[General] On particle radius & spin

Dr Grahame Blackwell grahame at starweave.com
Tue Jan 24 00:39:58 PST 2017


Richard,

I'm getting the feeling that one of us is losing the plot - and I don't think it's me.  Your use of terms like "rescue your foundering electron model" speaks of a level of desperation on your part - more like a schoolboy throwing stones than a scientist engaged in civilised debate.

Far from "keep hinting about legal action", I was simply observing that scientific rigor should be modelled after that of the courtroom, where precision and accuracy are of paramount importance and making untruthful assertions can land one in difficulties.  As a case in point I'd draw your attention to the fact that the "critical remark [you] made to [me] several years ago" was in fact, as I stated (below), 5th July (2016) - just over 6 months ago.  Following hot on the heels of your double-typo on an issue that you yourself clearly consider to be of importance, this doesn't speak well of your attention to detail.

I see nothing in either of your previous missives that brings us any closer to knowing how you think a photon can be electrically charged in addition to its time-varying formative electromagnetic field (or even what that means), nor on what experimental evidence you base that belief (for my part I have never, contrary to your apparent belief, proposed that a photon is in any way charged; as I've stated many times, it's my view, along with that of others, that the charge on an electron is the external manifestation of the electromagnetic field of an [uncharged] cyclic photon; the experimental evidence for this is: (a) the fact that two opposing photons, without any additional charge, do in fact transform to two charged particles in pair production; (b) the fact that the charge on an electron travels with the electron [of course] and so must be a part of the electromagnetic wave phenomenon that determines the path of that electron, including any preferential direction determined by interference effects; (c) the fact that an electromagnetic-field construct must necessarily give rise to electromagnetic field effects around its periphery, since EM fields do not have an abrupt cutoff).

Neither do I see anything in your missives that gives any clue as to how you believe that an increasing frequency of waveform can remain in synch with a decreasing frequency of helical cycle, in conformity with energy and time-dilation requirements respectively.

Since it seems that you're unwilling to vouchsafe any evidence or theory in support of either of these proposed phenomena, I take it that we're expected to take them on trust simply because they are required for your model.  This is in stark contrast to the extensive info that I've given which, without definitively proving every aspect of my model (I've never claimed that) does at least give a degree of theoretical and empirical-evidence underpinning to each and every one of those aspects.  You'll note also that none of my proposals violates Occam's directive by introducing new previously-unknown physical entities.

I'm sorry to have to say this as we've had some interesting conversations in the past. But given this serious imbalance in information provision and the confrontational nature of certain posts, I see no point in continuing this discussion.

Best regards,
Grahame
  ----- Original Message ----- 
  From: Richard Gauthier 
  To: Dr Grahame Blackwell 
  Cc: Nature of Light and Particles - General Discussion 
  Sent: Monday, January 23, 2017 6:01 PM
  Subject: Re: On particle radius & spin


  Hi Grahame,


     Thank you for pointing out my two typos where I wrote spin 1/2  and spin -1/ 2 photons when I meant  spin 1 and spin -1 photons , referring to photons detected in linearly polarized light. I’ve got spin 1/2 charged photons on my mind. The main point that I was making however is that you are proposing that the circling spin 1 photon in your resting electron model gradually turns into a spin 0 nearly-linearly-moving photon in your highly relativistic electron model, which would help rescue your foundering electron model by preserving its spin 1/2 hbar at relativistic velocities. I don’t think that this explanation will be successful, but that’s just my opinion. But the criticism is not just applicable to your electron model. John and Martin’s 1997 electron model as well as Vivian’s model and Chip’s model may also be subject to the same criticism of having too high a spin at relativistic velocities. 


     I am obviously not claiming originality by using hf=gamma mc^2 in an electron model or in relativistic circulating-photon electron models.  Please give me a little credit here.  I earlier wrote that de Broglie used this same equation when deriving his de Broglie wavelength for a relativistic electron. But I don’t recollect seeing the related photon wavelength lambda=h/(gamma mc) used in constructing other relativistic electron models composed of a circulating photon-like object, or in deriving the de Broglie wavelength from a circulating-photon-like-object electron model. 


