a pseudo-tensor because in LNIF's the energy-momentum of the non-geodesic detectors powered by non-gravity forces makes a contribution to the vacuum gravity field that, by the equivalence principle, cannot be locally distinguished from the "real gravity field." Garbage in -> garbage out. Ask a stupid question, get a stupid answer. Trying to globally conserve total energy, trying to conserve total linear and angular momentum in a generally curved and torsioned spacetime is a stupid thing to try to do. We already know this from Noether's theorem. This is simply because the global Poincare group is locally gauged and all we can hope for is to locally conserve the total stress-energy current densities, which in fact is the case.
((-detguv)^1/2Tuv(matter))^,v + (-detguv)^1/2(LC(observer))u^v^wTvw(matter) = 0
Actual observations given above show that the total energy of the universe is not conserved. It's time to slay that Sacred Cow.
What the pure mathematicians, who lack physical understanding do not get, is that any representation of curved space-time guv is observer dependent i.e. relative to any conceivable network of ideal local observers on arbitrary worldlines inside the local light cone field. For example, in the non-rotating black hole outside the event horizon rs/r < 1
g00 = -1/g11 = 1 - rs/r
is only for that special class of static LNIF "shell" (J.A. Wheeler's term) observers at fixed r without orbital angular momentum. They need to fire rockets to stay in place. Note that warp drive "UFO" observers see a different metric field representation. What "Diff(4)" (local T4) frame shifts do is to connect different networks of local observers. That's the physical meaning of the abstract math missed by many of the formalists in the field. The local relation between objective reality and the observer's experience is
ds^2(objective observer invariant) = guv(observer dependent)dx^udx^v
= (Tetrad)^a(Tetrad)a
Space-time physics is local only because curved space-time is emergent from a local vacuum ODLRO world hologram Higgsian field with several coherent Goldstone phases that encode the 10^122 bits of our universe retrocausally from far future Omega to past Alpha at The Creation in our deSitter Universe.
http://qedcorp.com/APS/Adam.jpg
http://qedcorp.com/APS/desitter.jpg
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://lifeboat.com/ex/bios.jack.sarfatti
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
Tuesday, December 26, 2006
Total energy of the universe is not conserved
"The Question is: What is The Question?" John Archibald Wheeler
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_12_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_51_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_46_jpg.htm
The total energy of the universe is obviously not conserved in the standard model that fits observations to ~ 1% precision.
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_08_jpg.htm
The total w = -1 dark energy repulsive cosmic antigravity field accelerating the 3D space expansion of the universe is obviously not conserved. The total w = -1 dark energy content of our universe from Rocky Kolb's first slide above scales as a(t)^3.
The total w = 0 on-mass shell finite rest mass matter-energy is conserved scaling as a(t)^0 = 1.
The total zero rest mass w = +1/3 on light cone radiation energy is not conserved, it scales as a(t)^-1 -> zero from the cosmic redshift. Note that the chemical potential of radiation is zero, therefore there is no general global conservation law for radiation.
The general point here is that global space-time conservation laws are not fundamental unlike the local versions, which are satisfied e.g.
Tuv(matter)^;v = 0
locally in 1915 GR with the (LC) connection covariant partial derivative ;v.
Global conservation laws require
[Tuv(Matter) + tuv(Matter-Gravity)]^,v = 0
where ,v is the ordinary partial derivative.
This cannot be done in general in curved space-time with tuv(Matter-Gravity) as a kosher localized T4 tensor. tuv(Matter-Gravity) is a pseudo-tensor because in LNIF's the energy-momentum of the non-geodesic detectors powered by non-gravity forces makes a contribution to the vacuum gravity field that, by the equivalence principle, cannot be locally distinguished from the "real gravity field." Garbage in -> garbage out. Ask a stupid question, get a stupid answer. Trying to globally conserve total energy, trying to conserve total linear and angular momentum in a generally curved and torsioned spacetime is a stupid thing to try to do. We already know this from Noether's theorem. This is simply because the global Poincare group is locally gauged and all we can hope for is to locally conserve the total stress-energy current densities, which in fact is the case.
((-detguv)^1/2Tuv(matter))^,v + (-detguv)^1/2(LC(observer))u^v^wTvw(matter) = 0
Actual observations given above show that the total energy of the universe is not conserved. It's time to slay that Sacred Cow.
What the pure mathematicians, who lack physical understanding do not get, is that any representation of curved space-time guv is observer dependent i.e. relative to any conceivable network of ideal local observers on arbitrary worldlines inside the local light cone field. For example, in the non-rotating black hole outside the event horizon rs/r < 1
g00 = -1/g11 = 1 - rs/r
is only for that special class of static LNIF "shell" (J.A. Wheeler's term) observers at fixed r without orbital angular momentum. They need to fire rockets to stay in place. Note that warp drive "UFO" observers see a different metric field representation. What "Diff(4)" (local T4) frame shifts do is to connect different networks of local observers. That's the physical meaning of the abstract math missed by many of the formalists in the field. The local relation between objective reality and the observer's experience is
ds^2(objective observer invariant) = guv(observer dependent)dx^udx^v
= (Tetrad)^a(Tetrad)a
Space-time physics is local only because curved space-time is emergent from a local vacuum ODLRO world hologram Higgsian field with several coherent Goldstone phases that encode the 10^122 bits of our universe retrocausally from far future Omega to past Alpha at The Creation in our deSitter Universe.
http://qedcorp.com/APS/Adam.jpg
http://qedcorp.com/APS/desitter.jpg

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://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
"The Question is: What is The Question?" John Archibald Wheeler
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_12_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_51_jpg.htm
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb2/Kolb2_Page_46_jpg.htm
The total energy of the universe is obviously not conserved in the standard model that fits observations to ~ 1% precision.
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_08_jpg.htm
The total w = -1 dark energy repulsive cosmic antigravity field accelerating the 3D space expansion of the universe is obviously not conserved. The total w = -1 dark energy content of our universe from Rocky Kolb's first slide above scales as a(t)^3.
The total w = 0 on-mass shell finite rest mass matter-energy is conserved scaling as a(t)^0 = 1.
The total zero rest mass w = +1/3 on light cone radiation energy is not conserved, it scales as a(t)^-1 -> zero from the cosmic redshift. Note that the chemical potential of radiation is zero, therefore there is no general global conservation law for radiation.
The general point here is that global space-time conservation laws are not fundamental unlike the local versions, which are satisfied e.g.
Tuv(matter)^;v = 0
locally in 1915 GR with the (LC) connection covariant partial derivative ;v.
Global conservation laws require
[Tuv(Matter) + tuv(Matter-Gravity)]^,v = 0
where ,v is the ordinary partial derivative.
This cannot be done in general in curved space-time with tuv(Matter-Gravity) as a kosher localized T4 tensor. tuv(Matter-Gravity) is a pseudo-tensor because in LNIF's the energy-momentum of the non-geodesic detectors powered by non-gravity forces makes a contribution to the vacuum gravity field that, by the equivalence principle, cannot be locally distinguished from the "real gravity field." Garbage in -> garbage out. Ask a stupid question, get a stupid answer. Trying to globally conserve total energy, trying to conserve total linear and angular momentum in a generally curved and torsioned spacetime is a stupid thing to try to do. We already know this from Noether's theorem. This is simply because the global Poincare group is locally gauged and all we can hope for is to locally conserve the total stress-energy current densities, which in fact is the case.
((-detguv)^1/2Tuv(matter))^,v + (-detguv)^1/2(LC(observer))u^v^wTvw(matter) = 0
Actual observations given above show that the total energy of the universe is not conserved. It's time to slay that Sacred Cow.
What the pure mathematicians, who lack physical understanding do not get, is that any representation of curved space-time guv is observer dependent i.e. relative to any conceivable network of ideal local observers on arbitrary worldlines inside the local light cone field. For example, in the non-rotating black hole outside the event horizon rs/r < 1
g00 = -1/g11 = 1 - rs/r
is only for that special class of static LNIF "shell" (J.A. Wheeler's term) observers at fixed r without orbital angular momentum. They need to fire rockets to stay in place. Note that warp drive "UFO" observers see a different metric field representation. What "Diff(4)" (local T4) frame shifts do is to connect different networks of local observers. That's the physical meaning of the abstract math missed by many of the formalists in the field. The local relation between objective reality and the observer's experience is
ds^2(objective observer invariant) = guv(observer dependent)dx^udx^v
= (Tetrad)^a(Tetrad)a
Space-time physics is local only because curved space-time is emergent from a local vacuum ODLRO world hologram Higgsian field with several coherent Goldstone phases that encode the 10^122 bits of our universe retrocausally from far future Omega to past Alpha at The Creation in our deSitter Universe.
http://qedcorp.com/APS/Adam.jpg
http://qedcorp.com/APS/desitter.jpg

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://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
http://www.flickr.com/photos/lub/sets/72157594439814784
Monday, December 25, 2006
Cosmic voids from dark zero point energy fields of negative pressure
re: http://www.shipov.com
In Einstein's 1915 GR prior to the introduction of the teleparallel Kibble-Shipov torsion field with the 6 anholonomic angular pre-Calabi-Yau coordinates for the orientation of the Einstein-Cartan tetrad frame mobile {e^a}
(Riemann Curvature)uvwl = (Weyl Vacuum Curvature)uvwl + (1/2)[(curved metric)uwT(non-gravity source)vl + (curved metric)vlT(non-gravity source)uw - (curved metric)ulT(non-gravity source)vw - (curved metric)vwT(non-gravity source)ul] - (1/3)[(curved metric)uw(curved metric)vl - (curved metric)ul(curved metric)vw]T(non-gravity source)
Tuv(Dark Energy/Matter) = (String Tension)/\zpf(curved metric)uv
/\zpf = (Quantum of Area of World Hologram)^-1(1 - |Higgs Vacuum ODLRO Order Parameter|^2)
/\zpf > 0 is repulsive blue-shifting universal anti-gravity field (e.g. cosmic voids & Type 1a supernovae)
/\zpf < 0 is attractive red-shifting universal gravity field (e.g. Galactic halos & filaments)
Dark regions are where /\zpf > 0, bright filaments are where /\zpf < 0.
http://heasarc.nasa.gov/docs/cosmic/sheets_voids.html
Problem is how to put Shipov's torsion field as a replacement for /\zpf, which he does in one of his papers on dark energy and torsion.
re: http://www.shipov.com
In Einstein's 1915 GR prior to the introduction of the teleparallel Kibble-Shipov torsion field with the 6 anholonomic angular pre-Calabi-Yau coordinates for the orientation of the Einstein-Cartan tetrad frame mobile {e^a}
(Riemann Curvature)uvwl = (Weyl Vacuum Curvature)uvwl + (1/2)[(curved metric)uwT(non-gravity source)vl + (curved metric)vlT(non-gravity source)uw - (curved metric)ulT(non-gravity source)vw - (curved metric)vwT(non-gravity source)ul] - (1/3)[(curved metric)uw(curved metric)vl - (curved metric)ul(curved metric)vw]T(non-gravity source)
Tuv(Dark Energy/Matter) = (String Tension)/\zpf(curved metric)uv
/\zpf = (Quantum of Area of World Hologram)^-1(1 - |Higgs Vacuum ODLRO Order Parameter|^2)
/\zpf > 0 is repulsive blue-shifting universal anti-gravity field (e.g. cosmic voids & Type 1a supernovae)
/\zpf < 0 is attractive red-shifting universal gravity field (e.g. Galactic halos & filaments)
Dark regions are where /\zpf > 0, bright filaments are where /\zpf < 0.
http://heasarc.nasa.gov/docs/cosmic/sheets_voids.html
Problem is how to put Shipov's torsion field as a replacement for /\zpf, which he does in one of his papers on dark energy and torsion.
Saturday, December 23, 2006
Russian Space and Psychotronic Torsionic Weapons Systems Study 1
"Returning to the question of Russian Resurgence, it may be remarked how 'gently' (except in some of national republics of f. USSR) proceeded the controlled (by secret KGB/GRU elite: nation's hidden 'Second Ring of Power', acting only during grave emergencies: cf. Prokhanov's 'Mr Hexogen' & debriefings of defector Golitsyn in '60s) decay" of overstuffed with both conventional & nuclear weapons former (?) global superpower.
No essential national assets (such as functional integrity of esoteric centers of power - not to say about nuclear arsenals) have been damaged; - and so much lamented by Old Paradigmers "collapse of academic science" had done to Russia very much good, - having liberated free thought from tyrannical domination of stupid carriers of obsolete dogmas (indeed, under Soviet regime perspectives of torsionic research in Russia would be incomparably dimmer).
Neither does present any problem for Russia so much lamented "brain drain" of best minds. Rather, the situation is reverse: wide emigration of top Russian experts, - which remain strongly spiritually connected to their tenacious Motherland, - does expand the area of Russian influence.
(In special cases - when a highly trained Russian expert has fair chances to obtain sensitive position in Western establishment - such persons (which had been specially targeted by secret Russian psychotronic services since '30s) are being, without their knowledge, remotely "psychotronically treated": that is, their minds are "telepathically entangled" with minds of their controllers/"minders"; - which are capable, via this link, literally "to see through their eyes & feel their thoughts": cf. on p. 161 of A. Robbins' "Unlimited Power"; Ballantyne Books, 1989 - and also L. Niven's "Mote in God's Eye" & chapter "Suckers and Suicides" in S. Lee's "Dunn's Conundrum".)
