Norman Albers

I think it is not nice to expel discussion because it does not answer everything at once. I have not claimed anything beyond a linear theory of response from the vacuum polarizability.

Farsight, I do see that you have described a spiralling "Moebius doughnut" and that there are coherent orbits described which track twice around in a different path before meeting their start. This is topologically fun, but where's the angular momentum accounting?

[bIGTEETH] Good one Klaynos. [/bIGTEETH] One night a friend and I were listening to a far radio-skip of some southwest US evangelist, who earnestly told us you can believe this because IT IS TRUE.

Somewhere in a far distant forum somebody dissed me as laying out "fake matter". The more I think of it, the more I think this person is slowly becoming enlightened...

Now that's funny. I consider upright bipedalism to be an unproven, unfinished experiment, for instance. Surely the most disunified thing around here is us.

I don't expect to rattle anything off but I certainly am laboring over the mathematics of relativity in particle near-fields. I have finally written what I think are the relevant inhomogeneous Einstein field equations to my electron study, and am working to figure what orders of m are implied, since the field equations boil down to the O(m) terms. (m is geometric mass and since it is arbitrary the equations must be satisfied in all expressed orders of it.)

I've listened to good physicists invoke "handwaving arguments" to put off what most see as niggling details, but they are no substitute for scarce logic. (This is another of my cartoons in Pitfalls of Theoretical Physics.)

This I am comfortable with. I am proceeding with a mathematical hypothesis and my goal is to find the end of its usefulness.

Yes, no, yes, no, but I think you are all being blind.

I figure the expanding event horizon scenario holds for accretion in the large, but this is not at all clear for a "particle" falling in. My book solves this as: [math] r-2m=8\pi e^{-(t-t_0)c/2m}[/math] and the authors say, "It is thus apparent that r=2m is approached but never passed by the falling body if one uses t as a time label... it corresponds to the proper time of an observer at rest far away from the central body. Thus in the finite proper time in which a test body falls to r=2m we would expect that the entire evolution of the physical universe exterior to r=2m has already occurred, so that the physical meaning of further fall becomes questionable in the context of Schwarzschild geometry."

You may be confusing what happens when. Why can I not argue that the proper time experienced by those "falling through" never gets to happen, to the "outer observers"? This is not a simple mapping of delayed light pictures. Where it gets interesting, to my understanding, is that the asymptote is only logarithmic, so that within ponderable time, we get to quantum separations from the horizon. Otherwise, you cannot have your relativistic spacetime cake and eat it too.

Collapse in the more analytically soluble models occurs asymptotically in time, though the time constant is not that long; you tell me...

If there is a near-field permittivity that increases as inverse-square radius, then radiation will go in a circle. If the parameters of such a singularity are right, then rotation and precession cancel helicity and you get frozen phase.

Cotton candy measuring other cotton candy.

Thank you for very helpful teachings, BenTheMan. Just considering wave packets from my perspective, with higher and higher frequency, the intensity of field strength in a photon gets hugely higher. If you assume there is conformal shrinking with higher k, as I do using a "number of cycles", or rather an envelope parameter of a certain strength (the FSC) dictated by the vacuum response, then fields must rise by the fourth power. It's clear to me that at some point you are going to hit a fundamental phase change and you describe how we are in a further regime. I figured we are around muon mass-energy, but you put the whole enchilada right in my face.

Harking back to pair production from high-luminosity light-fields, check out this reference to DESY free-electron laser plans, and the mention of Schwinger pair production. http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVN-43856N6-F&_user=10&_coverDate=06%2F21%2F2001&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=0d6b1d20cfa94bb0c16b9fc52cbb4a90 ........Good suggestion from BenTheMan; we certainly know Maxwell's equations fail on the level of quanta, but I offer a path here and hope to publish with solidspin a furthering of the Schroedinger equation. Someone with your knowledge could certainly help, Ben. Further question: why is there an energy ceiling on photons as you mentioned? Do higher-energy bosons take over the scenario?

