[General] Reply to Chip on particle radius & spin

[Dr Grahame Blackwell]

Chip et al.,

With reference to your notes below on particle radius and spin: theyre's more to say on the whole radius thing, which I will hopefully add shortly, but I feel I should respond to your notes since I said "a few days" almost a week ago.

It's been noted by others and myself before that a photon-formed electron will have spin (/ angular momentum) by virtue of (a) the momentum of the photon acting cyclically, and (b) the angular momentum of the photon itself.  One apparent anomaly is that, as the speed of the electron increases towards c, the formative photon becomes increasingly linear, being fully linear at that limiting speed (which can of course only be theoretical, a limiting state never reached); this creates the apparent anomaly that, in the limit, the electron will have at least the full spin-1 of its formative photon.  Even at much lesser electron speeds the photon's own spin component must be a consideration.

The only possiblility by which this could be nullified (since I think we're all agreed that a static electron will have spin-1/2 just by virtue of the photon's linear momentum) is that the formation of the electron must surely cancel out that photon spin component, either by the cyclic motion of the photon acting in the opposite sense or by a rotation (spinning motion), in the opposite sense, of the electron itself.  This has to be left for further thought (I have some thoughts on it) - but it clearly doesn't add to the spin of the electron which, as agreed, is 1/2 just from photon linear momentum.

Back to that momentum-induced spin: the static electron has spin-1/2 due to photon linear momentum.  As the electron moves, progressively faster, the momentum of that photon increases due to increasing electron speed (and so increasing photon frequency).  BUT - and this is the absolutely crucial point - the motion of that photon is now helical, a combination of cyclic and linear.  ONLY the cyclic component of that photon momentum will contribute to electron spin (/ angular momentum) - the linear component manifests as the linear momentum of the electron itself, gamma m v (where m is rest-mass); that cyclic component is Eo/c - WHATEVER the speed of the electron - this is quite apparent from the 'relativistic' energy-momentum relation.  In other words, in order to maintain that spin-1/2 for the electron, the radius of the electron also has to be kept constant, as the cyclic linear-momentum component of the formative photon is similarly constant.  If the radius of the electron is reduced then its angular momentum (/ spin) will be reduced in direct proportion.  This analysis totally supports the view that electron diameter remains invariant (which is also supported by other considerations - more on that later).

[In brief: to regard the full increased momentum of the higher-frequency photon as contributing to electron angular momentum is an over-simplification.]

As Albrecht and others have observed in recent posts, experimental evidence interpreted as electron diameter is at best an indication of cross-section of effective consequences; diameter inferred from such experimental readings cannot be taken as a definitive statement of particle size - there is clearly a lot of 'wiggle room' (literally!) in this.  The observations above on invariant electron spin would appear to be rather more precisely definitive.

With regard to the 'relativistic' effective total mass of the moving particle, I'd wholly agree that this is gamma m (where m is again rest-mass) - but we don't need to go via spin considerations to get to that, it's implicit in the raised frequency of that formative photon, in line with E = mc^2 {which again is not at all dependent on SR - but that's another story].

Best regards,
Grahame




----- Original Message ----- 
From: Dr Grahame Blackwell 
To: Nature of Light and Particles - General Discussion 
Sent: Sunday, January 08, 2017 10:10 PM
Subject: Re: [General] On particle radius


Hi Chip,

Many thanks indeed for your succinct and well-presented case ('succinct' is clearly a useful word in this discussion - as well as a good strategy!).
I need to go through this carefully and thoroughly and see how it relates to my own understanding of the situation.  As we're all agreed, we all have things to learn from each other and (here I DO agree with Vivian's metaphor) each have some aspect of the elephant (in the room?) to contribute.  I'm really looking forward to considering what you've said below and hopefully assimilating it into a fuller understanding on my own part of the issues that need to be taken into consideration.

I'll come back to you when I've processed it thoroughly (may take a few days) and have some thoughts to offer.

Thanks again,
Grahame
  ----- Original Message ----- 
  From: Chip Akins 
  To: 'Nature of Light and Particles - General Discussion' 
  Sent: Sunday, January 08, 2017 9:22 PM
  Subject: Re: [General] On particle radius


  Hi Dr Graham Blackwell

   

  I like the way you clearly and succinctly write.

   

  Let me explain some of the reasons why I feel the radius of the electron decreases with velocity.

   

  In order to accelerate the electron at rest, we must apply energy (force through distance).

  The only way to apply energy to the electron, when we get down to the basis, is to add energy to its existing confined wave structure.  Planck's rule suggests that this confined wave structure with energy added has a wavelength which is (h c)/E. If this is the case and the momentum of this wave remains p=E/c, then in order to be a spin ½ hbar particle, it seems the electron must have a radius which is r = (h c)/(4 pi E). Where E is the new total energy with velocity throughout this paragraph.

   

  Then when we calculate the mass of this particle from its confined momentum (as Richard has pointed out) we get the expected relativistic (total) mass of the moving particle. m = E/(r w c) = E/c^2= E Eo Uo. Which is exactly equivalent to m = y m. [where w = c/r (angular frequency)].

   

  This is the only scenario I have found where all of the expected parameters are accommodated, and I have searched extensively for other possibilities.

   

  We also note that the scattering cross-section of an electron at relativistic velocities is very small, and agrees with these assumptions quite well.

   

  In order for the electron radius to remain the same size with velocity I think we have to ignore things which seem quite important, and these specific things appear to be required in order to tie several of the pieces of the puzzle together. It seems the picture is just not complete unless the radius of the electron is reduced with velocity.

   

  Thoughts?

   

  Chip



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