[General] position

[John Williamson]

Hello Andrew and everyone,

I think Andrew has raised a very important point which has, indeed, not yet been widely picked up on.

The electron is, experimentally, spherically symmetric. Not only because it must be to give the projection of angular momentum into any spatial direction, as Andrew says and as observed, but also because it is simply measured to be so in HEP and trapping experiments (to enormous precision) - as John M has commented. What is required is a parameterisation for which this is the case. Now torii and spheres are both particular projections of hyperspheres so that should be a clue.

What it means, necessarily I think, is that the toroidal or disk form cannot be in space per-se. This is simply excluded experrimentally. This is not such a big problem - one merely needs to model the photon in the proper space (field-space or momentum space for example) and then project the result onto to the 3D components of space in a particular space-time frame using a proper projection. This need not be such a big deal - solid state physicists work in momentum space (k-space) all the time.

A few years ago I picked up a java applet due to Fergus Murray which does  paired rotations in 4D and projects them to a 2D screen. I then checked the underlying maths (OK - good work!) and modified the applet a bit so I could let it vary in the ways I wanted (please find code attached). It is a bit of a toy model for our purposes because it is really a pair of planar rotations in two perpendicular 2D sub-spaces parameterised by time. In other words the spatial metric is (+,+,+,+) and not the tempero-spatial (+,-,-,-) of reality. Also it is really 4+1 dimensional - like a 4D movie. Nonetheless if you run it you can see how the projections are BOTH toroidal in detail AND yet spherically symmettric if you average over time.

Regards, John W.
________________________________
From: General [general-bounces+john.williamson=glasgow.ac.uk at lists.natureoflightandparticles.org] on behalf of Andrew Meulenberg [mules333 at gmail.com]
Sent: Monday, April 27, 2015 8:00 PM
To: Nature of Light and Particles - General Discussion; Andrew Meulenberg
Subject: Re: [General] position

Dear Richard,

Something that no one seems to have mentioned/noticed is that the bound photon, as a stationary electron, should have a spherical rather than a circular path. Only in this manner can it have angular momentum in all and any directions. Also, when moving, even slowly, relativistic effects will 'flatten' the sphere in the direction of motion. This flattening will raise the energy, increase the inertia, and introduce the E-field distortions called magnetic field, B.

The path distortion from the spherical with motion gives a helical path for some portion of the photon length. The path is much more complicated for elements of the path that are not normal to the direction of motion. The photon itself may be a standing wave moving at c. If so, elements of the wave move faster than c and later move slower than c. In the electron, the same thing may happen. Only the average velocity is limited to c. Since the photon is a wave, the phase velocity can greatly exceed c, before the electron velocity becomes relativistic.

Andrew

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