[General] double photon cycle, subjective v objective realities

John Duffield johnduffield at btconnect.com
Wed Jul 13 00:31:13 PDT 2016


John W:

 

I’ve tried to describe spin at various times. See for example this:
http://physics.stackexchange.com/a/172447/76162. We start off with your
toroidal photon, but a gif rather than static image: 



 

See Adrian Rossiter’s torus animations:
http://www.antiprism.com/album/860_tori/index.html. Then you mentally
inflate it like an inner tube:  



Keep inflating until you’ve got a spherical symmetry which matches
experiment:



This also matches the S-orbital depiction:

 



 

Note that because you started with a sinusoidal field variation and you
wrapped it into a spin ½ double loop, every point in the loop is the sum of
two field-variation components. These add up to the same field variation all
round, and the result is a standing field. See this in chapter 27 of "The
Feynman Lectures on Physics Volume II: Mainly Electromagnetism and Matter":

 

“Finally, in order to really convince you that this theory is obviously
nuts, we will take one more example — an example in which an electric charge
and a magnet are at rest near each other — both sitting quite still. Suppose
we take the example of a point charge sitting near the center of a bar
magnet, as shown in Fig. 27-6 Everything is at rest, so the energy is not
changing with time. Also, E and B are quite static. But the Poynting vector
says that there is a flow of energy, because there is an E X B that is not
zero. If you look at the energy flow, you find that it just circulates
around and around. There isn't any change in the energy anywhere —
everything which flows into one volume flows out again It is like
incompressible water flowing around. So there is a circulation of energy in
this so-called static condition. How absurd it gets!”  

 

Re your email, some good stuff there, many thanks. But might I politely
point out that if you add a photon you add energy: the spin up or down of an
electron combined with a proton is not quite the same thing as the spin of
an electron all on its own. IMHO a spin flip is a bit like turning a rubber
torus over when it’s elastically attached to something in the middle. 

 

Regards

JohnD

 

From: General
[mailto:general-bounces+johnduffield=btconnect.com at lists.natureoflightandpar
ticles.org] On Behalf Of John Williamson
Sent: 13 July 2016 06:11
To: Nature of Light and Particles - General Discussion
<general at lists.natureoflightandparticles.org>
Cc: Nick Bailey <nick at bailey-family.org.uk>; Mark, Martin van der
<martin.van.der.mark at philips.com>
Subject: Re: [General] double photon cycle, subjective v objective realities

 

Ok Richard, I will try,

 

Gentlemen, I think you are entirely missing the point about (quantum) spin.
It is not primarily about a value. It is primarily about the (experimental)
fact that it comes in two varieties “up” or “down”. These two states follow
an exclusion principle. 

 

In other words the spin of an elementary electron or proton is in no way
like a little spinning top. Forget about it. Not even close. In no way an
analogy. 

 

It is BOTH far far smaller (pretty much zero) and far far bigger than that,
of which more later.

Hopefully, this does not come as a complete surprise. You all already know
this to be true.

Now the important experimental stuff for spin comes from (at least) four
different fields. I cannot teach you all (or any!) these in an email. In
fact, aspects of these I could not teach you at all as I do not master all
of them and some of you know more about one or two of them than do I.
Ignorance knows (little or) no bounds! However I am (supposed to be) expert
in a couple of the relevant fields so - with that disclaimer here goes 


 

Firstly, the strongest evidence (as far as I know – this is not my field)
for the value and the coupling of the photon spin and electron spin comes
from atomic and molecular physics and the “allowed” transitions emitting and
absorbing photons.  The limiting “spin” of the electron and photon is
strongly related, in that (if one accepts angular momentum conservation) one
is half (or double) the other. The analogy is a spin up” system (+1/2) emits
a spin 1 photon (+1) flipping to spin down (-1/2). The photon is
subsequently absorbed by a spin “down” which flips to a spin “up”. This is
just a sketch, and of course lots of transitions which are not “allowed” do
happen – but they have probabilities which are much lower. Anyway, in this
context it  could look as though “spin” was a purely electromagnetic
phenomenon. This would be the world-view one came away with if this was all
one knew.

 

The big surprise is, if one steps out of this field and looks at others,
that spin is not just characteristic of the electromagnetic “strength”. It
is strong. It is stronger than strong!

