Wheeler on the relation of gravity to the electro-weak-strong interactions – local gauge and string theories:
“What of the other forces of nature? Every other force – the electric force that rules the motion of the atomic electrons, the weak nuclear force that governs the emission of electrons and neutrinos from radioactive nuclei, and the strong nuclear force that holds together the constituents of particles heavier than the electron – demands … a geometry of more than four dimensions, perhaps as many as ten. The extra six dimensions are envisaged as curled up into an ultra-small cavity, with one such cavity at each point in spacetime. … The theories of the unification of forces with greatest promise today all have this striking feature that they, like the battle-tested, but simpler and older Einstein gravitation theory, build themselves on the [vanishing] boundary of a boundary principle, though in a higher dimensional version … Elie Cartan’s penetrating insight … from the grip of spacetime on mass to the grip of mass on spacetime, and from the automatic conservation of momentum-energy … the unfolding of all this from ‘the one-dimensional boundary of the two-dimensional boundary of a three-dimensional region is zero’ and the ‘two-dimensional boundary of the three-dimensional boundary of a four-dimensional region is zero.’” Pp. 9,10
All four interactions are boson local gauge theories of different groups of local frame transformations also called “gauge transformations” needing the mathematics of fiber bundles. Maxwell’s electromagnetism mediated by spin 1 massless spin 1 vector photons corresponds to the internal U(1) group that can be pictured as a circle “fiber” at each point on the “base” spacetime. Think of the circle as a one handed Salvador Dali clock. The clock hand can be moved locally at each spacetime point independently of all the other clocks at other spacetime points only because there is an induced connection field, analogous to the Levi-Civita connection (more precisely its more fundamental spin connection from which it derives) connecting the different fibers. Moving each local clock hand arbitrarily induces a gauge transformation in the connection field. The connection field supplies a covariant derivative and parallel transport of objects through the fiber space corresponding to world lines in the projected base space-time beneath it. The disclination curvature in closed loops in the fiber space corresponds to the electromagnetic field tensor. Similarly for the SU(2) group of the weak interaction which has three “flavor” quanta called the spin 1 vector W-bosons with electric charges +1, 0, -1 of the electron’s charge. Now we have a three-dimensional hyper-sphere bounding a four-dimensional internal fiber space not to be confused with spacetime. These W-bosons have rest masses from the Higgs spin 0 boson because of a kind of superconductivity that forms in the moment of inflation from a false vacuum at the Alpha Point creation of our observable universe (aka “causal diamond”) bounded in the past by an observer-dependent particle horizon and in the future by an observer-dependent de Sitter dark energy event horizon. Both of these cosmological horizons have quantum thermodynamic hologram computational capacity and they emit Hawking radiation. Our past history pre-selected particle horizon emits retarded Hawking radiation to us here-now along our past light cone. Our future destiny post-selected de Sitter event horizon sends us back-from-the-future advanced Wheeler-Feynman Hawking radiation that happens to have the same energy density as the anti-gravity dark energy accelerating the rate of expansion of three-dimensional inter-galactic space. This is not a meaningless random Darwinian coincidence. There is the w-problem that dark energy needs w < -1/3 whilst retarded Hawking radiation has w = +1/3. However, we also have the Unruh effect here that the w = +1/3 Hawking blackbody radiation seen in LNIFs whose temperature is proportional to its local proper accelerometer reading, looks like w = -1 zero point radiation in coincident LIFs both connected to each other by tetrad transformations via the Einstein Equivalence Principle (EEP).
Returning to the strong interaction, the internal group is SU(3) with eight massless spin 1 vector gluon quanta corresponding to an eight-dimensional hyper-sphere fiber bounding a nine-dimensional internal fiber space at each point in spacetime. The spin 0 Higgs boson does not directly interact with the eight “color” gluons that bind the spin ½ quarks into hadrons. The photon does not directly interact with itself, unlike the three weak massive W-bosons and the eight strong massless gluons which do interact with themselves respectively as well as with each other. Each boson charge of the internal groups is a hermitian generator of the Lie algebra of the unitary Lie group. SU2 and SU3 Lie algebras have non-vanishing commutators of these internal charges. This implies Heisenberg uncertainty relations for simultaneous quantum measurements of the internal weak flavor and strong color charges. It is this incompatibility of the charges that causes the self-interactions.
