Norman Albers

I have a theoretic question here. Given a real, symmetric matrix G, is there a complex square-root matrix such that [math] S^T S=G[/math]?

Well said kleinwolf. The choice of coordinate representation is critical, I think. You allow or disallow certain geometries by setting the real domain of especially the radial coord. We should be able over the next five years to discern black hole event horizons. If we can it is a blow to, say, Puthoff's dark gray hole construction from isotropic coords. I do think his degenerate event horizons share characteristics with particles. The discussion from Joshi comes from the more orthodox Schwarzschild perspective, as he investigates non-uniform possibilities. . . . . . . Do be careful not to combine different discussions, kleinwolf. Since cosmologic effects are long-distance and small in the near, we say that a near-field from a large and/or rotating mass is set in a Minkowski flatspace in the far.

Ah yes, after cleaning up my terminology this makes sense.

Thanks, I shall ponder... OK, can't this state be excited by absorbing a photon, say, to level spin-2? I am imagining the particle spins parallel and an orbital vector parallel also. Don't we go up in angular momentum quantum numbers with excited energy levels? [Tell me current notations.] Merged post follows: Consecutive posts mergedSometimes the terms 'ortho' and 'para' are used to refer to relative spins. I am asking about a parallel particle spin state with unit orbital AM also.

Can an orbiting electron/positron ensemble be in an excited spin-2 state? Is orbital AM still quantized in units of [math]\hbar[/math]? It seems the latter answer is yes, as you could say the particles orbit about a common center, so the problem is not so different from a massive atomic center.

The metric tensor produced in GR for rotating masses is real-valued. I am looking at null light-speeds, which may be complex-valued. They are expressed as the square root of the ratio of two metric terms, and so must be complex, just because the ratios may be negative. If I can connect my reasoning on gravitational vacuum polarizability with these theoretics, there ought to be a complex tensor expresson for polarizability of the vacuum. Merged post follows: Consecutive posts mergedI must make an important qualification about the metric tensor terms being real. The point of my recent study of the Kerr electron angular momentum object is that we must acknowledge and understand the coordinate system used to solve and express the metric. The fully axially symmetric representation is entirely real but this is coordinate-dependent. Transformed back to Cartesian coordinates there is a singular ring where the metric term itself, and not just its square root, is complex.

It seems you are thinking along the same lines I am, and yes that is the behavior in the isotropic coords. What is real? This does depend where you are, at least as observed by others elsewhere. I am trying to extend the usefulness of the externally flat Cartesian coords. by realizing a polarizability tensor. I suspect the use of isotropic coords. is misleading and motivated by the universality of local observations of the SOL. {P.S. Type '/math' and '\rho'.}

Whatever you assume for the near-field problem, the metric must be based on the Minkowski flat space in the far, yes. Thanks for noting the behavior as r goes to zero. I am staring at that and not knowing what to say, but I am speaking to the assumptions we make going into this, yah? . . . .OK I think we need to agree on coordinate names. I call the isotropic radial coord. "[math]\rho[/math]" as opposed to the original "r". In the isotropic metric of the first post, as you take [math]\rho[/math] to zero, the coefficient of the time differential goes to unity, but that of the space differentials blows up. So kleinwolf which coordinate are you thinking about?

What I have been investigating lately is the angular momentum singularity for a "small" mass. For stellar events the mass term in the GR equations is much larger (usually) than the AM term. The opposite is true for any particle. There is a ring-like singular solution in GR for an electron at roughly E-13 meters, though it is of very small, namely Schwarzschild, dimension. This is in addition to the center mass singularity as we are accustomed to except this would be at E-57 meters or so. . . not so relevant. I do not yet know the implications of this GR ring.

I am reading in Feynman Lectures Vol. II, chapter 31 on polarizability tensors. He offers here the machinery which I say is applicable to the vacuum per se. I am seeking a clear expression of the implications of the Schwarzschild and also rotating Kerr metrics, in such a parallel statement. There is a rich realm of implications between strongly rotating large masses, and then again, particles as strongly rotating tiny masses. Merged post follows: Consecutive posts mergedI am feeling my way to a unified field consistent with all we can now comprehend, and maybe there is something for me to express between the differential relations of GR and the interpretations of quantum vacuum physics.

My apology, I had not seen Bernard Madoff's name in print, and that obviously explains the bronze piggy bank.

I should clarify the line in post #54, "Resistance ... at a complex right angle to conductance." I am confusing a couple of things, since we are dealing with conductance either with or without time-dependent loss, and distinctly, with the complex plane comprising inductance, "resistive" flow, and capacitance, where current may or may not be in phase with voltage.

National Public Radio yesterday reported that in New York someone is selling a NADOLF DOLL, which is a piggy bank of his head, and the plug on the bottom doesn't work. . . . . . . . . . . . It is of cast bronze.

