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"The unquestioning acceptance of the
Copenhagen interpretation of quantum theory has, in the last
40 years or so, held back progress on the development of alternative
theories. ... Blind acceptance of the orthodox position cannot
produce the challenges needed to push the theory eventually
to its breaking point. And break it will, probably in a way
no one can predict to produce a theory no one can imagine."
The grand unified theory of Randell L. Mills:
a natural unification of quantum mechanics and relativity
? This could well evolve as being true. At any rate, Mills
proposes such a basic approach to quantum theory that it deserves
considerably more attention from the general scientific community
than it has received so far. The new theory appears to be
a realization of Einstein's vision and a fitting closure of
the "Quantum Century" that started in 1900 with
Max Planck's work on black-body radiation and his subsequent
postulate of energy quanta.
It was Einstein's lifelong dream to unify
the quantum world with his theory of (special and general)
relativity [2]. Even though he was one of the three eminent
fathers of quantum mechanics - besides Planck and Bohr - Einstein
had serious doubts about the uncertainties that were a basic
feature of its theoretical framework. In his response to Born's
interpretation of the wave function as a probability-field
("ghost-field") he made the now famous statement:
"I am at all events convinced that He does not play dice."
[1,2]
In addition, of course, quantum mechanics
is fundamentally inconsistent with relativity. The somewhat
forced unification in Dirac's approach was hardly satisfying
to that great genius of an Einstein: "I incline to belief
that physicists will not be permanently satisfied with ...
an indirect description of Reality, even if the [quantum]
theory can be fitted successfully to the General Relativity
postulates." [2] Einstein's dream for a unified field
theory envisioned a "programme which may suitably be
called Maxwell's ... ." As his biographer Abraham Pais
put it, his vision called for "start[ing] with a classical
field theory, a unified field theory, and demand[ing] of that
theory that the quantum rules should emerge as constraints
imposed by that theory itself." [2]
Randell L. Mills proposes such a unified field
theory. He outlines a quantum theory for the atomistic world
that is fully consistent with "Maxwell's programme":
It is founded solely upon the classical laws of physics in
the framework of Einstein's relativity with an additional
Lorentz-invariant scalar wave equation for de-Broglie matter
waves. This additional wave equation is completely compatible
with Maxwell's vector wave equation of electromagnetism. The
key for quantization of the steady-state is the well known
physical law that a steady-state of moving charge or matter,
with or without acceleration, must not radiate either electromagnetic
or gravitational waves. This postulate was originally derived
from Maxwell's Equations in 1986 by Hermann Haus for a moving
charge [3] and was generalized by Mills as follows: the steady-state
eigenfunction of charge/matter has to be free of Fourier components
synchronous with waves traveling at the speed of light. The
condition is equivalent to the violation of phase-matching
for the exchange of energy in coupled mode theory.
Retrospectively, the non-radiation postulate
is the only quantization condition that seems to make perfect
sense. Applied to the central force field of a hydrogen atom,
Mills derives eigenfunction solutions that correspond to concentric
spherical shells (called "orbitspheres") with radii
that are integer multiples n of the Bohr radius ao.
These eigenfunctions can be naturally interpreted as two-dimensional
charge/mass density functions of the electron confined to
a spherical surface. Charge/mass points on the orbitsphere
move along great circles with a fixed magnitude of linear
velocity in a strictly coordinated motion to each other (the
orbitsphere is not a rigid spinning globe).
All electromagnetic field energy is trapped
inside the orbitsphere as in a resonant cavity with perfectly
conducting walls, except for a static magnetic field produced
by the surface currents of the orbitsphere. In the excited
states n > 1 this trapping is meta-stable. The well-known
quantized energy states of the hydrogen atom are predicted
by Mills' solutions.
As a corollary, Mills derives the properties
of the electron spin and the Bohr magneton in agreement with
the Stern-Gerlach experiment. These properties arise out of
a constant "spin-term" in the angular function required
in the solutions to satisfy the condition of negative
definite charge (or positive definite mass) everywhere
on the orbitsphere for any set of quantum numbers. Mills assigns
to this spin-term the quantum number s = 1/2. Thus,
the spin is a natural by-product of the theory, whereas in
the traditional quantum mechanics of Schrödinger and
Heisenberg it had to be introduced artificially.
In the ground state (n = 1, l
= 0) Mills derives a homogeneous charge/mass distribution
on the orbitsphere surface, in the excited states (n
> 1, l > 0), on the other hand, the charge distribution
becomes non-uniform and generates, together with the central
charge of the nucleus, multipoles. Transition probabilities
would follow from classical multipole radiation theory. At
ionization the orbitsphere would expand to infinity, thus
becoming the wavefront of a quasi-plane de-Broglie wave traveling
away from the central nucleus, and once "free" from
the nucleus, the electron orbitsphere would collapse into
a spinning disk in order to conserve angular momentum.