"Natural telepathic links" in minds/souls of Russian emigrants around the globe, - now lying dormant, - might be activated, tremendously increasing their capacity, after beginning of full-scale functioning (in the mode of "global-scale psi-broadcaster") of long-projected "New Ahnenerbe": nationwide center where will be concentrated (like in Himmler's Ahnenerbe but on much higher modern level - and with much better financing!) all esoteric explorations (including non-conventional Leading Edge scientific disciplines like torsionics - which'll be harmonically synthesized, without annoying interference of "professional skeptics", with achievements of Ageless Wisdom).
As sources of inspiration/paragons for this enterprise of global importance will be taken not only such classical examples as first in the world Dr Barchenko's psi-research lab & Himmler's Ahnenerbe, but also such more modern outfits as GRU-sponsored Rejdak's Intl Assn for Psychotronic Research (which functioned as cover for "reborn Ahnenerbe" during Communist regime in f. Czechoslovakia) & Britain-based Scientific and Medical Network, many respected members of which are sympathizing these ideas.
(From this viewpoint there might be regarded as highly significant appearance in the last - No. 51/2006 - issue of influential Moscow weekly "Zavtra" ("To-Morrow"): www.zavtra.ru (which is regarded as an organ of Russian special services' elite: its Editor-in-Chief A. Prokhanov openly says about his close ties with GRU) of a large article bearing tritle "Putin is a target of PSI-weapons"; - where, - after wide (but not very deep) review of modern weapons of PSI/informational warfare, - there is made an appeal to increase measures of psychotronic defence of President & other VIPs, using most advanced modern technologies of psi-defence (including Internet-based).
Calls are made to the Ministry of Defence to organize special "Strategic Psychotronic Forces", which must constantly monitor minds of leaders of "potential enemy states".)"
Report today from Moscow by a Secret Agent for MASINT.
re: http://www.shipov.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://lifeboat.com/ex/bios.jack.sarfatti
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
The Russian Torsionic Space Weapons Program is partially described in
The precursor to 6D Calabi-Yau space of the M-Theory Dream, it's hardly even a "program" yet, is already in the Kibble 1961 -> Shipov tetrad-based curvature + torsion extension of Einstein's point test particle curvature only theory of 1915.
The tetrad as "internal fiber" analog has 6 independent periodic angular degrees of freedom (in Euclidean metric) corresponding to the 6 dimensions of Calabi-Yau space.
Given a base space-time of dimension n, the number of extra independent degrees of freedom to orient the n-bein in the base space is
n(n + 1)/2 - n = n^2/2 + n/2 - n = n(n -1)/2 = number of undirected edges of the n-simplex.
The Poincare group has 10 parameters = 4x5/2
The conformal group has 15 parameters corresponding to n = 5 the Kaluza-Klein model with one extra base space dimension giving the 5-bein fiber needing 15 - 5 = 10 angles.
The n-beins or "oriented points" are proto "extended objects" like strings are. They are the non-vibrating ground states of the strings -> branes.
The pre-string physics must be implicit in eq (49).
The A4 curvature + torsion geodesic equation is (52). This is not the same as Einstein's 1915 geodesic curvature only equation.
The geodesic equation says that the objective covariant acceleration of the test particle relative to the given connection vanishes.
(54) -> (56) show that the Euclidean kinematical acceleration for the A4 geodesic observer who experiences no g-force. Therefore the Einstein equivalence principle in its original sense continues to be obeyed for the center of mass motion even in the A4 theory beyond Einstein's.
Newton's picture of inertial compensation for the weightless geodesic observer works in the extended theory where the torsion force exactly cancels the Newtonian gravity force on the A4 geodesic.
Both Einstein's (LC) and Shipov's A4 geodesic observers report the same experience, weightlessness. They both report special relativity working locally near them. The presence of curvature is not relevant to the last statement. They both report approximately zero kinematical acceleration d^2x^i/dt^2 = 0 for nearby geodesic test particles in the slow speed weak curvature field regime. However they have different informal language explanations.
1915 T4* (AKA GCT) Einstein observer says his LC connection vanishes at origin of his LIF.
The A4 Shipov observer says his GCT non-tensor LC connection is not zero, but it is exactly cancelled by his GCT tensor torsion T =/= 0 connection.
Note that the A4 connection has independent physical meaning from (LC) i.e.
A4 connection derives from locally gauging the 10-parameter Poincare group P10.
The (LC) connection derives from locally gauging the 4-parameter T4 subgroup of P10.
The cotorsion T connection derives from locally gauging the 6-parameter Lorentz subgroup O(1,3) of P10
therefore
(LC) = A4 - T
is meaningful in this context, but not in Z's where he only had 1915 GR i.e. only T4 locally gauged so that T = 0.
On Dec 22, 2006, at 1:15 PM, Jack Sarfatti wrote:
Gennady Shipov's teleparallel A4 geometry then has two distinct metric structures:
The Einstein translational metric of 1915 GR
ds^2 = e^ajeaidx^idx^j = e^aea
and the "Calabi-Yau"-like
d@^2 = T^abiT^bajdx^idx^j = T^abT^ba
Note that
d@^ba = T^bajdx^j is a 2-tangent fiber indexed 1-form
That is, for a world 4-vector infinitesimal displacement dx^i, d@^ba is the infinitesimal rotation of the e^b tetrad about the e^a tetrad and vice versa with a negative sign.
This, therefore, is the physical origin of Calabi-Yau space in string theory. It is, perhaps, a missing "organizing" idea of string theory.
The 3rd rank T4* world torsion tensor fields in terms of the tetrad tensor fields are
Ojk^i = e^iae[k,j]^a = (1/2)e^ia(ek,j^a - ej,k^a) = - Okj^i
,j is ordinary partial derivative
Here I use Shipov's notation where i,j = 0,1,2,3 (not 1,2,3 as below using u,v as world T4* tensor indices)
The contorsion T^ijk is a variation on the above torsion field. How appropriate that term is will be discussed later.
T^ij,k = - O^ij,k + g^i^m(gjsOmk^s + gksOmj^s)
g^i^m(gjsOmk^s + gksOmj^s) = g^i^m(Omkj + Omjk)= O^ikj + O^ijk
D is the symmetric torsion free Levi-Civita connection from 1915 plain vanilla GR.
Shipov proposes a symmetric "source" stress-energy tensor for 1915 GR built from the contortion tensor alone
Tjm("Matter")~ D[iT^i|j|m] + T^is[iT^s|j|m] - (1/2)gjmg^p^n{(D[iT^i|p|n] + T^is[iT^s|p|n]}
|...| means "exclude the ... index from the [ ] antisymmetrization or the ( ) symmetrization.
What Shipov does not show is how to get the lepton-quark spinor fields plus the electroweak-strong gauge boson fields all coming from this single contortion. However, that may be possible because Shipov does have a 9D + 1 space like string theory and for the same reason - spatially extended test particles not point particles.
That is, Shipov most show that this is the Ur "Master Field" of all the fields in the standard model at least. Since his structure is like string theory this may not be impossible.
The Einstein vacuum equation Rim = 0 entails
D[iT^i|j|m] + T^is[iT^s|j|m] = 0
The generalized geodesic equation is
d^2x^i/ds^2 + [(LC)^ijk + T^ijk](dx^j/ds)(dx^k/ds) = 0
Einstein's 1915 GR has
T^ijk(dx^j/ds)(dx^k/ds) = 0
Note that this equation can be true even if T^ijk =/= 0 in special cases.
Shipov calls this a "teleparallel A4" space-time because he uses the constraint that the generalized curvature tensor is zero i.e. globally flat for the extended A4 connection.
non-symmetric A4 connection = symmetric non T4* tensor 1915 GR Levi-Civita connection
+ antisymmetric T4* tensor contorsion
i.e. the covariant curl of the A4 connection with itself vanishes identically, i.e.
Define the 4th rank T4* tensor
P^ijkm = 2T^i[|k|j|m] + 2T^is[kT^s|j|m], then
S^ijkm = R^ijkm + P^ijkm = 0 "teleparallel"
There are 2 other key constraint's here.
,k is ordinary partial derivative
;k is T4* zero torsion 1915 GR covariant partial derivative
|k is A4 non-zero torsion covariant partial derivative for the local 10-parameter Poincare group
e^a[k|j] + T^i[kj]e^ai = 0
and the A4 Bianchi identities, which are
P^i[|kjk]m = 0
Shipov's theory is a special case of Kibble 1961 which has a non-symmetric stress tensor as I recall? The Poincare group has 10 parameters.
4 translations that when locally gauged give the General Coordinate transformations.
When not locally gauged there is no problem with global conservation of total`energy and momentum of non-gravity fields. You cannot have that global conservation in general when locally gauged. There is still local conservation however. Also the stress energy of gravity by itself is not local.
3 space rotations, which when not locally gauged lead to conservation of angular rotational momentum
3 Lorentz boosts.
The four A4 geodesic equations
d^2x^i/ds^2 + [(LC)^ijk + T^ijk](dx^j/ds)(dx^k/ds) = 0
are only for the CM motion.
There are 6 other equations of motion for the variation of the orientation of the 4 tetrad fields
e^a = e^audx^u
under teleparallel transport using the A4 Kibble 1961 connection
= 1915 GR (LC) + Contorsion
Those 6 are simply
e^a[k|j] + T^i[kj]e^ai = 0
for a single a since all 4 a are relatively rigidly fixed to each other i.e. a 4D rigid body, and the world indices k,j appear anti-symmetrized.
The teleparallel A4 geometry then has two distinct metric structures:
The Einstein translational metric of 1915 GR
ds^2 = e^ajeaidx^idx^j = e^aea
and the "Calabi-Yau"-like
d@^2 = T^abiT^bajdx^idx^j = T^abT^ba
Note that
d@^ba = T^bajdx^j is a 2-tangent fiber indexed 1-form
That is, for a world 4-vector infinitesimal displacement dx^i, d@^ba is the infinitesimal rotation of the e^b tetrad about the e^a tetrad and vice versa with a negative sign.
This, therefore, is the physical origin of Calabi-Yau space in string theory. It is, perhaps, a missing "organizing" idea of string theory.
On Dec 21, 2006, at 10:15 PM, Jack Sarfatti wrote:
"Diff(4)" = "GCT" = "local T4" = T4* here.
Einstein's 1915 GR from the modern POV of local gauge theory is the universal local gauging of the T4 invariance of the actions of all non-gravity fields. The local variable compensating gauge potential is warped tetrad e^au fundamental gravitational field A^au analogous to Au in U(1) EM and Au^a in Yang-Mills theory of the weak SU(2) and SU(3) strong forces. SU(2) has the vacuum ODLRO Higgs field with Goldstone phase coherence and it breaks left-right chiral symmetry (parity - broken mirror symmetry).
Tensors transform multilinearly homogeneously under representations of a given group.
Einstein's geometrodynamic objects like the metric field guv and the torsion-free Levi-Civita connection (LC)uv^w = (LC)vu^w are composite objects
guv = e^au(Minkowski)abe^bv = (I^au + A^au)(Minkowski)ab(I^bv + A^bv)
For the Schwarzschild static solution outside the event horizon for static LNIF observers
e^00 = (1 - 2rs/r)^1/2
e^01,2,3 = 0
e^11 = (1 - 2rs/r)^-1/2
e^i,j = &^ij Kronecker delta for i,j = 1,2,3
In the weak field limit
A^00 ~ -rs/r = GM/c^2r = -(Gh/c^3)(Mc/h)(1/r) = -[(Planck Area)/(Compton wavelength)](1/r)
rs/r ~ Lp(Theta^0Phi^0,0 - Theta^0,0Phi^0)
Fix a gauge, i.e. select a degenerate ODLRO vacuum where Theta^0 = pi
Phi^0 ~ Lp(Mc/h)(ct/r)(1/pi)
Phi^0,0 = Lp(Mc/h)(1/pir)
A^11 ~ +rs/r
all other A^ai = 0
note the linear elastic and nonlinear plastic terms in the expansion of the metric field.
I^a is curvilinear in LNIF representations. It is Kronecker delta in LIF representations.
(Globally Flat Curvilinear Metric)uv = I^au(Minkowski)abI^bv
Only (Minkowski)ab is the constant 4x4 diagonal matrix in the geodesic representation.
(LC)uv^w = (1/2)e^wa[e^au,v + e^av,u] = e^wae^a(u,v)
,u = d/dx^u ordinary partial derivative
The T4* covariant partial derivatives are themselves T4* tensors.
DB^w/dx^u = B^w,u + (LC)^wuvB^v
more complicated for higher rank tensors
The T4* geodesic equation is
covariant absolute translational general relativistic acceleration of CM of test particle vanishes is
D^2x^w/ds^2 = d^2x^w/ds^2 + (LC)^wuv(dx^u/ds)(dx^v/ds) = 0
d^2x^w/ds^2 = special relativistic acceleration
(LC)^wuv(dx^u/ds)(dx^v/ds) = LNIF acceleration
Geodesic equation says
GR acceleration = SR acceleration + LNIF acceleration = 0
"Newton's First Law" = geodesic equation
In all mechanical theories. Curvature is irrelevant because this translational equation is only for the exact mathematical point center of mass CM of the extended test particle.
The LIF corresponds to geodesic normal coordinates where (LC)^wuv = 0 at the LIF ORIGIN.
The Newtonian inertial forces are already in (LC) without any torsion. This is shown explicitly by C. Lanczos.
(1/2)[(LC)^i^0k - (LC)^k^0i] = (1/2)(g0k,i - g0i,k) ~ CurlU = H
U = gravimagnetic potential (g01,g02,g03)
"On the Problem of Rotation in the General Theory of Relativity"
Kornel Lanczos, 1923
The inertial force in a non-inertial frame on test particle of rest mass m in 1915 torsion-free GR is
F^i(inertial) = m(LC)^r^siVrVs
Vr is special relativity 4-velocity
When V/c << 1 SLOW SPEED Galilean limit of near absolute simultaneity.
