Below I have included an edited version which should be more clear than
the original post.
From:
Neil
Topic:
The problematical nature of photon spin
Message:
1 of 9
Sent:
Wed, 1 Dec 1999 03:34:21 GMT
[NOTE: Edited and modified]
I wish to direct attention to what appears to be a very serious problem
concerning the spin of photons. The angular momentum of photons (hbar
each, regardless of energy) has been found to carry the equivalent of
literal angular momentum (Ref. the Richard Beth experiment, reported
1936 in Physical Review.) Furthermore, the spin of photons is presumed
to be directed either parallel or antiparallel to the direction of
propagation (s = +/hbar*unitk). There can be some ambiguity about this
for a single photon, but as N increases, the classical situation is
approached of a circularly polarized propagating wave. As far as we
know, the AM of such waves is parallel or antiparallel to the line of
propagation (who ever heard an optical physicist refer to the "angle of
tilt" of the spin with respect to the direction of the beam?) I refer
here to the spin component of AM (the part not dependent on a reference
point. Orbitaltype AM is dependent on the choice of reference point.)
Consider the case of pulses of CPol light emitted in opposite
directions from a source (as seen in its rest frame) of zero initial
spin AM. If both pulses are righthanded (relative to their respective
directions, of course), then the net angular momentum of the source
(and the system as a whole) remains unchanged. However, suppose that we
are observing this emitter from a reference frame in which the emitter
is moving rapidly in a direction perpendicular to its restframe
directions of propagation of the photons. For us, the two beams are
tilted in the direction of emitter motion, forming a "V" shape. If the
spin of photons actually must be parallel to the direction of
propagation  which is relative to the state of motion  then their
spins are tilted relative to their original orientations and no longer
cancel each other out. Specifically, there is now a component of
angular momentum in the direction of motion. This is not consistent
with the conservation of angular momentum! We started out with zero net
angular momentum, and that should be agreed upon by all observers
before and after emission, since there has been no interaction with the
outside world. (We could collect the spin from the photons.)
What makes other versions of this problem even more challenging than
the first one is that the perpendicular component of mechanical angular
momentum is relativistically transformed to be gamma factor times more
than the rest component. (Verify this for yourself by directly using
the velocity addition formulae and insert into s = sum of gamma*m*v*r
in the perpendicular axis case where the orientation and calculations
are simple.) This causes problems on its own because the acceleration
of a gyroscope can increase its spin "kinematically" without torque
input  c.f. the Thomas precession. Here I am interested in the
application to the photon problem. In a case where the photons were
opposite handed, their emission perpendicular to the line of motion
would leave net spin of the source. The spin of the source would be
increased by the gamma factor, but the spin of photons (which must
cancel out the spin of the source in any frame) is always hbar apiece.
The number of photons remains the same in all frames. Hence, not only
the direction but the magnitude of the photon spins will not be what we
need to fix things up!
Does anyone have any ideas about this? Is light more complicated than
we thought? Or is the conservation of angular momentum in trouble?
References to any prior posing/resolution/contention would be
appreciated along with your own views.
Neil Bates
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Your reasonings about the conservation of angular momentum are
probably the most unexpected thing I have ever read on these
forums.
Your two main postings:
http://www.deja.com/=dnc/getdoc.xp?AN=559426069
http://www.deja.com/=dnc/getdoc.xp?AN=559772601
Your argument that the photon spin cannot be parallel to the
propagation direction of the photon in all cases is intimately
related to stellar aberration. The simplest way to understand
the aberration principle consists in dealing with rain (without
wind) and a moving observer.
1 2 3 4 5 1 2 3 4 5
     / / / / / /
1 2 3 4 5 1 2 3 4 5
     / / / / / /
1 2 3 4 5 1 2 3 4 5
     / / / / /
X X'
>
Observer at rest observer moving wrt the medium
Whereas the observer at rest is only hit by raindrops of number 3
observer X' is hit by raindrops of increasingly higher numbers.
By replacing the raindrops by arrows we get two different
directions for the moving observer:
         
V V V V V V V V V V
/ / / / / /
         
V V V V V V V V V V
/ / / / / /
         
V V V V V V V V V V
And if we replace the arrows by photons with spin in direction
of the arrows, then we get your result of an "angle of tilt of
the spin with respect to the direction of the beam".
