[General] Reply to Chip on particle radius & spin

Richard Gauthier richgauthier at gmail.com
Sun Jan 15 18:27:45 PST 2017






Hello Chip, Grahame, Vivian, John W, Alex, Hodge and others,

    Alex, congratulations on your latest “bag model” article on arXiv. Do you have any suggestions on how we can get on arXiv? Does your bag model’s radius change by increasing the model's speed relativistically? Someone in an Academia.edu article discussion group I am in asked me if I had heard of your work. I was pleased to say “yes”.

    The below diagram (figure 1 in my SPIE article at https://www.academia.edu/15686831/Electrons_are_spin_1_2_charged_photons_generating_the_de_Broglie_wavelength ) represents the relationships among momentum, energy and velocity for the relativistic spin-1/2 charged photon model of the electron. The figure also applies to some other helical photon-like object models of the relativistic electron because the total photon-like object’s momentum P=gamma mc is the hypotenuse of a momentum triangle where p=gamma mv is the longitudinal component of the photon-like object's momentum (and equals the the momentum of the relativistic electron being modeled), while mc is the transverse component of the photon-like object’s total momentum P=gamma mc, as shown by the pythagorean formula P^2 = p^2 + (mc)^2 .  Since P=E/c  for the photon-like object, where the energy of the helically-moving  photon-like object is E=gamma mc^2 , the 90-degree momentum triangle relating P, p and mc corresponds to the relativistic energy-momentum equation for an electron: E^2 = p^2 c^2 + m^2 c^4 as is evident if you just substitute P=E/c into the momentum triangle formula  P^2 = p^2 + (mc)^2 .

   If the above momentum triangle relationship is agreed for all our helical models of the relativistic electron , the only quantitative difference among Graham’s, Vivian’s, Chip’s and my helical photon models in this regard is the helical radius R's dependence on gamma, compared to the resting electron’s trajectory radius Ro=hbar/2mc (shown by the oval’s transverse radius at the left end of the figure).   My spin-1/2 charged photon model predicts that the helical radius R is given by R=Ro/gamma^2 = hbar/(2mc gamma^2) as shown in the figure,  (which equals 1/2 in this diagram where the value used for gamma in the diagram is  gamma = sqrt(2) = 1.414 so also v= c/sqrt(2) = 0.707c in the diagram. The value of theta in the figure is therefore 45 degrees. Grahame’s electron model predicts that R=Ro for all values of gamma. Vivian predicts that R=Ro/gamma which would equal 0.707 Ro in this example.  I’m not sure what Chip’s model predicts for the radius of the helically trajectory (I think it is R=Ro/gamma) which however is not necessarily the same as the radius of the helically moving photon-like object itself. Chip, Vivian and I seem to agree that the photon radius decreases as R=Ro/gamma for highly relativistic values of gamma, while Grahame doesn’t as far as I know have a prediction for the radius of a photon-like object (as distinct for his prediction of the constant radius of the trajectory of the photon-like object of Ro for all values of gamma. 

   In Graham’s electron model, the orbital value alone for the angular momentum is always mc x Ro = hbar/2 even at highly relativistic velocities. Any additional angular momentum such as spin-1 or even spin-1/2 of the helically-moving photon would add a component of this spin at highly relativistic velocities to this orbital angular momentum value of hbar/2, giving a total z-component of spin greater than hbar/2 at highly relativistic velocities, which is contrary to experiment. Chip also doesn’t seem to take into account the spin of the photon-like object itself in his calculation of the total spin of his relativistic model of the photon as the electron’s momentum increases, which forces him to decrease the radius of his photon model as Ro/gamma (as I understand him) to keep the total spin of his electron model equal to hbar/2. But it is clear from the diagram that the transverse momentum component of the circulating photon-like object remains mc even at highly relativistic electron values, so his calculated value of orbital spin should actually decrease if his R decreases with increasing gamma.

