[General] double photon cycle, subjective v objective realities

Dr Grahame Blackwell grahame at starweave.com
Tue Jul 12 06:23:41 PDT 2016


Hi Chip, Richard, John W,

 

I think we all realised, from Chip’s email if not before, that there’s an issue to be addressed with regard to a photon’s angular momentum in the overall behaviour of a photon-formed electron.

 

It seems to me that, whatever photon-based electron model any one of us chooses to put forward, when that electron is in motion then there will be a component of that formative photon’s angular momentum in the direction of motion of the electron (i.e. about any axis in that direction).  More than this, my preliminary investigations suggest that it would take a very creative model indeed to ensure that the rise in that component with increase in electron speed would be exactly balanced by a drop-off in the component from the photon’s linear momentum to give the electron a constant angular momentum.

 

[A ‘quick fix’ would of course be to propose a linearly polarized photon with zero spin – i.e. 50/50 superposition of left and right circularly polarized elements.  This, though, is rather a cop-out as it removes a possible explanation for other electron features, notably charge; it also doesn’t feel right.]

 

I believe we’re all agreed that:

(a) There’s more than enough evidence to confirm that the concept of an electron (and likely also other elementary particles) being formed from a closed-loop photon is totally valid;

(b) Formation of an electron involves a double-loop per wavelength of the photon, at least for the static electron.  All else aside this is clearly indicated by zitterbewegung.

 

I’m guessing we all also agree on the validity of the so-called Relativistic Energy-Momentum Relation (whether or not we subscribe to the idea of objective frame symmetry).  There are quite a few points that can be drawn from that, as I see it.

 

Most importantly, the REMR represents the full momentum of a moving electron (i.e. momentum of its formative photon) in terms of linear and cyclic components.  Expressed diagrammatically, these three components form a right-angled triangle that defines the relative directions of the instantaneous velocity components (linear, cyclic, overall) of that photon (since these must necessarily follow momentum component directions).

 

It’s pretty clear, first of all, that if the linear velocity component is v (as it is) and the overall velocity is anything other than c (in directions as given by REMR) then the cyclic velocity component will not be orthogonal to the linear component (as it must be).  From this I believe that we can confirm that the velocity (at least the mean velocity) of an electron-forming photon must be c; I think this rules out certain proposals.

 

Secondly, that velocity triangle gives cyclic velocity component as c/gamma.  Those who subscribe to SR’s objective frame symmetry would presumably expect the double-loop to complete in a time gamma tau, where tau is the time for that double-loop for a static electron (since from the static perspective that double-loop in the moving electron would have to correspond with the time-dilated interval in the moving frame).  I also see the double-loop completing in that time, since I regard energy flow as the underlying mechanism driving the passage of time; a slower rate of time-experience (time dilation) is the consequence, rather than the cause, of that reduced looping rate.

 

Whichever is the case, a looping rate reduced by a factor gamma and achieved by a flow speed component also reduced by a factor gamma indicates a constant path-length, i.e. a constant radius for the cyclic path of the formative photon.  This appears to be an inescapable conclusion from consideration of the REMR and time dilation.

 

[For completeness I should add that SR frame symmetry requires that each double-loop is also seen as exactly one full single wavelength from within the moving frame; for me this raises an irreconcilable contradiction in SR.]

 

Back to that photon spin

==================

 

Clearly either electron spin increases with speed of the electron’s linear motion – or it doesn’t.  If it doesn’t then this implies some aspect of quantum mechanics that needs further consideration.  Rather more significantly for us, I believe it also rules out the whole concept of electrons being formed from looping photons.

 

That last seemingly outrageous statement follows from the tendency towards flat-lining of the formative photon as an electron tends towards speed c.  Unless we consider that photon to be other than circularly polarized – which I believe raises serious difficulties with other aspects of the model – then this means that the electron’s angular momentum in its direction of motion tends to at least hbar – which is clearly inconsistent with constancy of electron angular momentum with increasing speed.

 

Rather less problematic (as I see it) is the notion that the electron’s angular momentum in its direction of motion increases with its speed.  I don’t know of any experimental evidence showing conclusively that this is not the case, if others do then of course that would be of interest.

