Norman Albers

I could show you one of my favorite lines in Dirac's little black book on QM. The first third of the book is his exposition, tight mathematical prose, followed by math presentation. Right in the middle of the first part he says, "I give here the quantum mechanics of things of mass m and charge e. These are the eigenvalues we always measure and so I use them!" (I paraphrase only lightly.)

When we witness macroscopic superconductivity, is this describable by the term quantum nonlocality? Severian, it would be helpful if you would elaborate on your comments on normalizability and Dirac....................Oops, sorry for confusing things. You got it below.

Enoch is seeking with righteous curiosity. I have been working to describe photons and electrons as excitations of the vacuum, the laws of which we know, IMHO, only dimly. I grope with inhomogeneous field ideas, assuming Nature is indeed unified, and that only our understanding is not.

Some Western writer in a second marriage said, "I treat holidays with the same due respect I give rattlesnakes."

After looking at the construction of the stress-energy tensor for electromagnetic energy, it seems it is valid in the usual expression: [math]T_{ab}=[F_{ac}{F^c}_b + \frac{1}{4} g_{ab}F_{cd}F^{cd}] [/math], even for inhomogeneous fields, namely those including charge and current. I am assuming an entirely electromagnetic identity to the electron so there is no need to identify a mass density term, as if there were particle masses, and furthermore there is no need to run the source term [math]\rho U[/math] through the gravitation equations. The electric field already shows, or implies the charge density field, so I just talked myself out of a job. Not so for the magnetic field, however.

Great study, FrankM. That is a substantial amount of current at this scale. I don't know much else about the situation other than that you are grounding current into the local earth. I had wondered about surface/air changes in electric field but this discussion speaks to response from "creatures of length" to lateral distributions.

With the next day's perspective, it is not important to see the -2m/r singularity alleviated, because it would exist at a non-physical size. What I see is that just as I was able to plug my electron field into the Reissner-Nordtsrom machinery, I have three other terms to attempt the same: in an inhomogeneous stew one accounts for source terms in charge and current and also for field energy terms. (I do the same when I calculate total angular momentum.) This is mathematically exciting because, say, [math]\rho U[/math] in this model has stronger dependence at the origin than does the square of electric field. I am just mastering the tensor curl formalisms I need to present the magnetic terms. I do not mean to derail this thread. I mean to stimulate discussion of how both quantum mechanics and relativity can and must be moved further, to further synthesis. You might say, who needs a static model of electrons? This is static only if your thinking stops here. In the case of my similar meditations on photons, a PhD candidate has become quite excited about constructing photon position operators, and feels he has the overall structure. He is taking off with his knowledge of QFT, as impressed with my field manipulations as I am by what he can do. I describe what you might expect from a plasma physicist looking at the vacuum as a superconducting availability. He sees the key to constructing a nonlocal representation.

I gather the Reissner-Nordstron approach to the electron was discarded because it produces this embarassing positive asymptote in the gravitation potential. What I can offer here, if there is any usefulness in the idea of inhomogeneous charge nearfields, is that inside of the millimeter radius there would be a slow rising of the graph of [math]g_{oo} [/math]. Realize that this term is scaled to the characteristic length of E-30 meters as noted above, and is near Planck length. Much inside of the classical radius (E-15)m, I have shown that the "shading function" approach of my electric field, designed to cancel out terms of order <-2,-1> in radius as you go to the origin. also make the electric term in the gravitation metric expression drop out, leaving terms in -1/r. I see here a possible next move in this chess game. The untenable electric infinities have been removed. What has been solved was a gravitational equation for free space, in terms of a "point mass" possibility, but with the additional electric field energy specifically accounted for. Realize that the -2m/r term shows up as a constant of integration, simply. I suspect that if I developed the relativistic forms (Einstein equations) with the total energy densities included, as have done in my studies, then also the -1/r term would be balanced off, cancelled in the limit.

In low-order regimes we interpret this metric as equivalent to the classical gravitational potential [math]\phi[/math] expressed in: [math]g_{oo}=1+2\phi/c^2[/math]. Thus the original Schwarzschild soln. comes down from a farfield of unity, crosses the axis (becomes zero) at r=2m, and continues to tank downwards. This is not the case with the electric energy part of the gravitational field. This should not be confused with fields themselves. To wit, the forces of an electron on another, to this reckoning, are always forty-two magnitudes in ratio. Thus in a sense we are talking of a 'gravitational flea on an electric elephants back'. In the large, electric forces do not seem to be important as they seem to have opportunity to neutralize at small scale. It is, however, correct to say here that gravity has become repulsive, seen as a rising potential going inward, rather than falling. Protons, too, will show this, scaled by their mass being about 2,000 electron masses; neutrons will not.