   I would also like to know if John W agrees with the momentum right triangle relations here for a relativistic electron model. I believe that he thinks that the radius of a photon decreases as 1/gamma from various energy considerations. And Hodge? John M?

     Richard

Figure 1.  Velocity, momentum and energy relationships for the charged photon model moving along its helical trajectory. The velocity and momentum 

vectors of the charged photon and its components related to the electron being modeled are indicated.



> On Jan 15, 2017, at 5:04 AM, Chip Akins <chipakins at gmail.com> wrote:
> 
> Hi Dr Grahame Blackwell
>  
> You have made some good points. 
>  
> At one time I thought the electron was composed of a circulating photon which had its spin altered so that the negative portion of the electric field lines always point outward.
>  
> I am no longer of that opinion. There are several reasons for the change of opinion. Just as there are several reasons I changed my opinion about SR.
>  
> The energy configuration of the electron is different from that of a confined photon in several ways. There is no reason to hold onto the full energy configuration of the photon when modeling the electron, in fact it leads to difficulties and errors in my opinion.  It seems that the laws which govern the movement of energy in space support a few simple configurations.  The electron’s rest mass/energy comes from the threshold which space imposed on this specific configuration of energy.
>  
> Yes. The concept of radius is potentially misleading when discussing the electron simply because it consists of a set of fields with a finite focus point. But we are able to calculate the mean transport radius of the momentum density, which is confined and rotating, and which would yield a spin angular momentum of ½. If we assume the energy in the electron to display the same momentum as the energy in the photon of the same energy, then this is a pretty simple calculation.
>  
> I am not sure the idea that the momentum internal to the electron remains constant when the electron is accelerated is correct. When we accelerate the electron we add energy to the electron.  The energy we add is added directly to the energy which is already in the electron. The new momentum term with energy added is still Total Energy/c, so we now have more momentum, which means the radius must be smaller to yield spin ½.
>  
> Consider that space only allows electrons to exist at rest at a specific rest energy. Any electron with more energy than this is moving. In fact space requires an electron with a specific amount of energy (above the rest energy) to always move at the same speed. The law of inertia is built into the particle. The confined propagation pattern of the energy in the electron is altered from the rest condition by the addition of energy. Once energy is added the electron must move, it can no longer be at rest. So the added energy becomes part of the energy in the electron. Which in turn increases the momentum of the energy in the electron.
>  
> It seems this increase in energy must therefore also do two things. 1) Increase the confinement force due to increased energy. 2) Reduce the radius to maintain a spin ½ configuration.
>  
> This issue of the confinement force seems to be of great importance.  For Planck’s rule to hold, E=hv, there must be a force related to energy.  This force is simply the equal and opposite reaction of space which opposes the displacement which energy causes. Such a force clearly defines a particle confinement mechanism.
>  
> I could continue, but this email would become quite lengthy.
>  
> Thank you for your thoughts and insight.  I have looked at this issue from so many different perspectives but still find it fascinating.  For now I still feel there are very many indications that the radius of the electron must contract with velocity. I am not yet able to see how the pieces could all fit any other way.
>  
> And no, I do not think there is a photon inside an electron.  I think the energy of an electron can be released and become a photon. But you can’t change the configuration of the energy of a photon, convert it to an electron, and have it still be a photon.
>  
> Thoughts?
>  
> Chip
>  
>  
> From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org <mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org>] On Behalf Of Dr Grahame Blackwell
> Sent: Saturday, January 14, 2017 5:41 PM
> To: Nature of Light and Particles - General Discussion <general at lists.natureoflightandparticles.org <mailto:general at lists.natureoflightandparticles.org>>
> Subject: [General] Reply to Chip on particle radius & spin
>  
> 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 <mailto:grahame at starweave.com>
> To: Nature of Light and Particles - General Discussion <mailto:general at lists.natureoflightandparticles.org>
> 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 <mailto:chipakins at gmail.com>
>> To: 'Nature of Light and Particles - General Discussion' <mailto:general at lists.natureoflightandparticles.org>
>> 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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