      I think that it’s interesting that you now keep hinting about legal action in reference to a critical remark I made to you several years ago, just when your electron model is under severe scrutiny (as every model here should be). Perhaps you would prefer me to back off from these constructive criticisms of your model in a friendly forum? Just when we’re making some progress? 


     Good luck.
        Richard


    On Jan 23, 2017, at 4:45 AM, Dr Grahame Blackwell <grahame at starweave.com> wrote:


    Richard,

    I really feel that as a scientist you should be aware of the clear distinction between 'wonder' and 'assert' - whether used in a scientific discussion or in a courtroom (the two contexts are actually quite similar, both require more rigor than you appear willing to apply).  You most certainly were NOT 'wondering' when you categorically stated - wrongly - in your post to the group received 5th July: "You have such a strong belief in the correctness of your own model of physical reality derived from spun-light models of particles that you offer a series of online classes to teach it to others for a fee."  If you don't consider this assertion, which is an outright untruth, a 'brickbat' then I'm slightly at a loss to know what you would consider you'd have to say to justify that term.

    Also, I consider your 'sincere apology' to be rather hollow when it's followed in the next sentence by the insinuation that I've been nicking your work.  This is (a) patently ludicrous when 'your work' consists in this case of the increase in energy by factor gamma in a moving electron - a fundamental aspect of photon energy and of the energy-momentum relation used by ALL in this field; (b) yet another reversal of the facts, since you yourself purchased a copy of my book 'Tapestry of Light', almost nine years ago - which on pp59-65 clearly explains the increase in energy required for increasing speed of a particle, illustrated graphically with a series of right-angled triangles for increasing speeds showing even for the non-technical the Pythagorean relationship between speed and energy that you suggest I appropriated from you (You chose not to study my book published that same year giving the detailed math behind this view of material particles).  So your claim that "you know where and I don't", referring to my use of that relationship, is also untrue.

    [If we need to go further back than that, almost 13 years ago my model, including this detail, was published by the Scientific & Medical Network on their website, and reproduced in the Italian periodical 'Scienza e Conoscenza' in October 2004.]

    I wholeheartedly agree that part of the purpose of this forum is to critique the work of others - constructively.  I emphasise that last word because I don't feel that erroneous (mischievous?) adverse comments on the work of others fit that description.  I feel also that, if one wishes to query the rigor of others' work against the benchmark of empirically-verified facts, one really should take the trouble to get those facts right.  In this respect you may wish to reconsider your statement in your previous last email:"The detected photons always have either spin 1/2 or spin -1/2."

    I have other things to do than to pick out your errors, but I will address your other points in your previous email shortly.  I hope you find this constructive criticism useful.

    Best regards

    ----- Original Message ----- 
      From: Richard Gauthier
      To: Dr Grahame Blackwell
      Cc: Nature of Light and Particles - General Discussion
      Sent: Monday, January 23, 2017 4:41 AM
      Subject: Re: On particle radius & spin


      Hello Grahame,


         If I have attributed to you any statements that are the reverse of what you have actually said, then I do sincerely apologize. I don't remember your using the relativistic electron’s photon wavelength h/(gamma mc) in your electron model prior to me mentioning it or using it in my work. But if you did I either missed it or forgot it, and would appreciate your pointing out to me an example where and when you did, since you know where and I don't. I am in the process of critiquing your electron model as I have critiqued John and Martin’s, Vivian’s, Chip’s and Albrecht's in the past, as they are all double-looping models with some similarities to mine. I think all of us want to be fair-minded in our critiques. If your model stands up to all the scrutiny that we can apply to it, that will be great. If we were to give you or anyone here a “free ride” on possibly questionable issues, we would not be doing our duty to the scientific research process and this could slow down    progress towards better models. So there’s nothing personal going on here. I would not like to waste my own time for months or years thinking I had a good scientific model if it was really full of mathematical and/or conceptual errors and was a dead end. And such errors, if they exist, come out sooner or later anyway (less embarrassing if they come out sooner rather than later) unless no one cares enough to notice them and point them out. My own photon and electron models have evolved over the past 25 or more years starting with some initial insights, and I’m sure they will continue to evolve.


