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Introduction
I still believe in the possibility of a model of reality–that
is, to say, of a theory which represents things themselves
and not merely probabilities of their occurrence.
— (Albert Einstein)1
1.1 The method of theoretical physics
After the Bohr-Heisenberg philosophy had demanded the abandonment of all attempts to produce a visualizable theory of atomic
structure and fields, and focus instead on the mere description of
sense data, physics began to hit an impasse. As a result, theory has
descended into two unproductive epistemologies, rationalism and
empiricism, the exclusivity of which Popper has argued against in
his Logik der Forschung (1935).2
For those physicists who have taken a rationalist position, visual
clarity has been sacrificed at the altar of mathematical economy. As
Baggott aptly puts it
Some modern theoretical physicists have sought to compensate for this loss of understanding [. . . and have] been
led – unwittingly or otherwise – to myth creation and fairy
tales [. . .] wrestling with problems for which there are as
1
Albert Einstein, ‘On the method of theoretical physics’, Ideas and Opinions
(New York: The Modern Library, 1994), p. 302.
2
Karl Popper, Logik der Forschung (Vienna: Verlag von Julius Springer,
1935); see English translation ‘The problem of demarcation’, The Logic of
Scientific Discovery (Routledge, 2002), pp. 10–16.
1
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yet no observational or experimental clues to help guide
them towards solutions. They have chosen to abandon the
scientific method [. . .] for a ‘post-empirical science’. Or
if you prefer, they have given up [. . . and] these theorists
have been guided instead by their mathematics and their
aesthetic sensibilities.3
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Paul Dirac, who focused exclusively on mathematical form and for
whom the creation of a visual model was not a desirable goal, might
well have been the inspiration for this movement:
the main object of science is not the provision of pictures,
but it is the formulation of laws governing phenomena and
the application of these laws to the discovery of new phenomena [. . .] In the case of atomic phenomena no picture
can be expected to exist in the usual sense of the word
‘picture’ by means of which is meant a model functioning
essentially on classical lines.4
Mathematics is a language that should be used to convey the geometrical structure of Nature, not presented as a representation of Nature
itself. Such a structure is to be discovered by an iterative process
of postulate and test against the results of experiments. If an idea
falls short against experiment it is to be adjusted. It is a metaphysical mistake to disconnect from empirical data altogether, and believe
that the criterion of formal economy in mathematical structure is the
sole guide to what the fundamental concepts might be. It would be
like asserting that, given two men in dialogue, the one who speaks
more articulately expresses the greater degree of reality. Mathematics must not be the content of the theory but a means of expressing the content, and the content must be a visualisable geometrical
3
Jim Baggott, Farewell to Reality, How Fairytale Physics Betrays the Search
for Scientific Truth (Constable, 2013), pp. xii–xiii.
4
Paul Dirac, The Principles of Quantum Mechanics, fourth edition (Oxford
University Press, 2000), p. 10.
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Introduction
page 3
3
model honed from its repeated improvement as new experimental
data is accommodated. Even four hundred years ago, Francis Bacon
had the wisdom to suggest that “mathematics, [. . .] ought only to
give definiteness to natural philosophy, not to generate or give it
birth.”5
Those physicists who have elected to follow an empiricist
approach have completely abandoned the program of geometrically
elucidating the unobservable world that must lie behind our perceptions.6 In confining themselves to the description of phenomena, the
concepts that any such scheme attempts to represent, being only one
level removed from our unprocessed sense data, cannot possibly be
fundamental enough to embrace a unifying scheme. In his Treatise,
Maxwell had the integrity to recognise the need for a realistic geometrical model:
A knowledge of these things [whether or not a current is
material] would amount to at least the beginnings of a complete dynamical theory of electricity, not, as in this treatise,
as a phenomenon due to an unknown cause, subject only
to the general laws of dynamics, but as a result of known
motions of known portions of matter, in which not only the
total effects and final results, but the whole intermediate
mechanism and details of the motion, are taken as objects
of study.7
It will be argued in this work that his progress was impeded by
attempting to construct light rays from a matter ether rather than the
proposal presented here, matter from a light-ray ether. Unfortunately,
5
Francis Bacon, Novum Organon, Book I, XCVI, (1620); in James Spedding, Robert Leslie Ellis, and Douglas Denon Heath, The Works of Francis
Bacon, Vol. VIII (Boston: Taggard and Thompson, 1863), p. 128.