Fi(inertia) ~ Fi(Centrifugal) + Fi(Coriolis) + Fi(?)
summation convention here is restricted to i = 1,2,3
Fi(Centrifugal) ~ (m/g00)(LC)^0^0i
Fi(Coriolis) ~ (2m/g00)(LC)^0^siVs
There is also a quadratic inertial force
Fi ~ (m/g00)(LC)^r^siVrVs
not mentioned in Newtonian classical mechanics courses.
Start in a geodesic representation of globally flat Minkowski spacetime i.e. no real intrinsic warp GCT tensor fields of either curvature or torsion.
ds^2 = dx^2 + dy^2 + dz^2 - dt^2 c = 1
Go to a rotating non-inertial frame at constant rotation speed w about the z axis, in this rotating non-inertial global frame
ds^2 ~ dx'^2 + dy'^2 + dz'^2 - 2wy'dx'dt + 2wx'dy'dt - [1 - w^2(x'^2 + y'^2)]dt^2
where in this Galilean approximation
1 >> w^2(x'^2 + y'^2) = w^2r^2 in cylindrical coordinates, w pseudo 3-vector along z-axis
Fi(Centrifugal) ~ (m/g00)(LC)^0^0i ~ mwxwxr'
Fi(Coriolis) ~ (2m/g00)(LC)^0^siVs ~ 2mwxv'
On Dec 21, 2006, at 2:38 PM, Jack Sarfatti wrote:
Informal language
Shipov's term "accelerated locally Lorentzian frame" are "like those of elevators in free fall" are what MTW call LIF's. The "accelerated" is from Newton's picture.
The Einstein 1915 geodesic equation for the center of mass motion of an extended test body (i.e. we ignore its self-field) is
c^2D^2x^u/ds^2 = c^2d^2x^u/ds^2 + c^2(LC)^uvw(dx^v/ds)(dx^w/ds) = 0
where formally
ds^2 = guvdx^udx^v = e^aue^bv(Minkowski Metric)ab
However, to be more rigorous
D^2x^u/ds^2 = (D/ds)(D/ds)x^u
Tetrads are e^au = I^au + A^au(WARP)
In a globally flat spacetime region
A^au(WARP) = 0 globally in the specified region.
A^au(WARP) is the compensating gauge potential from localizing the spacetime symmetry group T4 on all non-gravity actions analogous to localizing U(1) internal symmetry only on charged source fields.
I^au -> Kronecker delta in a geodesic not translationally accelerating and not rotating inertial frame.
However in a non-geodesic translationally accelerating and/or rotating non-inertial frame then I^au is an arbitrary curvilinear field with zero Riemann curvature.
is the local fundamental invariant under both local Lorentz transformations and GCTs that are locally gauged T4 translation group transformations called loosely "Diff(4)."
(LC)^uvw = (LC)^uwv is the non-tensor Levi-Civita connection field for parallel transport of tensors on world lines in the curved 4D base spacetime of the (co)tangent bundle.
c^2D^2x^u/ds^2 is the GCT covariant tensor absolute acceleration of the test particle that is zero!
Only in a locally coincident non-geodesic frame (LNIF) will this geodesic test particle have a non-vanishing Newtonian-Euclidean acceleration c^2d^2x^u/ds^2 =/= 0 i.e.
c^2d^2x^u/ds^2 = - c^2(LC)^uvw(dx^v/ds)(dx^w/ds)
The measured acceleration of the test particle relative to the non-geodesic LNIF observer is called an "inertial force per unit test mass" in the 1915 GR without torsion fields.
The idea is that in "local geodesic normal coordinates"
(LC)^uvw = 0 at the origin of those local coordinates only AKA Einstein equivalence principle.
So to a good approximation, the local LIF Guy sees c^2d^2x^u/ds^2 = 0. The coincident local LNIF Gal does not see that as zero. Both, however agree that the first-rank GCT tensor covariant acceleration of the test body is zero. That is,
c^2D^2x^u/ds^2 = 0 FOR ALL OBSERVERS
this is Newton's First Law - works even in GR on geodesics even when there is curvature.
(LC) is 100% non-tensor i.e. its only tensor piece is zero and that is a local frame invariant fact.
So moral - be careful to distinguish "GCT covariant tensor kinematics" from Poincare group covariant kinematics.
Note that
c^2d^2x^u/ds^2 is a special relativity Poincare group tensor, but it is not a 1915 GR localized T4 group tensor. That tensor is c^2D^2x^u/ds^2.
On Dec 21, 2006, at 1:44 PM, Jack Sarfatti wrote:
Useful fact to remember
hc, e^2 , Gm^2
quantum electricity gravity
all have the same physical dimensions.
Their 3 distinct ratios
hc/e^2
Gm^2/e^2
Gm^2/hc
are all dimensionless numbers.
On Dec 21, 2006, at 1:19 PM, Jack Sarfatti wrote:
From the local gauge theory POV Shipov's new coupling seems to come from locally gauging the 15 parameter massless twistor conformal group with vacuum ODLRO to give the gauge quanta mass. The conformal quanta would be spin 1 forming entangled massive pairs of spin 0, spin 1 & spin 2. I think Tony Smith previously suggested something along these lines?
Shipov's new physics in his 1972 thesis was to add in the effects of hyperbolic boosts to uniformly accelerating frames in Maxwell's electrodynamics - no gravity G at all - no equivalence principle here?
On Dec 21, 2006, at 1:12 PM, Jack Sarfatti wrote:
There is a typo in Shipov's eq. (0.1) for his "geometrized electrodynamics." He writes
Rik - (1/2)gikR = (8pie/mc^4)Tik
(8pie/mc^4) has the wrong physical dimensions. The correct formula is
(e/mc^2)^2 = (Classical Electron Radius)/mc^2 i.e. (string tension)^-1
This is to be compared to G/c^4 with the same physical dimensions converting pressure to curvature.
Note that numerically this is ~ 10^-13 cm/10^-3 Gev ~ 10^-10 cm/Gev
In contrast G/c^4 ~ 10^-33cm/10^19Gev = 10^-52 cm/Gev
therefore Shipov's electro-gravitic coupling is 42 powers of 10 more powerful than Newton's gravity.
Is this equation true?
Shipov says he derived it in 1972 extending Einstein's special relativity electrodynamics to include uniformly accelerating frames. Are those the 4 conformal boosts?
Now if this is really so, it suggest a whole new approach to the metric engineering of warp and wormhole in which, perhaps, the alleged alien ET flying saucers are able to replace the usual much too weak G/c^4 coupling of stress-energy density to curvature with the (e/mc^2)^2 electro-gravitic coupling 42 Powers of Ten stronger. That's a whole new ball game. Note I am not saying, at this stage, that they are doing that OUT THERE. I am thinking on it. Such a coupling would need a massive graviton with a mass ~ ~ hc/(nanometers). It obviously cannot be a long-range field or it would destroy the universe.
On Dec 20, 2006, at 6:47 PM, Jack Sarfatti wrote:
Note that Shipov constructs a symmetrical Yang-Mills type source tensor from his torsion field with the torsion field analogous to the EM/Yang-Mills fields. This may not be general enough because Kibble 1961 says that the local gauging of the 10-parameter Poincare group will give a non-symmetrical piece to the stress-energy tensor i.e. a non-symmetric metric and Einstein tensor as considered in one of Einstein's attempts at a classical unified field theory. C. Lanczos shows that in such a theory there is propellantless propulsion. So this idea needs not to be forgotten.
On Dec 20, 2006, at 6:35 PM, Jack Sarfatti wrote:
Both Shipov and I independently associate anti-gravitating repulsive dark energy with variable local torsion fields.
My basic argument in e.g.
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
Guv(vacuum) + /\zpfguv = 0
if the torsion field is zero globally
Guv^;v = 0
Therefore
/\zpf^,v = 0
since
guv^;v = 0
One way to have /\zpf^,v =/= 0 in vacuum is to have the additional torsion field beyond Einstein's 1915 theory.
Note that even without torsion
/\zpf^,vguv + Tuv^;v(non-gravity source fields) = 0
http://www.shipov.com
The complete paper can be downloaded from http://www.shipov.com/science.html
e^am are the tetrad components, T^abm are the torsion field components, R^abkm are the curvature field components.
Note that Shipov's (45) is analogous to the ODLRO superflow field in liquid Helium II below the Lambda Point where the zero point energy dominates.
vm = (h/m)(Phase),m
In equation (84) Shipov gets a quintessent field from a particular model of the torsion tensor field leading from the torsion field version of the Yang-Mills type source (39) to (83).
In my theory Shipov's Lambda in (84) is
/\zpf(xi) = (Quantum of Area)^-1(|Vacuum ODLRO Higgs Field|^2 - 1)
that is repulsive positive dark energy density when positive and is attractive dark matter density when negative, assuming here w = -1.
"Returning to the question of Russian Resurgence, it may be remarked how 'gently' (except in some of national republics of f. USSR) proceeded the controlled (by secret KGB/GRU elite: nation's hidden 'Second Ring of Power', acting only during grave emergencies: cf. Prokhanov's 'Mr Hexogen' & debriefings of defector Golitsyn in '60s) decay" of overstuffed with both conventional & nuclear weapons former (?) global superpower.
No essential national assets (such as functional integrity of esoteric centers of power - not to say about nuclear arsenals) have been damaged; - and so much lamented by Old Paradigmers "collapse of academic science" had done to Russia very much good, - having liberated free thought from tyrannical domination of stupid carriers of obsolete dogmas (indeed, under Soviet regime perspectives of torsionic research in Russia would be incomparably dimmer).
Neither does present any problem for Russia so much lamented "brain drain" of best minds. Rather, the situation is reverse: wide emigration of top Russian experts, - which remain strongly spiritually connected to their tenacious Motherland, - does expand the area of Russian influence.
(In special cases - when a highly trained Russian expert has fair chances to obtain sensitive position in Western establishment - such persons (which had been specially targeted by secret Russian psychotronic services since '30s) are being, without their knowledge, remotely "psychotronically treated": that is, their minds are "telepathically entangled" with minds of their controllers/"minders"; - which are capable, via this link, literally "to see through their eyes & feel their thoughts": cf. on p. 161 of A. Robbins' "Unlimited Power"; Ballantyne Books, 1989 - and also L. Niven's "Mote in God's Eye" & chapter "Suckers and Suicides" in S. Lee's "Dunn's Conundrum".)
"Natural telepathic links" in minds/souls of Russian emigrants around the globe, - now lying dormant, - might be activated, tremendously increasing their capacity, after beginning of full-scale functioning (in the mode of "global-scale psi-broadcaster") of long-projected "New Ahnenerbe": nationwide center where will be concentrated (like in Himmler's Ahnenerbe but on much higher modern level - and with much better financing!) all esoteric explorations (including non-conventional Leading Edge scientific disciplines like torsionics - which'll be harmonically synthesized, without annoying interference of "professional skeptics", with achievements of Ageless Wisdom).
As sources of inspiration/paragons for this enterprise of global importance will be taken not only such classical examples as first in the world Dr Barchenko's psi-research lab & Himmler's Ahnenerbe, but also such more modern outfits as GRU-sponsored Rejdak's Intl Assn for Psychotronic Research (which functioned as cover for "reborn Ahnenerbe" during Communist regime in f. Czechoslovakia) & Britain-based Scientific and Medical Network, many respected members of which are sympathizing these ideas.
(From this viewpoint there might be regarded as highly significant appearance in the last - No. 51/2006 - issue of influential Moscow weekly "Zavtra" ("To-Morrow"): www.zavtra.ru (which is regarded as an organ of Russian special services' elite: its Editor-in-Chief A. Prokhanov openly says about his close ties with GRU) of a large article bearing tritle "Putin is a target of PSI-weapons"; - where, - after wide (but not very deep) review of modern weapons of PSI/informational warfare, - there is made an appeal to increase measures of psychotronic defence of President & other VIPs, using most advanced modern technologies of psi-defence (including Internet-based).
Calls are made to the Ministry of Defence to organize special "Strategic Psychotronic Forces", which must constantly monitor minds of leaders of "potential enemy states".)"
Report today from Moscow by a Secret Agent for MASINT.
re: http://www.shipov.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://lifeboat.com/ex/bios.jack.sarfatti
http://video.google.com/videoplay?docid=-1310681739984181006&q=Sarfatti+Causation&hl=en
The Russian Torsionic Space Weapons Program is partially described in
The precursor to 6D Calabi-Yau space of the M-Theory Dream, it's hardly even a "program" yet, is already in the Kibble 1961 -> Shipov tetrad-based curvature + torsion extension of Einstein's point test particle curvature only theory of 1915.
The tetrad as "internal fiber" analog has 6 independent periodic angular degrees of freedom (in Euclidean metric) corresponding to the 6 dimensions of Calabi-Yau space.
Given a base space-time of dimension n, the number of extra independent degrees of freedom to orient the n-bein in the base space is
n(n + 1)/2 - n = n^2/2 + n/2 - n = n(n -1)/2 = number of undirected edges of the n-simplex.
The Poincare group has 10 parameters = 4x5/2
The conformal group has 15 parameters corresponding to n = 5 the Kaluza-Klein model with one extra base space dimension giving the 5-bein fiber needing 15 - 5 = 10 angles.
The n-beins or "oriented points" are proto "extended objects" like strings are. They are the non-vibrating ground states of the strings -> branes.
The pre-string physics must be implicit in eq (49).
The A4 curvature + torsion geodesic equation is (52). This is not the same as Einstein's 1915 geodesic curvature only equation.
The geodesic equation says that the objective covariant acceleration of the test particle relative to the given connection vanishes.
