## Monday, December 13, 2004

How big is the electron?

Jack, since you know so many physicists let me ask you some things.

In your theory and in the physics community in general,

1. How big is an electron, what's its radius?

The classical ball size of an electron is

e^2/mc^2 ~ 10^-13 cm

The quantum size is

h/mc ~ 10^-11 cm

The classical "ball" is surrounded by a virtual electron-positron plasma that extends out from 10^-13 cm to 10^-11 cm

This is the NAIVE picture.

Problem is that Bohr's Copenhagen -> Von Neumann interpretation says THERE ARE NO ELECTRONS as Newton's "hard massy balls" - there are only "quantum waves" or "qubits" that "collapse" to make localized "clicks" on counters. This is Wheeler's "Smoky Dragon" mysticism. That is, there are NO HIDDEN VARIABLES.

In quantum electrodynamics the bare electron is a point particle. This leads to problems of infinite renormalization parameters.

There is then the scattering theory of "form factors" - complicated.

Also high energy scattering of electrons on protons and neutrons shows the latter have three point like scattering centers - consistent with "quarks". Quarks and leptons are "unified" in gauge theory. Well not quite.

Bohm's theory does allow the HIDDEN VARIABLES i.e. Newton's hard massy balls that are "guided" by the Bohr quantum pilot waves. It's like a ball rolling on a landscape of hills valleys and saddle point mountain passes. These are the Bohmian trajectories of the hidden variables.

Then there is the idea that electrons and quarks are really little microgeons i.e. localized regions of pure vacuum with CONFORMAL CURVATURE fields like rotating charged black holes. Burinski is working on that now in Moscow. However you need strong short range gravity G* ~ 10^40G on the scale of e^2/mc^2 ~ 1 fermi for this to work. Maybe the extra space dimensions kick it for nuclear physics. Also for the stable electron you need a special solution that does not have Hawking radiation - that is part of Kerr-Newman.

The microgeons will "shrink" if probed with a big kick in a high-resolution scattering Heisenberg microscope experiment. They look more and more like point particles as you increase the momentum transfer - at least up to a critical value, where maybe they start looking bigger again in Susskind's IR/UV duality of string theory.

One nice thing about rotating micro-geons in strong short range gravity is that they automatically obey the universal Regge slope law

Spin of hadronic resonance ~ alpha'E^2

alpha' ~ (1 Gev)^-2

This is the basic data for string theory and of course black holes and strings are two sides of the same coin!

Also no hierarchy problem in this picture where the quantum gravity Planck scale Lp is actually at ~ 1Gev. I published this in 1973 and Abdus Salam invited me to ICTP because of that.

2. What is the equivalent lineal mass density (kg/m) of the vacuum?

Meaningless question.

The naive zero point energy of the vacuum WITHOUT the COHERENCE that is the basis for my theory of the emergence of Einstein's General Relativity as a "More is Different" post-inflationary macro-quantum coherent phase modulation is

Vacuum Energy Density ~ hc/Lp^4

This is MUCH TOO BIG. The dark energy density is

~ hc/(c/H)^4

Where H = today's FRW Hubble parameter R^-1dR/dt.

If you use Lp ~ 10^-33 cm Hal's PV gives is off by 122 Powers of Ten. That is a colossal failure compared to GR's colossal success of 10^-14 in the 1916 + 13 pulsar data that won a Nobel Prize!

Hal Puthoff has no solution to this problem in PV. He hand waves it away as he genuflects to ET. :-)
http://www.guntheranderson.com/v/data/thevatic.htm
http://www.hyperdictionary.com/dictionary/genuflect

I'm doing a comparison of GR and PV and, I'd like to compare it to your
model as well. However, I'm getting mixed input about the radius of an
electron. The Particle Data Group lists it as the classical radius of 2.818
fm. Milonni on the other hand says it is point-like and 10^-2 fm but its
charge is spread out by the interaction with the ZPF to about the Compton
wavelength, ~10^3 fm. The classical radius is "bogus". Do you agree?

Sort of. See above. PV is worthless, a complete waste of time.

1. It violates general coordinate transformation covariance of the dynamical action.

2. It is incompatible with the LOCAL equivalence principle used in GR (e.g. Cartan tetrads).

3. It is seriously incomplete e.g. it cannot describe rotating bodies and the now observed gravimagnetic Lense-Thirring frame drag of the Cartan tetrads.

4. PV fails every experimental test beyond the 3 trivial classic tests in new observations like 1913+16 pulsar where GR works beautifully to a precision of 10^-14!

The above opinion on Hal's PV is the consensus of several top physicists at GR 17
e.g. Cliff Will, Matt Visser, Bill Unruh ...

Since at less than 1/2 the Compton wavelength we get the possibility of e-p
pair creation, this would seem to fit well with your model of the vacuum. So
I'm hoping you can give me some specifics to compare to.

Thank you!
main_engineering