In any case I have now more understanding for the (otherwise IMO
absurd) claim that photons are pointlike particles. If photons
have a lenght of e.g. some wavelengths, wouldn't then 'Lorentz
Ether Theory' at least in principle allow to detect our movement
wrt the ether, because the central longitudinal axis (and maybe
even the pointing vector?) of the photons would be tilted wrt
their (apparent) propagation direction?
Cheers, Wolfgang
http://members.lol.li/twostone/E/physics1.html
Thanks for posting, Wolfgang.
If we imagine that the orientation of photon spins is the same in all
reference frames, then the fact that the direction of light travel
depends on observer motion means that photon spins can be tilted at an
angle relative to that direction. It may be true that photon spins are
indeed like that  which would allow conservation of angular momentum
in this case. However, everything known in optics and quantum mechanics
concerning the nature of circularly polarized light affirms that the
spins of photons (and the corresponding spin of pulses of many photons)
is in fact parallel to the line of motion of the light for any
observer. If so, then we have a problem for the conservation of angular
momentum because of the spin component produced in the direction of
motion of the source. Because of how light emitted from a source
behaves (constant velocity), the angle of tilt of the spins would
produce an anomalous change delta S in the angular momentum of the
system given by:
delta S = N*hbar*v/c *x^ ,
where N is the number of photons per pulse, and x^ is the unit vector
in the direction of motion of the source.
Here's the choice: we have to have either conservation of angular
momentum and then unknown new properties of light, or we keep light as
we think we know it, and lose conservation of angular momentum. I don't
know what nature does with this, but the theoretical conumdrum is
evident.
Neil Bates
 ////  / wave propagation
 ////  / wrt observer
 //// v v
 ////
 ////  wave front wrt
observer
waves wrt rest waves wrt
frame observer moving observer
>
Fig. 1
The observer at rest has no problem to determine the exact direction
to the source, because both the propagation direction and the line
perpendicular to the wave front point to the same direction.
The moving observer gets the correct direction to the source only in
the case he measures the wave front (the principle of the ears). If
he measures the propagation direction of the wave (the principle of
the eye), he will get an aberration shifted angle.
By using both methods he can determine his own velocity wrt the
medium (if the wave speed is known).
I suppose that radioastronomy has shown that the wave fronts show
the same aberration angles as the propagation directions.
Let us assume that the earth moves at 300 km/s = 0.001 c wrt the rest
frame of a star. The direction from the star to the earth is
perpendicular to the earth's surface which is parallel to the earth's
velocity wrt the rest frame.


v
 surface of the earth = x'frame
> movement wrt rest frame
Fig. 2
SR (in the same way as 'Lorentz Ether Theory') predicts an aberration
angle for the propagation direction of light from the star. But what
about the wave fronts of radio waves?
In order to determine the direction of the wave front we measure the
arrival of the same wave front at different locations. We expect that
a front arrives at first at higher values of the x'coordinate.
/
/
. v
.
. x'coordinate
> .
Fig. 3
This is exactly what SR (and LET) predicts, because the simultanous
arrival of the wave front in the rest frame (Fig. 2) is not
simultanous in the earth's frame:
t' = t  0.001/c * x (gamma can be neglected)
Wolfgang Gottfried G.
Yes. The moving observer also observes a positiondependent phase
offset compared to the mediumrestframe observer. But it doesn't
affect your analysis significantly. This is just a different way of
saying that to the moving observer the wave crests are not
perpendicular to the wave's propagation direction. The details
depend upon the observer's relative velocity wrt the medium and wrt
the wave direction in the medium.
> [...]
> The moving observer gets the correct direction to the source only in
> the case he measures the wave front (the principle of the ears). If
> he measures the propagation direction of the wave (the principle of
> the eye), he will get an aberration shifted angle.
Unless the wave satisfies Maxwell's equations in vacuum and has
propagated for many wavelengths (so it's not near field). In that
case, both observation methods give aberrationshifted angles, because
the E and H fields are orthogonal to the Poynting vector and so are
their wave crests. One could also say this is so because the Maxwell's
equations are Lorentz invariant.
Ditto for QED.
> I suppose that radioastronomy has shown that the wave fronts show
> the same aberration angles as the propagation directions.
Stellar aberration is observed at all wavelengths, including verylong
baselineinterferometry, which should easily observe the variations you
seek (when the baseline is parallel to the earth's orbit), but doesn't.
