Norman Albers

I struck out on my own (either way!) by letting electrodynamics be inhomogeneous. Now this concept of polarization is as a runaway locomotive, and seems to offer a deep new perspective on GR. . . . . Sorry, I lose track of the point and forget what's been said where. I can explain the thrust of the idea is that the behavior of light (null geodesics) is equally explained by a medium of increasing dielectric constant. This is offered by the vacuum polarization, in two degrees: radial and transverse. To my amazement there is a very nice equivalence here and the algebra of dielectric runaway explains the event horizon and the whole shot. Are you ready for this? When the "thickened vacuum" reaches a polarization density of R=3epsilon-nought, you have a horizon. Inside, behavior is fascinating and analytic! I say we can picture a Euclidean manifold with dielectric stuff and enjoy exactly the differential geometry given to us. We said, "There shall be a Reimannian geometry where space and time are such and such." We are speaking about the backdrop of both energy and mass since mass is energy basically in circles. In a stronger dielectric waves are compressed in outside coordinate measure, but space and time are as they should be for travelers in it. Can the two be distinguished? I suggest not, and that we've found the darned rubber sheet!

The following is an actual question given on a University of Washington chemistry mid-term. The answer by one student was so "profound" that the professor shared it with colleagues, via the Internet, which is, of course, why we now have the pleasure of enjoying it as well : Bonus Question: Is Hell exothermic (gives off heat) or endothermic (absorbs heat)? Most of the students wrote proofs of their beliefs using Boyle's Law (gas cools when it expands and heats when it is compressed) or some variant. One student, however, wrote the following: First, we need to know how the mass of Hell is changing in time. So we need to know the rate at which souls are moving into Hell and the rate at which they are leaving. I think that we can safely assume that once a soul gets to Hell, it will not leave. Therefore, no souls are leaving. As for how many souls are entering Hell, let's look at the different religions that exist in the world today. Most of these religions state that if you are not a member of their religion, you will go to Hell. Since there is more than one of these religions and since people do not belong to more than one religion, we can project that all souls go to Hell. With birth and death rates as they are, we can expect the number of souls in Hell to increase exponentially. Now, we look at the rate of change of the volume in Hell because Boyle's Law states that in order for the temperature and pressure in Hell to stay the same, the volume of Hell has to expand proportionately as souls are added. This gives two possibilities: 1. If Hell is expanding at a slower rate than the rate at which souls enter Hell, then the temperature and pressure in Hell will increase until all Hell breaks loose. 2. If Hell is expanding at a rate faster than the increase of souls in Hell, then the temperature and pressure will drop until Hell freezes over. So which is it? If we accept the postulate given to me by Teresa during my Freshman year that, "It will be a cold day in Hell before I sleep with you," and take into account the fact that I slept with her last night, then number two must be true, and thus I am sure that Hell is exothermic and has already frozen over. The corollary of this theory is that since Hell has frozen over, it follows that it is not accepting any more souls and is therefore, extinct...... leaving only Heaven, thereby proving the existence of a divine being which explains why, last night, Teresa kept shouting "Oh my God." THIS STUDENT RECEIVED THE ONLY "A"

More clearly: I have discounted our tenet that the radiation field only carries quantized bundles. I am working with 'infinitesimal' inhomogeneity (regions of diverging E or charge) but admit above that this is the question, really.

My prior work shows that the mechanism which localizes E&M energy does not sense the total energy of a wave packet, and on these grounds I have challenged the quantum theory of the radiative vacuum: it is not intrinsically quantized. I have to be more sympathetic to Q polarization theory because I agree there that electrons are the only stable state cooked out of the vacuum at this level. However, I have already trashed the idea that only units of charge exist in the fields. If I am shown that Q polarizations with brief existence fill the bill, I will reconsider. Do you see I am at the nexus of energy density becoming localized and am seeking and finding further possibilities in field mathematics, and trying to let these results tell us what the vacuum theory has to be? One of the blue-stars here already admitted that QM does not talk of the kind of currents I do. For me this was wonderful news.

Thank you, ajb. I need to learn quantum theory of polarizations in the vacuum; I am not there yet. I am at a place of taking electrodynamics further and dialing more than I ever thought I would. I sneaked into the basement and am wreaking some glorious havoc. . . . . .In my work on electrons and photons I show how vacuum polarization is necessary to create a limited wave packet. Also, the electron may be understood as nothing but dipoles. I do not know yet how this relates to present theory. My construction requires from the vacuum regions of diverging E-field (I simply allow them to exist) of 'infinitesimal' nature compared with what we are talking about. Can the current theory supply this? There is in my electron model, significant curvature only in a near range which does not contain much energy inside it. In photons, I have not yet reached for the high energy range.

I have achieved the first part of a paper in which my ideas of polarization of the vacuum lead to a new understanding of General Relativity. It is not yet sufficiently finished to post at my URL but people may e-mail me for PDF.

[math][ik,m] = \tfrac{1}{2}(\frac{\partial g_{im}}{\partial x^k}+\frac{\partial g_{km}}{\partial x^i} - \frac{\partial g_{ik}}{\partial x^m})[/math], and [math]\{^m_{ik}\} = g^{mn}[ik,n][/math]. This took quite a while to learn to compose, yes!!! How satisfying to speak the same language. Party at the TOWER.

