> From: Jack Sarfatti <sarfatti@...>

> Date: November 1, 2005 1:42:44 PM PST

> To: Gennady Shipov <shipov@...>

> "Jack!

>

> Please answer to me the following questions:

>

> 1. What group is located in your theory?

>

> If the Poincare's group, is located:

>

> 2. What quantities are the structural functions of the group of

> translations and to what equations they satisfy?

>

> 3. What quantities are structural functions of the group of

> rotations and to what equations they satisfy?"

>

>

> I assume you mean "localized" by "located".

>

> u,v ... indices raised and lowered with guv etc.

>

> I,J ... indices raised and lowered with nIJ (Minkowski)

>

> Equivalence Principle (EEP) is

>

> guv = (Iu^I + Bu^I)nIJ(1^Jv + B^Jv)

>

> ds^2(P) = guv(P)dx^udx^v

>

> P = {x} mod Diff(4)

>

> Step 1 Localize T4 the translation subgroup of Poincare Group

>

> The curved tetrad B is the compensating gauge potential from T4

>

> B ~ dx^u&IBuP^I(Goldstone Phase)

>

> Bu^I = eu^I - Iu^I

>

> |u^I = Kronecker delta MAP connecting tangent space frames to base

> space frames in ALIGNMENT when B = 0.

>

> The globally flat Minkowski space-time is degenerate, i.e. tangent

> space and base space MERGE, which is why we can have global frames.

> Curvature splits off local tangent fibers from the curved base space.

>

> P^I are the 4 Lie algebra generators of T4, their conjugate phases

> are 4 dimensions of the base manifold.

>

> Given the above preliminary structure, define the Cartan 1-form

> SPIN-CONNECTION W^IK implicitly from

>

> e = e^I&I same for 1 & B

>

> &I are base tangent vectors

>

> &Idx^J = 1I^J duality of wave Cartan form and particle Cartan co-

> form.

>

> i.e. dx's are wave front isophase surfaces

>

> & are particle directional propagation vectors

>

> De^I = d(1^I + B^I) + W^IK/\(I^K + B^K) = dB^I + W^IK/\(I^K + B^K)

> = 0 ZERO TORSION CONSTRAINT

>

> Therefore, W^IK determined completely from B^I.

>

> Map W^IK to Levi-Civita connection

>

> W^IK = dx^uWu^IK

>

> This is LOCAL DIFF(4) scalar INVARIANT (nice feature of this Cartan

> notation. This is the INTRINSIC GEOMETRY that is Diff(4) INVARIANT

> and LOCAL in Einstein's sense of P = {x} = Coset Space of Manifold/

> Diff(4).

>

> It seems that Witten, Baez et-al do not know this? Hard to believe.

> Hence their odd statements about non-existence of LOCAL Diff(4)

> gauge invariant observables in Quantum Gravity?

>

> Levi-Civita = {u^vw} = Wu^IKeI^ve^Kw

>

> 1915 GR Cartan Structure eqs are the same FORM as U(1) EM & SU(2)SU

> (3)Yang-Mills, but now for T4:

>

> R^IK = DW^IK = curvature 2-form

>

> R^IK = dx^udx^vRuv^IK

>

> DR^IK = 0 Bianchi identities

>

> D*R^IK = *J^IK(T4 sources) ---> Guv = kTuv(Matter)

>

> D*J^IK(T4) = 0 local conservation of matter current densities

>

> Step 2 BEYOND 1915 GR locally gauge O(1,3)

>

> SIK ~ 6 generators of O(1,3). Their conjugate phases are 6 extra-

> dimensions of the "oriented" base manifold.

>

> SIK ~ dx^uSuIK(Goldstone Phase)

>

> D' = D + S^IJ/\. ...

>

> Extended Curvature 2-form is

>

> R'^IK = D'W^IK = R^IK + S^IJ/\W^JK

>

> Note the torsion-curvature coupling term S^IJ/\W^JK

>

> The field equations are

>

> D'R'^IK = 0 Bianchi

>

> D'*R^IK = *J'^IK(T4) Einstein Marble - Wood

>

> D'*J^IK(T4) = 0 Current conservation

>

> Similarly the TORSION 2-form is

>

> T'^IK = D'S^IK = dS^IK + W^IJ/\S^JK + S^IJ/\S^JK

>

> with field equations

>

> D'T'^IK = 0 Bianchi

>

> D'*T^IK = *J(O(1,3)) Einstein

>

> D'*J(O(1,3)) = 0 Current conservation

>

> This is at least classical UNIFIED FIELD THEORY FORMALLY speaking.

>

> Same basic template for ALL fields for ALL continuous symmetry

> groups internal & space-time.