(54) -> (56) show that the Euclidean kinematical acceleration for the A4 geodesic observer who experiences no g-force. Therefore the Einstein equivalence principle in its original sense continues to be obeyed for the center of mass motion even in the A4 theory beyond Einstein's.
Newton's picture of inertial compensation for the weightless geodesic observer works in the extended theory where the torsion force exactly cancels the Newtonian gravity force on the A4 geodesic.
Both Einstein's (LC) and Shipov's A4 geodesic observers report the same experience, weightlessness. They both report special relativity working locally near them. The presence of curvature is not relevant to the last statement. They both report approximately zero kinematical acceleration d^2x^i/dt^2 = 0 for nearby geodesic test particles in the slow speed weak curvature field regime. However they have different informal language explanations.
1915 T4* (AKA GCT) Einstein observer says his LC connection vanishes at origin of his LIF.
The A4 Shipov observer says his GCT non-tensor LC connection is not zero, but it is exactly cancelled by his GCT tensor torsion T =/= 0 connection.
Note that the A4 connection has independent physical meaning from (LC) i.e.
A4 connection derives from locally gauging the 10-parameter Poincare group P10.
The (LC) connection derives from locally gauging the 4-parameter T4 subgroup of P10.
The cotorsion T connection derives from locally gauging the 6-parameter Lorentz subgroup O(1,3) of P10
therefore
(LC) = A4 - T
is meaningful in this context, but not in Z's where he only had 1915 GR i.e. only T4 locally gauged so that T = 0.
On Dec 22, 2006, at 1:15 PM, Jack Sarfatti wrote:
Gennady Shipov's teleparallel A4 geometry then has two distinct metric structures:
The Einstein translational metric of 1915 GR
ds^2 = e^ajeaidx^idx^j = e^aea
and the "Calabi-Yau"-like
d@^2 = T^abiT^bajdx^idx^j = T^abT^ba
Note that
d@^ba = T^bajdx^j is a 2-tangent fiber indexed 1-form
That is, for a world 4-vector infinitesimal displacement dx^i, d@^ba is the infinitesimal rotation of the e^b tetrad about the e^a tetrad and vice versa with a negative sign.
This, therefore, is the physical origin of Calabi-Yau space in string theory. It is, perhaps, a missing "organizing" idea of string theory.
The 3rd rank T4* world torsion tensor fields in terms of the tetrad tensor fields are
Ojk^i = e^iae[k,j]^a = (1/2)e^ia(ek,j^a - ej,k^a) = - Okj^i
,j is ordinary partial derivative
Here I use Shipov's notation where i,j = 0,1,2,3 (not 1,2,3 as below using u,v as world T4* tensor indices)
The contorsion T^ijk is a variation on the above torsion field. How appropriate that term is will be discussed later.
T^ij,k = - O^ij,k + g^i^m(gjsOmk^s + gksOmj^s)
g^i^m(gjsOmk^s + gksOmj^s) = g^i^m(Omkj + Omjk)= O^ikj + O^ijk
D is the symmetric torsion free Levi-Civita connection from 1915 plain vanilla GR.
Shipov proposes a symmetric "source" stress-energy tensor for 1915 GR built from the contortion tensor alone
Tjm("Matter")~ D[iT^i|j|m] + T^is[iT^s|j|m] - (1/2)gjmg^p^n{(D[iT^i|p|n] + T^is[iT^s|p|n]}
|...| means "exclude the ... index from the [ ] antisymmetrization or the ( ) symmetrization.
What Shipov does not show is how to get the lepton-quark spinor fields plus the electroweak-strong gauge boson fields all coming from this single contortion. However, that may be possible because Shipov does have a 9D + 1 space like string theory and for the same reason - spatially extended test particles not point particles.
That is, Shipov most show that this is the Ur "Master Field" of all the fields in the standard model at least. Since his structure is like string theory this may not be impossible.
The Einstein vacuum equation Rim = 0 entails
D[iT^i|j|m] + T^is[iT^s|j|m] = 0
The generalized geodesic equation is
d^2x^i/ds^2 + [(LC)^ijk + T^ijk](dx^j/ds)(dx^k/ds) = 0
Einstein's 1915 GR has
T^ijk(dx^j/ds)(dx^k/ds) = 0
Note that this equation can be true even if T^ijk =/= 0 in special cases.
Shipov calls this a "teleparallel A4" space-time because he uses the constraint that the generalized curvature tensor is zero i.e. globally flat for the extended A4 connection.
non-symmetric A4 connection = symmetric non T4* tensor 1915 GR Levi-Civita connection
+ antisymmetric T4* tensor contorsion
i.e. the covariant curl of the A4 connection with itself vanishes identically, i.e.
Define the 4th rank T4* tensor
P^ijkm = 2T^i[|k|j|m] + 2T^is[kT^s|j|m], then
S^ijkm = R^ijkm + P^ijkm = 0 "teleparallel"
There are 2 other key constraint's here.
,k is ordinary partial derivative
;k is T4* zero torsion 1915 GR covariant partial derivative
|k is A4 non-zero torsion covariant partial derivative for the local 10-parameter Poincare group
e^a[k|j] + T^i[kj]e^ai = 0
and the A4 Bianchi identities, which are
P^i[|kjk]m = 0
Shipov's theory is a special case of Kibble 1961 which has a non-symmetric stress tensor as I recall? The Poincare group has 10 parameters.
4 translations that when locally gauged give the General Coordinate transformations.
When not locally gauged there is no problem with global conservation of total`energy and momentum of non-gravity fields. You cannot have that global conservation in general when locally gauged. There is still local conservation however. Also the stress energy of gravity by itself is not local.
3 space rotations, which when not locally gauged lead to conservation of angular rotational momentum
3 Lorentz boosts.
The four A4 geodesic equations
d^2x^i/ds^2 + [(LC)^ijk + T^ijk](dx^j/ds)(dx^k/ds) = 0
are only for the CM motion.
There are 6 other equations of motion for the variation of the orientation of the 4 tetrad fields
e^a = e^audx^u
under teleparallel transport using the A4 Kibble 1961 connection
= 1915 GR (LC) + Contorsion
Those 6 are simply
e^a[k|j] + T^i[kj]e^ai = 0
for a single a since all 4 a are relatively rigidly fixed to each other i.e. a 4D rigid body, and the world indices k,j appear anti-symmetrized.
The teleparallel A4 geometry then has two distinct metric structures:
The Einstein translational metric of 1915 GR
ds^2 = e^ajeaidx^idx^j = e^aea
and the "Calabi-Yau"-like
d@^2 = T^abiT^bajdx^idx^j = T^abT^ba
Note that
d@^ba = T^bajdx^j is a 2-tangent fiber indexed 1-form
That is, for a world 4-vector infinitesimal displacement dx^i, d@^ba is the infinitesimal rotation of the e^b tetrad about the e^a tetrad and vice versa with a negative sign.
This, therefore, is the physical origin of Calabi-Yau space in string theory. It is, perhaps, a missing "organizing" idea of string theory.
On Dec 21, 2006, at 10:15 PM, Jack Sarfatti wrote:
"Diff(4)" = "GCT" = "local T4" = T4* here.
Einstein's 1915 GR from the modern POV of local gauge theory is the universal local gauging of the T4 invariance of the actions of all non-gravity fields. The local variable compensating gauge potential is warped tetrad e^au fundamental gravitational field A^au analogous to Au in U(1) EM and Au^a in Yang-Mills theory of the weak SU(2) and SU(3) strong forces. SU(2) has the vacuum ODLRO Higgs field with Goldstone phase coherence and it breaks left-right chiral symmetry (parity - broken mirror symmetry).
Tensors transform multilinearly homogeneously under representations of a given group.
Einstein's geometrodynamic objects like the metric field guv and the torsion-free Levi-Civita connection (LC)uv^w = (LC)vu^w are composite objects
guv = e^au(Minkowski)abe^bv = (I^au + A^au)(Minkowski)ab(I^bv + A^bv)
For the Schwarzschild static solution outside the event horizon for static LNIF observers
e^00 = (1 - 2rs/r)^1/2
e^01,2,3 = 0
e^11 = (1 - 2rs/r)^-1/2
e^i,j = &^ij Kronecker delta for i,j = 1,2,3
In the weak field limit
A^00 ~ -rs/r = GM/c^2r = -(Gh/c^3)(Mc/h)(1/r) = -[(Planck Area)/(Compton wavelength)](1/r)
rs/r ~ Lp(Theta^0Phi^0,0 - Theta^0,0Phi^0)
Fix a gauge, i.e. select a degenerate ODLRO vacuum where Theta^0 = pi
Phi^0 ~ Lp(Mc/h)(ct/r)(1/pi)
Phi^0,0 = Lp(Mc/h)(1/pir)
A^11 ~ +rs/r
all other A^ai = 0
note the linear elastic and nonlinear plastic terms in the expansion of the metric field.
I^a is curvilinear in LNIF representations. It is Kronecker delta in LIF representations.
(Globally Flat Curvilinear Metric)uv = I^au(Minkowski)abI^bv
Only (Minkowski)ab is the constant 4x4 diagonal matrix in the geodesic representation.
(LC)uv^w = (1/2)e^wa[e^au,v + e^av,u] = e^wae^a(u,v)
,u = d/dx^u ordinary partial derivative
The T4* covariant partial derivatives are themselves T4* tensors.
DB^w/dx^u = B^w,u + (LC)^wuvB^v
more complicated for higher rank tensors
The T4* geodesic equation is
covariant absolute translational general relativistic acceleration of CM of test particle vanishes is
D^2x^w/ds^2 = d^2x^w/ds^2 + (LC)^wuv(dx^u/ds)(dx^v/ds) = 0
d^2x^w/ds^2 = special relativistic acceleration
(LC)^wuv(dx^u/ds)(dx^v/ds) = LNIF acceleration
Geodesic equation says
GR acceleration = SR acceleration + LNIF acceleration = 0
"Newton's First Law" = geodesic equation
In all mechanical theories. Curvature is irrelevant because this translational equation is only for the exact mathematical point center of mass CM of the extended test particle.
The LIF corresponds to geodesic normal coordinates where (LC)^wuv = 0 at the LIF ORIGIN.
The Newtonian inertial forces are already in (LC) without any torsion. This is shown explicitly by C. Lanczos.
(1/2)[(LC)^i^0k - (LC)^k^0i] = (1/2)(g0k,i - g0i,k) ~ CurlU = H
U = gravimagnetic potential (g01,g02,g03)
"On the Problem of Rotation in the General Theory of Relativity"
Kornel Lanczos, 1923
The inertial force in a non-inertial frame on test particle of rest mass m in 1915 torsion-free GR is
F^i(inertial) = m(LC)^r^siVrVs
Vr is special relativity 4-velocity
When V/c << 1 SLOW SPEED Galilean limit of near absolute simultaneity.
Fi(inertia) ~ Fi(Centrifugal) + Fi(Coriolis) + Fi(?)
summation convention here is restricted to i = 1,2,3
Fi(Centrifugal) ~ (m/g00)(LC)^0^0i
Fi(Coriolis) ~ (2m/g00)(LC)^0^siVs
There is also a quadratic inertial force
Fi ~ (m/g00)(LC)^r^siVrVs
not mentioned in Newtonian classical mechanics courses.
Start in a geodesic representation of globally flat Minkowski spacetime i.e. no real intrinsic warp GCT tensor fields of either curvature or torsion.
ds^2 = dx^2 + dy^2 + dz^2 - dt^2 c = 1
Go to a rotating non-inertial frame at constant rotation speed w about the z axis, in this rotating non-inertial global frame
ds^2 ~ dx'^2 + dy'^2 + dz'^2 - 2wy'dx'dt + 2wx'dy'dt - [1 - w^2(x'^2 + y'^2)]dt^2
where in this Galilean approximation
1 >> w^2(x'^2 + y'^2) = w^2r^2 in cylindrical coordinates, w pseudo 3-vector along z-axis
Fi(Centrifugal) ~ (m/g00)(LC)^0^0i ~ mwxwxr'
Fi(Coriolis) ~ (2m/g00)(LC)^0^siVs ~ 2mwxv'
On Dec 21, 2006, at 2:38 PM, Jack Sarfatti wrote:
Informal language
Shipov's term "accelerated locally Lorentzian frame" are "like those of elevators in free fall" are what MTW call LIF's. The "accelerated" is from Newton's picture.
The Einstein 1915 geodesic equation for the center of mass motion of an extended test body (i.e. we ignore its self-field) is
c^2D^2x^u/ds^2 = c^2d^2x^u/ds^2 + c^2(LC)^uvw(dx^v/ds)(dx^w/ds) = 0
where formally
ds^2 = guvdx^udx^v = e^aue^bv(Minkowski Metric)ab
However, to be more rigorous
D^2x^u/ds^2 = (D/ds)(D/ds)x^u
Tetrads are e^au = I^au + A^au(WARP)
In a globally flat spacetime region
A^au(WARP) = 0 globally in the specified region.
A^au(WARP) is the compensating gauge potential from localizing the spacetime symmetry group T4 on all non-gravity actions analogous to localizing U(1) internal symmetry only on charged source fields.
I^au -> Kronecker delta in a geodesic not translationally accelerating and not rotating inertial frame.
However in a non-geodesic translationally accelerating and/or rotating non-inertial frame then I^au is an arbitrary curvilinear field with zero Riemann curvature.
is the local fundamental invariant under both local Lorentz transformations and GCTs that are locally gauged T4 translation group transformations called loosely "Diff(4)."
(LC)^uvw = (LC)^uwv is the non-tensor Levi-Civita connection field for parallel transport of tensors on world lines in the curved 4D base spacetime of the (co)tangent bundle.
c^2D^2x^u/ds^2 is the GCT covariant tensor absolute acceleration of the test particle that is zero!