Good damn questions from several points of view, and I have one or two that are not orthodox. Light is pretty much a transverse disturbance, no? Electric fields jiggle side to side, and at right angles to this are magnetic fields doing the same. Just for this to be happening, we have to cop to an electric permittivity and its magnetic counterpart. I did a study on photons where I figured out a possible electromagnetic field envelope of a localized wave packet of light, really the most basic field model one could execute. I said, if there is a transverse field disturbance with a Gaussian envelope, like a fat cigar or bullet [[words escape me]] then this implies the vacuum or something is supplying response, and this may be understood as a superconducting sort of thing. We all agreed at the start of electrodynamics, that the vacuum cooks, in some responsive fashion. I allowed an expression on the right-hand-side (RHS) of the Maxwell equation that we usually set to zero. This is a good electrodynamic study. WHAT IS PHYSICS? THE QED light-field is not the same and it shows the broader wave nature of photons, like going through "both slits" of a close pair in a diffraction setup. So maybe light doesn't propagate in the neat little bullets I describe and there is a more subtle essence to the field. I think, however, that at the atomic absorption event, my picture of wave packet is realized. The atom may stably exist at quantized energy levels, and the absorption or emission may be seen as a superposition of the two wave states. This is literally a dipole radiator configuration as expressed in the QM 'dipole radiation matrix element'. At some point I think Nature answers to electrodynamic questions, but the fundamental field is deeper than this.

The Michelson-Morley determination that given a plus or minus speed of the Earth at points a half-year apart, there is no such change in the measurement of the SOL. Here is a section I lift from the opening of a paper by Hal Puthoff, where he lays out the Polarizable Vacuum approach to GR. I feel he pulls his punches to say: "Although conceptually straightforward, the curved space-time approach can seem rather abstract to beginning students, and often lacking in intuitive appeal. During the course of development of GR over the years, however, alternative approaches have emerged that provide convenient methodologies for investigating metric changes in less abstract formalisms, and which yield heuristic insight into what is meant by a curved metric." He goes on to describe a scalar field in which electromagnetic and gravitational responses of space are allowed to change smoothly over space. I am trying to build a construction with, a priori, a complex tensor field.

I don't see why you say that. Every observer perceives the same SOL in their own locale. The vacuum is thus Lorentz invariant.

These days I see spacetime as percolating desire. Remember, physics is relatively the same in different frames, but that does not mean permittivity and permeability are absolutely the same. Quite the opposite is the case. For this reason I dared to write of "thickening of the vacuum". I am currently setting my dreamcatcher for theoretics using what I call null speeds of light, which are what an observer at one gravitational point perceives of light moving at another locale. This vector field becomes imaginary (complex) in different regimes.

Einstein was only convinced he had really accomplished something when he figured the perihelion shift of the planet Mercury. It's orbit is an oval, and this slowly moves around in the large sense. Later, shifts of light sources passing behind other massive objects showed bending of light-paths. This is predicted in GR.

In Southwest Oregon, Josephine County has given its Soil and Water Conservation Service $85K for small farm canola crop planting. Described as useful for marginal soils without irrigation (a spring crop, I guess?) this is being supported also by a Eugene-based Northwest Seed Crushers Company who will actually contract to farm your little 5- or 10-acre field, if not contract for your seed crop to crush for oil. My colleague solidspin who is actually into the biodiesel industry deeper than you can imagine, says yes but soybeans are what I need for biodiesel. Stay tuned, folks. For optimum fuel-oil soybeans, but canola yields oil and also feedstock-grade meal. Merged post follows: Consecutive posts mergedOne local farmer jumped right in and is doing 80 or so acres and is considering his other few hundred acres.

It would be nice to hear from people knowledgeable in quantum theory, concerning the possible disturbances alluded to in this article, as we integrate ????????? quantum probability amplitudes of some sort I guess, and I am weak here in theoretics.

Generally, I agree, Swansont. I suspect I came on something more profound in seeing that the Compton wavelength is [math] 4\pi[/math] greater than the GR expression for the geometric angular momentum radius. Over good beers, we might agree that ultimately we will see deeper unity.

I read last summer that in Europe somewhere there is a prototype flywheel bus. I guess we mount it vertically, no?¿?

pioneer I feel you have no hook on which to hang your "simple mass preference". I do like your statement about positrons being massive. Any localization of energy is. I feel you are ignoring a great deal of physical truth in symmetries. The mystery is of symmetry breakdown. Energetic encounters, whether of accelerator or "cosmic ray" nature, give particle pair production.

I call it being 'hipneck' and I certainly am, goddang flippin' betcha, sumbuck. Kirby AND HIS WIFE hiked up through my yard, and I sort of chickened out, only because when I showed him the dead tree from his land hanging toward me, he agreed I could take it out. Dang, oh well.

The expression of [math]4\pi[/math] usually indicates that an integration over three-space has taken place, and this is the solid angle. Swansont, interesting to read this surprising definition. Surprising to me because I assume such essences.