Martin, thanks, my book has the "geometric mass" or Scwarzschild radius as [math] m=\kappa M/c^2[/math]. The metric result is [math]g_{oo}= 1-2m/r + \kappa e^2/[r^2(4\pi \epsilon_o^2c^4m_e)][/math]. For electrons or any other particle, actually, the Schw. radius is way below the Planck length; the graph in the nearfield is dominated by the electric term and shows only a small dip where the first order term shows. We know the electric force is "much stronger" but this is examining the subtleties. . .I just edited the incorrect power of 'c',and [math]M=m_e[/math]. Note that I am elucidating the original solution. In my thread on 'Reissner...' I develope nearfield possibilities suggested by a spreading out of the region of divergence, or charge density. which change this picture, though not until dimensions at and below classical radius. . . . . . . .more time passes . . . . .ARGHHH, I blew some of the numbers, though the substance of the discussion offered remains. Now I calculate the Schwarzschild electron radius as 7E-58; I had something upside-down and if you figure the radius where the two r terms cancel. Actually this is the point where the graph, which would have been the Scwarzschild (1-2m/r) and falling down through zero from a farfield of 1, goes back up across the r-axis. Twice this radius is where the curve has its minimum. . . . . . .After much numerical chaos I again got the result of a tenth of a millimeter. I got confused trying to simplify the expression to: [math] g_{oo}= 1 - R_m/r + (R_e/r)^2[/math]. The quantity [math]R_e[/math] is about 0.4E-30.

The result of all this is that in the far field the gravitational effects of an electron's electric field die off faster than the term supposedly given by its mass. Conversely, as you go in close, the term created by the modelling of electric field energy dominates the gravitation expression, and actually gravitation changes sign! I have not dealt with this previously so it is a wonderland to me. Now most of us agree that our physics falls apart, or comes together, at the Planck length, so we never get to the smaller radii at which electron gravitation becomes major in the small. Remember the "rubber membrane" of GR strong fields? I'm speaking of where the sheet changes from tension to compression for a charged particle.

I am finding much to do and learn around the analysis of the Reissner-Nordstrom metric. Please check me on the units and quantities here: I calculate the Schwarzschild radius of the electron to be 4E-60 meters. On the other hand, the second term in the metric expression, positive in the inverse square of radius, has a characteristic length of 1.3E-22 m. The electric energy overwhelms the gravitational term in the nearfield, so that there is manifest no event horizon. There is a small dip in the graph and it seems strange that I calculate the point at which the [math]g_{oo}[/math] plot again crosses the x-axis is only about a tenth of a millimeter. Now we are not talking about much gravity here, but the scale is most interesting.

No I cannot, and am just barely approaching what you so beautifully express here. Thank you for showing this.

I do not mean to be flip here. I am involved in exciting discussions taking off from my realizations of the electron field itself, as well as gravitation studies, of the states of the vacuum polarizability in these different but not totally distinct regimes. Severian, I like that statement of spin being another degree of freedom. It is the intrinsic particle characteristic and THE NEWS is that the different levels of angular momentum interact. As a senior in college this struck me like a freight train.

Strictly speaking it takes an asymptotically long time to fall to an event horizon. I've been hung up on this, as it is true, BUT, the dependence of the separation of a falling body to the horizon becomes logarithmic: [math] r-2m=8me^{-c(t-t_o)/2m} [/math]. If we work out the scales at a mass of our sun, it has a Scwarzschild radius of only 1.5 kilometers. The characteristic decay time in the exponential is this divided by c, or about 0.5E-4 seconds. Thus in just one second, the exponential developes thousands of orders of magnitude, or thousands of decimal points. This is way beyond kilometers reducing to microns; that is a magnitude shift of E-9. Thus it does not take long for a radially falling object to get quantum mechanically close, or to atomic and particle scales. Thus there is much theoretic ferment here at the meeting of quantum mechanics and relativity. My own guess is that inside the horizon, the vacuum is in a fundamentally different phase state and we should not assume physics is as it was outside.