 

Obviously if angular momentum does increase then that must be by virtue of its being transferred from elsewhere.  Since increase in velocity must be caused by an input of energy – a real or virtual photon – then the most obvious course is to consider a Compton scattering event that increases the velocity of the electron.

 

It’s known that in general Compton scattering leads to a change in polarisation state of the scattered photon.  From what little I’ve seen, such changes have been calculated from theory and confirmed in principle by experiment; that theory doesn’t generally include the notion of an electron’s angular momentum varying with speed, as far as I know.  That (likely) omission would make negligible difference in all but the most extreme case: increase of electron speed from sub-relativistic to highly relativistic in a single step – since the change in scattered-photon spin would correspond to the change in v/c for the electron.

 

To summarise: The concept of an electron formed from a circularly-polarised photon looping at constant radius for all speeds of the electron appears to be consistent with all experimental evidence, other than maybe definitive evidence on electron radius at speed* (unless electrons moving at high speed have been shown, and not just inferred, to have spin ½); this observation is based on the assumption that no evidence exists of photon polarisation state changes in high-energy Compton scattering events with sufficient powers of discrimination (i.e. accuracy) to definitively show that no angular momentum has been passed from the photon to the electron, other than that accounted for by a change in direction of motion of the electron.

* I have yet to look at this.

 

Of course this is just my view, based on my understanding of available scientific data.  I’d be interested to hear other views on these observations

 

[Richard, I hope it’s clear from the above why I have reservations over your proposed v=sqrt(2)c spin-1/2 photon model of the electron.  In particular I can’t see how that model can be reconciled with the Relativistic Energy-Momentum Relation in terms of correspondence of directions for components of momentum and velocity.]

 

Regards to all,

Grahame

  ----- Original Message ----- 
  From: Richard Gauthier 
  To: Nature of Light and Particles - General Discussion 
  Sent: Friday, July 08, 2016 6:13 AM
  Subject: Re: [General] double photon cycle, subjective v objective realities


  Hello Grahame,


      Unfortunately the situation is not so simple. Neither of our published electron models includes a specific photon model with its own spin, where this photon model moves along the helical trajectory described in our models. If that photon moving along the helical trajectory has a spin that is is independent of the energy of the photon (which is the nature of photons) then as the photon's trajectory in the your double-loop constant helical radius electron model gets more and more straight with increasing electron speed, then the spin of this circulating photon adds more and more to the spin 1/2 of your electron model produced by its circling transverse component of momentum mc at constant radius R. The result is that a circulating spin 1 photon along your constant radius R helical trajectory would give your electron model a total spin of one and a half units of spin hbar at highly relativistic velocities. A circulating spin 1/2 photon traveling along your constant radius R trajectory would give your electron model a total spin of  1/2 + 1/2 = 1 unit of hbar of spin at highly relativistic velocities. It is only if the radius R of the photon’s helical trajectory decreases with increasing velocity to become insignificant (compared to R in a resting electron) at relativistic velocities that the spin of the electron model at relativistic velocities will equal only the spin of the photon composing the electron model. Ideally the helically circulating photon model of the electron will have longitudinal spin component 1/2 hbar at all velocities of the electron model from very slow velocities to very highly relativistic velocities. 


      I have an unpublished internally superluminal (v=c sqrt(2) ) helically circulating spin-1/2 photon model whose spin remains 1/2 at all energies, which may be suitable for modeling the electron. I described this photon model in this email list in the past. The radius of my published spin-1/2 charged-photon electron model’s photon trajectory decreases as 1/gamma^2 with increasing electron velocity, so this does not produce the complication described above when the helical radius of the photon’s trajectory is a constant R at all electron velocities.


            Richard


    On Jul 7, 2016, at 1:00 AM, Dr Grahame Blackwell <grahame at starweave.com> wrote:


    Thanks Richard,

    That's precisely what I've been trying to say, without in any way resting on any generally-accepted results that might be regarded as consequences of SR (and so open to question).