6
Denial of the existence of this world amounts to asserting that our sense
data has no origin.
7
James Clerk Maxwell, A Treatise on Electricity and Magnetism, 2 vols,
Vol. 2 (Clarendon Press, 1891), §574.
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in his commentary on the electromagnetic field, Lorentz did not share
Maxwell’s philosophy
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we need by no means go far in attempting to form an image
of it and [. . .] we can develop the theory to a large extent and
elucidate a great number of phenomena, without entering
upon speculations of this kind. Indeed, on account of the
difficulties into which they lead us, there has of late years
been a tendency to avoid them altogether and to establish
the theory on a few assumptions of a more general nature.8
At least Maxwell found a supporter in Larmor
The time has fully arrived when, if theoretical physics is not
to remain content with being merely a systematic record of
phenomena, some definite idea of the connexion between
aether and matter is essential to progress.9
There are problems that still remain unresolved from this era. Reporting on the work of his father Carl Anton Bjerknes, Vilhelm Bjerjnes
has declared
We have theories relating to these [E-M] fields, but we have
no idea whatever of what they are intrinsically, nor even
the slightest idea of the path to follow in order to discover
their true nature.10
In more recent times, David Deutsch has called for a return to the
contemplation of the world beyond the senses:
Being able to predict things or to describe them, however
accurately, is not at all the same thing as understanding
8
H. A. Lorentz, The Theory of Electrons (Leipzig: B. G. Teubner, 1916),
p. 2.
9
J. Larmor, Aether and Matter (Cambridge University Press, 1900), p. x.
10
Vilhelm Friman Koren Bjerknes, Fields of Force: A Course of Lectures in
Mathematical Physics Delivered December 1 to 23, 1905 (New York, The
Columbia University Press, 1906), p. 1.
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Introduction
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them [. . .] Facts cannot be understood just by being summarized in a formula [. . .] Scientific theories explain the
objects and phenomena of our experience in terms of an
underlying reality which we do not experience directly
[. . .] To [some scientists . . .] the basic purpose of a scientific theory is not to explain anything, but to predict the
outcomes of experiments [. . .] This view is called instrumentalism (because it says that a theory is no more than
an instrument for making predictions).11
In the last century, the focus has been mainly on the ‘particle’ and
‘wave’ concepts. The photographs of tracks in a Wilson cloud chamber undoubtedly point to directed emissions.12 However, Wilson as
well as those who followed him assumed that each of these directed
emissions was a ‘particle’, that is, a solid undefined substance contained in a arbitrarily small but finite bounded spherical volume. On
the other hand, the work of Davisson and Germer in which an electron beam passing through a crystal of nickel showed that the beam
intensity depended on the scattering angle, clearly pointed to a wavelike interference effect. This diffraction phenomenon required that
the emission was not confined to a small localized spherical volume
but that it needed a lateral spatial extent in order for parts of it to
interfere with other parts.13 Davisson and Germer assumed, as did
those that followed them, that they were witnessing a wave front of
11
David Deutsch, The Fabric of Reality (The Penguin Press, 1997), pp. 2–3.
In his critique of General Relativity, Lavenda states “we have not made any
theoretical progress in the hundred years that general relativity, and the
nearly fifty years that string theory, have been around. It’s time for a new
start and to wipe the slate clean”, see Bernard Lavenda, Where Physics Went
Wrong (World Scientific Publishing, 2015), p. 209.
12
C. T. R. Wilson, ‘On a method of making visible the paths of ionizing
particles through a gas’, Proceedings of the Royal Society A, 85 (1911),
p. 285–88.
13
C. Davisson and L. H. Germer, ‘Diffraction of electrons by a crystal of
nickel’, Physical Review, 30 (1927), p. 705–40.
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matter. However, neither the ‘particle’, ‘wave’, nor ‘wave-particle’
theories has led to the desired clarification of mass, charge, and field.
Taking all this into account, it is the abandonment of the program of finding a geometrical-mechanical theory of the electric and
magnetic fields at the turn of the twentieth century that needs to be
addressed. It should now be accepted that no combination of a ‘particle’ and a ‘wave’ theory can lead to a deeper understanding of Nature.