If the effect you claim actually happened, the rotation of the earth
would completely negate VLBI (they average over many hours for noise
reduction). The aberration angle of ~20 arcseconds is _enormous_
compared to their angular resolution; it's large even to optical
instruments. In fact, if the effect you claim were true, I doubt it
would be possible to focus any large telescope on any star at all!
So does your analysis disprove the ether?  No. LET survives, as does
SR and every ether theory in the class of theories I discuss. Your
analysis does refute several simple ether theories, but they were
already refuted long ago.
Your analysis also highlights a difference between water waves and light
waves. But most of us already knew they were different (:)).
Tom Roberts tjro...@lucent.com
Good post on an important topic. The answer to your final
question {is light [ and Professor Berry reminds us that
the photon is the simplest quantum object known ] more
complex than we think?} is yes if you listen to those who
pretend to describe photons without pictures. The tilt you
mention is very real. Here is away to say what Professor
Berry discovered in the mid 1980s. The question of
independence [usually described as perpendicularity in
polarization] and matched polarization is more complex
than was previously understood until his discovery of
Berry Phase. I call it the HV [ Hamilton Visualization]
because it is a rediscovery of Hamilton's work from the
mid 1800s. You won't get much response on the questions
in these forums because little is known by the
participants about Berry Phase. John Baez, who you
mentioned, has commented on it in one of his weeks.
There is extensive literature,try LANL preprints,
especially in theoretical physics and the book of
articles including originals from Professor Berry by
World Scientific titled "Geometric Phases in Physics".
Good seeing. JD

Sent via Deja.com http://www.deja.com/
Before you buy.
: If we imagine that the orientation of photon spins is the same in all
: reference frames, then the fact that the direction of light travel
: depends on observer motion means that photon spins can be tilted at an
: angle relative to that direction. It may be true that photon spins are
: indeed like that  which would allow conservation of angular momentum
: in this case.
Special Relativity is based on the assumption that only two directions
are involved in electromagnetic radiation:
1) the propagation direction
2) the direction of the wave front
The angle between these two directions remains orthogonal under the
Lorentz transformation.
The photon spin constitutes a third direction (an axis of the
radiation), and for very obvious reasons such an axis does change its
angle wrt the propagation direction under the Lorentz transformation.
See my previous posts for details:
http://www.deja.com/=dnc/getdoc.xp?AN=560135431
http://www.deja.com/=dnc/getdoc.xp?AN=561141721
: However, everything known in optics and quantum mechanics
: concerning the nature of circularly polarized light affirms that the
: spins of photons (and the corresponding spin of pulses of many photons)
: is in fact parallel to the line of motion of the light for any
: observer.
I am in general very skeptical of the spin concept. Im my opinion it
doesn't make sense to attribute on the one hand the quantity hbar to
each single photon and on the other hand to believe in Heisenberg's
uncertainty principle which denies the empirical relevance of such a
small quantum.
And the assumption that all photons have the same spin despite of
having energies which vary over many many orders of magnitude seems
rather absurd to me.
I also do not believe in circularly polarized photons. Jackson's
'Classical Electrodynamics', Second edition, 7.2, introduces
circularly and elliptically polarized waves as a combination of
linearly polarized waves. I see no convincing reasonings or
empirical evidence suggesting that circularly polarized radiation
is not simply composed of linearly polarized photons.
: If so, then we have a problem for the conservation of angular
: momentum because of the spin component produced in the direction of
: motion of the source.
I suppose that the concept of angular momentum does not belong
to the classical theory of e.m. waves. Have you ever heard that
the angular momentum of a beam of a given energy is INVERSELY
proportional to the frequency of the radiation?
I think that your PHOTON SPIN PARADOX is evidence against both
photon spin and angular momentum of e.m. radiation.
Linearly polarized beams carry no obvious angular momentum, do they?
If they do not, then also a combination of two beams resulting in
circularly polarized light cannot carry angular momentum, can it?
Gruss, Wolfgang
Not in QED. And that's basically the only theory in which photons
appear or are defined. In QED the spinor components are intermixed by
a Lorentz transform, in precisely the proper amount to keep the photon
spin aligned with its direction of motion in any inertial frame.
> then we have a problem for the conservation of angular
> momentum because of the spin component produced in the direction of
> motion of the source.
Not really. You just need to compute components of angular momentum in
_the_same_ direction.