Mills' orbitspheres, the electron eigenfunctions
of the atom, emerge as complete charge/matter equivalents
of standing electromagnetic waves in a resonant cavity. The
compatibility of the respective wave equations allows a harmonic
self-consistent description of electron (charge/mass) and
electromagnetic-field (energy) distribution in the atom. It
would bring back determinism to quantum theory, a heroic task
that Schrödinger set out to accomplish with his wave
mechanics but, to his own dismay [1], tragically failed to
do.
If, then, the charge/mass density functions
of Mills were the correct solutions, the "real thing"
that Einstein's "inner voice" predicted [1,2], what
are Schrödinger's wave functions? In order to find some
answer to this question one has to realize that in the case
of time harmonic motion the steady-state Schrödinger
equation is identical to the steady-state charge/matter
wave equation in Mills' theory, specified for the non-relativistic
limit. The connection is provided by the de-Broglie relation
combined with conservation of energy. What is vastly different,
of course, is the boundary condition! The Haus criterion
in Mills' theory, which was outlined above, leads to non-radiating
eigenfunctions. This situation is equivalent to a perfectly
closed lossless resonant cavity. Schrödinger's
boundary condition, on the other hand, requires that the wave
function vanishes at infinity and is well behaved anywhere
else. As demonstrated by Mills, the resulting eigenfunctions
have Fourier transforms with components traveling at the speed
of light and, thus, should involve radiation. Schrödinger's
eigenfunctions can be considered the normal modes of a spherical
resonator of infinite extent.
In such a context, how could Schrödinger's
solution describe a steady-state that has some physical meaning?
To this reviewer it is quite conceivable that such a state,
for each set of quantum numbers, can be characterized by the
superposition of two dynamic states: one would consist of
a continually contracting orbitsphere emitting "virtual"
photons, whereas the other one would constitute the reverse,
the orbitsphere continually expanding and thereby re-absorbing
these photons, where the principle quantum number n
refers to the "home" orbit and the angular quantum
numbers (s,l,m) determine the angular charge/mass distribution
on the contracting and expanding orbitsphere surface. No net
emission or absorption of photons takes place. Such a quasi-dynamic
state could, perhaps, best be compared with the superposition
of a lasing resonant cavity emitting a light beam to infinity
(there vanishing just like a spherical wave) and its time-reversed
counterpart, i.e. a lossy cavity absorbing the opposite light
beam as it travels from infinity into the cavity. This would
result, in effect, in a leaky resonant cavity with
lossless feedback from infinity.
Obviously, the described hybrid quasi-dynamic
state could not be a real state. Rather it should be viewed
as a virtual state. As such, it is expected to provide
some statistical information about the possible dynamic behavior
which the real steady-state of a Mills charge/mass
eigenfunction may be subjected to. In the hydrogen atom the
statistics would refer to all possible expansion and contraction
events starting from a particular orbitsphere with a given
set of quantum numbers: the orbitsphere expansion/contraction
events are an endless "Monte Carlo game" forced
onto the Schrödinger eigenfunction by perfect feedback
from infinity! Thus, in a quasi-dynamic sense, one could consider
a Mills orbitsphere of a given set of quantum numbers as being
statistically "projected" onto a Schrödinger
wave function of the same set of quantum numbers. To make
this projection complete the latter needs to be generalized
by adding the spin-term in the angular function which Schrödinger
did not consider.
Such a view point would lead to the conclusion
that the statistical interpretation of the Schrödinger
wave function remains compatible with the unified field theory
of Mills. However, the statistics became purely classical,
they were totally equivalent, e.g., to the statistics of thermodynamics:
statistics of, in effect, an infinite number of real individual
events that proceed in a completely deterministic way without
the intervention of a measurement apparatus. Hence, Heisenberg's
uncertainty principle would lose all its mystique, in the
context of the Mills theory it just became the charge/mass-density-function
equivalent of the classical relation between the decay time
and bandwidth of a damped harmonic oscillator and its spatial
twin for propagating waves!
The unified theory of Mills provides a simple,
exceptionally pleasing, resolution of the conceptual problems
with the traditional quantum mechanics of Schrödinger
and Heisenberg. In fact, this resolution is amazingly close
to Einstein's vision [2]: Quantum mechanics is revealed as
incomplete but remains a valid branch of statistical physics.