Starting in 2001, I looked at all the ways you could try to put two halves of a sinusoidal form around a loop. I actually looked at energy densities of these tested forms. Notice that in my electron theory I hypothesize a near-field current circulation, a thing which QM sidesteps. Investigating [math]A_r [/math] and [math]A_\theta[/math] forms always yielded something untenable, geometrically if not energetically. There were alternating quadrants of +/- infinite density, so I moved on to work with [math]A_\phi[/math] and this does yield reasonable near-fields. If there is circulation as I propose, the revolution equals phase precession which would be expected, so you produce a consistently outward (or inward) electric field, one of the same phase all around. For a few months in 2003 I walked around exclaiming "Moebius doughnuts!" to wondering friends. I have not shown why electron spin is 1/2-bar. You can imagine remnants of the form of photon going around in "frozen phase" but I rather see it as a different stable state of the same energy of photons which underwent interaction. This should not raise eyebrows because we work with conservation of energy, no? I am working to form a theoretic vision where we realize all the phenomena we speak of as manifestations of the vacuum polarizability. I do find Farsight romantic and mathematically wanting, and stuck on preserving individual photons. I am doing something more subtle.

There is no frame of reference where the photon is stopped. One cannot speak of a "center of mass" frame of reference, but rather a "center of momentum" frame.

Thanks for the good source, tranx. It is more clear than some others I've seen so I will chew on it. Clearly precise distance cannot matter if "precise" means "same number of wavelengths".

Thanks for a knowledgeable answer, Klaynos.

Seeing developments in metamaterials a few months ago I asked if a reduction in the permittivity of the "vacuum" medium, somewhat below unity, could be engineered ???

Do they need to measure at the same time in their common frame? What if one is further?

My photon model has a longitudinal-scalar mode, though I have not thought about its polarization. This comes by assuming the vacuum supplies inhomogeneous response, and is simply implied if you make the statement, "There exists a wave packet described by [math]A_y=A_0 cos(kX)e^{-a^2(X^2+y^2+z^2)},A_z=A_0sin(kX)e^{-a^2(X^2+y^2+z^2)},X=x-ct. [/math] The fact that the transverse components fall off in the transverse directions means the field has divergence. This is equated through the Lorentz gauge to [math] \nabla\cdot A=-c^{-2}\dot U [/math]. This scalar potential is an "accordian mode", and has to be integrated carefull by parts since t appears twice.

We enter the model saying there is spherical symmetry. I'll quote from Adler, Bazin, Schiffer, Introduction to General Relativity: (p.186) "The limiting form of the line element at large distances from the origin may be expected to be Lorentzian... The reasoning which follows is based on plausibility only, in order to guess a heuristically reasonable and convenient line element. We should expect the line element to be invariant under inversion of the coordinate interval [math]dx^0[/math] (representing time); that is, [math]ds^2[/math] should be invariant under the replacement of [math]dx^0[/math] by [math]-dx^0[/math]. This dictates that we use Gaussian coordinates in which the off-diagonal elements [math]g_{0i}[/math] of the metric tensor are zero and the line element has the form [math]g_{00}(dx^0)^2+g_{ik}dx^idx^k [/math] with the [math]g_{ik}[/math] independent of the [math]x^0[/math]. This is referred to as a static metric; it is to be distinguished from a metric which is merely independent of time, or stationary. Second, if there is to be no preferred angular direction in space, the line element should be independent of a change of [math]d\theta[/math] to [math]-d\theta[/math] and a change of [math]d\phi[/math] to [math]-d\phi[/math]... so the metric tensor must be entirely diagonal for the type of solution we desire." I enjoy the mathematical clarity and honesty here.

Swansont, when I last communicated with Seb Doniach, Prof. of QM physics at Stanford, he described the dueling x-ray sources being set up at the accelerator storage rings, to, as he put it, "boil the vacuum" and yield pair production. Has this happened?