However, there is a third way which has recently been receiving attention in the laboratory, and that is the notion of optical14 and electron
vortices.15 These vortex tubes are directed emissions with a limited
cross-section in common with particles, but they also have lateral
extent in common with waves, in the form of a vortex field. In Chapters 7, 8, and 9, a new theory of the toroidal mass ring is developed
based on the curved helical trajectories of circular polarized rays.
These are vortex rings with two component rotations, one around the
axis of the ring tube, and the other around the ring circumference,
and it is suggested that it is the curvature of the Poynting vector
that generates the accompanying vortex momentum field of which
there is a magnetic (tube-concentric) and electric (ring-concentric)
component.
Einstein has made the point that many others have made since,
that
neither Maxwell nor his followers succeeded in elaborating a mechanical model for the ether which might furnish a satisfactory mechanical interpretation of Maxwell’s
laws of the electro-magnetic field. The laws were clear
14
M. Padgett and L. Allen, ‘Light with a twist in its tail’, Contemporary
Physics, 41 (2000), pp. 275–85.
15
Uchida, M., and A. Tonomura, ‘Generation of electron beams carrying
OAM’, Nature, 464 (2010), pp. 737–9.
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Introduction
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and simple, the mechanical interpretations clumsy and
contradictory.16
However, a structural model of mass and charge is absolutely
necessary before reliable progress can be made in a unified
theory.17
This present work returns to the problems of the late nineteeth century and shows how Coulomb’s law, the Lorentz force
law, the attraction and repulsion of parallel conductors, electromagnetic induction, and the hydrogen atom ground state can all
be obtained from a theory of the mass vortex ring. The concepts
of mass, charge, and electric potential energy which have previously had no visualizable basis, arise naturally from this theory.
An experimental test is proposed for non-conservation of charge
in which the flight of cathode rays in a magnetic field is reversed
in order to observe whether or not their deflection also reverses.
A further test is proposed for the speed of cathode rays through
crossed electric and magnetic fields which it is suggested has been
overestimated.
However, a theory need not offer new predictions to be instructive.
In 1543, when Copernicus published the De revolutionibus orbium
coelestium,18 there was an important feature of his heliocentric theory
16
Albert Einstein, ‘An address delivered on May 5th, 1920, in the University
of Leyden’, Sidelights of Relativity (London: Methuen & Co Ltd, 1922),
p. 7.
17
Pauli’s view was that “a complete unified theory would have to account
for the internal structure of particles”, in John Hendry, The Creation of
Quantum Mechanics and the Bohr-Pauli Dialogue (D. Reidel Publishing
Company, 1984), p. 14.
18
Nicolaus Copernicus, De Revolutionibus Orbium Coelestium (Nuremberg: Johannes Petreius, 1543).
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that immediately raised it above the Apollonius–Ptolemy geocentric model of deferents, epicycles, and equants.19 The seven doublerotation geocentric models that had been proposed to account for
the motions in the then-known solar system20 could be replaced by a
unified model that employed single-rotation circular orbits. Although
the Copernican system could provide no better agreement with data
than the geocentric theory, it dramatically reduced the number of
independent hypotheses required for the model to function. In fact,
a better agreement had to wait for Kepler’s introduction of elliptic
orbits,21 a development that finally secured the heliocentric system’s
advantage over its predecessor. An example such as this suggests that
even if a new theory offers no new results, the principle of theoretical
economy is an important measure of the ‘truth’ content of any theory
that has been proposed to imitate the machinery of Nature.
My wish for the mass ring theory outlined in these pages, is that
those with a greater mathematical facility might identify any imperfections, recognise its utility, and press its application further. As
Popper very wisely said:
We must be clear in our own minds that we need other
people to discover and correct our mistakes (as they need
19
In the system first proposed by Apollonius of Perga (c.262–190BC), the
Earth is slightly offset from the center of a circle known as a ‘deferent’. A
smaller circle, the ‘epicycle’, on which circumference a heavenly body is
lodged, runs around the inner circumference of the deferent. Ptolemy added
an ‘equant’, an observation point close to the center of the body’s orbit, from
which vantage point the epicycle covers equal areas in equal times.
20
Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.
21
Kepler’s first and second laws were first published in 1609 in Johannes
Kepler, Astronomia nova [A new astronomy] (Prague: 1609), pp. 167, 294.
The third law had to wait until 1619 in Johannes Kepler, Harmonices Mundi
[The Harmony of the World] (Austria: Johann Planck, 1619), p. 189.
