Title: A second high energy Hawking radiation predicted Abstract: Hawking's horizon surface area-entropy A black body radiation peaks at wavelength ~ A^1/2 ~ Unruh temperature T^-1 for distant observers This is not the complete story. There should be a second asymptotic redshifted higher Unruh temperature component with peak wavelength ~ proper quantum thickness of the horizon ~ geometric mean of UV cutoff L with A^1/2) = (LA^1/2)^1/2 with energy density ~ T^4 ~ hc/L^2A. The two Hawking surface and thickness radiations form a Carnot limited heat engine. L = Lp corresponds to random black body gravity waves. L ~ h/mc for virtual electron-positron pairs stuck to the horizon corresponds to far field thermal photons. These back of the envelope heuristic shortcuts apply both to observer independent black hole horizons as well as observer-dependent past and future cosmological horizons bounding the causal diamond. In the case of gravity wave thermal Hawking thickness radiation hc/Lp^2A is the observed dark energy density if we use the future deSitter horizon entropy A. The Unruh effect suggests that the w = + 1/3 black body radiation (gravity or EM) for accelerating detectors corresponds to w = -1 for the distant local inertial frame detectors.
Jack Sarfatti15) Woodward’s Chapter 1: Newton’s rotating bucket. I agree with Rovelli in his book “Quantum Gravity” Ch. 2 that we do not need Mach’s Principle here. Everything is local field theory. The extended test particle, in this case Newton’s bucket filled with water on a twisted cord will behave in the same way even if the universe is empty. The water surface will go concave independent of the distant matter of the stars and beyond. This is because special relativity’s globally flat Minkowski spacetime is a solution of Einstein’s general relativity field equations – even if unstable that is not relevant here. Therefore, the volume elements of the rotating water are being pushed off the timelike geodesics of Minkowski spacetime with non-zero radially inward centripetal proper acceleration by the real electrical forces of the material. Of course there is no obvious way to Popper falsify this issue. With regard to p. 22 on whether we should use the virtual spacelike spin 2 graviton “force” picture against a non-dynamical background-dependent globally flat Minkowski background. Kaluza and Klein tried to extend the equivalence principle, to geometrize the electromagnetic force by introducing an extra curled up dimension of space. This led to modern day controversial superstring theory, which not only introduces six extra space-dimensions (seven in M-theory) but makes the space a non-commuting matrix space. Feynman showed in his Cal Tech course on gravity, that one can apply his QED Feynman diagrams to the spin 2 tensor field on Minkowski space, but that we need to sum an infinite number of his tree diagrams to arrive at Einstein’s gravity field equations as a non-perturbative emergent collective effect similar to the “More is different” (P.W. Anderson) emergence of the Higgs-Goldstone spontaneous broken U1 gauge symmetry ground state of the BCS superconductor. There is also the issue of the non-tree diagrams with closed vacuum loops with problems of renormalizability. Similar problems arose with the weak-strong spin 1 Yang-Mills gauge theory. G. ‘tHooft solved that with spontaneous broken symmetry of the vacuum. Why does that not also work for spin 2 gravity? Einstein’s 1916 general relativity corresponds to the local gauging of the globally rigid ten-parameter Poincare Lie symmetry group of his 1905 special relativity. As shown by T.W.B. Kibble at Imperial College, London in 1961, this gives the extended Einstein-Cartan theory with two independent dynamical curvature and torsion fields. Curvature comes from localizing the six-parameter Lorentz space-time rotation subgroup generated by angular momentum and boosts. Curvature corresponds to disclination topological defects on a “world crystal lattice” (Hagen Kleinert, Free University of Berlin). Torsion comes from localizing the four-parameter translation group generated by the 4-momentum. Torsion corresponds to disclination defects in the world crystal lattice. Einstein’s 1916 model is the limiting case of Einstein-Cartan with the adhoc constraint of zero dynamical torsion put in by hand. Indeed, these local translations are precisely the general curvilinear coordinate transformations of Einstein’s 1916 papers that describe the actual relationships between physically coincident timelike massive observers with proper accelerations from real forces pushing them off local timelike geodesics. The presence or absence of local tensor curvature is not directly relevant. The dynamical background independent curvature field of course bends the timelike and lightlike (null) geodesics away from what they would be