Before discussing the evidence for that note that the experimental
properties of spin have been the starting point for many beautiful theories.
Alex, for example, has used this. In this he has been following Kerr, Newman
Carter and others – all beautiful and short! papers. He argued in 1973 that
if the spin density is what it is there must be some strong force at play.
He and others have ascribed this to gravitation, within the framework of GR.
Though others, Carter for example, attribute this to a breakdown of the
theory of gravitation. Whatever the “force” confining the spin is it
certainly large. This is not to mention the (infinitely) large forces one
needs to contain a point charge. This is a point where Alex and I disagree
(though it is only in a name) – for me gravitation is a weak thing – I would
just prefer to call the strong stuff something else to avoid confusion.
Effectively, Martin and also started from this in our 1997 paper, noting
that if the initial photon was spinning at one unit, the resultant
double-loop electron spun with half a unit.

 

Anyway, this is the task at hand, gentlemen, one needs (eventually) to
explain all of this simultaneously, not just bits of it. 

 

Another beautiful, and more recent theory in another field also takes spin
as a starting point. This is Carver Mead’s “Collective electrodynamics”.
Also very beautiful and I recommend you all read it. He takes spin as a
central paradigm in solid state physics and derives much of value and beauty
from this.

 

However I diverge a bit. Lets get back to what is known from experiment, and
in particular with what happens at high energy.

 

This is completely astonishing.

 

Firstly one must realize that there is no difference in the energy of an
elementary particle for spin “up” or “down”. I do not mean “no difference”
figuratively here. The energy difference is zero. One only observes a
difference at all in the presence of an external magnetic field – and this
is a tiny tiny fraction of the mass-energy of the particles concerned. Now
one can prepare a set of particles in a given spin state rather easily
electromagnetically – and with very low energy input (like zero!). If one
does this, and subsequently accelerates the spin up or spin down particles
while maintaining that spin and then bash them into one another, things at
least as amazing as what happened in Rutherfords experiment happens. One
expects very little at the scale of the strong interaction. One has only
inputted a little eentsy bit of energy into the spin component far away and
long ago. All gone now. For this reason one does not really measure the
(tiny) spin of an elementary particle as a number in HEP – one observes its
effects – and these are astonishingly large.

 

What actually happens in collisions is MONSTROUS.

 

This was first done at the zero gradient synchrotron at Argonne (the clue of
maintaining the spin is in the name). Look at Scientific American May 1979.
Nice pictures. Shocking. Disproves the quark model! Oh dear.

 

Take the probability of scattering of unpolarised protons on protons as a
base. Call it 1. Remember this scattering is dominated by the strong
interaction at high energies. At 4-momentum transfers of the order of the
proton mass the spin parallel probabilty is about 2 and for spin
antiparallel about a half.  It is as if one had wrapped ones tank in blue
cling film – and discovered that shells then passed right through it half
the time, whereas if one used red cling film the shells tended to blow it
up, even if they missed it a bit. Further, if one tries to decompose the
results in terms of the internal parton (quark) spin it does not work at
all. The quark model breaks down. It was largely the complete refusal of the
HEP community to accept this experimental fact and chase it down that led me
to leave it in disgust in the mid eighties.

 

Experimentally, more astonishing still one finds a beautiful resonance, a
little below the proton mass-energy, where the protons become even more
transparent. Utterly astonishing (and still completely unexplained)
behavior. Look at it! Quantum spin is crucial. The “exclusion principle” is
not infinitely potent, but remains potent up to energies exceeding the total
mass-energy of the elementary particles themselves. Further, there is very
clear structure (in energy) in its potency. Explain that! We do in terms of
the double-loop model – see below.

 

Subsequent experiments using polarised targets and polarized beams all found
such kinds of behavior. Conclusion: whatever spin is it is involved with
generating interactions as strong or stronger than the so-called strong
interaction. Conventionally, one ascribes these to “exchange” forces though
the detail of what is supposedly exchanged in the framework (of QCD, for
example) throws up serious contradictions in the detail. Normally, this
would have meant that one threw away ones theory and came up with something
better, but the scientific method seems to have gone out of fashion in these
circles and this has yet to happen (to my knowledge).

 

Coming back to our discussion. Even if one could line up the whole electron
or proton as a pure spinning top, oriented with spin up (in the classical
sense) one would not observe anything like this. The energy would be limited
to the energy in the spin. One sees much more. These particles do not behave
AT ALL like little spinning tops. NO way. Not a bit. Forget about it!

 

In the context of solid state physics one also sees astonishing effects
associated with spin. Mad magnets. Spin blockade in quantum dots.
Ridiculously high Tc superconductors. Giant magneto-resistance. Lots more
“exchange” stuff way beyond standard QM or EM.

 

Conclusion: a proper understanding of the underlying nature of quantum spin
will prove crucial in developing a proper theory of how it all works. 