[math] \Gamma^r_{ik}= -\{^r_{ik} \}[/math]

In Reimannian geometry is it then the same as the Christoffel symbol of the second kind?

Good linguistics and laTeX discussion, thanks.

Thanks, I'll check out current expressions before casting my work in 4-D relativistic notation! (How was that, "klattu niktu barrata" or something in a sci-fi story?)

Adler, Bazin, and Schiffer, "Introduction to General Relativity". Great mathematician's book, ca. 1975.

How so commas, for ordinary differentiation? I'm used to: . . . [math] \partial/\partial r= \partial_r= F_{|r}[/math], and I am just seeing Sweetser using nabla for covariant differentiation, as Severian offers . . .[math]{\cal D}_r=\nabla_r=F_{||r}[/math]. . . . . . . . . I am pretty much usually thirty years behind the times, but then too the times are always a-changin'.

I will lighten up about screaming sprouts, as I think it to be the smallest degree of 'slaughter' by which we can feed ourselves. I find a narrow viewpoint about plants, though. They use CO2 and produce oxygen; they shade and protect the earth from the elements of wear; they alter the water ecology of each area. These are what IMM says are 'external' benefits, no?

Thanks! Your covariant derivative symbol is nice and clear. My text uses two vertical (small) lines between indices to distinguish from ordinary differentiation. This is economic notation when you are in the thick of it, tensorially speaking. (Ah'll be damned, I just found that symbol on the keyboard. Awesome. Not.) . . .(Speaking 'ex post post', [math]F_{uv||\gamma}[/math]).

A funny woman walking out the door last week asked, "Why do cowboys all have the same size of balls? ? ? ? ? ? ? ? ? ? ? ? So they can pull each others' trailers, silly!"

There have to be cool ways but one is to figure a limit with polygons inscribed, taking the ratio of circumference as sum of chords, to radius. This seems less than profound, though: [math] \lim_{n\to\infty} n\sin{\pi/n}[/math]

[math] [F_{uv\vline\gamma}]=0[/math], and [math]\nabla_vF^{uv}= s^u[/math] laTeX queries: the bracket on the first term should be a brace, for antisymmetrization or generalized curl. How do we print that, and also a double vertical line symbol for covariant diffs? Also, the 'evaluated at' vline?

Plants are sensitive to many things. The only question should be the level of suffering and pain inflicted. You seem to judge that since they don't have a nervous system like us they are on a level of no pain. What are we saying here? I certainly do credit animals with more similarities to us than do many people, and to me they have feelings. Plants respond to chemical signals, etc., but this is a good place of discussion.

I researched and found that only some of the buffalo meat here is local but it is a cooperative involving other Northwest states like Idaho. They have space in grasslands. To me the 'moral' questions are treatment of the animal, use of land and resources, and quick and painless slaughter. I assume that if my head is blasted off I won't long feel it. This is the tough point and it is where we must get in touch with our inner Neanderthal. Like I said, I hear the sprouts scream!

When you talk about long-term fasting, there is a trick reason why you can't just drink water and quiet down to alpha state. Cells continue to die and need to be replaced! We are a successful rate process, as long as we are.

The ideal conductor supports currents but no charge densities, but this is not the case with real materials. There are atomic centers and mobile electrons. Granted, the latter are 'spread' out in their freedom but I can still see atomically local variations in charge density.

This is carried on in the thread "Inhomogeneous field theory..."

Some fields near the center of the electron model become arbitrarily large as radius goes to zero (charge density, radial B-field), there must be a general relativistic solution constructed to adequately represent the inner region. In stellar research we acknowledge that when energy density exceeds, maybe, 10^15 gm/cc, neutron star range, the metric tensor becomes notable. I am working now to structure this analysis, observing that, at least in the basic studies I have available, we deal with either: 1) charges on massive particles which we represent at low-beta, so that a simple matter continuity equation may be used to start, neglecting E&M densities. This yields the source tensor: [math]S^{ij}=c^{-2} (F^i_a F^{aj}+ 1/4g^{ij} F^{ab} F_{ab})[/math]; 2) an electron field outside of a point source, and so divergenceless. This gives us the electron field solution of the Nordstrom-Reissner metric: [math] g_{00}= c^2(1-2m/r-C\epsilon^2/2c^2r^2)[/math]. I have a third approach becuase I deal with charge as only infinitesimal field divergence in a region, and it moves at lightspeed. So I construct a 4-vector: [math] s^i=\rho (1,-1,-1,-1)[/math] which should yield something workable to add essentially to the Schwarzchild solution. I'll let you know, and I would appreciate help understanding what I'm talking about! Namely, what is the essence of our restriction in the first case; then, is it necessary to work with the Minkowski tensor, and not a potential form? I work in the latter as does QED.

A Higgs boson walks into an Irish town and sees no one around. Finding the people all crowded into the church, he enters and jostles his way down the aisle, at which point the priest ceases the liturgy. "Please don't stop because of me," he says. Answers the priest, "But you are Higgs and are supposed to give mass!"