We have a similar situation with gravity as a local gauge fiber bundle. We now have four mutually commuting tetrad charges that form the momentum-energy Hermitian observables in the LIF tangent space-fiber over spacetime base space. However, in addition we have the six spin-connection charges consisting of three space-rotation angular momenta and three Lorentz boosts. All ten of these charges form the non-commuting Lie algebra of the Poincare group, which unlike the electro-weak-strong unitary groups is not compact. However, the failure of the ten charges of the Poincare group to mutually commute completely causes the non-linear self-interaction of the massless spin 2 tensor gravitons of classical GR. The classical near fields of all of these four basic interactions consist of “super conducting” macro-quantum coherent Glauber states of off-shell virtual bosons with all possible polarizations. This is in contrast to the far-field radiations consisting of Glauber coherent states of massless photons or massless gravitons with only two transverse polarization states. One point of interest is that the gravity quanta are spin 1 vector bosons at Dirac square root LIF tetrad/spin connection level of the formalism. Einstein’s 1916 GR is a constrained limiting case of the local gauge theory just described in which zero dynamical dislocation torsion is imposed ad hoc giving only dynamical geodesic deviation disclination curvature. In this limiting case, the six spin-connection components are no longer an independent dynamical field, but are determined from the LIF tetrads (consisting of a spacelike triad and a timelike tangent vector). One can also use the complex Penrose light cone null tetrads. These spin 1 vector boson tetrad fields then entangle in pairs to get spin 0, spin 1 and spin 2 “gravitons.” However, the spin 0 and spin 1 must get rest masses via the Higgs bosons because we do not directly detect them at macroscopic distances.
Jack SarfattiWheeler’s Version of Einstein’s Geometrodynamics Rocklike (IT) spacetime, in addition to David Bohm’s thoughtlike (BIT) quantum potential Q that operates from beyond spacetime, tells mass how to move on free-float weightless timelike geodesics where accelerometers measure zero local proper tensor acceleration. That is the action. The reaction is mass telling spacetime how to curve. If Einstein’s 1916 geometrodynamics is merely a limiting case of Cartan’s extension to it, then quantum spin and possibly orbital angular momentum of mass tell spacetime how to torsion causing dislocation cracks in the quantum gravity world crystal lattice of Hagen Kleinert, which must have a Fermi lattice spacing of 10-15 meters not Planck spacing of 10-35 meters if the ‘t Hooft-Susskind causal diamond observable universe is a hologram simulation is correct. This suggests a Yukawa strong finite-range micro gravity picture of nuclear forces with spin 0, spin1 and spin 2 components at the 1 Gev scale. Abdus Salam had such a spin 2 f-gravity idea in the early 1970’s, which, as I pointed out to him corresponded to the universal slope of Regge trajectories of hadronic string theory resonances that could be pictured as Kerr-type quantum black holes. Their Hawking radiation evaporation time would correspond to their instability. As of 2013 there is a newer model connecting two SU(3) theories to quantum gravity.
Returning to Wheeler: 1) Equivalence principle 2) Geometry 3) Geodesic equation of motion of point test particles (aka Newton’s 1st Law first-order partial derivatives of the metric tensor field describe fictitious inertial pseudo-forces on the test particle corresponding to real forces on the detector) 4) Intrinsic tensor curvature geodesic deviation (disclinations of vectors parallel transported around closed loops in spacetime) from second order partial derivatives of the metric tensor field describing relative covariant tensor accelerations between two neighboring geodesic test particle each with zero g-force proper acceleration.
One must use the LIF to distill the intrinsic geometry of the real Einstein gravity field. The LNIF is fool’s gold, MAYA, illusion, the shadow on the wall of Plato’s Cave that has ship wrecked many a careless mariner including Isaac Newton listening to the wiles of Circe. The LNIF is contingent random noise, all sound and fury a tale told by an idiot, and believed by sorry bastards, a fairy tale, a mask. Only Einstein escaped the Cave that Newton was trapped in. Of course, Newton had a good excuse. Newton’s “gravity force” is simply the real quantum electrodynamic force sustaining the static LNIFs. It is a fictitious pseudo-force as far as the observed test particle is concerned without any intrinsic objective reality, same ontic status as Coriolis and centrifugal pseudo-forces all parts of the LNIF Levi-Civita Christoffel symbols that depend only on first order partial derivatives of the metric tensor field. Einstein’s equivalence principle (EEP) relegates them to Prospero’s phantoms, the illusions of the Wizard of Oz behind the theater curtain of the world stage.
Jack SarfattiFermi Normal Coordinates for the LIF’s Image of Intrinsic Geometry “The metric tensor can indeed be written using the Riemann (curvature) tensor, in a neighborhood of a spacetime event, in a freely falling non-rotating local inertial frame to second order in the separation δxi where i,j,k,l are spacelike (outside local light cones with origins at the spacetime event of interest) 1,2,3 indices. The Taylor series expansion to lowest non-vanishing order is g00 ~ - 1 – R0i0jδxiδxj for the gravity redshift g0k ~ - (2/3)R0ikj δxiδxj for the LIF drag gravimagnetic field gkl ~ δkl – (1/3)Rkilj δxiδxj for the curved spacelike 3-geometry The relative covariant tensor acceleration between two freely-falling geodesic test particles each with zero local proper tensor acceleration, is d2δxα/dt2 ~ R^α0μ0δxμ is the equation of geodesic deviation