 

Martin and I have explained these effects with our models in terms of the
interference of the internal fields of the elementary particles – doubling
the mass-energy if the interference is precisely in phase (leading to an
exclusion) and giving zero energy if in antiphase. We talked about this in
our early work leading to the 1997 paper. I talked about this at CYBCOM in
2008 and presented a paper arguing this in 2012 (proceedings of MENDEL
2012). This is how one makes fermions from bosons – tie them up into a
double loop. Martin has been looking at this in more detail in the context
of much weaker overlaps in the solid state. 

 

So – if one looks one sees effects larger even than the E = hbar nu one
would ascribe to the full mass energy of the elementary particles. This is
something I should have mentioned before. In the formula above hbar takes
the role of an elementary, quantized angular momentum. That is the angular
momentum (spin energy) accounts for ALL the energy of the photon. In this
sense, for a circularly polarized photon, all of its energy is rotational.
This does not mean that the photon is rotating like a little massive ball on
a stick. Not at all. No ball. No stick.  It is the EM field that carries the
rotation. The rotation appears at its simplest, as the differential of the
(perpendicular) differential of a (perpendicular) vector.  More properly,
one may wish to see it (as measured in experiment) as the differential of
one vector times the differential of the differential of another (at least
another phase (loop)). I said before the rotation “axis” must be viewed as
at least complex, and in my view more complex than complex (complex is only
2D and one needs at least 4 dimensions to describe it dynamically)  to give
any hope of explaining the body of experimental facts. Three complex vectors
would do it (for example). Cheers Alex – but I think one could make it
simpler that that! 

 

Gentlemen, coming back to the discussion about the spin of the moving
electron -if we take angular momentum to be conserved then the spin of an
electron passing you fast is exactly the same as one passing you slow as JD
said as – think about it – you have not spun it up or down by accelerating
yourself. One may wish to try to explain this in terms of the spin of tops,
relativistic or otherwise (also conserved) but one is then not getting into
a discussion about the really interesting stuff about spin at all.

 

Regards, John.

  _____  

From: General
[general-bounces+john.williamson=glasgow.ac.uk at lists.natureoflightandparticl
es.org] on behalf of John Duffield [johnduffield at btconnect.com]
Sent: Tuesday, July 12, 2016 7:23 PM
To: 'Nature of Light and Particles - General Discussion'
Subject: Re: [General] double photon cycle, subjective v objective realities

 

Can I chip in to say that IMHO Compton scattering takes  a “slice” off the
photon and gives it to the electron in an asymmetrical fashion. As a result,
the electron moves. It moves because it’s a circulating photon that’s no
longer a symmetrical circulating photon. It’s hard to visualize this, but
simplify the electron to a photon going round in a circular path. When
Compton scattering occurs, energy is added so the wavelength reduces, but
asymmetrically. It’s like drawing say 355 degrees of a circle, then without
lifting your pen, drawing another 355 degrees of a circle, and so on:

 



 

As for the exact details of what happens with a fast-moving electron, I’m
not sure. I am reminded of extending a slinky, but I know that an electron
doesn’t change just because I move past it fast. And I wish that all
physicists only had that to disagree upon. 

 

Regards

JohnD

 

From: General
[mailto:general-bounces+johnduffield=btconnect.com at lists.natureoflightandpar
ticles.org] On Behalf Of Chip Akins
Sent: 12 July 2016 16:25
To: 'Nature of Light and Particles - General Discussion'
<general at lists.natureoflightandparticles.org
<mailto:general at lists.natureoflightandparticles.org> >
Subject: Re: [General] double photon cycle, subjective v objective realities

 

Hi Again Grahame

 

One issue I have been contemplating is the “spin mode” of the energy in the
photon and the electron.

 

You said
”[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.]”

 

But perhaps that is not a “quick fix” at all.  It may well be that
characterizing the electron as a confined photon is actually a quick fix and
that the energy in the electron is configured in a completely different
“spin mode” than that of the photon. We already know that the electron spin
is, at the very least, different than the photon spin, so we might be trying
to force fit the photon solution where it does not apply at all (except that
the energy can be configured in two completely different stable modes).

 

Thoughts?

 

Chip

 

From: General
[mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.
org] On Behalf Of Dr Grahame Blackwell
Sent: Tuesday, July 12, 2016 8:24 AM
To: Nature of Light and Particles - General Discussion
<general at lists.natureoflightandparticles.org
<mailto:general at lists.natureoflightandparticles.org> >
Subject: Re: [General] double photon cycle, subjective v objective realities

 

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 <mailto:richgauthier at gmail.com>  

To: Nature of Light and Particles - General Discussion
<mailto:general at lists.natureoflightandparticles.org>  

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
<mailto: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 <mailto:richgauthier at gmail.com> 

To: Nature of Light and Particles - General Discussion
<mailto:general at lists.natureoflightandparticles.org> 

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
<mailto: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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