> Here's the choice: we have to have either conservation of angular
> momentum and then unknown new properties of light, or we keep light as
> we think we know it, and lose conservation of angular momentum. I don't
> know what nature does with this, [...]
What nature "truly does" is unknowable to us mere humans, but I know what
QED does with this, and it's not what you claim. In QED angular momentum
is indeed conserved, and photon spins must behave as QED predicts or that
would not be possible.
Tom Roberts tjro...@lucent.com
True.
> The photon spin constitutes a third direction (an axis of the
> radiation), and for very obvious reasons such an axis does change its
> angle wrt the propagation direction under the Lorentz transformation.
This is not true in QED. The spinor components are intermixed by a
Lorentz transform in such a way to keep the photon spin aligned with
its direction of propagation.
Yes, in classical E&M the polarization vector of an E&M wave is
independent of its propagation direction. Yes, the angle between
polarization and propagation can change under a Lorentz transform.
But angular momentum will still be conserved (other angular momentum
vectors also change directions under that Lorentz transform).
> I am in general very skeptical of the spin concept. Im my opinion it
> doesn't make sense to attribute on the one hand the quantity hbar to
> each single photon and on the other hand to believe in Heisenberg's
> uncertainty principle which denies the empirical relevance of such a
> small quantum.
Without photon spin one cannot conserve angular momentum in atomic
transitions (which emit photons). Heisenberg's uncertainty principle
does not say what you seem to think.
> And the assumption that all photons have the same spin despite of
> having energies which vary over many many orders of magnitude seems
> rather absurd to me.
Maybe Nature does seem "absurd" to you, but She is under no constraint
to behave as you would wish. In order to conserve angular momentum in
both atomic and nuclear transitions, the photon must have spin 1 even as
it varies over many order of magnitude in energy. This has been solidly
established over many decades of atomic and nuclear spectroscopy.
> I also do not believe in circularly polarized photons. Jackson's
> 'Classical Electrodynamics', Second edition, 7.2, introduces
> circularly and elliptically polarized waves as a combination of
> linearly polarized waves. I see no convincing reasonings or
> empirical evidence suggesting that circularly polarized radiation
> is not simply composed of linearly polarized photons.
Jackson is not discussing photons, he is discussing classical
electrodynamics (note the title of his book!).
In fact, there _IS_ no evidence about what you claim  photons are
a theoretical construct, and you are free to project them onto a
linearlypolarized basis or onto a circularlypolarized basis. Both
give the same prediction for any observable quantity, of course.
> I suppose that the concept of angular momentum does not belong
> to the classical theory of e.m. waves.
Yes, it does. Jackson surely covers it (but I haven't looked). Think
about it  _anything_ which carries momentum must also be capable of
carrying angular momentum; look up the Poynting vector, which
quantifies the momentum of a classical E&M wave.
> Have you ever heard that
> the angular momentum of a beam of a given energy is INVERSELY
> proportional to the frequency of the radiation?
Not particularly. Why would you think so? I think in classical E&M it
would depend upon how the beam is generated. In QED this is (loosely)
so because the number of photons is not the same for equaltotalenergy
beams of different frequencies, but again it depends upon how the beam
is generated.
> I think that your PHOTON SPIN PARADOX is evidence against both
> photon spin and angular momentum of e.m. radiation.
I think it is really a lack of understanding of what photons are
in modern physics.
> Linearly polarized beams carry no obvious angular momentum, do they?
> If they do not, then also a combination of two beams resulting in
> circularly polarized light cannot carry angular momentum, can it?
Yes. Think about how you must manipulate the charges generating
the wave and you will be able to figure it out (classically, of
course)  to sum two linearlypolarized waves to have circular
polarization they must be (loosely) 90 degrees out of phase; that
is equivalent to moving the charges circularly.
Tom Roberts tjro...@lucent.com
This is only correct if the source is stationary in the medium.
In the case where you have the source and the detector stationary
to each other, but with the medium flowing past them, then
wavefronts will _not_ be perpendicular to the direction to
the source in the source/detectors stationary frame.
You can interpret this as an anisotropy in the medium in
the source/detector frame.
> By using both methods he can determine his own velocity wrt the
> medium (if the wave speed is known).
>
> I suppose that radioastronomy has shown that the wave fronts show
> the same aberration angles as the propagation directions.
Right.
> Let us assume that the earth moves at 300 km/s = 0.001 c wrt the rest
> frame of a star. The direction from the star to the earth is
> perpendicular to the earth's surface which is parallel to the earth's
> velocity wrt the rest frame.