         As for your website and online physics teaching, I was at one point wondering, after looking over your site, if you were including your own metaphysical approach and physical hypotheses in your online physics instruction, which seemed directed towards physics newcomers. You assured me that you were not. So I dropped the subject. I would not call any of this “hurling brickbats” but I understand that you could have taken my comments in a different way than I intended. 


      with best wishes,


           Richard




        On Jan 21, 2017, at 3:12 PM, Dr Grahame Blackwell <grahame at starweave.com> wrote:


        Oh Richard,

        I really do wonder sometimes about your lines of reasoning.  And ‘disconfirm’ ?? – I didn’t even know that was a word!  Poor old Occam must be spinning in his grave!  What with ‘disprove’, ‘refute’, ‘rebut’ – ‘disconfirm’ must surely be a case of “multiplying entities (words) beyond necessity”.

        On a slightly different point: in polite conversation it’s generally considered courteous for two parties to alternate in asking questions and responding to the other’s questions; if one just follows the other’s answers with yet more questions it can seem a bit more like an interrogation than a discussion.  Having (as you noted) offered quite a bit of info in reply to your critique of my model, I was hopeful that you would in turn respond to my simple question; instead you’ve chosen not to reply to that but rather asked yet more questions of your own.  Something in me wonders if that’s an avoidance strategy – but I’m sure you do in fact have a simple explanation to offer with regard to your curious concept of a ‘charged photon’.

        Since your two questions are fairly easy to answer, I’ll do that now in the hope that you will respond in like manner by making everything clear about this elusive ‘charged photon’, in a way that fits with existing knowledge.

        [More seriously, Richard: I had reason a while ago to caution you about grossly untrue and potentially libellous comments that you posted regarding      content of my website; now I find you attributing to me statements that are precisely the reverse of what I've actually said, and inviting others to find fault with my work on the strength of that misinformation; I feel you might be wise to check your facts more carefully before hurling such brickbats, they may rebound with consequences that you might not wish.]

        You’ve asked about the wavelength of the helically-moving photon in my electron model – at least, I think you have.  My uncertainty is caused by the fact that you appear to be switching between two different things as if they’re one and the same thing.  Those two things are the electromagnetic wave frequency of the photon that forms the electron and the periodicity of the cycle pattern of that photon around its helical path.  In this you appear to be dealing with the de Broglie Clock Paradox by completely ignoring it.

        As you’ve observed, my photon’s constant-radius helical trajectory has a cycle frequency that decreases as the photon’s speed increases, and so also its energy.  As photon energy increases by factor gamma then cycle frequency decreases by factor 1/gamma.  This is fully in line with experimental evidence and also fully to be expected: a clock moving with the electron would show that helical trajectory completing one full cycle in precisely the same time as would be shown by a static clock for an electron at rest.  This is known as ‘time dilation’, proposed by Einstein and demonstrated by various experimental observations, notably that by Gouanère, Catillon et al in respect of electrons; another elementary particle with no substructure, the muon, has also been shown to demonstrate so-called ‘relativistic’ time dilation in terms of its decay rate and so also, one must infer, in terms of the effect of motion on its underlying structure.  [My model of particle structure proposes that this is in fact the reason for such time dilation: energy takes longer for a complete cycle through/around a particle; since it must necessarily be energy that propagates effects of time, it naturally follows that time will propagate more slowly with regard to a moving particle.]  Observation and theory match perfectly.

        In respect of a rather different matter, the frequency of the formative photon for an electron, I agree with you again that the frequency of that photon      increases by factor gamma in accordance with the speed of linear motion of the photon.  So, without question – again I agree with you 100% – the ‘frequency’ of the formative photon wave, measured against the increased (‘time-dilated’ by factor gamma) duration of each complete cycle of the helical path of that photon, will indeed be increased by factor gamma^2.  This again is fully in line with existing theory, and such experimental evidence as is available: time dilation is an established fact, even for individual particles without substructure, so each complete helical cycle will take longer by a factor gamma; frequency of the formative wave, as evidenced by experimental evidence on energy content and also by consideration of the ‘relativistic’ energy-momentum relation, is indeed increased by factor gamma for a moving particle; simple multiplication gives the inevitable result that we both agree applies in my model.

