Norman Albers

Someguy, what do you think about entropy if the universe were cyclic?

I assumed a Gaussian structure in the paper you may read at the cache in my signature. What is not at all usual in my approach is allowing the vacuum to be a responsive source of charge and current density. This works beautifully if you allow a diffuse superconducting response such as I found expressed in the mathematics.

No! Also, I used to have a bad 'tude for Eddington because he dissed Chandrasekar, but now I am using the Eddington transform of the Schwarzschild metric and I think he was monster good. FARSIGHT, take each hand and form a hitch-hikers' thumb. Consider the thumb to represent yang and the pinky end to be yin. Now join the thumbs and consider what shows to the outside. Only yin. Now join the pinky ends; what shows???THIS IS ALL YOU NEED TO KNOW ABOUT CHARGE.

The Kerr solution can be derived as a generalization of the Schwarzschild field. Eddington offered a coordinate transform of the time variable: [math]\bar x^0 = x^0 + 2m\log\left| r/2m - 1 \right| [/math]. This yields a form of the metric termed degenerate. From here, substitution of a complex variable where we wrote z gives expression of a system with angular momentum. If I am correct, I have expressed the Minkowski and stress-energy tensors and can apply the Eddington transform to the latter to yield a right-hand side to the Einstein field equations. It looks like it yields first, second, and third orders in the arbitrary m. I would appreciate comments on my methodology.

Nice, Martin. This is a very high continental divide, and I take it as a very good sign that I end up talking relativity in the QM section and a little quantum nature in the relativity section. This is where I am working.

"...gonna make a mess outta you." Bob Dylan Take heart, it looks like a black hole!

My textbook says "One would see the surface falling freely in precisely the same menner as the test particle discussed, that is, it would shrink asymptotically toward radius 2m." I found the other relevant quote: "When the necessary light nuclei have been used up, the fusion process ceases, the stellar equilibrium cannot be maintained, and in some cases the gravitational force collapses the star, shrinking it to a size asymptotically approaching its Schwarzschild radius. Thus for radii slightly greater than 2m and times that are finite the geometry becomes that which we have discussed: the asymptotically collapsing start would appear as a black hole." Curiouser and curiouser.

Hey DanJFarnan, I think you are clueless. To other folks, cool I shall check your suggested refs. I came a surprisingly neat answer, if my handling of the concepts is correct. BenTheMan, you seem to be implying that gravitational force blows up as you approach the horizon. I am doubtful about this, but don't yet know how to write it. I have really strong SPIDERMAN STRING, and we don't have to go all the way there to learn something. Thwppp!............OK, Spyman, that's a killer reference article, thank you. According to this rather knowledgeable writeup, I should credit BenTheMan for his note on tension rising asymptotically........<time passes> OK I came up with an expression for grav. acceleration and I'd like to know if it's good. Start with the expression I gave elsewhere: http://www.scienceforums.net/forum/showthread.php?t=28046&page=3 relating time and distance for an infalling small body. Differentiate both sides by t, and you can write: [math]1=L'®\frac{dr}{cdt}[/math], where L® is the RHS of the first equation. Differentiate again and work out: [math] \frac{d^2r}{cdt^2}=-\frac{L''}{L'}\left( \frac{dr}{cdt}\right)^2. [/math] This has the characteristic as radius nears the horizon of the numerator being finite but the denominator having a zero........<more time passes> DAMN, I figured backwards, the denominator blows up so I cannot say the acceleration does. What is being expressed is in "far-field" coordinates, and this makes sense to me because the infall does seem forever suspended to the far string-holder. Maybe both things are true, and this is just not the expression for the force experienced by the test probe. Even Spiderman Silk cannot stand here.

Let's assume the BH has negligible angular momentum.

Not yet knowing the answer and needing to know how to work better with this material, I propose a gedanken experiment on apporaching black holes. From a station somewhat distant, we lower slowly a small weight on a long, strong string. We are not orbiting, but maintaining our position by other means. How much string will we let out as it appproaches the event horizon? How much more there is there, radially speaking? We may call this black hole string theory.

Light also seems to slow approaching an event horizon. Remember it is observed from outside going to infinite redshift, meaning it is becoming not observable. You can only describe crossing a horizon if you choose the reference frame there. Yes, truly compared to the far observer, this never happens in a finite time, and you have to deal with cosmologic questions of what ever gets to happen. The point about duh fizziks is that we try to do quantum mechanics on a horizon, and this is beyond me now. Bogoliubov is one name I associate here.

Occassionally, pots must get cracked. This is how Joao Mageuijo describes it in his book, Faster Than the Speed of Light: "The first time I threw my solution to the cosmologic problems into discussion, an embarrassed silence followed. I was aware that a lot of work neede to be done before my idea could attract some respect; and that, as it was, my idea would look completely crackpot... People would chake their heads, at best say, 'Shut up and don't be stupid,' and at worse just be very British and say noncommitally, 'Oh, I don't know anything about that'... When I started labelling my idea VSL (varying SOL), someone suggested that it stood for 'very silly'. You can't take anything that happens at these meeting personally. In fact, the easiest way to drive yourself crazy in science is to take challenges to your ideas as personal insults, even those that are expressed with contempt or venom, and even when you are absolutely sure that those around you think you are a fool. That's science. Every new idea is gibberish until it survives ruthless challenge."

Cool, now we can get to duh fizziks. With each passing time constant unit measured by a somewhat distant observer, the coordinate r by which they measure the infalling "test" is reduced by another order of magnitude, so in not too long it seems they are very close but it is an exponentially stretched-out deal. Radius is a funky marker if you don't realize what's going on here. One can relate the differential change in radius by the ratio of the metric terms evaluated at the two locales, the outer observer and the infaller. You must also acknowledge the stretching of time. All this can only be stated differentially, and there is singularity at the horizon. You must be careful, these things really do totally suck. The first solution I wrote is completely general, I think.