>

> On Nov 1, 2005, at 3:15 AM, Gennady Shipov wrote:

>

>>

>> ----- Original Message -----

>> From: Jack Sarfatti

>> To: ROBERT BECKER

>>

>> Subject: Re: Local Curvature & Torsion fields as Nonlocal Bohm-

>> Aharonov Topological Singularities

>>

>>

>> On Oct 31, 2005, at 2:39 PM, ROBERT BECKER wrote:

>>

>>> "Jack, Gennady -

>>> ?

>>> I am going to take a leap and jump in here. As I read the debate

>>> on this issue, there appears to be some distinct points of

>>> difference, but the overall approach may not be completely

>>> different.

>>> ?

>>> I cannot intelligently comment on Gennady's complete statement

>>> that Riemannian geometry can not be a group manifold because it

>>> lacks the Cartan Structure Equations. But perhaps I can say a few

>>> things about parts of this statement."

>> Jack Sarfatti

>>

>> There may be a problem of the Russian --> English translation here

>> since, e.g. Rovelli's book Ch 2 clearly shows Cartan structure

>> equations for 1915 GR without torsion. How to generalize correctly

>> to torsion is not completely obvious. I need another go at that.

>>

>> Only 2 key principles:

>> 1. Locally gauge every continuous group, both internal & space-time.

>>

>> 2. Enforce equivalence principle by making weak force Higgs vacuum

>> coherence mechanism also the source of emergent c-number gravity.

>> Note that we have running coupling constants - weak force gets

>> stronger at higher energy.

>>

>> Side point:

>>

>> Heisenberg's uncertainty principle is INCOMPLETE, i.e.

>>

>> &r ~ h/&p + (G*/c^3)&p

>>

>> G* is effective gravity parameter at scale &r.

>>

>> Simplest Higgs mechanism in the standard model has TWO complex

>> scalar fields for SU(2)weak

>>

>> i.e. n = 4 real fields.

>>

>> But only one complex scalar field develops the local order

>> parameter VEV =/= 0. It is electrically neutral.

>>

>> Remember U(1)hyperchargeSU(2)weak has 4 generators, combinations

>> of which make ONE electric charge neutral massless photon and 3

>> massive Weak bosons. Not the Higgs bosons, which is another part

>> of the theory.

>> From this POV I only have 2 real fields, n = 2, so in 3 space 1 +

>> d' + r = 3. Stable defects d' = d - n = 1 string vortices rather

>> than point defects. The two real VEV's give me 1 Goldstone Phase

>> to make gravity with from

>>

>> B = (hG/c^3)^1/2'd' (Goldstone Phase)

>>

>> On the other hand, there are other possible models.

>>

>> Of the 4 real fields, 3 feed mass to the W-bosons and the

>> remaining massless one is the photon.

>>

>> In this model N - K = 1 is dim of H, which in this case is U(1).

>> K = 3 = number of broken generators of G = U(1)xSU(2) has N = 4

>> and if n = 4, i.e., U(1) acts as multiple of identity on the two

>> complex fields, rather than my earlier n = 6, then there is only 1

>> Higgs boson that should be ~ 250 Gev, which is the critical

>> temperature for the onset of the VEV at least at this cosmological

>> epoch. Presumably it was much larger when the universe was smaller

>> consistent with the strength of the weak coupling decreasing as

>> universe expands.

>>

>> <349D287C-6199-4C9B-AD21-B0AB0A0BD807>

>>

>>>

>> OK,? Einstein-Cartan tetrad, showing the LIF tangent fiber indices

>> explicitly

>>

>> e^I = 1^I + B^I

>>

>> B^I also from local gauging of T4 to Diff(4)

>>

>> The 1 + B split is Diff(4) INVARIANT

>>

>> Hence B = 0 really is a globally flat spacetime.

>>

>> Zero torsion 2-form means

>>

>> De^I = 0

>>

>> where the SPIN CONNECTION is the 1-form W^IK

>>

>> D = d + W^IK/\

>>

>> De^I = dB^I + W^IK/\B^K = 0

>>

>> Therefore W determined from B, which comes from SINGULAR nonlocal

>> Bohm-Aharonov "Flux-without-flux" 'd'(Goldstone Phase) d' = 1

>> vortex string singularities in simplest Higgs model that will not

>> give a stable Hedghog where we need d' = 0.

>>

>> The curvature 2-form is

>>

>> R^IK = DW^IK = dW^IK + W^IJ/\W^JK

>>

>> Bianchi identity is

>>

>> DR^IK = 0

>>

>> Einstein's field eq. is

>>

>> D*RIK = *J(Matter)

>>

>> Local conservation of matter current density is

>>

>> D*J(Matter) = 0

>>

>> That's 1915 GR in a NUTSHELL using SAME Cartan form eqs as in EM

>> or Yang-Mills theory.

>> SAME FORMAL TEMPLATE.

