[General] light and particles group

Richard Gauthier richgauthier at gmail.com
Wed Jan 25 10:22:42 PST 2017


Hi Chip,
  The only experimentally measurable linear momentum of a relativistic
electron is the electron's relativistic linear momentum p=gamma mv, not
 E/c All other momenta such as the relativistic electron's inner transverse
momentum mc and the total momentum P=E/c of a helically-circulating
photon-like object hypothesized to form the relativistic electron are
speculation. BUT the relationship of this one measurable electron momentum
p= gamma mv  to  the two speculative momenta mc and P= E/c  is  P^2 = p^2 +
(mc)^2 because this is mathematically equivalent to the relativistic
energy-momentum equation of the electron E^2 = p^2 c^2 + m^2 c4  as I have
shown elsewhere and which you can confirm by substituting P=E/c into the
momentum equation P^2 = p^2 + (mc)^2. This Pythagorean momentum
relationship P^2 = p^2 + (mc)^2  implies that the measurable momentum
p=gamma mv and the speculative momentum mc are perpendicular to each other
and add vectorially to produce the speculative total momentum P=E/c which
corresponds to the momentum of the helically-circulating photon-like object
composing the electron. (You don't need to call this a photon-like
object but it has the relationship P=E/c of a photon, and has energy
E=hf=gamma mc^2 and follows c=f lambda as well.)  Now, if you want to
further speculate that the hypothetical helically-circulating photon-like
object's momentum P=E/c is not the total momentum but is only the
longitudinal component of the momentum pt = sqrt(2) P = sqrt(2) E/c of a
hypothetical transluminal energy quantum (or call it what you like)  that
is helically circulating superluminally around this helically-circulating
hypothetical photon-like object of momentum P=E/c ,  I will be happy to
join you in this speculation. But I think that your equation pt = sqrt(2)
E/c may have to be modified somewhat because the photon-like object of
momentum P=E/c is moving at light speed in a helical trajectory rather than
in a straight trajectory where your formula pt = sqrt(2) E/c would apply
exactly.

On Wed, Jan 25, 2017 at 6:02 AM, Chip Akins <chipakins at gmail.com> wrote:

> Hi Richard
>
>
>
> I do not feel that p=E/c is the total momentum, but rather the normal
> measureable momentum. Since it is the momentum measured longitudinally. It
> is then just one vector component of the total momentum, the total momentum
> is more likely pt = sqrt(2) E/c.
>
>
>
> I do not think there is a photon inside the electron. I think the energy
> in the electron can become a photon.  That energy can be an electron, or a
> photon, but not both at the same time.
>
>
>
> Chip
>
>
>
> *From:* General [mailto:general-bounces+chipakins=gmail.com at lists.
> natureoflightandparticles.org] *On Behalf Of *Richard Gauthier
> *Sent:* Wednesday, January 25, 2017 12:37 AM
> *To:* Nature of Light and Particles - General Discussion <general at lists.
> natureoflightandparticles.org>
> *Subject:* Re: [General] light and particles group
>
>
>
> Hi Chip (and all),
>
>    Thanks for summarizing your approach to calculating electron spin from
> your model.
>
> You quoted Wikipedia:
>
>
>
>  Please see PHOTON in Wikipedia… *“The photon also carries a quantity
> called spin angular momentum that does not depend on its frequency. The
> magnitude of its spin is sqrt(2) hbar and the component measured along its
> direction of motion, its helicity, must be ±ħ.”*
>
>
>
> I did vector calculations for the total angular momentum L= R x p of both
> my spin 1 hbar and spin 1/2 hbar transluminal energy quantum photon models.
> The results were as follows for L^2 , which is the square of the total
> angular momentum of the photon models.
>
>
>
> For the spin 1 hbar photon model:     L^2 = 2 hbar^2  + (Et)^2  where E is
> the energy of the photon and t is the time (arbitrary starting time) for
> the mathematical helical motion of the energy quantum.
>
>
>
> For the spin 1/2 hbar charged photon model:   L^2 = 2 (hbar/2)^2 + (Et)^2
> for E and t as above.
>
>
>
> This shows that as t -> 0  (remembering that the starting point of t is
> arbitrary in the models, the above total angular momentum equations for the
> photon models reduce to  L= sqrt(2) hbar  for the spin 1 photon model and
> L= sqrt(2) (hbar/2) for the spin 1/2 photon model. This is the quantum
> mechanical result for the total spin of a spin 1 photon (as mentioned above
> in the Wikipedia quote) , remembering that Sz = hbar  and hbar/2 are the
> z-components of spin of a photon or electron respectively that are actually
> measured in photon and electron experiments. I had  never previously done
> these calculations for the total spin of my spin 1 and spin 1/2 charged
> photon models (whose equations are summarized in my recent article at
> https://www.academia.edu/30899196/Transluminal_Energy_
> Quantum_Model_of_a_Spin-_Charged_Photon_Composing_an_Electron ) which is
> attached below. So the fact that the result for the total spin sqrt(2) hbar
> of my spin 1 model photon is consistent with the quantum mechanical result
> for a spin 1 photon  is a very nice result. The expression (Et)^2 in the
> total angular momentum L^2 result is curious. But I think this part of the
> result is because in the calculation of L=R x p ,  R is measured from the
> origin (x=0, y=0, z=0) of the coordinate system in which the helical motion
> is given.  Since for large values of t,  R increases with time
> approximately as R=ct, while p = (E/c) sqrt(2) for the transluminal energy
> quantum of the photon models, the vector calculation of L= R x p =~  ct x
> (E/c) (sqrt (2)= Et is also increasing with time (which accounts for the
> (Et)^2 contribution to the total value of L^2 for both the spin 1 and spin
> 1/2 transluminal energy quantum photon models when t is large compared to
> the period t = 1/f of the photon.
>
>
>
> Chip, I also noticed in your calculation for the spin of your electron
> model in your email below,  you calculate the electron spin as s=r x p
> where p =E/c = gamma mc is the momentum of the helically moving photon. But
> we have seen that the transverse component of this total momentum p=E/c of
> the helically moving photon is only Ptrans = Eo/c = mc  and not E/c = gamma
> mc. So when this Ptrans=Eo/c is multiplied by r = (c h)/(4pi E)=(c
> h)/(4pi gamma Eo)  in your model, the result is S = r x Ptrans = h/(4 pi
> gamma) = hbar/(2 gamma) and not hbar/2 as you state below in your email.
> And you have apparently left out the contribution of the spin of the
> helically moving  photon itself in your calculation of the total spin of
> the helically moving photon model of the electron.
>
>
>
>   I hope this is useful.
>
>        Richard
>
>
>
>
>
>
>
>
>
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