[General] Gamma from self-confined light

[John Williamson]

Hmm,

I’ve realized that the previous email is far too cryptic for most folk to get much out of it. Let my try to explain why the problem is hard – and not easily addressed by using the standard approach of simple (inertial) relativity.

The main problem is that of postulating a circulating photon, without the proper mathematics to describe this. Such a circulating photon is continuously strongly accelerated; that is it is in a non-inertial frame. Applying the standard simple mathematics for relativity is then bound to get your mind in a twist. One can do the maths for a photon bouncing back and forth fairly simply (as in eqs 18 to 20) and for one bouncing sideways (one has to realize here that field transform only perpendicular to a boost, where space and time transform only along the boost – but this is known). Stuff going round and round in circles needs better maths and insight though. Sorry guys, one really really needs the maths and not just some “losse kreet” about something is something else. One needs a properly relativistic rotating wave-function which transforms properly in every frame to describe this. Now here comes the hard bit: one cannot write a conventional (complex) wave-function in terms of space and time. Whose space? Whose time? These are different for every distinct angle theta in the rotation. On then needs to find a wave function which one can accelerate and will remain a valid wave function under such operations. This needs a Dirac mathematics (at the very least). Such a wave-function is, I propose, equation 21 in the paper attached to the last email, but this is not easy to understand. In the first place the exponents are not complex but hyper-complex (Dirac) elements of a 4D space-time (as they must be). Secondly, although the spatial and temporal components are explicit, and defined for any frame, the wave function as a whole is not in vector-space but bivector space – so one needs, at minimum, to understand this. Without help I think that only Martin has a chance here. Also, the wave-function given is in Cartesian form. The “3” direction for a hydrogen-like solution must then be azimuthal. One must then apply the spherical harmonics in the usual way – but this is not right either for an isolated electron – one really needs (probably) the half-integer Legendre polynomials of the first and second kind (the Ps and Qs) with a matching condition at their interface. Folk, (Merzbacher, for example) have tried and failed with this kind of approach in the past. I think it is pretty much doomed to failure of one tries to use simple complex wave-functions, as they do not incorporate the right relativistic (rotational) transformations and will give a sign error on the interface. If one is lucky one may be able to engineer an even number of errors in such an approach!

Even after (if) one has got ones head around all of this the answer to the main question is still missing: what is making the photon go round and round in the first place? What is the confinement mechanism for the electron charge? This is what we should really be discussing. Viv suggests that this may be a QED type interaction with the rest of the Universe. As I have said in previous emails this is a candidate. Martin calculated (estimated) this decades ago and it is at least of the right order.
I have done QED calculations in the past (with big computer programs), but this was so long ago I do not even have the code on an old-fashioned floppy.  If anyone has any expertise here (with QED) please get in touch and we can discuss it.

For me, the local force arises, in analogy to the Lorentz force, as a product of the multi-vector field with its derivative: GdG. This is outlined in my other SPIE paper last year. These two approaches are not mutually exclusive: one can see the rest mass inherent in particles as a balance of the interaction with the rest of the universe – one positive one negative – leading to a total mass-energy of the universe of exactly zero (as is consistent with that which is observed in experiment). Action and re-action for the self-confinement of the particles we observe in nature.

I could go on, but should get onto to working on the paper explaining some aspects of this a bit better. It has been sitting untouched since I last had any time over Christmas last year! If anyone feels up for it I will be looking for volunteer proof-readers for it soon – I hope.

Regards,
-John.

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