Norman Albers

This is day 29 of "editorial evaluation" at Journal of Mathematical Physics after peer review. I am a very lonely man, though it is greatly satisfying to Google on "gravitation vacuum polarization".

Thank you, Severian. I certainly had not recalled "Jacobian" here, but I dig it. The task at hand is to construct a one-to-one mapping of coordinate transform, in an efficient easily notated manner. We all have wonderfully convoluted minds so knock yourselves out conceptualizing things, but communicate them simply to me. [Now about the possibilities of negative radii... you probably don't want to open this box with me here, considering my latest ruminations on black holes, down in the kitchen of Speculations. I am on day 21 of editorial review at JMP] Sarahisme: All this exchange is good, and both of you have shown me how to notate things I never have. We must know formally how to follow our nose when we need to. We must trail good strings behind us when we wander into cubist landscapes.

It is consistent to cover the plane with radius positive and angle covering 2pi. It's just style, here, but since when do we speak physics of negative radii? String people do a neato thing doing 1/r beyond the small Planck limit, but I don't see physical sense in negative values. Like I said it's only a matter of self-consistent notation here.

Thanks for further lessons in laTex. Do you see the two triangles? You know what you're doing but it is a bad habit to write negative radii.

Why is this unique? I am 57 years old and an accomplished piano rebuilder with an MS(Stanford) and BS(Princeton) . Vocabulary changes but challenges of expression don't. How do you say it? Did you vizualize the domain or did you proceed as you showed me? I was outfoxed. Remember in high school it was the word problems to be expressed algebraically that separated the masses.

I'm trying to say that we try to separate integration variables but when they cannot separate you have to express the integration limits as you have. The domain being described in (b) is |y|'s less than |x|'s, and that is right triangles on their sides, yah? Thus one-half of a total square. Laughing is good - I am continually surprised at how I cannnot ass'u'me people see things similarly. I used the word 'dependent' because the range of |y| depends on |x|. This is a bit strange because they are both "independent variables" of f(x,y).

You have psyched out what makes me slow. I guess we have to break down the logic to independence and dependence, in the new set of variables. So it's not just all <x,y> in a square, but rather a chosen half of this! Congratulations, thanks for showing me something. The challenge is to know how to proceed in this process.

I have realized the first important result from my theorization of Gravitation and Vacuum Polarization. Permittivity for light propagation on a transverse path inside a black hole is negative, meaning that an imaginary square root speaks of absorption of transverse waves. Radial propagation is as we had pictured it. http://laps.noaa.gov/albers/physics/na

My apologies. I was outfoxed by the second statement. I guess the domain describes a square and you see this. Now, a few hours later it looks to me like you have one-fourth the answer, not one-half like you thought. You write for one quadrant, if both <x,y> go +/-.

Reconsider your limits on the second one. There is less here than meets the eye in the stated domain.

Radius does not go through zero unless you've got some truly cool physics.

Ah, yes, 'non-Euclidean' stuff. Remember M.C.Escher and the tower. Does he use converging lines, or only messed-up meeting lines to make things go round and round?

I built a house with log pole frame and studs filled in. My windows are level and I know that to test a level gauge you simple turn it around to see if it reads the same. Regarding Phi's flowing water, one could imagine a gentle flow having ripples going upstream looking like backflow. Think phase versus group velocities.

This is the eighth day of editorial review on this two-page paper on gravitation at the Journal of Mathematical Physics (AIP). Too bad folks are afraid to think outside the box that holds us back.

Wikipedia has enough on negative index to mess up my mind. I have only recently myself approached the plus/minus possibility on the square root of permittivity times permeability. These guys are not in Kansas and the index is negative. I am going to my room.

I need to get straight about relative indices. What is negative here, precisely? Is index of refraction less than one but positive? This would imply negative polarizability, I guess. What is the speed of light here? It is predicted that these things give opposite Doppler shift!

No, cloaks are not about to happen but spheres and lenses are! Negative index metamaterials can theoretically channel light around a region. In a different game, conductive nanocoatings block emission/scattering, the Goldfinger effect one better. In this case you would not see what's behind, just a lack of light I guess? Gcol's point of not seeing out is well taken. We shall have 100-meter periscopes, I don't know.

The idea is to channel the light from behind the object to project out the front, not to make a cloth that is transparent. Not that I'm arguing with your fashion preferences, Severian.

[bIG TEETH] Good'un, mate! Very funny stuff. Supposedly something weird happened with the Navy in the "Philadelphia incident" in the '40's.

Right now it's tuned to one frequency by the construction. I forgot the other part of the plot: negative index of refraction! Yes that would complete my lensing cloud, wouldn't it? Commend me to DARPA. In my paper on gravitation permittivity does all manner of things. On the way to my electron model are three others with different assumptions where it goes negative. I rejected those for electrons but now it's in my face for gravitation and I welcome it. . . . . . . . . Let's see, optics guess: a giant torus of optically more dense gas, blown like a smoke-ring, and/or a center (axial) region of optically thinner gas. The point I guess is to create index gradient outward.

According to Science News this is indeed happening, and is a channeling of light issue. How would you make a Navy destroyer seem to disappear? I think I could if I could blow a cloud of dense gas in front and behind. What do you think?

I have submitted this paper to Nature Physics and to JETP.

My cache at http://laps.noaa.gov/albers/physics/na now has the 2-page pdf.

I disagree. I am speaking about light bending in a medium of higher permittivity, in this case smoothly increasing toward a gravitational mass. I am letting the vacuum polarization field, whatever that is, supply this. In my electron paper I showed that angular permittivity goes to infinity at the center. That's what set the stage for this realization. My perspective is that of an electrodynamicist allowing mathematics to speak to physics to derive from clear phenomenologic needs what the vacuum has to be cooking up. I don't yet even know the quantum formulations here but expect to be faced with them real soon! I am conversant in general relativity tensor theory, and the great news is that it's quite cool and that this is interpretable as the 'rubber sheet'. It works; I'd be happy to e-mail you two pdf pages.

I have equated the appropriate metric terms with the square root of a local permittivity/dielectric field. Don't tell anyone.