    If we agree that the transverse momentum component of the electron is a direct consequence of the rotational component of its formative photon (as I hope we do!) then that rotational component is acting at radius R of the electron at that time from its centre.  Angular momentum is given by linear tangential momentum multiplied by radius - so angular momentum of the electron is mcR.  Since mc is constant, R must also be constant if angular momentum is invariant (which I believe we agree it is).

    Just one further point: Richard, you refer to m as the electron's invariant mass.  If we regard mass as that quality of an object that resists acceleration (and so is proportional to the instantaneous force required to induce an instantaneous acceleration), then my research indicates that the mass is not invariant - though it will appear so from measurements taken within the electron's moving frame.  My analysis shows that objective mass varies with speed and the relationship E = mc^2 is applicable only for an objectively static object/particle.  The m referred to above, as I see it, is the objective rest-mass of the electron (i.e. its mass when objectively static), which corresponds to the energy required to maintain the formative structure of the electron (as opposed to that required to maintain its linear motion).  This is of course constant.

    Best regards,
    Grahame
      ----- Original Message ----- 
      From: Richard Gauthier
      To: Nature of Light and Particles - General Discussion
      Sent: Thursday, July 07, 2016 6:42 AM
      Subject: Re: [General] double photon cycle, subjective v objective realities


      Chip and Grahame,
         Lets be specific to the electron to avoid unnecessary vagueness. The moving electron (composed of a circulating photon) has a constant transverse internal momentum component mc and a longitudinal external momentum component p=gamma mv. These two momenta add vectorially (by the Pythagorean theorem) to give  P^2 = p^2 + (mc)^2  where P=E/c is the momentum P=gamma mc of the helically circulating photon of energy E = gamma mc^2 that is the total energy of the linearly moving electron, modeled by the helically moving photon. This relationship is equivalent to the relativistic energy-momentum equation for a moving electron: E^2 = (pc)^2 + m^2 c^4 which, substituting E=Pc,  gives  (Pc)^2 = (pc)^2 + (mc^2) c^2 .. Dividing by c^2 gives P^2 = p^2 + (mc)^2 as given above. So as the electron speeds up, the transverse momentum component mc of the electron’s total (internal plus external) momentum P remains constant even for a highly relativistic electron. The electron’s constant transverse internal momentum component mc corresponds to (and leads to a derivation of) the electron’s invariant mass m.
          Richard


        On Jul 6, 2016, at 10:18 AM, Dr Grahame Blackwell <grahame at starweave.com> wrote:


        Yes Chip,

        Certainly the momentum of the confined wave increases - but that increased momentum should not ALL be reckoned as ANGULAR momentum of the electron.

        We know that a component of the momentum of that photon is linear - it's the linear momentum of the electron in motion.  There is another component of that photon that's orthogonal to that, i.e. in the direction of the cyclic motion of the photon.  As the linear velocity of the electron increases, the linear component of the photon momentum increases - however the orthogonal, cyclic, component of that photon momentum does NOT increase, since the 'pitch angle' of the helical motion of that photon increases with linear electron velocity, and so also with photon frequency, so as to precisely cancel out the effect of that increased frequency in the resolved-component cyclic direction.

        The angular momentum of the electron, dictated by the angular momentum contribution of the photon, does NOT depend on the FULL momentum of the photon - it ONLY depends on that component of the photon that acts cyclically, i.e. the component that's orthogonal to the linear motion of the photon.  That component remains constant (as long as the radius of the photon cycle remains constant).

        For example, if an electron is travelling with linear speed 0.6c then its formative photon is travelling in a helical path which, if we were to flatten it out (as in relativistic energy-momentum relation) we'd find that formative photon having a linear motion component of 0.6c and cyclic speed component of 0.8c.  This means that the ANGULAR momentum imparted by the photon will only be 0.8 of that which it would give if it were travelling fully cyclically at speed c (as for a static particle).  Since the frequency of the photon will be increased by a gamma factor of 1/0.8 for such motion, the decreased (0.8) contribution of momentum for increased (1/0.8) frequency will be exactly what it was for the static particle.

        I hope that helps make things clearer.

        Best regards,
        Grahame

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