Norman Albers

No but I like your statements and questions, nstansbury. You are messing with a powerful idea. In my electron nearfield I assumed a describable near-field charge density. This manifests polarization as in a dielectric and I freely interpret it as a relativistic increase of the vacuum polarizability. Thus it is a degenerate black hole: vacuum permittivity blows up asymptotically but this requires 'only' a finite local polarizability increase. This is quite similar to the 'dark gray holes' of H.Puthoff and Polarizable Vacuum Theory. In the other study on possible photon radiation field localization, I simply let it be so by declaring the existence of the Guassian packet. By solving for the implied electrodynamics, we witness charge and current densities which are understandable as responses from a superconducting medium. I believe the processes I illuminate here are manifest in atomic absorption and emission. On the other hand, you find me at the point of just trying to pull my head out of the sand and consider the larger quantum field picture. Maybe the best I can say at the moment is, aren't QM wave functions spacelike entities? P.S., When we broached a thread on negative index of refraction, I recall us all "going to our rooms" and I did not hear further! [On the atomic level, you can write out the wave function product of the two states of a transition, combine the imaginary exponents of the 'z' components, and see a radiating antenna and an EM wave. This, in the quantum theory, is the dipole transition matrix element, and interpreted as a probability. I add on my list of things to do today, look at that and see it corresponds to my 'scrunched up' wave packet. Bets?]

Aren't Type I supernovae our standard candle for figuring density?

Do we observe only galaxies, then, at such distances? Thinking high luminosity, maybe quasars? How far out do we measure the population of novae?

Clarifying my statements in post #13, when I shorten the "fuzziness" or falloff envelope of my assumed wave packet, the first order terms yield a picture of two opposed dipoles. I have the first four orders of integration by parts and the other set of terms is at right angles and out a bit in the 'X' dimension, namely maxima in an expression of: [math] Xe^{-a^2 X^2} [/math]. So each is served with a twist. This is more like Fig. 3 in the paper offered by Jacques. It is a poor choice of words to say "opposed dipoles". This is so in an axial sense, but to look at it there are similarly oriented dipoles above and below the axis.

Back to the cosmologic models, I have been spending time with the Friedman (Robertson-Walker) and DeSitter metric solutions of the Einstein field equations, and would appreciate feedback on my observations. If the curvature tensor terms could go to zero in a far-expansion state, this implies a fixed R(t), the usually expanding radius of the system. This sounds not reasonable, so I look further to the DeSitter form. Here we set the 'Hubble constant', or R'/R, to an unchanging value. Realize that in the "midlife" stage this was a decreasing quantity. If I am correct this implies a constant Riemann scalar (tensor contraction) of: [math] {R^a}_a = 12H^2 [/math], and an exponential late expansion... A DeSitter metric implies that the sum of mass-energy and pressure are zero. Then specifically, they satisfy: [math] \frac {8\pi G}{c^4} P = \Lambda - \frac {3} {c^2} H^2 [/math], with [math] \rho + P/c^2=0[/math]. I'd appreciate hearing what we can observe about the balance of the two terms on the RHS of the equation. In the "middle age" epoch the Friedman (Robertson-Walker) metric recognizes a source field of isotropic mass-energy distribution and negligible pressure. Stars and galaxies have separated to where their average random motions are small in kinetic contribution. The Hubble constant varies inversely with time. Therefore one can see the possibility that it eventually comes down to equal [math] \Lambda[/math]. At this level the residual vacuum pressure becomes siginificant. Total energy goes down through zero as the regime yields to the DeSitter form. I'll be looking at the late-stage Friedman behavior.

Have you checked out Anthony Lisi's work and reaction lately? I am just starting to read a textbook on geometric algebra. It frightens me but my friend solidspin is there to coach. He says, this is it.

In the inimitable words of my brother, when faced with the stupendous, that's pretty cool !!!

Cool, it seems we agree that a single moderate star at a billion LY is 'pretty weak'?

Janskys, I love it. Now tell me the answer! . . . . . OK, helpful conversions: energy of one EV (photon) is 1.6 E-19 Joule.