>
> 
> 
> v
>
>  surface of the earth = x'frame
> > movement wrt rest frame
>
> Fig. 2
>
> SR (in the same way as 'Lorentz Ether Theory') predicts an aberration
> angle for the propagation direction of light from the star. But what
> about the wave fronts of radio waves?
SR (+ Maxwell) predicts that the wavefronts will be
perpendicular to the wave vector (direction of propagation)
in any frame of reference.
Thus the aberration of the wavefronts will be the same as
the aberration of the direction.
> In order to determine the direction of the wave front we measure the
> arrival of the same wave front at different locations. We expect that
> a front arrives at first at higher values of the x'coordinate.
>
> /
> /
> . v
> .
> . x'coordinate
> > .
>
> Fig. 3
>
> This is exactly what SR (and LET) predicts, because the simultanous
> arrival of the wave front in the rest frame (Fig. 2) is not
> simultanous in the earth's frame:
>
> t' = t  0.001/c * x (gamma can be neglected)
Right.
(But for a typo. v = c*10^4 assuming solar frame to be "rest frame"))
You may explain why the wavefront will be perpendicular to
the wave vector in any frame this way.
However, stellar aberration do _not_ falsify the Galilean ether
you started out with, not even if you consider your wavefronts.
There _is_ a difference, but the difference is not measurable.
SR pedicts arcsin(v/c) while "Galilean ether" predicts arctan(v/c).
With v/c = 10^4, the difference is minute (ca. 5*10^13 radians).
So why can the "Galilean ether" explain why the non aberrated
wave front is received by a parabolic radio antenna which is at
an angle to the wave front? The reason is that the anisotropy of
the medium due to it's motion. The waves reflected from the
"upstream" part of the antenna will arrive at the focal point
faster than the the light reflected from the "downstream" part
of the antenna. To compensate for that, the antenna must have
an angle to the wave front. You can analyse any kind of antenna
you like, and you will find that the antenna must always point
in the direction of propagation, and _not_ perpendicular to
the wave front, to receive the signal.
This is in fact the reason why a directional light source in
"Galilean ether" always will emit light in the direction of
it's optical axis, unaffected by any ether wind.
So stellar aberration does not falsify a Galilean ether.
But since this ether is falsified by experiments like MMX,
it is not very interesting.
Paul
:: According to classical wave theory, a movement wrt a medium
:: results in two different wave directions depending on the way
:: of measurement.
::
::  ////  / wave propagation
::  ////  / wrt observer
::  //// v v
::  ////
::  ////  wave front wrt
:: observer
:: waves wrt rest waves wrt
:: frame observer moving observer
:: >
:: Fig. 1
::
:: The observer at rest has no problem to determine the exact direction
:: to the source, because both the propagation direction and the line
:: perpendicular to the wave front point to the same direction.
::
:: The moving observer gets the correct direction to the source only in
:: the case he measures the wave front (the principle of the ears). If
:: he measures the propagation direction of the wave (the principle of
:: the eye), he will get an aberration shifted angle.
:
: This is only correct if the source is stationary in the medium.
I don't think that the movement of the source is relevant. By
"direction to the source" I mean "direction to the source at emission
time". Wrt the medium the wave fronts are always perpendicular to
the propagation direction, aren't they?
: > In order to determine the direction of the wave front we measure the
: > arrival of the same wave front at different locations. We expect that
: > a front arrives at first at higher values of the x'coordinate.
: >
: > /
: > /
: > . v
: > .
: > . x'coordinate
: > > .
: >
: > Fig. 3
: >
: > This is exactly what SR (and LET) predicts, because the simultanous
: > arrival of the wave front in the rest frame (Fig. 2) is not
: > simultanous in the earth's frame:
: >
: > t' = t  0.001/c * x (gamma can be neglected)
: You may explain why the wavefront will be perpendicular to
: the wave vector in any frame this way.
If it is explained classically as you suggest then one must not
explain it a second time by a SR first order effect.
: However, stellar aberration does _not_ falsify the Galilean ether
: you started out with, not even if you consider your wavefronts.
Are you sure? Look again at Fig. 1. If the moving observer starts
moving in the opposite direction, the direction of the wave fronts
remains unchanged. In my opinion, stellar aberration of wave fronts
constitutes maybe the most simple and convincing argument for
relativity of simultaneity.