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Introduction
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9
us); especially those people who have grown up with
different ideas in a different environment.22
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Although the theory of the vortex mass ring presented here leaves
many unanswered questions, my aim has been merely to focus attention to a point where I believe others might better direct their efforts.
In the words of Francis Bacon, “I have only taken upon me to ring a
bell to call other wits together”.23
1.2
Overview of the work
Chapter 2 deals with the theory of the Maxwell–Faraday fields.
A detailed background to this work is given, covering the early experiments on static electricity, the one- and two-fluid theories of electricity, the experimental confirmation of Coulomb’s law, the Laplace and
Poisson equations, and the work of Oersted and Ampère on electrodynamics. Faraday’s experiments on electromagnetic induction are
treated in detail, results which were cast into formal principles by
Lenz and Neumann. In §2.4, the work of James Clerk Maxwell is
examined in considerable detail, providing an exposition in his own
notation of his derivation of the equations of electrodynamics which
he first presented in his four papers ‘On physical lines of force’, Parts
I–IV (1861–2). Since Maxwell was unable to provide a visualizable
model for his equations, the emphasis in §2.4 is on what he did rather
than what he understood. It is clear from the concluding discussion
that as the twentieth century approached, contemporary physicists
were still searching in desperation for a workable model of mass,
22
Karl Popper, In Search of a Better World, translated by Laura J. Bennett
(Routledge, 2000), p. 202.
23
Written in Bacon’s own hand, Lambeth Palace Library MS 650.28.
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charge, and field, one that did not have the ‘particle’ as its conceptual
basis.
Theories relating to the behaviour and structure of the electron
are the subject of Chapter 3. An historical review is given of the
late nineteenth work on cathode rays through the development of the
Geissler tube. The rays were shown to be deflected by electric and
magnetic fields as well as transmit linear momentum, and a measurement of their charge-to-mass ratio was made. However, no one
seems to have succeeded in establishing that they generate a magnetic
field. The mass ring theory developed in Chapters 7, 8, and 9, suggests that they do. In §3.3, the Lorentz–Zeeman effect is discussed
where orbiting negative charges were proposed as being responsible
for the shift of the two sodium D lines in a magnetic field. There
followed various experiments, most notably by Owen Richardson,
to show that atoms have a circulating current and that the magnetization of a cylindrical bar can produce a net angular momentum.
This work was taken up by Einstein and De Haas who showed that
the magnetic moment of an iron molecule is due to the circulation
of electrons, although their result for the ratio of the electron’s angular momentum to magnetic moment was shown to be in error by
a factor of two. The converse effect, that a stationary iron cylinder becomes magnetized on being accelerated around its axis, was
investigated by Samuel Barnett who obtained a positive result when
measuring the magnetization of a steel rod. After a brief discussion
of electron spin, in §3.6, the various hypotheses of electron structure
are examined including Lorentz’s charged solid sphere and Parson’s
charge ring.
The theory of blackbody radiation is treated in Chapter 4. Here,
the Stephan-Boltzmann law is derived based on Bartoli’s relation
between radiation pressure and energy density. The total power radiated is proportional to the fourth power of the temperature and Boltzmann’s theoretical use of the Carnot engine cycle to justify this law
is analysed in detail. A treatment of Wien’s displacement law for
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11
the constancy of λT in the heat radiation distribution function is
given in §4.3. Here, use is made of the principle of energy conservation, Stefan’s law, and the Doppler shift of radiation wavelength
during an adiabatic expansion. The work of Lummer and Pringsheim
(1899), and the long wavelength experiment of Rubens and Kurlbaum
(1901) played a central role in perfecting the radiation laws of Wien,
Rayleigh, and Planck. In fact, it was the attempt to find agreement
with the latter that led Planck to his formula. A critique is given of the
standing-wave theory of the blackbody spectrum showing its many
difficulties, and the incorrect definition of a probability in Planck’s
original derivation is also pointed out. In 1916, Einstein analysed the
rates of emission and absorption of heat radiation and developed his
‘coefficients’ model. Eight years later, he received a paper from Bose
which abandoned the use of oscillators and presented a new statistical
counting method based on a six dimensional phase space. However,
despite their ingenuity, none of these theories provide a clear insight
into the emitting and absorbing structure that the radiation interacts
with, but only serve to illustrate that it is possible to produce the
same agreement with experience from several independent theoretical bases. In §4.10, a new vortex tube approach to Planck’s law is
employed in which the main assumption is that a heat ray consists of
a number of linked unidirectional wavelengths which can be emitted
or absorbed together. This idea is also connected to the subsequent
development of the OAM mass ring theory.