>>

>> Enter TORSION from local gauging of O(1,3) that is GLOBAL in 1915 GR.

>>

>> This gives TORSION 1-form Potential S^IK where now

>>

>> D' = D + S/\

>>

>> Therefore, the CURVATURE 2-form is now

>>

>> R'^IK = D'W^IK = R ^IK+ S^IJ/\W^JK

>>

>> Note the TORSION-CURVATURE COUPLING S/\W

>>

>> The TORSION 2-form is?

>>

>> T'^IK = D'S^IK = dS^IK + W^IJ/\S^JK + S^IJ/\S^JK? =/ = 0

>>

>> The Bianchi identities are

>>

>> D'R' = 0

>>

>> D'T' = 0

>>

>> The FIELD EQUATIONS are

>>

>> D'*R' = *J(Translation)

>>

>> D'*T' = *J(Rotation)

>>

>> The LOCAL current conservation laws are

>>

>> D'*J = 0 (both)

>>

>> Everything is MOD Diff(4,) i.e. Einstein's "local coincidences" P

>> = {Diff(4) Orbits of manifold points} as explained by Rovelli Ch 2.?

>>

>> One can add Yang-Mills fields from internal symmetry groups

>> trivially into

>>

>> D" = D' + A^IK/\

>>

>> where A^IK = A^IKaT^a

>>

>> T^a are the charges of G which spontaneously breaks to H etc.

>>

>>> ?

>>> "A formalism is not a geometry. The Cartan Equations of Structure

>>> arising from the what is often called the Cartan Moving Frame

>>> Method, which I think is synomous with Gennady's Oriented Point

>>> Method, provides a formalism upon which one can impose additional

>>> constraints and assumptions."

>>

>> Yes, Gennady uses a 10Dim manifold from the local gauging of O

>> (1,3), which will be internal parameters in my notation

>>

>> i.e. Bu^I ~? BuP^I

>>

>> The 4 P^I form Lie algebra of T4 for 4D translations

>>

>> Su^IK ~ SuL^IK

>>

>> L^IK are the 6 O(1,3) Lie algebra generators for 4D rotations.

>>

>> There are conjugate phases @^I & @^IK, I =/= K, for each, i.e. a

>> 10 Dim manifold of "dynamical phases" (not Goldstone phases of

>> VEV's of course)

>>> ?

>>> "From what I can see, Jack?is?using the Cartan Structure

>>> Equations in his derivation. However, I do not think Gennady's

>>> objection is to Jack's use of the Cartan Structure Equations

>>> specifically. What Gennady appears to be saying is that the

>>> Curvature Form which appears in the Equations of Structure is?not?

>>> the same kind of mathematical object as the Curvature that shows

>>> up in the Riemannian Differential Geometry of GR. Gennady is

>>> correct on this so far as I know."

>>

>> Yes, but there is a TETRAD MAPPING connecting them.

>>

>> R^IK = Ruv^IKdx^udx^v

>>

>> Ruv^wl = Ruv^IKeI^wel^K

>>

>> The base space u,v indices ARE HIDDEN in the Cartan formalism,

>> that is AUTOMATICALLY DIFF(4) SCALAR LOCAL INVARIANT in sense of P

>> "local coincidences" of course.

>>

>>

>>> "What shows up in the Equations of Structure is what Vargas calls

>>> the "Total Curvature", of which the classical Riemannian

>>> Curvature is only a piece."

>>

>>

>> That's exactly my

>>

>> R' = D'W = R + S/\W

>>

>> The difference is the direct torsion-curvature coupling.

>>

>> If you want TELEPARALLELISM, then I suppose that means

>>

>> R' = 0

>>

>> T' =/= 0

>>

>>> "By making the assumption that Torsion vanishes, one obtains

>>> Riemannian GR and a Riemannian Curvature."

>>

>> Yes, that's simply S = 0 in my notation.

>>

>>> "(One can readily use the Cartan formalism to recover Riemannian

>>> GR, it just does not contain the full richness of the mathematics

>>> that can be obtained from the Cartan formalism if one does not

>>> make the vanishing Torsion assumption.)

>>> ?

>>> Therefore, if the vanishing Torsion assumption is used, then the

>>> more restricted version of the Curvature Form shows up in the

>>> Equation of Structure and the full theory is not obtained. Jack

>>> in the first part of his derivation?does?appear to be using a

>>> vanishing Torsion assumption, which forces the Curvature in

>>> Jack's equations to not be the full Total Curvature of the Cartan

>>> formalism. So, in this sense, Gennady is correct that there is a

>>> discrepancy."

>>

>> Not really. I simply did that at first for PEDAGOGY to show how to

>> get Einstein's 1915 theory as THE FIRST BABY STEP. After a few

>> FUMBLES I think I got the TORSION extension of GR above

>> (correcting some previous errors).