Modelling the collapse of a "dust ball" yields an asymptotic solution such as BenTheMan are wrassling with in the Quantum Mechanics thread. However the time constant is the Schwarschild radius divided by the speed of light, so maybe 10^-4. As Ben points out, the theory reaches its own limit, like a guide who takes us to the high mountain divide, and then says, I leave you here to find a further guide.

The position of the infalling object is described by coordinate r. What happens as this approaches the event horizon? Correct, here I am not dealing with any back reaction; this is what is meant by describing an infalling "small test particle or object". When we allow ourselves to feel confused we are in danger of learning something.

At the electromagnetic level. I offer an addition to the Schroedinger equation or to the allowed forms considered. Without this, there is an inadequate connection between electrodynamics and QFT. I work with assumed transverse divergence on the scale of the fine structure constant.

NO! The entire first term becomes insignificant compared to the log, so basically you have to figure the limit with the two terms of the log argument involving [math]r_o[/math] forming a constant other than 8. I tried to warn you, this'll make you stupid. I won't tell you how long I trashed yesterday, and we'll give you credit for lunchtime, also. Basically the RHS becomes: [math] -2m \log K \frac{\sqrt r -\sqrt{2m}}{\sqrt r + \sqrt{2m}}[/math]. Last year I enjoyed the following exchange with Hal Puthoff:..........(NA) You mean someone else dares talk sense? I'm still asking about the geometric stretching, basically the distinction between radial and transverse. ----- Original Message ----- From: Puthoff@aol.com To: singularities@clab.net Sent: Wednesday, October 18, 2006 6:21 PM Subject: Re: isotropics In a message dated 10/18/2006 6:32:38 P.M. Central Daylight Time, singularities@clab.net writes: (NA) As time crunches to a crawl even in your dark gray singularity we can say things are not happening at our clocking. (HP) Absolutely. (NA)It seems to me immense mistakes have been made here, by people talking about blithely going through a horizon, etc, not that you say this in particular. (HP)I agree. Another way of saying it. As the velocity of light seen from our frame drops to zero (approaching an event horizon) we (in our frame) we'll never see a particle go thru the event horizon, since its velocity cannot exceed the local velocity of light "down there," and that has dropped to zero. (For the exponential case, we will never see a particle reach a singularity at the origin.) So even though a rider on a particle would not note anything strange in his frame, he might notice that external clocks seem to be going so fast that eons will go by "out there" while he approaches the event horizon (or singularity for the exponential case) and therefore rightly assumes that the outsider would never see him make the progress he himself considers himself making. Pretty straightforward, in a way! Hal

The far-field metric is assumed to be a Lorentzian flat-space so r is that radial coordinate. As you go inward, things are compressed by the appropriate metric expression; there is more there, there. If the starting point of an infalling object is not "really far away", it amounts to a lessening of the coeff. of [math]8\pi[/math]. It's a cute challenge to analyze this and I cussed for a while today, but it is a variation of the limit one can figure as r>=2m. You really don't want to see the full display, and I don't want to compose it. It ought to be clear why I said that we logarithmically approach the horizon... but also that "we get" infinitesimally close in a reasonable coordinate time. Physics here is a glorious mess. . . .MY APOLOGIES BUT DYSLEXIA STRIKES. . .where I wrote [math]8\pi[/math] it should read 8m. For a test body falling from rest at radius [math]r_0[/math], the trajectory is described by: [math] c(t-t_0) = \frac{2}{3\sqrt{2m}}(r_0^{3/2} - r^{3/2} +6m\sqrt{r_0} - 6m\sqrt{r}) \;\; -2m\log{\frac{(\sqrt{r_0}+\sqrt{2m})(\sqrt{r}-\sqrt{2m})}{(\sqrt{r}+\sqrt{2m})(\sqrt{r_0}-\sqrt{2m})}} [/math]. When we consider approaching the event horizon, the singularity from the 'zero' in the numerator of the logarithm takes over, and you can have fun working out the correct [math] \lim_{r\to 2m} [/math].

Is quantum mechanics based on DeBroglie waves being associated with mass?

I am considering the Kerr metric as the exterior solution to my electron problem, but with the limit taken for small mass but significant geometric angular momentum. When we allow both 'mass' and 'angular momentum' to be small, we get the expansion for the Lense-Thirring form. In particle scales, however, Schwarzschild radius is very small compared to geometric angular momentum (E-57 to E-13), so we can choose to ignore the terms involving 'm' and obtain a form describing metric anisotropies governed by rotation, and its expression in the vacuum. The regime is described as a~r>>2m.

Mitigating is faint praise. In the late 1940's a group at Princeton had to meet secretly and at night to avoid being known as practicing expression of Feynman diagrams. These were ridiculed by most for a few years. Then, rather quickly accepted. Freeman Dyson related this story.

I treat charge as simply a change of rules: rather than relegating all the sourcing of an electric field to a point, I let there be near-fields characterized by divergence. Naively one might start saying, ah, magic mystery monopole goop. Much more fun, though, to move on to dipole density, because it really does show more essentially how what appears as charge is innies and outties of polarization. Quantum mechanics supplies us with the virtual ingredients needed. Electrons are a stable singularity given a supply of very short-lived and short radius dipole manifestations. This allows a vision of electrons as process. There are near-field circular currents; electrodynamically I started with allowed charge density, and treat it as a massless availability so the current may be written as [math]\rho©[/math].

You may call my several mathematical excursions poorly founded in the physical universe but you may not call them poor mathematics.

BEN I think not but will try to work it out. It is not such a strong constraint, but is the far-field in the sense that r/2m>>1.