Although the present work is focused mainly on the structure of
mass and charge, and how these give rise to electric and magnetic
fields, a brief survey of the early theories of atomic structure is presented in Chapter 5. This assists as a background to the attempt to
set up a theory of a bound oscillation state for the proton and electron orbital angular momentum (OAM) mass rings in §9.7 of Chapter 9. The work of Nicholson and Bohr in producing a preliminary
sketch of the hydrogen atom is outlined in §5.2 followed by Bohr’s
introduction of the reduced mass correction in §5.3. Sommerfeld’s
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theory of the fine structure hydrogen atom is then set forward in
detail covering Wilson’s action integrals, the quantum conditions for
elliptic orbits, elliptic precession, and both the non-relativistic and
relativistic derivation of the fine structure energy levels. Finally, §5.5
gives a brief survey of the introduction of Heisenberg’s matrix multiplication rule for a mechanics of observables.
The most modern of the historical chapters is Chapter 6 where
the latest research on the spin and orbital angular momentum of light
is reviewed. Section 6.2 begins with the Faraday effect where a circularly polarized ray which has spin angular momentum (SAM) is
rotated on passing along the magnetic field lines imposed on a diamagnetic or paramagnetic material. This was subsequently given a
mathematical treatment by George Airy, the Astronomer Royal in
1846. The work of John Henry Poynting from 1884 on the linear
momentum of light is taken up in §6.3 in which he formulated the
energy per unit volume in terms of electric and magnetic fields. Over
twenty years later, he suggested that light also carries angular momentum, a property that was detected by Richard Beth in 1936. The Beth
experiment involves a half-wave plate suspended on a quartz fiber
which is given an oscillatory rotation in a horizontal plane. By reversing the sense of circularly polarized light at the two ends of each plate
oscillation, a torque is transmitted to the plate and the angular amplitude is affected. Later experiments by Bruce Garetz and Peter Arnold
in 1979 also demonstrated that circularly polarized light can impose
a torque on a half-wave quartz plate. The plate was given an initial
rotation with angular frequency ωR and they reported that circularly
polarized light rotating in the same direction as the plate was reduced
in its angular frequency by 2ωR while the plate gains angular momentum 2, and a ray rotating in the opposite direction has a gain of 2ωR
while the plate loses 2. Marco Beijersbergen of Leiden University
has noted that light can be given orbital angular momentum (OAM)
in which the Poynting vector rotates in a helical path about its propagation axis. This work on the SAM and OAM of light rays is the
starting point for the mass ring theory that is developed.
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13
Fig. 1.1 The three stages of constructing an OAM mass ring. (a) A leftcircularly polarized Poynting vector is bent into a closed circuit to form an
SAM ring or rest mass. (b) The system is set in motion along the x axis as an
optical OAM vortex or mass in motion. A field occurs around the Poynting
vector due to its curvature with tangential field momentum pf inversely
proportional to radius rf and linear momentum p|| independent of radius.
(c) The motion along the x axis is bent into a closed tube to create an OAM
mass ring with fields (dotted). The dual curvature of the Poynting vector
produces a tube-concentric magnetic field momentum and a ring-concentric
electric field momentum, where α is the fine structure constant.
Chapters 7, 8, and 9 introduce a new theory of the OAM mass
ring and its momentum fields, see Figure 1.1. The first of these chapters explains the ring construction and its properties. The basic elements of the theory are left- and right-circularly polarized rays. These
have spin angular momentum (SAM) +1 and −1, respectively. An
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optical vortex can be formed from these rays where the Poynting vector rotates around a linear axis as the beam progresses along it. This
is known as optical orbital angular momentum (OAM) and §6.5 is
referenced which reviews the decade of experimental work on this
issue as summarized by Padgett and Allen.24 It is suggested in §7.3.2
that due to the curvature of the Poynting vector, a vortex momentum
field circulates the given optic axis, a notion which has possibilities
for accounting for interference and diffraction phenomena, where a
single directed OAM ray tube is affected by its appropriately directed
lateral vortex field. A suggestion for the construction of a SAM mass
ring is given in §7.4.1. A SAM mass ring at rest takes the form of
an optical vortex brought to rest, in that the Poynting vector that
rotates around the axis is brought into a closed circuit. Here its mass
is proportional to its radius of rotation about this axis. When this ring
receives energy parallel to its axis, the Poynting vector moves along
the axis in a helical trajectory in the form of an optical vortex. This
is also a SAM mass ring in motion.
