Moment of the Poynting vector is not spin


A common opinion that moment of the Poynting vector is spin is a common
delusion. A Laguerre-Gaussian beam without an azimuth phase structure
is used for proving this. This delusion causes many conflicts,
vagueness, and paradoxes concerning electromagnetic angular momentum.
Meanwhile, spin is present obviously in a circularly polarized light.
But the standard electrodynamics has not caught sight of it. Standard
spin tensor is zero. The only way to resolve the paradoxes is to use an
electrodynamics spin tensor.

-----It is a matter of common opinion that
j = r x <ExB> (1)
encompasses both the spin and orbital angular momentum density of
electromagnetic field. In particular, they think that a circularly
polarized Laguerre-Gaussian beam without an azimuth phase structure,
for example, with the mode indices l = 0, p = 1 has only spin angular
momentum density
s = r x <ExB>,
and has no orbital angular momentum [1], [2 p. 299], [3 - 6]. But,
this LG mode contains one dark ring of radius r_1 = \sqrt{1/2}, and we
have <ExB>^\phi > 0 for r < r_1 and for r > r_2 = \sqrt{3/2}, and
<ExB>^\phi < 0 for r_1 < r < r_2. This shows clearly that a moment of
the Poynting vector is dependent of the choice of origin.
Zambrini and Barnett [6] calculate the moment of a part of a beam
relative to the beam axis, but a translation of the coordinate system
changes this moment. This shows clearly that a moment of the Poynting
vector is not intrinsic angular momentum, i.e. a moment of the Poynting
vector is an orbital angular momentum rather than spin.
-------If a target absorbs our beam, the target experiences a density
of orbital forces. The component of the Maxwell tensor [7, p. 609]
shows that these forces are positive if the Zambrini's part of the beam
is in the domain r < r_1 or r > r_2, but these forces are negative in
the middle domain r_1 < r < r_2. Note that the middle domain is twice
as big as the central disk.
-------Imagine that the target is divided into three concentric parts
by circles of r_1 and of r_2. Then the inner disk (r < r_1) and the
outer ring (r > r_2) should rotate clockwise, but the middle ring (r_1
< r < r_2) should rotate anticlockwise. Reasoning along similar lines
we must conclude that small particles, which are trapped off axis near
the circle of maximum intensity at r_2, should not orbit the beam axis.
But when diffusing towards r < r_2 they should orbit anticlockwise,
while when diffusing towards r > r_2 they should orbit clockwise. This
proves that the force (8) bears no relation to a spin.
--------It is easy to calculate power P(r) and torque \tau(r) which the
target accepts. This calculation shows that there is lack of torque in
central parts of the target. A part of the target near the axis almost
does not receive the angular momentum. Using two terms of the Taylor
expansion yields that the ratio \tau(r)/P(r) = 0. In other words, the
central part receives energy, but does not receive the angular
momentum. This proves once more that the angular momentum (1) is an
orbital angular momentum rather than spin. Attention was paid on this
fact in [8].
--------At the same time, if we isolate the small central part of the
target and illuminate it by the beam or by a plane circularly polarized
wave, the part will receive j (1) per unit time that equals to P/\omega
because -j per unit time will be carried away by the edge of the
part's shade. It was explained in [9]. However, neither plane wave
nor our beam in its central part carry the angular momentum of a type
(1). Thus this angular momentum (1) is not spin.
--------Meanwhile, spin is present obviously in a circularly polarized
light. But the standard electrodynamics has not caught sight of it.
Standard electrodynamics' spin tensor is zero. This causes many
conflicts, vagueness, and paradoxes concerning electromagnetic angular
momentum. I quote here some evidences of this phenomenon.
"Experimental observations appear to be in conflict with theoretical
considerations" [6].
"If the above expression (1) was in fact the correct angular momentum
flux density, then the angular momentum of a circularly polarized plane
would be zero. Since the correct classical angular momentum density
must agree with the classical limit of the quantum angular momentum
density, this must be incorrect." [10]
"The angular momentum of a classical electromagnetic plane wave of
arbitrary extent is predicted to be exactly zero. However, finite
sections of circularly polarized plane waves are found experimentally
to carry angular momentum." [11]
"A circularly polarised plane wave has a linear momentum density only
in the z-direction. When this is crossed with r to give the angular
momentum density, there is no contribution in the z-direction. Thus,
such a beam has no angular momentum to transfer to a waveplate, yet,
Beth was able to make such a transfer - a paradox." [3]
The only way to resolve the paradoxes is to use the electrodynamics
spin tensor [12 - 14]. The spin tensor explains the Beth's
experiment. The use of the spin tensor is presented at web sites
www.mai.ru/projects/mai_works, www.sciprint.org.