        What baffles me is why exactly you think that this self-evident fact is so unspeakable (“doesn’t make sense”) – not only that, but you invite others to      think likewise.  This may be because you appear to turn this relationship on its head (without explanation) and claim that I’m proposing N = gamma^2 helical turns per wavelength *; this is clearly incorrect, what I’m actually proposing is gamma^2 wavelengths of the formative photon per (double) helical turn – exactly the opposite of your claim (and fully in line with theory and experimental evidence, as I’ve shown above).  I can’t help feeling that you’ve been bamboozled by your fixation with SR into believing that the two are one and the same thing – a feat that takes a pretty extreme level of belief in something for which, as far as I know, NO experimental evidence is available (i.e. fixed relationship of photon wavelength to helical cycle).  [Being charitable, it appears that you’ve totally befuddled yourself over turns/wavelengths and wavelengths/turns – not a sign of clear thinking.]

        [* Your quote: “the number N of helical turns per wavelength … your N=gamma^2 result doesn’t make physical sense“.]

        I’d be most interested to hear how you square the circle of increasing wave frequency and decreasing helical cycle frequency, in line with theory and experiment, whilst the two remain synchronised…

        As to the second of your questions below: I thought I’d already explained this, it seems I need to do so again.  I hope we’re agreed that spin-1 is applicable for circularly polarised photons, elliptically polarised photons have a lesser degree of spin (dependent on eccentricity), plane polarised waves have zero spin.  Even Wikipedia, with all its failings, appears to have this one right.

        There’s some agreement, too, that electric charge is an artefact of cyclic circularly-polarised electromagnetic wave motion.  Since any increase in energy of a particle such as an electron must be the consequence of a photon (real or virtual) being transferred from some other entity, it seems likely that this transfer is in the form of a plane polarised photon (otherwise the electron’s electric charge might arguably be increased or decreased).  A plane polarised photon combining with the static electron’s formative photon would have the effect of ‘diluting’ the degree of circular polarisation of the latter; this would in turn have the effect of reducing the spin of the electron’s formative photon (now higher frequency, but elliptical – frequency doesn’t affect photon spin, ellipticity does).

        So it is that, in my model, the spin of the formative photon reduces as the linearity of the photon’s path increases – so for the “very large gamma” that you refer to, the spin of the formative photon tends to zero and so would not add anything to the constant spin-1/2 that my constant-radius model gives for an electron.

        [As a footnote: I note that you’ve been soliciting support from others for your model, including Hodge; no disrespect to Hodge, but since as I understand it your model rests fundamentally on a wave-form photon, I’m not sure that agreement from one who rejects the very idea of a photon being wavelike would help your cause.]

        Over to you – I’m really keen to hear your rationale for this charged photon, with experimental evidence.

        Best,
        Grahame

          ----- Original Message ----- 
          From: Richard Gauthier
          To: Dr Grahame Blackwell
          Cc: Nature of Light and Particles - General Discussion
          Sent: Thursday, January 19, 2017 2:09 PM
          Subject: Re: On particle radius & spin


          Graham,
            A small typo correction in my email. The factor of 1/2 (helical turns per photon wavelength) in my email should be a factor of 2 helical turns per photon wavelength. In the resting electron the photon makes 2 circular loops per Compton wavelength, producing the zitterbewegung frequency fz=2mc^2/h. The ratio of 2 helical turns per photon wavelength remains in my relativistic electron model. This does not affect the main argument in the email.
              Richard


            On Jan 18, 2017, at 6:34 PM, Richard Gauthier <richgauthier at gmail.com> wrote:


            Hi Grahame (and others)


               Thanks for the detailed critique of my electron model and further information on your model. It’s a lot to reply to so first I’ll start with one question about your electron model.