To provide the mass with charge and electromagnetic field properties, the motive SAM mass ring needs to be linked end-to-end with
others in order to form a more elaborate OAM mass ring. This consists of n SAM mass rings in helical motion in a closed ring or toroidal
structure. The rotation of the Poynting vector around the ring circumference takes place at speed αc, where α is the
√fine structure constant,
and the rotation around the tube has speed c 1 − α2 . There are now
two curved trajectories of the Poynting vector and each generates a
momentum field around it. The field around the tube becomes the
magnetic momentum field and runs in the opposite direction to the
electric field vector, while the ring concentric field accommodates
the electric momentum and holds the magnetic field lines. Electric
charge is defined in relation to an OAM ring plane normal, where
24
M. Padgett and L. Allen, ‘Light with a twist in its tail’, Contemporary
Physics, 41 (2000), pp. 275–85.
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15
a positive angular momentum about this normal, as determined by
the directions of the circularly polarized components, constitutes a
positive charge and a negative angular momentum results in a negative one. There are two main consequences of this construction:
(i) a magnetic field exists around a charge whether or not it is in
motion; (ii) a non-conservation of charge can occur by reversing
either the direction of motion of the OAM ring or the direction
in which it is approached. There is already experimental evidence
for the non-conservation of topological charge in an optical vortex,
which can occur without external influence while the beam is in
transit.25
In order to account for the effects of repulsive and attractive fields,
in §7.4.2 a novel type of acceleration is introduced. The traditional
acceleration, where a mass at rest with respect to some frame absorbs
energy and its total mass is thereby increased, is denoted here as
‘active’ acceleration. However, consider a mass at rest in this reference frame. If the frame absorbs energy and accelerates instead of
the mass, it cannot be expected that the rest mass is seen to increase
since it has not physically taken on any energy. This is denoted
here as ‘passive’ acceleration. By analysing the OAM rings in both
cases, it is found that for active acceleration, the total action in the
ring plane is preserved while the absorbed action is redistributed
into linear action of the ring along its axis. For passive acceleration, the ring plane action diminishes, but the loss is compensated by
an increase in linear action of the ring thus preserving the original
action. It is suggested that the former is the basis of a repulsive electric interaction while the latter is associated with an attractive one.
Chapter 7 concludes with a discussion of interlaced helical Poynting
vectors in the OAM ring, thus opening up the possibility that stable
25
See G. Molina–Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M.
Wright, ‘Observation of the dynamical inversion of the topological charge
of an optical vortex’, Physical Review Letters, 87 (July 2001), 023902.
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multi-nucleon and multi-electron rings can be constructed without
the need for additional ad-hoc forces. The first method of producing
an electron vortex beam with OAM was devised by Uchida and Tonomura in 2010, 26 and was subsequently improved by Veerbeck et al.27
The production of interlaced electron beams carrying |l| > 1 units
of OAM in an electron vortex beam has been reported by McMorran et al.28 Their experimental work lends considerable weight to
the theory of the OAM mass ring to be developed in the pages that
follow.
The linear magnetic momentum delta-field is developed in
Chapter 8, which is the effective magnetic field when target and
source are in relative motion. The mechanism of an OAM ring deflection in a magnetic field is applied to parallel conductors as well as
to a charge under the effect of the Lorentz force, and it operates as
follows, see Figure 1.2. Each of the n SAM elements in the OAM
ring (or toroid) has a tube-concentric circuit of momentum p2 . As the
OAM ring passes along the x axis through the magnetic delta-field set
in the z direction, the magnetic momentum field in the x direction has
a differential flow, where pfa > pfb , which imposes a clockwise
momentum rotation (with respect to the B field line) around each of
the tube-concentric circuits at a, b, c, d.29 Circuits that are diametrically opposed in the ring have opposite sense rotational momenta
imposed by the field. With opposing rotations, the circuits a and d
26
Uchida, M., and A. Tonomura, ‘Generation of electron beams carrying
OAM’, Nature, 464 (2010), pp. 737–9.