Only in a locally coincident non-geodesic frame (LNIF) will this geodesic test particle have a non-vanishing Newtonian-Euclidean acceleration c^2d^2x^u/ds^2 =/= 0 i.e.
c^2d^2x^u/ds^2 = - c^2(LC)^uvw(dx^v/ds)(dx^w/ds)
The measured acceleration of the test particle relative to the non-geodesic LNIF observer is called an "inertial force per unit test mass" in the 1915 GR without torsion fields.
The idea is that in "local geodesic normal coordinates"
(LC)^uvw = 0 at the origin of those local coordinates only AKA Einstein equivalence principle.
So to a good approximation, the local LIF Guy sees c^2d^2x^u/ds^2 = 0. The coincident local LNIF Gal does not see that as zero. Both, however agree that the first-rank GCT tensor covariant acceleration of the test body is zero. That is,
c^2D^2x^u/ds^2 = 0 FOR ALL OBSERVERS
this is Newton's First Law - works even in GR on geodesics even when there is curvature.
(LC) is 100% non-tensor i.e. its only tensor piece is zero and that is a local frame invariant fact.
So moral - be careful to distinguish "GCT covariant tensor kinematics" from Poincare group covariant kinematics.
Note that
c^2d^2x^u/ds^2 is a special relativity Poincare group tensor, but it is not a 1915 GR localized T4 group tensor. That tensor is c^2D^2x^u/ds^2.
On Dec 21, 2006, at 1:44 PM, Jack Sarfatti wrote:
Useful fact to remember
hc, e^2 , Gm^2
quantum electricity gravity
all have the same physical dimensions.
Their 3 distinct ratios
hc/e^2
Gm^2/e^2
Gm^2/hc
are all dimensionless numbers.
On Dec 21, 2006, at 1:19 PM, Jack Sarfatti wrote:
From the local gauge theory POV Shipov's new coupling seems to come from locally gauging the 15 parameter massless twistor conformal group with vacuum ODLRO to give the gauge quanta mass. The conformal quanta would be spin 1 forming entangled massive pairs of spin 0, spin 1 & spin 2. I think Tony Smith previously suggested something along these lines?
Shipov's new physics in his 1972 thesis was to add in the effects of hyperbolic boosts to uniformly accelerating frames in Maxwell's electrodynamics - no gravity G at all - no equivalence principle here?
On Dec 21, 2006, at 1:12 PM, Jack Sarfatti wrote:
There is a typo in Shipov's eq. (0.1) for his "geometrized electrodynamics." He writes
Rik - (1/2)gikR = (8pie/mc^4)Tik
(8pie/mc^4) has the wrong physical dimensions. The correct formula is
(e/mc^2)^2 = (Classical Electron Radius)/mc^2 i.e. (string tension)^-1
This is to be compared to G/c^4 with the same physical dimensions converting pressure to curvature.
Note that numerically this is ~ 10^-13 cm/10^-3 Gev ~ 10^-10 cm/Gev
In contrast G/c^4 ~ 10^-33cm/10^19Gev = 10^-52 cm/Gev
therefore Shipov's electro-gravitic coupling is 42 powers of 10 more powerful than Newton's gravity.
Is this equation true?
Shipov says he derived it in 1972 extending Einstein's special relativity electrodynamics to include uniformly accelerating frames. Are those the 4 conformal boosts?
Now if this is really so, it suggest a whole new approach to the metric engineering of warp and wormhole in which, perhaps, the alleged alien ET flying saucers are able to replace the usual much too weak G/c^4 coupling of stress-energy density to curvature with the (e/mc^2)^2 electro-gravitic coupling 42 Powers of Ten stronger. That's a whole new ball game. Note I am not saying, at this stage, that they are doing that OUT THERE. I am thinking on it. Such a coupling would need a massive graviton with a mass ~ ~ hc/(nanometers). It obviously cannot be a long-range field or it would destroy the universe.
On Dec 20, 2006, at 6:47 PM, Jack Sarfatti wrote:
Note that Shipov constructs a symmetrical Yang-Mills type source tensor from his torsion field with the torsion field analogous to the EM/Yang-Mills fields. This may not be general enough because Kibble 1961 says that the local gauging of the 10-parameter Poincare group will give a non-symmetrical piece to the stress-energy tensor i.e. a non-symmetric metric and Einstein tensor as considered in one of Einstein's attempts at a classical unified field theory. C. Lanczos shows that in such a theory there is propellantless propulsion. So this idea needs not to be forgotten.
On Dec 20, 2006, at 6:35 PM, Jack Sarfatti wrote:
Both Shipov and I independently associate anti-gravitating repulsive dark energy with variable local torsion fields.
My basic argument in e.g.
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
Guv(vacuum) + /\zpfguv = 0
if the torsion field is zero globally
Guv^;v = 0
Therefore
/\zpf^,v = 0
since
guv^;v = 0
One way to have /\zpf^,v =/= 0 in vacuum is to have the additional torsion field beyond Einstein's 1915 theory.
Note that even without torsion
/\zpf^,vguv + Tuv^;v(non-gravity source fields) = 0
http://www.shipov.com
The complete paper can be downloaded from http://www.shipov.com/science.html
e^am are the tetrad components, T^abm are the torsion field components, R^abkm are the curvature field components.
Note that Shipov's (45) is analogous to the ODLRO superflow field in liquid Helium II below the Lambda Point where the zero point energy dominates.
vm = (h/m)(Phase),m
In equation (84) Shipov gets a quintessent field from a particular model of the torsion tensor field leading from the torsion field version of the Yang-Mills type source (39) to (83).
In my theory Shipov's Lambda in (84) is
/\zpf(xi) = (Quantum of Area)^-1(|Vacuum ODLRO Higgs Field|^2 - 1)
that is repulsive positive dark energy density when positive and is attractive dark matter density when negative, assuming here w = -1.
Sunday, September 03, 2006
Baron Munchausen Meets Rube Goldberg in Einstein's Elevator
PS No matter how hard the Baron fires his rocket motor, his non-geodesic world line must be inside the forward light cone at each point on that world line. The field of light cones is not parallel in curved space-time so that the bundle of non-geodesics available to the Baron is not identical to what it would be in globally flat space-time. Therefore, one must take the connection field of the source in some global coordinates like the asymptotic flat "Book Keeper coordinates" (Wheeler's term) in
ds^2 = (1 - 2M/r)dt^2 - (1 - 2M/r)^-1dr^2 + r^2(dtheta^2 + sin^2thetadphi^2)
to make the problem simpler let theta = pi/2 equatorial orbit
x^1 is radial r, x^3 is azimuthal phi, the only non-zero LC-connection components then are
(^010) = (M/r^2)(1 - 2M/r)^-1
(^133) = -r(1 - 2M/r)
(^100) = (M/r^2)(1 - 2M/r)
(^313) = 1/r
For the fiducial hovering LNIF shell observers at fixed r
dt(shell) = (1 - 2M/r)^1/2dt
dr(shell) = (1 - 2M/r)^-1/2dr
dphi(shell) = dphi
So for an arbitrary motion of the Baron subject to the above causal light cone restriction, one needs to find the GCT from the shell observer to the Baron to do find the Baron's coincident connection field relative to the shell observer.
i.e. symbolically we have the CONTINGENT inhomogeneous non-tensor transformation from non-geodesic LNIF Shell Observer to the non-geodesic LNIF Baron
(Baron) = (GCT)(GCT)(GCT)(Shell Observer) + (GCT)Grad(GCT)
This is not intrinsic. This is not of any fundamental theoretical interest. It is contingent even though one can formally relate it to curvature, it's Fool's Gold. It's a Chimera. It's The Siren beckoning. Also it is a very complex calculation in general not worth the effort since the Baron would do better to directly measure his local g with a scale.
On Sep 3, 2006, at 8:23 PM, Jack Sarfatti wrote:
The word "fictitious" is a bad one like "hidden variables" in Bohm's reinterpretation of quantum theory. You certainly "feel" a "fictitious" g and it will cause a pointer on a suitable detector to move. Therefore, fictitious forces, or inertial forces, are physical in that they are detectable. However, they are not tensors relative to the relevant symmetry groups, therefore, one cannot construct objective frame-invariants from them under those symmetry groups. In this subtle sense I meant "g-forces are not physical" or "g-forces are fictitious" although in a pragmatic experiential sense they are real!
The covariant equation for the NON-geodesic in ALL frames is
D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 + (Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = F^u(non-gravity)/m(test)
If Alice is LIF her connection vanishes and she sees the special relativity F = ma
D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 = F^u(non-gravity)/m(test)
What does the Baron see in his own LNIF rest frame when he fires a small rocket motor on his cannon ball?
D^2x^u(Baron)/ds^2 = (Connection Baron)^u00(dx^0(Baron)/ds)(dx^0(Baron)/ds) = F^u(Baron)/m(Baron)
(Connection Baron)^u00(dx^0(test)/ds)(dx^0(test)/ds) - F^u(non-gravity)/m(Baron) = 0
(Connection Baron)^000(dx^0(test)/ds)(dx^0(test)/ds) - F^0(non-gravity)/m(Baron) = 0
(Connection Baron)^i00(dx^0(test)/ds)(dx^0(test)/ds) - F^i(non-gravity)/m(Baron) = 0
i = 1,2,3 spacelike
The experienced "fictitious" inertial nongeodesic g-force in the Baron's frame is simply
g-force = {(Connection Baron)^i00}
= {F^i(non-gravity)/m(Baron)}
Notice that curvature is completely irrelevant i.e. gradients of the connection play no role whatsoever.
Let the Baron in his LNIF rest frame look at a Alice who is on a geodesic. The Baron's version of Alice's geodesic equation is
D^2x^u(Alice)/ds^2
= d^2x^u(Alice)/ds^2 + (Connection Baron)^uvw(dx^v(Alice)/ds)(dx^w(Alice)/ds) = 0
This simplifies to
= d^2x^u(Alice)/ds^2 + (Connection Baron)^u00(dx^0(Alice)/ds)(dx^0(Alice)/ds) = 0
= d^2x^u(Alice relative to Baron)/ds^2
+ F^i(non-gravity on Baron)/m(Baron)(dx^0(Alice relative to Baron)/ds)^2 = 0
Now above assumes Minkowski space-time.
Suppose all of the above happens in the vacuum curvature field of an SSS source
g00 = (1 - 2M(source)/r) = - 1/grr etc.
in the usual asymptotic coordinates.
Let Alice and the Baron be momentarily close to a given r,theta, phi, t.
For example, in the equatorial plane theta = pi/2 "1" = "r"
(SSS connection)^100 = M/r^2(1 - 2M/r) etc.
One would then have to find the GCT connecting the nearly coincident static shell observer to the Baron. If, for example, the Baron adjusted his rocket motor to be a shell observer, then the GCT is the trivial identity transformation and one can then use
(SSS connection)^100 = M/r^2(1 - 2M/r)
Actually doing a detailed calculation is not trivial.
From: Jack Sarfatti
Date: September 3, 2006 4:58:01 PM PDT
To: Sarfatti_Physics_Seminars@yahoogroups.com
Subject: Re: Zielinski fails to grasp the subtle beauties of Einstein's Vision
On Sep 3, 2006, at 1:16 PM, xerberos2 wrote:
Jack wrote:You misread Einstein's text ...
I'm not misreading his text. Einstein's text is very clear. He is
proposing to treat a fictitious inertial field as if it were a real
gravitational field, so that he can pretend that the accelerating
frame K' is not accelerating.
By "real gravitational field" he means in the sense of Newton's theory.
K' that is non-geodesic in curved space-time is locally equivalent to a geodesic inertial frame in flat space-time with a "real" gravity field. This is Einstein's bridge back to Newton's theory. "geodesic" has two different meanings in the same sentence here.
"Real gravitational g-field" is meaningful in Newton's theory in flat Euclidean 3D space with absolute simultaneity (Galilean relativity v/c ---> 0) where the Newtonian geodesics are straight lines in flat Euclidean 3D space with point test particles moving at constant speed along them. That's the Newtonian geodesic. There is zero g-force on Newton's geodesic.
"g-field" in Einstein's theory means exactly the same thing as in Newton's theory except that the notion of geodesic has changed. An Einstein geodesic projected down into 3D space is generally not a straight line nor is the test particle speed constant. For example the Earth's elliptical orbit around the Sun is geodesic relative to the Sun's curvature field - to a good approximation. Curvature is geodesic deviation. g-forces are non-zero only on non-geodesics created by non-gravity (essentially electromagnetic) forces. There is no necessary intrinsic relationship of a g-force event to the local curvature.
Now, what confuses Zielinski is the following: consider a cannon ball in free fall as in
http://www.zonalibre.org/blog/diversovariable/archives/baron-munchausen.jpg
Newton's explanation: the Baron and the cannonball are NOT on a geodesic, therefore, there is a real gravitational force per unit test mass on both the Baron and the cannonball relative to the frame K' (surface of Earth) that is "inertial" to a good approximation. It is the same real gravitational force per unit test mass g for both
g-force(Newton) ~ GM(Earth)/r^2
Therefore, the Baron feels weightless, i.e. no pressure on his behind from the cannonball since each are falling in exactly the same way at every moment. That is, there is zero g-force in the common rest frame of the Baron and the cannonball.
Einstein's explanation: the Baron and the cannon ball are on a timelike geodesic in curved space-time.
The covariant equation for the geodesic in ALL frames is
D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 + (Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = 0
This is the covariant
F = ma
with
F = 0
This form-invariant (local frame covariant) equation means.
OBJECTIVE TENSOR TEST PARTICLE ACCELERATION = 0
This is the DEFINITION of a GEODESIC!