Farsight, that reference is a whopper. I suspect I am exposing my confusion but that's how I learn! All of my expressions are correct, but correctly what? One has to include a metric multiplier to get local measures; I'll be reading to get to the facts of the relative frames of measure. . . . . . . time passes. . . . . The expressions above are in "coordinate variables", or those of a far observer in a flat space. My text makes it clear that a local observer experiences an interval: [math]d\tau=g_{oo}^{1/2}dt[/math]. This shows clearly the relative time dilation. However, I guess we need to rescale the distance measured by the near observer, and if this is the case then locally it balances out and speed-of-light is no different. The analysis I offered might be good for, say, trajectories of light near massive bodies insofar as this is observed "in the far".

I start by looking at the expression: [math]ds^2=(1-2m/r)(cdt)^2-\frac {1}{(1-2m/r) }dr^2-r^2d\Omega^2,[/math] where the last term refers to angular changes. I'm trying to learn the correct interpretations for different observers. A light path is characterized by [math] ds^2=0[/math], but we are free to separately consider change in radius, or transverse (sideways) change. Rearrange terms in a radial displacement: [math]0=(1-2m/r)(cdt)^2 - dr^2 [/math] and in such a measure, [math] (dr/cdt)^2 = (1-2m/r)^2[/math], or [math]dr/dt=c(1-2m/r).[/math] On the other hand, an angular change yields: [math] 0=(1-2m/r)(cdt)^2 - (rd\Omega)^2[/math], or [math] (rd\Omega)/dt=c(1-2m/r)^{1/2}.[/math] The metric term approaches zero near the event horizon, so the transverse term with the square root is larger. Here on Earth the metric term from the Sun's gravity can be calculated ([math]m=\kappa M/c^2[/math]) as roughly [math] 2m/r=2.5E-8[/math], and that from the Earth's gravity is about a magnitude smaller. This is the deviation from unity, and the square root for the transverse term can be approximated with a factor of 1/2. Thus, hereabouts transverse light is slightly faster than radial.

Hey, Swansont, what does an observer "near a BH" measure for speed-of-light radially, and distinctly, transversely? Bascule, at what point, namely what energy regime do we need to answer your question? I see in GR a a differential calculus which shows its own limitation. It is a set of mathematical possibilities to be answered by physics.

I associate all relativity as illuminating the essence of both light and matter forms as resonance of the vacuum polarizability. The latter is a fundamentally Lorentz-transformable E&M responsiveness, and it's increased availability, or density, is what manifests gravitation.

In the paper available in my cache (URL below) on gravitation I offered my take on the Polarized Vacuum (PV) theoretics started (perhaps) by R.Dicke in the 1950's. All the studies I have read to date posit a scalar function of permittivity of the vacuum, which is then expressed in the Scwarzschild metric to yield the distinct radial and transverse responses. I have enjoyed a lengthy correspondence with H.Puthoff who offers the isotropic solution of the gravitational singularity. This is simply the other reasonable possible assumption on physics going into the construction. We either let the same coefficient multiply differential changes in all three spatial dimensions, or we allow radial measure to change differently from transverse. In my study I directly substitute presumed changes of the vacuum polarizability as per dielectric hole theory, into the two distinct Schwarzchild results to be seen when we express light-speed. I think this is a good approach because it echoes what can be seen in the small in my electron study, namely the "thickening" of the polarizability field, but moreso, one in which we see a skewing of a randomly offered dipole population which reduces the nearfield radial population. I told Puthoff that one or the other of our two respresentations is more useful, and that whoever can tie this gravitation persepective in the large, to the vacuum field expectations in the small, wins. The isotropic approach yields solution with no event horizon per se, so Puthoff calls these "dark gray holes" where permittivity blows up as you apporach the center singularity rather than a spheric event horizon characterized by the same asymptotic behavior in [math]\epsilon_o[/math]. Both the PV gravitational singularity and my electron singularity may be described as degenerate event horizons. The dielectric respresentation offers the understanding of this "infinite slowing of light" to be caused by an increase of the local polarizability equalling 3, a quite finite state of affairs on the face of it.

Electrons are the identifiable manifestations of whatever you want to call the available vacuum. So is all the rest of this, namely, available resonances.

I stuttered fairly badly in the first decades of my life, so I cracked up at this, my first stuttering joke, from columnist Calvin Trillin: A Jewish boy goes seeking a job at the local radio station. Returning home dejected, he is asked by his father, "Why do you think you did not get the job, son?" Answers the boy, "A-A-Anti S-S-S-Semmmmatism. "

It would be beautifully twisted if my projects on localized forms in a superconducting vacuum led to quantum mechanics of nonlocality.

This is a spherically symmetric system, or nearly. You can go around the Earth and not fall off, at least off the Earth.

Like some southern US senator said, we know pornography when we see it. Quantum operators satisfying nonlocality are it.