27
Verbeeck, J., H, Tian, and P. Schattschneider, ‘Production and application
of electron vortex beams’, Nature, 467 (2010), pp. 301–4.
28
Benjamin J. McMorran, Amit Agrawal, Ian M. Anderson, Andrew A.
Herzing, Henri J. Lezec, Jabez J. McClelland, and John Unguris, ‘Electron
vortex beams with high quanta of orbital angular momenta’, Science, 331
(2011), pp. 192–5.
29
The magnetic momentum is inversely proportional to its distance from
source.
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Fig. 1.2 A negative (left) and positive (right) charge ring passing through a
magnetic field B set in the z direction with magnetic delta-field momentum
pfa > pfb in the x direction.
decrease in momentum, and to conserve local angular momentum
the ring radius at that location increases. At b and c, the reinforcing rotations increase the momentum and so the ring radius there
decreases. Consequently, the whole ring moves in the same direction
(gray arrows) along the y axis while conserving energy.
To apply this to parallel conductors, it is assumed that when there
is no potential difference across the ends of the wire, the magnetic
momentum fields of the positive and negative charge rings, although
arbitrarily orientated they cancel out. However, when a potential difference is applied, the ring axes align with the conductor, and the
electron ring motion which is passively accelerated reduces its magnetic field perpendicular to the conductor resulting in an excess of
positive charge magnetic field. Using these ideas, the correct deflection of parallel and anti-parallel currents in two parallel conductors is
obtained. So while the present view holds that a magnetic field cannot
exist without charge motion, this is modified to the position that an
OAM ring has a permanent magnetic field, part of which becomes
detectable when a ring that is cancelling its effect has its own field
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reduced. A Lorentz-type force is also derived in §8.4 together with
the correct radius of curvature.
Chapter 9 takes on the electric field. Here, the Coulomb field is
derived from a mass ring vortex as an effect of its ring-concentric
momentum field passing through another ring, see Figure 1.3. This
vortex rotation is analogous to Faraday’s tubes of electric field
lines. A mass ring (on the left of the diagram) that has an opposite sense momentum rotation pr3 to the electric momentum field
pf 3 it approaches (on the right of the diagram) experiences an attraction, while same sense rotations result in a repulsion. The former
is an example of the new ‘passive’ acceleration where no energy is
gained or lost by the ring, while the latter is an ‘active acceleration’
resulting in a gain of energy. It turns out that for a source mass ring
electric momentum field to affect a given target mass ring, its axis
has to pass through the area enclosed by the target ring. It is shown
Fig. 1.3 A positive (top left) and a negative (bottom left) charge mass ring
entering a positive electric field. Same sense rotations cause an increase
in mass ring action while opposite sense creates a decrease. In both cases,
action is redistributed into linear motion of the ring. The magnetic momentum field is pf 2 which is directed oppositely to the electric field E, and
the electric momentum field is pf 3 which is in the same direction as the
magnetic B field.
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19
that neighbouring source rings with axes that do not pass through the
target area have no effect.
The phenomenon of electromagnetic induction arises between two
rings that are coplanar. The magnetic field around one ring is moved
laterally, that is, perpendicular to its ring axis, towards or away from
a wire containing other rings. The protons re-orientate for least action
in their ring circuits taking the electrons with them. The lateral motion
of the source changes the electric field passing through the target rings
and results in a redistribution of the excess ring action in the electron
as motion along its ring axis. However, the theory also accommodates a further magnetic effect. The electron moves perpendicularly
through the source magnetic field and experiences a Lorentz-type
deviation from its linear path, reducing its own magnetic effect on
the source, and thus exposing an excess of stationary positive charge
magnetic field which in turn penetrates the source. The theory implies
that the reactive magnetic field generated in the target conductor as
a result of induction can be minimized by reducing the width of the
conductor in a direction connecting the source to the target, so an
experimental test is proposed.
Finally, a bound proton–electron oscillatory state is examined.
The electron and proton rings run along a common axis with parallel
ring planes and the electron ring oscillates backwards and forwards
over the much smaller proton ring. The electron must radiate energy
before entering this state and both the electron ring-concentric angular momentum and the proton field angular momentum penetrating
the electron ring are shown to be /2 at the point of radiation. The
ground state of hydrogen is derived which serves as an invitation to
investigate further the application of the OAM mass ring theory to
atomic structure.