THIS IS TRUE IN ALL FRAMES FOR ALL POSSIBLE CURVATURES INCLUDING GLOBALLY FLAT ZERO EVERYWHERE-WHEN.
D^2x^u(test)/ds^2 is the GCT tensor acceleration of the test particle. Its local frame-invariant scalar is
g = (D^2x^u(test)/ds^2D^2xu(test)/ds^2)^1/2
g = 0 on a geodesic - universally true!
Look more closely at the meaning of the geodesic equation. Let Baron Munchausen be on the test particle that is the cannonball in the above picture.
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2 + (Connection)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds) = 0
d^2x^u(Baron)/ds^2 = Newton's flat space + time kinematical acceleration that is not a GCT tensor.
(Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = inertial "force per test mass" that is a contingent artifact of the local frame of reference. This term even exists in globally flat spacetime when K' is accelerating from an electromagnetic force.
Let Alice be a nearly coincident to the Baron geodesic LIF in curved space-time. What Alice sees is
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2
= 0
(Connection Alice LIF) = 0
The size of Alice's LIF is such that the gradients in (Connection Alice LIF) are ignorable. You can think of the LIF as a ball at the bottom of a potential well with a very small zero point jiggle - this is only a rough analogy.
http://rsc.anu.edu.au/~sevick/groupwebpages/images/animations/capture_3D0282.jpg
Let Bob be a nearly coincident to the Baron non-geodesic LNIF observer, then in Bob's POV
D^2x^u(Baron)/ds^2
= d^2x^u(Baron)/ds^2 + (Connection Bob)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds)
= 0
(Connection Bob) =/= 0
Because an electromagnetic force is acting on Bob.
Finally in the Baron's rest frame, which in this case is also geodesic
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2
= 0
dx^i/ds = 0
i = 1,2,3 spacelike
dx^0/ds = 1
This covers all of the cases.
Homework Problem: Put an external force on the Baron. Describe all the cases.
In answer to Z's question about Wheeler. When Wheeler says gravity is curvature he means tensor "geodesic deviation" he does not mean contingent non-tensor non-geodesic "g-force."
"Gravity" and "gravity field" mean different things in different contexts. Usually this is not a problem for physicists to get the nuance intended in each specific. It is a problem for Z.
PS No matter how hard the Baron fires his rocket motor, his non-geodesic world line must be inside the forward light cone at each point on that world line. The field of light cones is not parallel in curved space-time so that the bundle of non-geodesics available to the Baron is not identical to what it would be in globally flat space-time. Therefore, one must take the connection field of the source in some global coordinates like the asymptotic flat "Book Keeper coordinates" (Wheeler's term) in
ds^2 = (1 - 2M/r)dt^2 - (1 - 2M/r)^-1dr^2 + r^2(dtheta^2 + sin^2thetadphi^2)
to make the problem simpler let theta = pi/2 equatorial orbit
x^1 is radial r, x^3 is azimuthal phi, the only non-zero LC-connection components then are
(^010) = (M/r^2)(1 - 2M/r)^-1
(^133) = -r(1 - 2M/r)
(^100) = (M/r^2)(1 - 2M/r)
(^313) = 1/r
For the fiducial hovering LNIF shell observers at fixed r
dt(shell) = (1 - 2M/r)^1/2dt
dr(shell) = (1 - 2M/r)^-1/2dr
dphi(shell) = dphi
So for an arbitrary motion of the Baron subject to the above causal light cone restriction, one needs to find the GCT from the shell observer to the Baron to do find the Baron's coincident connection field relative to the shell observer.
i.e. symbolically we have the CONTINGENT inhomogeneous non-tensor transformation from non-geodesic LNIF Shell Observer to the non-geodesic LNIF Baron
(Baron) = (GCT)(GCT)(GCT)(Shell Observer) + (GCT)Grad(GCT)
This is not intrinsic. This is not of any fundamental theoretical interest. It is contingent even though one can formally relate it to curvature, it's Fool's Gold. It's a Chimera. It's The Siren beckoning. Also it is a very complex calculation in general not worth the effort since the Baron would do better to directly measure his local g with a scale.
On Sep 3, 2006, at 8:23 PM, Jack Sarfatti wrote:
The word "fictitious" is a bad one like "hidden variables" in Bohm's reinterpretation of quantum theory. You certainly "feel" a "fictitious" g and it will cause a pointer on a suitable detector to move. Therefore, fictitious forces, or inertial forces, are physical in that they are detectable. However, they are not tensors relative to the relevant symmetry groups, therefore, one cannot construct objective frame-invariants from them under those symmetry groups. In this subtle sense I meant "g-forces are not physical" or "g-forces are fictitious" although in a pragmatic experiential sense they are real!
The covariant equation for the NON-geodesic in ALL frames is
D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 + (Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = F^u(non-gravity)/m(test)
If Alice is LIF her connection vanishes and she sees the special relativity F = ma
D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 = F^u(non-gravity)/m(test)
What does the Baron see in his own LNIF rest frame when he fires a small rocket motor on his cannon ball?
D^2x^u(Baron)/ds^2 = (Connection Baron)^u00(dx^0(Baron)/ds)(dx^0(Baron)/ds) = F^u(Baron)/m(Baron)
(Connection Baron)^u00(dx^0(test)/ds)(dx^0(test)/ds) - F^u(non-gravity)/m(Baron) = 0
(Connection Baron)^000(dx^0(test)/ds)(dx^0(test)/ds) - F^0(non-gravity)/m(Baron) = 0
(Connection Baron)^i00(dx^0(test)/ds)(dx^0(test)/ds) - F^i(non-gravity)/m(Baron) = 0
i = 1,2,3 spacelike
The experienced "fictitious" inertial nongeodesic g-force in the Baron's frame is simply
g-force = {(Connection Baron)^i00}
= {F^i(non-gravity)/m(Baron)}
Notice that curvature is completely irrelevant i.e. gradients of the connection play no role whatsoever.
Let the Baron in his LNIF rest frame look at a Alice who is on a geodesic. The Baron's version of Alice's geodesic equation is
D^2x^u(Alice)/ds^2
= d^2x^u(Alice)/ds^2 + (Connection Baron)^uvw(dx^v(Alice)/ds)(dx^w(Alice)/ds) = 0
This simplifies to
= d^2x^u(Alice)/ds^2 + (Connection Baron)^u00(dx^0(Alice)/ds)(dx^0(Alice)/ds) = 0
= d^2x^u(Alice relative to Baron)/ds^2
+ F^i(non-gravity on Baron)/m(Baron)(dx^0(Alice relative to Baron)/ds)^2 = 0
Now above assumes Minkowski space-time.
Suppose all of the above happens in the vacuum curvature field of an SSS source
g00 = (1 - 2M(source)/r) = - 1/grr etc.
in the usual asymptotic coordinates.
Let Alice and the Baron be momentarily close to a given r,theta, phi, t.
For example, in the equatorial plane theta = pi/2 "1" = "r"
(SSS connection)^100 = M/r^2(1 - 2M/r) etc.
One would then have to find the GCT connecting the nearly coincident static shell observer to the Baron. If, for example, the Baron adjusted his rocket motor to be a shell observer, then the GCT is the trivial identity transformation and one can then use
(SSS connection)^100 = M/r^2(1 - 2M/r)
Actually doing a detailed calculation is not trivial.
From: Jack Sarfatti
Date: September 3, 2006 4:58:01 PM PDT
To: Sarfatti_Physics_Seminars@yahoogroups.com
Subject: Re: Zielinski fails to grasp the subtle beauties of Einstein's Vision
On Sep 3, 2006, at 1:16 PM, xerberos2 wrote:
Jack wrote:You misread Einstein's text ...
I'm not misreading his text. Einstein's text is very clear. He is
proposing to treat a fictitious inertial field as if it were a real
gravitational field, so that he can pretend that the accelerating
frame K' is not accelerating.
By "real gravitational field" he means in the sense of Newton's theory.
K' that is non-geodesic in curved space-time is locally equivalent to a geodesic inertial frame in flat space-time with a "real" gravity field. This is Einstein's bridge back to Newton's theory. "geodesic" has two different meanings in the same sentence here.
"Real gravitational g-field" is meaningful in Newton's theory in flat Euclidean 3D space with absolute simultaneity (Galilean relativity v/c ---> 0) where the Newtonian geodesics are straight lines in flat Euclidean 3D space with point test particles moving at constant speed along them. That's the Newtonian geodesic. There is zero g-force on Newton's geodesic.
"g-field" in Einstein's theory means exactly the same thing as in Newton's theory except that the notion of geodesic has changed. An Einstein geodesic projected down into 3D space is generally not a straight line nor is the test particle speed constant. For example the Earth's elliptical orbit around the Sun is geodesic relative to the Sun's curvature field - to a good approximation. Curvature is geodesic deviation. g-forces are non-zero only on non-geodesics created by non-gravity (essentially electromagnetic) forces. There is no necessary intrinsic relationship of a g-force event to the local curvature.
Now, what confuses Zielinski is the following: consider a cannon ball in free fall as in
http://www.zonalibre.org/blog/diversovariable/archives/baron-munchausen.jpg
Newton's explanation: the Baron and the cannonball are NOT on a geodesic, therefore, there is a real gravitational force per unit test mass on both the Baron and the cannonball relative to the frame K' (surface of Earth) that is "inertial" to a good approximation. It is the same real gravitational force per unit test mass g for both
g-force(Newton) ~ GM(Earth)/r^2
Therefore, the Baron feels weightless, i.e. no pressure on his behind from the cannonball since each are falling in exactly the same way at every moment. That is, there is zero g-force in the common rest frame of the Baron and the cannonball.
Einstein's explanation: the Baron and the cannon ball are on a timelike geodesic in curved space-time.
The covariant equation for the geodesic in ALL frames is
D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 + (Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = 0
This is the covariant
F = ma
with
F = 0
This form-invariant (local frame covariant) equation means.
OBJECTIVE TENSOR TEST PARTICLE ACCELERATION = 0
This is the DEFINITION of a GEODESIC!
THIS IS TRUE IN ALL FRAMES FOR ALL POSSIBLE CURVATURES INCLUDING GLOBALLY FLAT ZERO EVERYWHERE-WHEN.
D^2x^u(test)/ds^2 is the GCT tensor acceleration of the test particle. Its local frame-invariant scalar is
g = (D^2x^u(test)/ds^2D^2xu(test)/ds^2)^1/2
g = 0 on a geodesic - universally true!
Look more closely at the meaning of the geodesic equation. Let Baron Munchausen be on the test particle that is the cannonball in the above picture.
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2 + (Connection)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds) = 0
d^2x^u(Baron)/ds^2 = Newton's flat space + time kinematical acceleration that is not a GCT tensor.
(Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = inertial "force per test mass" that is a contingent artifact of the local frame of reference. This term even exists in globally flat spacetime when K' is accelerating from an electromagnetic force.
Let Alice be a nearly coincident to the Baron geodesic LIF in curved space-time. What Alice sees is
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2
= 0
(Connection Alice LIF) = 0
The size of Alice's LIF is such that the gradients in (Connection Alice LIF) are ignorable. You can think of the LIF as a ball at the bottom of a potential well with a very small zero point jiggle - this is only a rough analogy.
http://rsc.anu.edu.au/~sevick/groupwebpages/images/animations/capture_3D0282.jpg
Let Bob be a nearly coincident to the Baron non-geodesic LNIF observer, then in Bob's POV
D^2x^u(Baron)/ds^2
= d^2x^u(Baron)/ds^2 + (Connection Bob)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds)
= 0
(Connection Bob) =/= 0
Because an electromagnetic force is acting on Bob.
Finally in the Baron's rest frame, which in this case is also geodesic
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2
= 0
dx^i/ds = 0
i = 1,2,3 spacelike
dx^0/ds = 1
This covers all of the cases.
Homework Problem: Put an external force on the Baron. Describe all the cases.
In answer to Z's question about Wheeler. When Wheeler says gravity is curvature he means tensor "geodesic deviation" he does not mean contingent non-tensor non-geodesic "g-force."
"Gravity" and "gravity field" mean different things in different contexts. Usually this is not a problem for physicists to get the nuance intended in each specific. It is a problem for Z.
Newton vs Einstein
On Sep 3, 2006, at 1:16 PM, xerberos2 wrote:
Jack wrote:You misread Einstein's text ...
I'm not misreading his text. Einstein's text is very clear. He is
proposing to treat a fictitious inertial field as if it were a real
gravitational field, so that he can pretend that the accelerating
frame K' is not accelerating.
By "real gravitational field" he means in the sense of Newton's theory.
K' that is non-geodesic in curved space-time is locally equivalent to a geodesic inertial frame in flat space-time with a "real" gravity field. This is Einstein's bridge back to Newton's theory. "geodesic" has two different meanings in the same sentence here.
"Real gravitational g-field" is meaningful in Newton's theory in flat Euclidean 3D space with absolute simultaneity (Galilean relativity v/c ---> 0) where the Newtonian geodesics are straight lines in flat Euclidean 3D space with point test particles moving at constant speed along them. That's the Newtonian geodesic. There is zero g-force on Newton's geodesic.
"g-field" in Einstein's theory means exactly the same thing as in Newton's theory except that the notion of geodesic has changed. An Einstein geodesic projected down into 3D space is generally not a straight line nor is the test particle speed constant. For example the Earth's elliptical orbit around the Sun is geodesic relative to the Sun's curvature field - to a good approximation. Curvature is geodesic deviation. g-forces are non-zero only on non-geodesics created by non-gravity (essentially electromagnetic) forces. There is no necessary intrinsic relationship of a g-force event to the local curvature.