Scalbers, thank you so much for your practical experience and observations. This is helping me move forward in challenging my thinking about the nature of the radiation field. Especially, since I have focused on possible electrodynamics of photon localization, I have underestimated the wave nature of the larger field. It makes sense that it takes the whole mirror to focus one photon. Can you get me into realworld magnitudes? I ran calcs on a star like our sun in power output, generalizing from 1,300 watts/square meter at Earth orbit radius. If such a star were one billion lightyears distant, I calculate that a 9-meter mirror would see only one photon per hour. Do we only observe galaxies here?

I think we can agree that the photon with unit angular momentum is what is detected by identifiable detectors which respond to quantum quantities. What, then, do we know of the 'detectors' and what do we know of the vacuum radiation field??? This question drives my studies and pushes me to further dimensions of understanding, I hope. I realize that when quantum electrodynamics and field theory make you feel queasy, you are starting to get it. It seems that quantum wave functions demand a spacelike reality outside the lightcone, in the language of relativity. Is this what others see? I figure the larger theory deals with such waves on a stochastic background. The fact is, there was a detectable coherent photon event.

If the mirror surface is perturbed, like you described, say, built of little flats at angles to the overall curve, is there no loss of some photons, a loss of luminosity or light collected? . . . . Clearly the individual photon detections do not interact. They all individually do whatever it is they do, and the interference patterns build up in discrete steps. The quantum wave probability function describes the overall effect. It seems you point out that if photons were only local EM wave packets at a small (centimeter, say) region, then the diffraction would be great. This is something that I would think takes many events to determine, however. Is there no way we can add the larger interference patterns from all parts of the mirror and come out with the finer result?

Excellent discussion, scalbers. My understanding fails where we try to compare physics of one photon to that of the ensemble falling at different reflection points on a parabolic mirror. You are saying that one photon "knows all" as I think John Wheeler espoused. I say, one photon lands with some uncertainty of momentum, and I am asking if many of them distributed around a mirror of many square meters, then establish the diffraction clarity or lack thereof?

It is good if a little bird poop does not throw off the usefulness of the device. We dutifully integrate over all possible paths. One photon has no fringes. The pattern is a buildup, yah?

So each photon has less diffraction, and it's not just a matter of signal to noise from more photons at distinct reflection points? I thought that in double slit experiments the two slits had to be within a few wavelengths to get strong interference fringes.

Does the photon have to 'sense' the entire mirror? Don't we build mirrors of many square meters to catch one here, one there?

Do you know the reflection happens without delay?

We're talking septillionths here. [sorry, you out-Greeked me.] I hear the free electron lasers give pulses of a 'few hundred' attosecs. This corresponds to a light-length of 0.06 microns. Now I need to find out the frequency here, also.

Arrghh, my decimals were also off! Now that we all know a femtosecond is E-15 sec., and an attosecond is E-18 sec., the pulse described multiplies to speed of light. What, however, is the "period"? It is the length of the pulse, and is the pulse one wavelength?

Yes, pardon me. This is different, being single photon production. The first questioner below asked also, what's the momentum, or frequency? In my modeling, I can allow the envelope decay parameter, 'a', to approach the propagation vector 'k'. As long as a/k<1, I can still generate an expansion series in the integration of dU/dt. It looks like the sheath does not lose its character. There is still an inner and outer, oppositely charged, double helix. One might imagine it as two opposite e-p dipole pairs manifesting from the vacuum on either side of center.

My colleague solidspin described pulses of 'a few hundred attoseconds' duration, so those described here last 65 attosecs. Were this the time for one cycle it would be 20 micron waves. My impression is that these are higher frequency sources on free electron lasers at accelerators. Is this correct here? In the paper from Jacques my model is depicted in Fig. 2.

Jacques this is a very beautiful article. I shall digest what it offers and talk later. For the last two days I have been trying to understand what I might or might not be able to analyze if the falloff of my envelope is comparable to the characteristic wavelength. BINGO! NORM

Thanks, Dave and ajb, I hope to lose my fear of convolution.

I need to take the Fourier transform of a product of three terms. The statements I have of the convolution theorem are thus: [math]\frac 1 {2\pi} \int dk F(k)G(k)e^{ik x} = \int du f(u)g(x-u) . [/math] How do we express the inverse, namely: [math] \int dx f(x)g(x)e^{-ik x} [/math]? Can I just follow my nose and write a similar convolution integral in k-space?

I vote for Klaynos for whatever office he cares to assume...