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Fwd: reply to Shipov's questions ON Cartan's CLASSICAL UNIFIED FIELD THEORY

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  • Jack Sarfatti
    Message 1 of 1 , Nov 1, 2005
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      Begin forwarded message:

      > 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?
      >>>
      >>>
      >>>
      >>>
      >>>
      >>
      >
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