Now, what confuses Zielinski is the following: consider a cannon ball in free fall as in
http://www.zonalibre.org/blog/diversovariable/archives/baron-munchausen.jpg
Newton's explanation: the Baron and the cannonball are NOT on a geodesic, therefore, there is a real gravitational force per unit test mass on both the Baron and the cannonball relative to the frame K' (surface of Earth) that is "inertial" to a good approximation. It is the same real gravitational force per unit test mass g for both
g-force(Newton) ~ GM(Earth)/r^2
Therefore, the Baron feels weightless, i.e. no pressure on his behind from the cannonball since each are falling in exactly the same way at every moment. That is, there is zero g-force in the common rest frame of the Baron and the cannonball.
Einstein's explanation: the Baron and the cannon ball are on a timelike geodesic in curved space-time.
The covariant equation for the geodesic in ALL frames is
D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 + (Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = 0
This is the covariant
F = ma
with
F = 0
This form-invariant (local frame covariant) equation means.
OBJECTIVE TENSOR TEST PARTICLE ACCELERATION = 0
This is the DEFINITION of a GEODESIC!
THIS IS TRUE IN ALL FRAMES FOR ALL POSSIBLE CURVATURES INCLUDING GLOBALLY FLAT ZERO EVERYWHERE-WHEN.
D^2x^u(test)/ds^2 is the GCT tensor acceleration of the test particle. Its local frame-invariant scalar is
g = (D^2x^u(test)/ds^2D^2xu(test)/ds^2)^1/2
g = 0 on a geodesic - universally true!
Look more closely at the meaning of the geodesic equation. Let Baron Munchausen be on the test particle that is the cannonball in the above picture.
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2 + (Connection)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds) = 0
d^2x^u(Baron)/ds^2 = Newton's flat space + time kinematical acceleration that is not a GCT tensor.
(Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = inertial "force per test mass" that is a contingent artifact of the local frame of reference. This term even exists in globally flat spacetime when K' is accelerating from an electromagnetic force.
Let Alice be a nearly coincident to the Baron geodesic LIF in curved space-time. What Alice sees is
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2
= 0
(Connection Alice LIF) = 0
The size of Alice's LIF is such that the gradients in (Connection Alice LIF) are ignorable. You can think of the LIF as a ball at the bottom of a potential well with a very small zero point jiggle - this is only a rough analogy.
http://rsc.anu.edu.au/~sevick/groupwebpages/images/animations/capture_3D0282.jpg
Let Bob be a nearly coincident to the Baron non-geodesic LNIF observer, then in Bob's POV
D^2x^u(Baron)/ds^2
= d^2x^u(Baron)/ds^2 + (Connection Bob)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds)
= 0
(Connection Bob) =/= 0
Because an electromagnetic force is acting on Bob.
Finally in the Baron's rest frame, which in this case is also geodesic
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2
= 0
dx^i/ds = 0
i = 1,2,3 spacelike
dx^0/ds = 1
This covers all of the cases.
Homework Problem: Put an external force on the Baron. Describe all the cases.
In answer to Z's question about Wheeler. When Wheeler says gravity is curvature he means tensor "geodesic deviation" he does not mean contingent non-tensor non-geodesic "g-force."
"Gravity" and "gravity field" mean different things in different contexts. Usually this is not a problem for physicists to get the nuance intended in each specific. It is a problem for Z.
On Sep 3, 2006, at 1:16 PM, xerberos2 wrote:
Jack wrote:You misread Einstein's text ...
I'm not misreading his text. Einstein's text is very clear. He is
proposing to treat a fictitious inertial field as if it were a real
gravitational field, so that he can pretend that the accelerating
frame K' is not accelerating.
By "real gravitational field" he means in the sense of Newton's theory.
K' that is non-geodesic in curved space-time is locally equivalent to a geodesic inertial frame in flat space-time with a "real" gravity field. This is Einstein's bridge back to Newton's theory. "geodesic" has two different meanings in the same sentence here.
"Real gravitational g-field" is meaningful in Newton's theory in flat Euclidean 3D space with absolute simultaneity (Galilean relativity v/c ---> 0) where the Newtonian geodesics are straight lines in flat Euclidean 3D space with point test particles moving at constant speed along them. That's the Newtonian geodesic. There is zero g-force on Newton's geodesic.
"g-field" in Einstein's theory means exactly the same thing as in Newton's theory except that the notion of geodesic has changed. An Einstein geodesic projected down into 3D space is generally not a straight line nor is the test particle speed constant. For example the Earth's elliptical orbit around the Sun is geodesic relative to the Sun's curvature field - to a good approximation. Curvature is geodesic deviation. g-forces are non-zero only on non-geodesics created by non-gravity (essentially electromagnetic) forces. There is no necessary intrinsic relationship of a g-force event to the local curvature.
Now, what confuses Zielinski is the following: consider a cannon ball in free fall as in
http://www.zonalibre.org/blog/diversovariable/archives/baron-munchausen.jpg
Newton's explanation: the Baron and the cannonball are NOT on a geodesic, therefore, there is a real gravitational force per unit test mass on both the Baron and the cannonball relative to the frame K' (surface of Earth) that is "inertial" to a good approximation. It is the same real gravitational force per unit test mass g for both
g-force(Newton) ~ GM(Earth)/r^2
Therefore, the Baron feels weightless, i.e. no pressure on his behind from the cannonball since each are falling in exactly the same way at every moment. That is, there is zero g-force in the common rest frame of the Baron and the cannonball.
Einstein's explanation: the Baron and the cannon ball are on a timelike geodesic in curved space-time.
The covariant equation for the geodesic in ALL frames is
D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 + (Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = 0
This is the covariant
F = ma
with
F = 0
This form-invariant (local frame covariant) equation means.
OBJECTIVE TENSOR TEST PARTICLE ACCELERATION = 0
This is the DEFINITION of a GEODESIC!
THIS IS TRUE IN ALL FRAMES FOR ALL POSSIBLE CURVATURES INCLUDING GLOBALLY FLAT ZERO EVERYWHERE-WHEN.
D^2x^u(test)/ds^2 is the GCT tensor acceleration of the test particle. Its local frame-invariant scalar is
g = (D^2x^u(test)/ds^2D^2xu(test)/ds^2)^1/2
g = 0 on a geodesic - universally true!
Look more closely at the meaning of the geodesic equation. Let Baron Munchausen be on the test particle that is the cannonball in the above picture.
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2 + (Connection)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds) = 0
d^2x^u(Baron)/ds^2 = Newton's flat space + time kinematical acceleration that is not a GCT tensor.
(Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = inertial "force per test mass" that is a contingent artifact of the local frame of reference. This term even exists in globally flat spacetime when K' is accelerating from an electromagnetic force.
Let Alice be a nearly coincident to the Baron geodesic LIF in curved space-time. What Alice sees is
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2
= 0
(Connection Alice LIF) = 0
The size of Alice's LIF is such that the gradients in (Connection Alice LIF) are ignorable. You can think of the LIF as a ball at the bottom of a potential well with a very small zero point jiggle - this is only a rough analogy.
http://rsc.anu.edu.au/~sevick/groupwebpages/images/animations/capture_3D0282.jpg
Let Bob be a nearly coincident to the Baron non-geodesic LNIF observer, then in Bob's POV
D^2x^u(Baron)/ds^2
= d^2x^u(Baron)/ds^2 + (Connection Bob)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds)
= 0
(Connection Bob) =/= 0
Because an electromagnetic force is acting on Bob.
Finally in the Baron's rest frame, which in this case is also geodesic
D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2
= 0
dx^i/ds = 0
i = 1,2,3 spacelike
dx^0/ds = 1
This covers all of the cases.
Homework Problem: Put an external force on the Baron. Describe all the cases.
In answer to Z's question about Wheeler. When Wheeler says gravity is curvature he means tensor "geodesic deviation" he does not mean contingent non-tensor non-geodesic "g-force."
"Gravity" and "gravity field" mean different things in different contexts. Usually this is not a problem for physicists to get the nuance intended in each specific. It is a problem for Z.
Saturday, September 02, 2006
Kibble's 1961 paper on gravity as a local gauge theory
Sean Carroll's text book lightly touches on this at the end. Sunny Auyang makes a short cryptic remark in her book on the philosophy of quantum field theory that is intriguing but too incomplete.
My original unique approach to gravity as an emergent collective phenomenon from the inflation process itself has the tetrads (AKA "vierbeins") as the macro-quantum emergent 4D covariant supersolid field in analogy with the 3D Galilean superfluid velocity field. The tetrad field is renormalizable spin 1 as a quantum field. Einstein's geometrodynamic field is quadratic in the tetrad field, therefore any residual zero point micro-quanta outside of the Bose-Einstein vacuum ODLRO condensate forming the random anti-gravitating dark energy are Einstein-Podolsky-Rosen entangled spin 2 triplet pair states of the spin 1 tetrad quanta.
T.W.B. Kibble's 1961 paper "Lorentz Invariance and the Gravitational Field" JMP 2, March-April 1961 was a marked improvement over Utiyama's partial solution of the problem that locally gauged only the 6-parameter homogeneous Lorentz group (AKA Poincare group) to get the spin connection 1-form w^ab = w^abudx^u for the parallel transport of orientations of the tetrad 1-forms e^a = e^audx^u, a = 0,1,2,3 AKA Cartan mobile frames. Utiyama had to stick in the curved metric ad-hoc - not very satisfactory. Kibble locally gauged the entire 10-parameter inhomogeneous Lorentz group. This was prior to the elegant math of fiber bundles in physics where the compensating local gauge potential comes from the principle bundle and the source fields come from an associated bundle. Gauge theories use internal symmetry groups G for action dynamics with the Poincare group as a rigid non-dynamical background enforcing globally flat spacetime without any gravity at all. The equivalence principle forces the Poincare group to be dynamical and this introduces an added layer of complexity, ambiguity and confusion when trying to cast gravity as a local gauge theory. One must use Dirac's idea of the "substratum" in which the tetrad fields are well-behaved spin 1 vector fields when quantized rather than the unrenormalizable spin 2 tensor fields. It is curious that Kibble, or Penrose later, did not locally gauge the 15-parameter massless conformal group that is the basis of twistor theory. Locally gauging the 4-parameter translation subgroup T4 of the 10-parameter Poincare group gives the Einstein-Cartan tetrads e^a as the compensating field. However, because of the equivalence principle, these tetrads are also in the associated bundle as source fields like the spinor electron field in U(1) QED. That is, the equivalence principle has a feature like Godel's self-reference. In a sense this is true of all non-Abelian gauge theories that are self-interacting forming "geons" or "solitons" or "glue balls" (QCD), i.e. the gauge field carries the source charge. In the case of gravity the source charge is stress-energy density. Although the spin 2 geometrodynamic field does not have a local stress-energy tensor, one cannot jump to that conclusion for the spin 1 tetrad field in the substratum. Locally gauging the 6-parameter homogeneous group O(1,3) gives a dynamically independent spin connection. Note, that in Einstein's 1916 theory, the spin connection is not dynamically independent. The tetrads are dynamically independent and forcing the constraint of zero torsion gaps to second order in closed loops of parallel transport means that the spin connection components are determined by the tetrad components. This is not so in the general case treated by Kibble in 1961.
"The extended transformations for which the 10 parameters become arbitrary functions of position may be interpreted as general coordinate transformations and rotations of the vierbein system."
Sean Carroll's text book lightly touches on this at the end. Sunny Auyang makes a short cryptic remark in her book on the philosophy of quantum field theory that is intriguing but too incomplete.
My original unique approach to gravity as an emergent collective phenomenon from the inflation process itself has the tetrads (AKA "vierbeins") as the macro-quantum emergent 4D covariant supersolid field in analogy with the 3D Galilean superfluid velocity field. The tetrad field is renormalizable spin 1 as a quantum field. Einstein's geometrodynamic field is quadratic in the tetrad field, therefore any residual zero point micro-quanta outside of the Bose-Einstein vacuum ODLRO condensate forming the random anti-gravitating dark energy are Einstein-Podolsky-Rosen entangled spin 2 triplet pair states of the spin 1 tetrad quanta.
T.W.B. Kibble's 1961 paper "Lorentz Invariance and the Gravitational Field" JMP 2, March-April 1961 was a marked improvement over Utiyama's partial solution of the problem that locally gauged only the 6-parameter homogeneous Lorentz group (AKA Poincare group) to get the spin connection 1-form w^ab = w^abudx^u for the parallel transport of orientations of the tetrad 1-forms e^a = e^audx^u, a = 0,1,2,3 AKA Cartan mobile frames. Utiyama had to stick in the curved metric ad-hoc - not very satisfactory. Kibble locally gauged the entire 10-parameter inhomogeneous Lorentz group. This was prior to the elegant math of fiber bundles in physics where the compensating local gauge potential comes from the principle bundle and the source fields come from an associated bundle. Gauge theories use internal symmetry groups G for action dynamics with the Poincare group as a rigid non-dynamical background enforcing globally flat spacetime without any gravity at all. The equivalence principle forces the Poincare group to be dynamical and this introduces an added layer of complexity, ambiguity and confusion when trying to cast gravity as a local gauge theory. One must use Dirac's idea of the "substratum" in which the tetrad fields are well-behaved spin 1 vector fields when quantized rather than the unrenormalizable spin 2 tensor fields. It is curious that Kibble, or Penrose later, did not locally gauge the 15-parameter massless conformal group that is the basis of twistor theory. Locally gauging the 4-parameter translation subgroup T4 of the 10-parameter Poincare group gives the Einstein-Cartan tetrads e^a as the compensating field. However, because of the equivalence principle, these tetrads are also in the associated bundle as source fields like the spinor electron field in U(1) QED. That is, the equivalence principle has a feature like Godel's self-reference. In a sense this is true of all non-Abelian gauge theories that are self-interacting forming "geons" or "solitons" or "glue balls" (QCD), i.e. the gauge field carries the source charge. In the case of gravity the source charge is stress-energy density. Although the spin 2 geometrodynamic field does not have a local stress-energy tensor, one cannot jump to that conclusion for the spin 1 tetrad field in the substratum. Locally gauging the 6-parameter homogeneous group O(1,3) gives a dynamically independent spin connection. Note, that in Einstein's 1916 theory, the spin connection is not dynamically independent. The tetrads are dynamically independent and forcing the constraint of zero torsion gaps to second order in closed loops of parallel transport means that the spin connection components are determined by the tetrad components. This is not so in the general case treated by Kibble in 1961.