The spin tensor was submitted to "JETP" on Jan. 27, 1999. It was
rejected more than 350 times by scientific journals. For example (I
show an approximate number of the rejections in parentheses): JETP
Lett. (8), JETP (13), TMP (10), UFN (9), RPJ (70), AJP (14), EJP (4),
EPL (5), PRA (2), PRD (4), PRE (2), APP (5), FP (6), PLA (9), OC (2),
JPA (4), JPB (1), JMP (4), JOPA (2), JMO (2), CJP (1), OL (1), NJP (2),
MREJ (3), arXiv (70).
In particular, JOPA rejected a paper "The Beth's experiment is under
review" on December 11, 2003 10:11 AM. Joanna Dingley, Publishing
Administrator, wrote, "I notice that the above paper has previously
been rejected from Journal of Physics A and New Journal of Physics. A
rejection from one Institute of Physics Publishing journal is a
rejection from all Institute of Physics Publishing journals. We will
therefore not consider this manuscript any further."
Then JOPA rejected a paper "A mirror reflecting a circularly polarized
plane wave receives spin" on September 26, 2005 9:54 AM. August Head,
Senior Publishing Administrator, wrote, "I am sorry to tell you that we
are unable to consider it for our journal as it has previously been
rejected. It is company policy that once an article has been rejected
from one Institute of Physics journal, we cannot consider it for
another. Your paper has therefore been withdrawn from consideration."
----Unfortunately, I cannot submit the paper to the arXiv because I am
blacklisted by the arXiv since 2001. See details at
http://www.ArchiveFreedom.org/freedom/Khrapko.html
http://groups-beta.google.com/group/USENET-talk-arXiv

------I am deeply grateful to Professor Robert H. Romer, Editor of AJP,
for publishing my question [8] (was submitted on Oct. 7, 1999) and to
Professor Timo Nieminen for valuable discussions (Newsgroups:
sci.physics.electromag). Unfortunately, Jan Tobochnik, the present-day
Editor of AJP, rejected my papers more than 20 times.

References
[1] L. Allen et al., Phys. Rev. A45, 8185 (1992)
[2] L. Allen et al., Progress in Optics XXXIX (Elsevier, Amsterdam,
1999).
[3] L. Allen, M. J. Padgett, Opt. Commun. 184, 67 (2000).
[4] A. T. O'Neil et al., Phys. Rev. Lett. 88, 053601 (2002).
[5] R. Loudon, Phys. Rev. A68, 013806 (2003)
[6] R. Zambrini, S. M. Barnett, J. Mod. Opt. 52, 1045 (2005)
[7] J D Jackson, Classical Electrodynamics (Wiley, 1999).
[8] R. I. Khrapko, Amer. J. Phys. 69, 405 (2001)
[9] J. W. Simmons, M. J. Guttmann, States, Waves and Photons
(Addison-Wesley, Reading, MA, 1970)
[10] T. A. Nieminen et al., physics/0408080
[11] A. M. Stewart, Eur. J. Phys., 26, 635 (2005)
[12] R. I. Khrapko, physics/0105031
[13] R. I. Khrapko, Measurement Techniques, 46, No. 4, 317 (2003)
[14] R. I. Khrapko, Gravitation & Cosmology, 10, No. 1-2, 91-98 (2004)

This paper is published at www.sciprint.org

R. Khrapko

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