Subject: Re: Electron is near perfect sphere? Good news for Bohmians from Imperial College, London? (Dr. Quantum)
On May 26, 2011, at 11:34 PM,
Ah! At last. Yes, getting semi-classical electrons right is pivotal in exotic physics. . . . :-)
Yes, however I need to fix my sloppy algebra yesterday done in haste, I think I switch sign conventions mid-way and it's not correct at the "stability" part, but the conclusion is.
Basically, if you use convention force = - Grad potential
+ e^2/r has Grad = -e^2/r^2 and the force is +e^2/r^2 repulsive pointing away from r = 0.
forgetting factors of m, c etc for now
If we also use - /
^2 for the potential
then its Grad is - 2/
so the force ~ + 2/
repulsive for / > 0 i.e. as in de Sitter metric g00 = 1 - /
^2 with a future event horizon at /
^2 = 1 in this static LNIF rep where we are at r = 0.
this is also the interior of George Chapline's dark star that I independently thought of BTW
attractive for / < 0 as in anti de Sitter metric without an event horizon.
it's the anti de Sitter case that is the Poincare stress strong zero point energy induced gravity glue opposing the self-repulsion of the extended hollow shell of electric charge.
v2 corrected!
PS a simple classical model
Old classical model
The self-energy electrical potential energy of the extended electron of radius a is
Vself = +xe^2/a > 0
x is a model-dependent dimensionless number of order unity
This is obviously unstable.
Add the virtual particle interior to the shell of charge e and rest mass m, this is a dimensionless effective potential per unit test mass energy
We now have a quantum corrected semi-classical effective potential
V(r) = Vself + VQM = +xe^2/mc^2r - /
^2
(note we can also consider a |/|^1/2 r term with a constant "force" as in the accelerating universe, but it has a vanishing 2nd derivative)
the critical point is
dV/dr = 0
-xe^2/mc^2r^2 - 2/
= 0
i.e. using the classical electron radius
re = e^2/mc^2
-xre /r^2 - 2/
= 0
-xre - 2/a^3 = 0
2/ = -xre /a^3
a^3 = -xre /2/
check the stability
d^2V/dr^2 = 2xre/a^3 + 2/ = -4/ + 2/ = -2/
stability requires / < 0, i.e. second derivative must be positive for stability in this function of a single real variable r
we can also put in "spin" as a dimensionless centrifugal potential in the rotating frame ~ (J/mc^2)^2r^-2 etc.
http://en.wikipedia.org/wiki/Maxima_and_minima
Please note: message attached
From: JACK SARFATTI <
To: Jonathan Post <
Cc:
Subject: Re: Electron is near perfect sphere? Good news for Bohmians from Imperial College, London?
Date: Thu, 26 May 2011 17:15:35 -0700
From: JACK SARFATTI <
Date: May 26, 2011 5:15:35 PM PDT
To: Jonathan Post <
Cc: david kaiser <
Subject: Re: Electron is near perfect sphere? Good news for Bohmians from Imperial College, London?
On May 26, 2011, at 3:47 PM, JACK SARFATTI wrote:
No that is no longer true once quantum gravity effects are included. I talk about it in my Journal of Cosmology article that Penrose allegedly vetted. Sure what you say was the case CLASSICALLY that's the famous problem that I claim I have solved.
Virtual fermion-antifermion pairs gravitate strongly enough on the Compton scale to counter-act the self-repulsion of the classical shell of electric charge.
Of course virtual bosons will anti-gravitate so in order for this scheme to work the density of virtual fermion pairs must exceed the density of the virtual bosons.
My model is similar to George Chapline's dark star on the macro-scale. He has repulsive dark energy (virtual bosons dominate) interior to the event horizon. In contrast, I have attractive dark matter (virtual fermion-antifermion pairs dominate) interior to the classical shell of charge.
On May 26, 2011, at 2:34 PM, Jonathan Post wrote:
I've published a refereed paper about why spherical shells or spherical cloud electrons don't work, as was well known early in the 20th century. To be blunt:
(1) each negative part repels each other negative part, and they explode;
well known - that's the classical Abraham-Lorentz-Poincare stress problem.
(2) when you use classical electromagnetism to see what happens when the shell or cloud is accelerated by a force, you get a differential equation that forces you to "pre-accelerate" the electron before t=0 just to be able to get displacement, velocity, and acceleration to agree with F=mA. That is, you get a mess that required a third derivative of displacement with respect to time. More terms just make things worse.
Yes of course, this is well known from Dirac e.g. Hoyle-Narlikar papers.
(3) It is a dirty little secret that vexed Schrodinger, Dirac, Einstein et al,. -- there is no workable semiclassical theory of the electron.
There is now.
Then Feynman invented QED and, as I say, the problem vanished. But the electrons must be true points. Zero radius.
Not any more. That's the conventional wisdom that is wrong.
v2 typo-corrected algebra: Electron is near perfect sphere? Good news for Bohmians from Imperial College, London?
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