"The extended transformations for which the 10 parameters become arbitrary functions of position may be interpreted as general coordinate transformations and rotations of the vierbein system."
Tuesday, August 29, 2006
Torsion Fields: Some toy model calculations
I. 1 + 1 string spacetime slice, neglecting Weyl conformal dilation but including energy and momentum translation generators i.e. A00 = Energy Generator, A11 = Linear Momentum Generator in sense of Noether's theorem relating symmetries to conservation laws for continuous groups. We mean appropriate matrix representations of the Lie algebra depending on what physical vector space they operate on, e.g. Cartan mobile tetrad local frames of reference for gravity and internal vector spaces for "charges" of U(1), SU(2) & SU(3).
The geometrodynamic gauge-covariant partial derivatives acting on Tuv(source) matter fields are
,u ---> ;u = ,u + (Connection)u^a^bAab
(use ' for base space indices)
;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11
+ (Connection)0'^1^0A10 + (Connection)0'^0^1A01
A01 = - A10 = space-time Lorentz boost
;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Linear Momentum)
+ [(Connection)0'^1^0 - (Connection)0'^0^1]A10
;0' = ,0' + (LC Connection)0'^0^0(Energy) + (LC Connection)0'^1^1(Linear Momentum)
+ (Tensor Torsion Field)0'^1^0(Lorentz Boost)
Note how the String Torsion Field is the Yang-Mills "Phase" of the Lorentz Boost.
The Equivalence Principle is encoded in the (LC Connection) terms.
Similarly for ;1
The tetrads tilt in infinitesimal displacements as:
ea(x + dx) = eb(x)(Connection at x)u^badx^u
e0(x + dx) = [(Connection at x)0'^00dx^0' + (Connection at x)1'^00dx^1']e0(x)
+ [(Connection at x)0'^10dx^0' + (Connection at x)1'^10dx^1']e1(x)
e1(x + dx) = [(Connection at x)0'^01dx^0' + (Connection at x)1'^01dx^1']e0(x)
+ [(Connection at x)0'^11dx^0' + (Connection at x)1'^11dx^1']e1(x)
II 2 + 1 slice for anyonic vacuum ODLRO fractional charge/quantum statistics "World Hologram Plate"
cc* + c*ce^i(Anyonic Phase) = 1
Anyonic Phase = 0 2D fermions
Anyonic Phase = pi 2D bosons
Control Anyonic Phase with perpendicular magnetic field on a 2D nano quantum well showing fractional quantum Hall effect.
Exotic matter effects are neither fermion nor boson.
What does that do to the spin-statistics connection?
Flux tubes pin to charged fermions. Effective charges are fractional like quarks, but only in 2D + 1 space-time "surfaces". In world holography there are no dynamically independent volume degrees of freedom for the geometrodynamic field, hence the Bekenstein bound for black hole thermodynamics and the amount of bits that can be packed into a Volume V ~ V^2/3/Lp^2 ~ (/\Lp^2)^-1 for our pocket universe on the cosmic landscape of parallel universes.
,u ---> ;u = ,u + (Connection)u^a^bAab
;0' = ,0' + (Connection)0'^a^bAab
;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11 + (Connection)0'^2^2A22
+ (Connection)0'^0^1A01 + (Connection)0'^1^0A10
+ (Connection)0'^0^2A02 + (Connection)0'^2^0A20
+ (Connection)0'^1^2A12 + (Connection)0'^2^1A21
;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +
(Connection)0'^2^2(Momentum2)
+ [(Connection)0'^0^1 - (Connection)0'^1^0]A01
+ [(Connection)0'^0^2 - (Connection)0'^2^0]A02
+ [(Connection)0'^1^2 - (Connection)0'^2^1]A12
;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +
(Connection)0'^2^2(Momentum2)
+ (TORSION)0'^0^1 (LORENTZ BOOST)01
+ (TORSION)0'^0^2 (LORENTZ BOOST)02
+ (TORSION)0'^1^2 (ROTATION)12
Similarly for ;1'
Note that in Einstein's 1916 theory, TORSION = 0, therefore the Lorentz boost and rotation terms vanish!
Homework, do this for 3D + 1.
On Aug 29, 2006, at 8:32 AM, Jack Sarfatti wrote:
Bottom Line
Gravity is "More is different" emergent from the Standard Model of quarks & leptons with gauge bosons. Standard quantum gravity theories are not even wrong, i.e. loop quantum gravity, string theory, canonical quantization are like trying to quantize elasticity theory.
This is the 11th dimension so to speak. 10 from the Poincare group.
From the principle fiber bundle
M(Base Space) = Cartan Mobile Tetrad Frame Fiber Bundle/(Poincare Group + Weyl Dilation)
dimM = 11?
This is intuitive - still thinking about it - non-rigorous.
That is, 4 translations of the tetrad local frame, 3 rotations, 3 boosts + 1 Weyl dilation. Each parameter "phase" "angle of rotation" is a "dimension" of M.
11 G-Orbit equivalence classes partition of the tetrad bundle.
G = Poincare Group + Weyl Dilation
(universal symmetry group for emergent spacetime physics)
Also an addition 4 special conformal transformations not accounted for (Tony Smith)
,u ---> ;u = ,u + (Connection)u^a^bAab
"Gauge covariant partial derivative" analog to internal symmetry Yang-Mills SU(2), SU(3) ...
{Aab} = Lie Algebra of G
The Cartan mobile tetrad frames tilt & stretch/contract relative to each other
ea(x + dx) = eb(x)(Connection at x)u^badx^u
(ea|eb) = (Minkowski metric)ab = nab
(eu|ev) = (Curvilinear Metric)uv = guv
e^a = eu^adx^u
eu = eu^a&a
Identity action = I = e^a&a = I' + B
F = dB ~ dTheta/\dPhi
Theta & Phi = Goldstone phases of vacuum ODLRO Higgs inflation field with 3 real components (in one toy model)
B ~ Theta/\dPhi - dTheta/\Phi
d^2 = 0
D = d + B/
DF = 0
D*F = *J
D*J = 0
Yang-Mills field equations for U(1)xSU(2)xSU(3) of standard model in false vacuum that is globally flat.
i.e. Gravity emergent from the Standard Model of quarks & leptons with gauge bosons.
On Aug 29, 2006, at 2:05 AM, Carlos Castro wrote:
Dear Jack :
Also in Weyl's geometry the non-metricity tensor Q is
zero as well.
The Weyl covariant derivative of the metric is zero.
Despite that the lengths of vectors change under
parallel transport (in Weyl spacetime )
the angle of two vectors remains the same ( conformal
property ) under paralell transport.
Best wishes
Carlos
I. 1 + 1 string spacetime slice, neglecting Weyl conformal dilation but including energy and momentum translation generators i.e. A00 = Energy Generator, A11 = Linear Momentum Generator in sense of Noether's theorem relating symmetries to conservation laws for continuous groups. We mean appropriate matrix representations of the Lie algebra depending on what physical vector space they operate on, e.g. Cartan mobile tetrad local frames of reference for gravity and internal vector spaces for "charges" of U(1), SU(2) & SU(3).
The geometrodynamic gauge-covariant partial derivatives acting on Tuv(source) matter fields are
,u ---> ;u = ,u + (Connection)u^a^bAab
(use ' for base space indices)
;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11
+ (Connection)0'^1^0A10 + (Connection)0'^0^1A01
A01 = - A10 = space-time Lorentz boost
;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Linear Momentum)
+ [(Connection)0'^1^0 - (Connection)0'^0^1]A10
;0' = ,0' + (LC Connection)0'^0^0(Energy) + (LC Connection)0'^1^1(Linear Momentum)
+ (Tensor Torsion Field)0'^1^0(Lorentz Boost)
Note how the String Torsion Field is the Yang-Mills "Phase" of the Lorentz Boost.
The Equivalence Principle is encoded in the (LC Connection) terms.
Similarly for ;1
The tetrads tilt in infinitesimal displacements as:
ea(x + dx) = eb(x)(Connection at x)u^badx^u
e0(x + dx) = [(Connection at x)0'^00dx^0' + (Connection at x)1'^00dx^1']e0(x)
+ [(Connection at x)0'^10dx^0' + (Connection at x)1'^10dx^1']e1(x)
e1(x + dx) = [(Connection at x)0'^01dx^0' + (Connection at x)1'^01dx^1']e0(x)
+ [(Connection at x)0'^11dx^0' + (Connection at x)1'^11dx^1']e1(x)
II 2 + 1 slice for anyonic vacuum ODLRO fractional charge/quantum statistics "World Hologram Plate"
cc* + c*ce^i(Anyonic Phase) = 1
Anyonic Phase = 0 2D fermions
Anyonic Phase = pi 2D bosons
Control Anyonic Phase with perpendicular magnetic field on a 2D nano quantum well showing fractional quantum Hall effect.
Exotic matter effects are neither fermion nor boson.
What does that do to the spin-statistics connection?
Flux tubes pin to charged fermions. Effective charges are fractional like quarks, but only in 2D + 1 space-time "surfaces". In world holography there are no dynamically independent volume degrees of freedom for the geometrodynamic field, hence the Bekenstein bound for black hole thermodynamics and the amount of bits that can be packed into a Volume V ~ V^2/3/Lp^2 ~ (/\Lp^2)^-1 for our pocket universe on the cosmic landscape of parallel universes.
,u ---> ;u = ,u + (Connection)u^a^bAab
;0' = ,0' + (Connection)0'^a^bAab
;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11 + (Connection)0'^2^2A22
+ (Connection)0'^0^1A01 + (Connection)0'^1^0A10
+ (Connection)0'^0^2A02 + (Connection)0'^2^0A20
+ (Connection)0'^1^2A12 + (Connection)0'^2^1A21
;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +
(Connection)0'^2^2(Momentum2)
+ [(Connection)0'^0^1 - (Connection)0'^1^0]A01
+ [(Connection)0'^0^2 - (Connection)0'^2^0]A02
+ [(Connection)0'^1^2 - (Connection)0'^2^1]A12
;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +
(Connection)0'^2^2(Momentum2)
+ (TORSION)0'^0^1 (LORENTZ BOOST)01
+ (TORSION)0'^0^2 (LORENTZ BOOST)02
+ (TORSION)0'^1^2 (ROTATION)12
Similarly for ;1'
Note that in Einstein's 1916 theory, TORSION = 0, therefore the Lorentz boost and rotation terms vanish!
Homework, do this for 3D + 1.
On Aug 29, 2006, at 8:32 AM, Jack Sarfatti wrote:
Bottom Line
Gravity is "More is different" emergent from the Standard Model of quarks & leptons with gauge bosons. Standard quantum gravity theories are not even wrong, i.e. loop quantum gravity, string theory, canonical quantization are like trying to quantize elasticity theory.
This is the 11th dimension so to speak. 10 from the Poincare group.
From the principle fiber bundle
M(Base Space) = Cartan Mobile Tetrad Frame Fiber Bundle/(Poincare Group + Weyl Dilation)
dimM = 11?
This is intuitive - still thinking about it - non-rigorous.
That is, 4 translations of the tetrad local frame, 3 rotations, 3 boosts + 1 Weyl dilation. Each parameter "phase" "angle of rotation" is a "dimension" of M.
11 G-Orbit equivalence classes partition of the tetrad bundle.
G = Poincare Group + Weyl Dilation
(universal symmetry group for emergent spacetime physics)
Also an addition 4 special conformal transformations not accounted for (Tony Smith)
,u ---> ;u = ,u + (Connection)u^a^bAab
"Gauge covariant partial derivative" analog to internal symmetry Yang-Mills SU(2), SU(3) ...
{Aab} = Lie Algebra of G
The Cartan mobile tetrad frames tilt & stretch/contract relative to each other
ea(x + dx) = eb(x)(Connection at x)u^badx^u
(ea|eb) = (Minkowski metric)ab = nab
(eu|ev) = (Curvilinear Metric)uv = guv
e^a = eu^adx^u
eu = eu^a&a
Identity action = I = e^a&a = I' + B
F = dB ~ dTheta/\dPhi
Theta & Phi = Goldstone phases of vacuum ODLRO Higgs inflation field with 3 real components (in one toy model)
B ~ Theta/\dPhi - dTheta/\Phi
d^2 = 0
D = d + B/
DF = 0
D*F = *J
D*J = 0
Yang-Mills field equations for U(1)xSU(2)xSU(3) of standard model in false vacuum that is globally flat.
i.e. Gravity emergent from the Standard Model of quarks & leptons with gauge bosons.
On Aug 29, 2006, at 2:05 AM, Carlos Castro wrote:
Dear Jack :
Also in Weyl's geometry the non-metricity tensor Q is
zero as well.
The Weyl covariant derivative of the metric is zero.
Despite that the lengths of vectors change under
parallel transport (in Weyl spacetime )
the angle of two vectors remains the same ( conformal
property ) under paralell transport.
Best wishes
Carlos
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