counterfactually in nondynamical Minkowski spacetime. Globally flat Minkowski spacetime is very special because it allows global frames of reference that extend over the whole universe. This is not possible when there are real tensor curvature gravity fields. Now we can only use local frames of reference, either local inertial LIFs (“frefos” Lenny Susskind) or local non-inertial LNIFs (“fidos” Lenny Susskind). Furthermore, we can only compare local frames that are physically coincident – with proper separations small compared to the locally varying radii of curvature. The components of curvature are the inverse squares of the several tensor radii of curvature. Formally, all the coincident LNIFs lie on the same “gauge orbit” in Lie group theory. They are all different representations of the same geometrodynamic curvature field seen from different perspectives in locally properly accelerating LNIFs. There are also the LIFs in which, Newton’s gravity force, is eliminated to a good approximation. Indeed, the connection between locally coincident LNIFs and LIFs are the sixteen tetrad components. These sixteen components form four first rank tensor fields, one of which describe the tangent 4-vector to the timelike world line of the COM of the LIF. The LIF tetrads themselves are quasi “Yang-Mills” spin 1 gravity fields that combine with in pairs to form the ten spin 2 symmetric tensor fields in accord with Einstein’s Equivalence Principle (EEP). Newton’s gravity force is represented by the Levi-Civita connection that vanishes at the center of mass (COM) of the LIF. However, the Levi-Civita connection components also describe all the fictitious inertial pseudo-forces found in Newton’s particle mechanics. They are explicitly, in the case of rotation, Coriolis, centripetal and Euler. Under conditions of constraint, for example, a moving bead constrained on a circular wire. Electrical contact real forces from the wire on the moving bead provide the real inward centripetal radial acceleration.
Jack SarfattiWe must be clear, what is meant by a “real force” as distinct from a “fictitious inertial pseudoforce.” This distinction depends on first distinguishing the measured object from the detector measuring its motion. Fictitious inertial pseudo forces do not act on the measured object. That is, an accelerometer clamped to the measured object will not show any local proper tensor acceleration (aka “g-force”). In fact, however, an identical accelerometer clamped to the detector will show a local proper tensor acceleration on the detector from some real force acting on it. Therefore, fictitious inertial pseudoforces are optical illusions, purely kinematical artifacts, that appear to act on the measured object, but are really acting on the measuring apparatus. For example, we standing still on surface of the Earth are static LNIFs with radially outward proper tensor accelerations in topsy turvy curved spacetime. Literally, we properly accelerate towards a freely falling cannon ball on a 4D timelike geodesic that is the parabolic orbit in ordinary 3D space. This is hard for many to wrap and warp their minds around. So here is where we come into conflict with Woodward’s idea. He appears to unconsciously shift meanings of “fictitious force” in his argument leading to false conclusions in my opinion. Therefore, I disagree with Woodward’s too vague ambiguous remark: “ Coriolis forces … do not be fooled, they are not the same as gravity …” p. 26 It depends what you mean by “gravity”. If one means the real gravity tensor curvature – then of course that’s correct. However, the proper context is Newton’s famous inverse square force and that is precisely in the same ontic category as the Coriolis, centrifugal and Euler fictitious pseudoforces. Indeed, C. Lanczos showed this explicitly for the Levi-Civita connection. The non-tensor Levi-Civita connection describes all the fictitious forces – the optical illusions seen by observers with proper local tensor accelerations on off-timelike geodesic world lines. The self-referential covariant curl of the non-tensor Levi-Civita connection with itself is the fourth-rank tensor curvature field of real gravity if it’s non-zero. However, the Levi-Civita connection is useful even in special relativity with zero curvature because it describes accelerating observers there as well.
Jack SarfattiThe meaning of “constraint” in this specific context is when the measured object and the measuring apparatus are clamped to the same rotating frame, e.g. a rotating disk. In this case, the clamp provides a real electrical contact force on the measured object must provide the inward radial acceleration magnitude square of rotation rate x distance to the axis of rotation. Of course, in accord with Newton’s third law, the measured object exerts and equal and opposite reaction contact force back on the clamp.