                Your electron model still doesn’t explicitly contain the relationship Lwavelength = h/(gamma mc) for the wavelength of your helically circulating photon, derived from hf= hc/Lwavelength = gamma m c^2 . Your photon’s constant-radius helical trajectory has a continuously DECREASING helically turning frequency as the energy of the electron increases. Your model's helical turning frequency decreases as 1/gamma with increasing electron energy, while its turning period T increases directly proportional to gamma. This implies that the length of one complete helical turn in your relativistic model is Lturn = gamma Lcompton). This means that with increasing gamma for your electron model,  more and more of your helically moving photon's wavelengths of value Lwavelength = h/(gamma mc) = Lcompton/gamma are included on a single helical turn of length Lturn = gamma Lcompton of your helically moving photon. The number N of wavelengths per helical turn in your model moving with relativistic speed given by gamma can be seen easily to be N= Lturn/Lwavelength = (gamma Lcompton)/ (Lcompton/gamma) = gamma^2 . So if two people observe your electron model go by with two different high energies (say gamma = 10 and gamma = 100, the person observing the gamma=10 electron go by will count 10^2 = 100 photon wavelengths per helical turn of your photon while the second person, observing the  gamma = 100 electron go by, will count 100^2 = 10,000 photon wavelengths per helical turn of your model (not counting the factor of 1/2 in helical turns per photon wavelength due to zitterbewegung double-looping). In my spin-1/2 charged photon model, the number N of helical turns per wavelength is INDEPENDENT of gamma and always equals 1/2 helical turn per photon wavelength (including the zitterbewegung double-looping factor.) To me (and perhaps to others?) your N=gamma^2 result doesn’t make physical sense so I want to confirm with you that this result is in fact implied by your model. This result alone could disconfirm your model if it doesn’t make physical sense. Also in your model I still don’t see why the constant spin 1/2 of the orbital motion of the photon would not for very large gamma simply add to the intrinsic spin of the photon (either spin 1 or spin 1/2), whose spin vector is directed essentially longitudinally like that of the spin 1/2 orbital motion, to give a total relativistic electron-model spin 1 1/2 or spin 1 respectively . Please let me know. Thanks.


                 Richard


              On Jan 18, 2017, at 7:29 AM, Dr Grahame Blackwell <grahame at starweave.com> wrote:


              Hi Richard (et al.),
              I feel I need to address your reference to my constant-radius electron model with your inference as to its apparently increasing spin angular momentum with increasing velocity.  There is actually no paradox there – in fact a clue as to the resolution of this issue is hidden in your own candidate photon.
              First I’d like to query that electron model of yours, based as you say on a “spin-1/2 charged photon”.  I have no problem with the spin-1/2 bit: as we know, the spin-1 (+ or -) characteristic of a photon is a consequence of its own circular polarisation, clockwise or anticlockwise.  So it follows that a plane polarised photon, being an equal combination of + & - circularly-polarised elements, will not exhibit any such spin; likewise an elliptically polarised photon, consisting of unequal parts of + & - polarisation, will somewhere between 0 and +/-1, depending on its eccentricity.  So spin-1/2 is a distinct possibility for a photon.
              I’m not clear, though, on what’s meant by a “charged photon”.  I don’t know of any entities arising from Maxwell’s equations that fit that term.  Indeed, it’s increasingly apparent that the phenomenon referred to as ‘static charge’ is itself an artefact arising from the electromagnetic fields that form a ‘charged’ particle.  I fully agree with John W & Martin vdM on this* – more than that, I believe it would be pretty well impossible to explain experimental findings showing the wavelike nature of an electron without this being the case.  [* Also that this formative photon must necessarily be circularly polarised.]
              If one talks of a ‘charged photon’, presumably the photon itself is still an electromagnetic construct?  In which case we have an electromagnetic construct with an electric charge attached to it (?) – two quite different electromagnetic constructs combined within the same entity (if I’ve misunderstood this completely, please put me right).  In this case, what’s the mechanism that persuades that charge to follow the interference-guided waveform to its destination in the Davisson/Germer experiment?  I just can’t see how it would work, on a number of fronts.  Surel that 'charge' must itself be wave-lie - so it's just part of the photon wave?
              The other thing that’s quite puzzling is: when photons (possibly virtual) are added into the electron to accelerate it, do they have to be these ‘charged photons’ as well?  If so, where do they come from?  If not, why not?  How do 'non-charged' photons combine with a 'charged' photon to increase its frequency?
              With regard to my own model, as you say it of course conforms with the energy-momentum relation.  It also creates the phenomenon experienced as ‘electric charge’ as an artefact of the time-varying electromagnetic field effects of its formative photon.  Those same effects, internally to the electron, interfere with one another (non-linearly, of course – so not coherent superposition) to create curvature in the photon path which, once initiated, is self-perpetuating; hence the ‘confinement’ of the photon.
              It’s clear that the linear momentum of the cyclic photon, completing one wavelength in a double-loop (as per zitterbewegung), gives the static electron an angular momentum equivalent to spin-1/2.  The intrinsic spin of the photon itself (being circularly polarised) will balance itself out over one cycle, contributing no additional spin to the electron.  Additional energy, leading to motion of the electron, will be plane polarised* – this is apparent from other considerations, notably in relation to gravitational effects (which fit very well with this model as extended electromagnetic effects of ‘massive’ objects), as well as non-increasing charge.
              [* This isn’t in any way a limitation on the energies that might accelerate an electron; it’s anticipated that the structure of any elementary particle would be self-regulated by interference effects that would mediate the energy exchange between particles – both particles generally obeying matching constraints.  Thus energy exchanges would be in the form of plane polarised waves.]
              This leads to a formative photon for an electron that becomes progressively more elliptical in its polarisation as the electron increases its speed.  It should be apparent that the increasing linear component of the formative photon itself thus has a decreasing degree of angular momentum.  From this it should in turn be apparent that: (a) the formative photon should asymptotically approach plane polarisation as the speed of the electron approaches c (and the photon path approaches the unattainable ‘flatline’ state); (b) the decreasing degree of circular polarisation will match the decreasing proportion of that photon acting cyclically, as opposed to linearly – so maintaining the balance between the reducing spin angular momentum of that photon and the compensating cyclical component of photon motion; (c) the linear momentum of the photon will contribute an unvarying element of angular momentum (at constant radius) to the electron (translating into a constant spin-1/2, regardless of electron speed), as already noted.
              As electron speed approaches arbitrarily close to c, its formative photon approaches arbitrarily close to a flatlining plane polarised form – whilst still maintaining a helical constant-radius path over an arbitrarily long cycle interval, matched by an arbitrarily high frequency such that the two combine to give a cyclic momentum component which gives a constant spin-1/2 at all electron speeds.
              In contrast to all other models seen, this proposed electron structure requires absolutely no add-ons or modifications to known features of a photon; the proposal of self-interference as a mechanism for ‘confinement’ of the looping photon seems virtually axiomatic, given the well-verified phenomenon of pair production from two linear photons with no apparent injection of any additional props.  Not least, this model with  its invariant loop radius for its formative photon offers a comprehensive detailed explanation for ALL phenomena grouped under the heading of Special Relativity (including, as Albrecht has observed, but not just, time dilation in accordance with Lorentz factor).
              More than this, it offers a cogent and robust rationale for the phenomenon referred to as ‘gravitation’, including a full explanation for the highly useful concept of ‘curved spacetime’ as a tool for calculating trajectories through areas of space subject to influences from massive bodies in motion.  Not least, it offers a fully coherent rationale for the phenomenon that we know as ‘time’, in a formulation that fits precisely with all known experimental and other empirical findings.  To cover ALL these bases without having to introduce ANY new concepts would, I believe, warm the heart of William of Ockham.


              Just to push the boat out a little further, this model also gives a sensible explanation of 'quantum indeterminacy' - without either of the antiquated myths of exponentially-increasing alternative universes OR 'God playing dice' (I'm with Einstein on the latter of these).
              Grahame


              ========
              ----- Original Message -----  
              From: Richard Gauthier
              To: Nature of Light and Particles - General Discussion
              Sent: Monday, January 16, 2017 2:27 AM
              Subject: Re: [General] Reply to Chip on particle radius & spin

               
              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.

















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