: So why can the "Galilean ether" explain why the non aberrated
: wave front is received by a parabolic radio antenna which is at
: an angle to the wave front? The reason is that the anisotropy of
: the medium due to it's motion. The waves reflected from the
: "upstream" part of the antenna will arrive at the focal point
: faster than the the light reflected from the "downstream" part
: of the antenna. To compensate for that, the antenna must have
: an angle to the wave front. You can analyse any kind of antenna
: you like, and you will find that the antenna must always point
: in the direction of propagation, and _not_ perpendicular to
: the wave front, to receive the signal.
What you describe is analogous to the roundtrip light speed
(radio telescope with focal point) whereas I mean something
analogous to the oneway light speed (radiointerferometer using
wire waves). The angular resolution of radiointerferometry is
much higher than the one of ordinary radio telescopes.
: So stellar aberration does not falsify a Galilean ether.
: But since this ether is falsified by experiments like MMX,
: it is not very interesting.
I'm not knowledgeable about radioastronomy, but I suppose that
wave fronts themselves have been measured precisely enough to
refute a static medium of electromagnetic radiation.
Gruss, Wolfgang
http://members.lol.li/twostone/E/physics1.html
Most astronomical observations are repeated.
> If it is explained classically as you suggest then one must not
> explain it a second time by a SR first order effect.
Classical and SR are different theories. Each must explain every
experimental observation. This is much easier when a new theory
includes the old one in an appropriate limit.
> I'm not knowledgeable about radioastronomy, but I suppose that
> wave fronts themselves have been measured precisely enough to
> refute a static medium of electromagnetic radiation.
I do not think they are accurate to 10^13 radian, which is what
would be required to do that. But other experiments do refute
such a static medium.
Tom Roberts tjro...@lucent.com
That was not my impression of the thread.
At least one poster pointed out the difference between
conservation and invariance.

James A. Carr <j...@scri.fsu.edu>  Commercial email is _NOT_
http://www.scri.fsu.edu/~jac/  desired to this or any address
Supercomputer Computations Res. Inst.  that resolves to my account
Florida State, Tallahassee FL 32306  for any reason at any time.
Ironically, Tom, you are explaining exactly why my paradox is real
after all. Measure angular momentum along the line of motion of the
source. Originally the source has no angular momentum, in either its
rest frame or the moving frame (this last point confused some
respondents.) It emits the pulses of CPol light which go in opposite
directions as seen in the rest frame. But in the moving frame, it is
moving (still without AM), and the light paths are now diagonal. If
their spin AM is parallel to those new directions of propagation, then
conservation of AM is not held since the vectors of light AM no longer
add to zero. (This is simple geometry, Tom. There is really no way out,
except perhaps to say that the orbital AM uncertainty of the pulses
overwhelms their spin AM  but that would just be random smearing, and
relative to reference point, not a specific counteracting vector.)
...
> > then we have a problem for the conservation of angular
> > momentum because of the spin component produced in the direction
> of
> > motion of the source.
> Not really. You just need to compute components of angular
> momentum in
> _the_same_ direction.
I'm not sure what you mean here. I have referred directly to the
orientations of the restframe versus the moving frame vectors of AM of
the light pulses, and it is a case of the vectors in the latter case
not adding up to zero, but having a component in the direciton of
motion of the source. Just like so: /
\
If you don't agree, please distinguish yourself from all of my other
respondents by actually showing how to fix things up, instead of just
talking loosely about how the fix might happen. (That includes posts in
other discussions about this, such as "Photon spin: no problem," etc.)
I don't think you can, not because of any lack of ability, but because
the problem can't be solved with what is now known about the subject.
Neil Bates
To me the question of the spin of the photon is not so
straightforward. It seems that the photon normally referred to has an
almost constant spin around 1. But there are other types of photons,
for instance those elated to gravity action  I think they are
conventionally called gravity waves. I think the spin issue is complex
for these waves, and I am not yet in the clear how to discuss their
spin.
In neither case would there be any problems with the continuity of the
angular momentum.
Download files at www.evolus.org contain a lot of material related to
these questions. One pertinent item would also be Pauli's exclusion
principle  a phenomenon created by photons.
Best regards
Willie
He did not say that the spin is an invariant, only that you
can use a helicity basis. Why you ignore the information given
to you in the sci.physics.research thread is unclear, but you
have done so. There is no paradox.