>>> ?

>>> "However, about 2/3 to 3/4 of the way down in Jack's sequence of

>>> equations, there appears a T', a "modified" Torsion, which is?not

>>> assumed to vanish.?So,?with this final set of equations, Jack

>>> seems to be satisfying Gennady's concern over the apparent use of

>>> a vanishing Torsion in the Cartan formalism."

>>

>> Yes. But also I have the CONNECTION to Higgs mechanism for origin

>> of inertia of leptons and quarks and GRAVITY so that SPIRIT of

>> equivalence principle is obeyed GRAVITY & INERTIA EMERGE TOGETHER!

>> Still lots of mopping up details of course. But basic idea I think

>> is sound. Everything FROM COHERENCE including ZPF COHERENCE i.e.

>> ZPF, like ALL EPR ENTANGLEMENTS is LOCALLY RANDOM but NONLOCALLY

>> COHERENT or PHASE-LOCKED. In contrast Higgs field CONDENSATE is

>> BOTH LOCALLY AND NONLOCALLY COHERENT. The origin of GRAVITY and

>> INERTIA TOGETHER is from the LOCAL COHERENCE. The DARK ENERGY/

>> MATTER is from the LOCAL w = -1 INCOHERENCE of the NONLOCALLY EPR

>> CORRELATED ZPF in the T = 0 Kelvin "Vacuum".

>>> ?

>>> "A few other comments:

>>> ?

>>> Assuming vanishing Torsion?yields GR. Assuming the?vanishing of

>>> the Total Curvature (in which case, the Torsion does not vanish)

>>> is called Teleparallelism (TP) and is one?primary leg of Vargas

>>> Theory."

>>

>> Yes, that's easy in my notation, that's

>>

>> R' = R + S/\W = 0

>>

>> T' = dS' + W/\S + S/\S =/= 0

>>

>> But why R' = 0 is not physically compelling for me. I prefer

>>

>> D'R' = 0

>>

>> D'*R = *J (Translation)

>>

>> D'T' = 0

>>

>> D'*T' = *J(Rotation)

>>

>> D'*J = 0 etc.

>>

>>> "Another difference is that Vargas Theory does not seek to

>>> introduce gauge fields into the frame forms (i.e. Jack's e) or

>>> into theory at all. Finally, no assumption of a spin-connection

>>> is made in Vargas Theory and the resulting "geometric" Maxwell-

>>> Einstein Equations resulting from the Torsion Equation of

>>> Structure do not have a rotating source. Torsion in Vargas Theory

>>> is not related to rotation, but rather, in a certain

>>> matehmatically detailed sense, to EM. The geometric Maxwell

>>> Equations essentially represent a geometrization of the EM (at

>>> that level of theory).

>>> ?

>>> Take care,

>>> ?

>>> Robert E. Becker"

>>

>> I think my theory makes more physical sense than Vargas theory

>> BECAUSE

>>

>> I get Gravity and Dark Energy/Matter and Inertia ALL EMERGING

>> TOGETHER in a way consistent with standard model of leptons &

>> quarks. My theory is very close to observation and is FALSIFIABLE.?

>>

>> In this way my theory is better not only than Vargas theory, it is

>> better than STRING THEORY and better than LOOP QUANTUM GRAVITY.

>>

>> I make some strong predictions of principle:

>>

>> 1. Dark Matter Omega ~ 0.23 is VIRTUAL NONLOCALLY COHERENT ZPF

>> that is LOCALLY RANDOM with positive pressure for compact sources.

>>

>> 2. Hence DARK MATTER DETECTORS will BE SILENT with RIGHT STUFF

>> same a Michelson-Morley not showing Ether Drift - barring some

>> bizarre claims to the contrary of course. No exotic on-mass-shell

>> quanta will explain Galactic Halo etc.

>>

>> 3. Quantum foam does not exist and high energy cosmic photons will

>> not show it!

>>

>> 4. Universal slope of Regge trajectories for hadronic resonances

>> is STRONG SHORT RANGE ZPF induced gravity.

>>

>> Basically Kerr solution J/h ~ GM^2/hc? (I published that in 1973)

>>

>> i.e. anticipated string-blackhole correspondance in 1973.

>>>

>>>

>>> Gennady Shipov

>>>

>>>

>>> Jack!

>>>

>>> Please answer to me the following questions:

>>>

>>> 1. What group is located in your theory?

>>>

>>> If the Poincare's group, is located:

>>>

>>> 2. What quantities are the structural functions of the group of

>>> translations and to what equations they satisfy?

>>>

>>> 3. What quantities are structural functions of the group of

>>> rotations and to what equations they satisfy?

>>>

>>>

>>>

>>>

>>>

>>

>