It is highly accurate when dealing with a large number of
quantum events, but utterly fails in the description of individual
"quantum jumps". Here, the unified theory of Mills
re-establishes determinism, as is demonstrated by Mills with
the example of electron scattering from a He atom: Schrödinger
's approach provides accurate results only for relatively
large scattering angles for which the statistics are expected
to be good. Mills's deterministic approach, however, provides
an accurate solution for the full angular range. Hence, traditional
quantum mechanics - a better term in the framework of Mills'
theory would be statistical quantum mechanics - is
related to the quantum laws of the Mills unified theory -
Mills calls it classical quantum mechanics - in a way
that is somewhat reminiscent of the relation between Newton's
mechanics and its generalization in special relativity. May,
at last, Einstein's spirit rest in peace?
Einstein's theory of relativity modified Newton's
law but yielded more: it predicted the equivalence of matter
and energy! What are the exciting new predictions of the grand
unified theory of Mills? This theory predicts the existence
of so-called "shrunken" atomic states, substates
below the ground state. These substates are non-radiating
electron orbitspheres at the simple fractions n = 1/2,
1/3, 1/4, ... of the Bohr radius ao (the "subharmonics"
of the atom!). The existence of these substates is consistent
with the above speculation for a new statistical interpretation
of Schrödinger's wave functions, since these wave functions
remain finite below the Bohr radius dropping to zero only
at the nuclear center.
The ground state is completely stable, so
the substates are generally inaccessible. According to Mills'
hypothesis, however, the atomic substates can be accessed
by interaction with the proper partner atom(s) or ion(s) in
a resonant energy exchange. For hydrogen, Mills calculates
this critical energy to be just twice the hydrogen ionization
energy from the ground state (2 x 13.6 eV). Once this energy
quantum is transferred from the hydrogen ground state orbitsphere
to the interacting partner atom(s) or ion(s) by exciting it
to a higher orbitsphere level, the hydrogen orbitsphere becomes
unstable and collapses to its next lower stable non-radiating
substate with additional release of energy. Thus, to activate
such a Coulomb field collapse the hydrogen atom has to absorb
- as Mills calls it - an "energy hole" of 27.2 eV.
According to Mills, absorption of multiples of energy holes
is also allowed for this activation, and the size of the energy
hole remains the same for activating further collapse from
any of the substates. Considerable shrinkage should, hence,
be possible in a catalytic process with the release of considerable
amount of energy.
Mills also predicts that atomic Coulomb field
collapse can proceed to such a degree that, with fusible atomic
nuclei, e.g. deuterons, fusion can set in: Mills predicts
the possibility of cold fusion or, in his terminology,
Coulombic annihilation fusion (CAF)! Fleischmann and Pons
[4] appear to be vindicated.
But the postulated Coulomb field collapse
itself is predicted by Mills to lead to the release of large
amounts of energy and by itself could explain the observed
excess heat in electrolytic cell experiments. The process,
thus, deserves earnest attention as a potential future energy
source. Mills has some convincing experimental evidence for
both catalytic exothermic formation of shrunken substates
of hydrogen (so-called "hydrinos"), as well as for
catalytic cold fusion. Only the future can tell, if these
catalytic processes can be made efficient enough to be viable
for useful energy production. As an encouraging sign, Mills
has designed a hydrogen gas energy cell based on his shrinkage
reaction that provides far superior performance than any of
the original liquid electrolytic cells.
A most exciting feature of the Mills theory
is, however, that it promises to be a true grand unified
theory: Mills applies the orbitsphere concept not only to
single and multiple electron atoms and ions, to the hydrogen
molecule and the chemical bond, but also to pair production
and positronium, and to the weak and strong nuclear forces.
Mills proposes that just three basic concepts, i.e., electromagnetism,
gravity, and mass/energy, suffice to describe all known phenomena
from the dimensions of the atomic nucleus to those of the
cosmos.
Mills' new "classical" quantum mechanics
is of beautiful conceptual simplicity and fully deterministic
without the uncertainties, quantum jumps and probability functions
of traditional quantum mechanics, without "spooky action
at a distance" [1]. This should be a pure joy for every
searching scientist! It appears that the scientific community
has taken little notice of this new theory. Considering its
revolutionary nature and seemingly far-out conclusions this
is perhaps not too surprising. On the other hand, critical
dialogue is necessary for any new and unconventional thinking
in order to mature and reach a high degree of rigor and precision
in its formulation. In view of the fact that recently receptiveness
for alternate views on quantum theory has increased, as e.g.
the renewed interest in the deterministic interpretation of
Bohm attests [5], it is hoped that the theory of Randell L.
Mills will find its deserved resonance.
Let me close, as I started this review, with
a quote from Jim Baggott [1]: "Science is a democratic
activity. It is rare for a new theory to be adopted by the
scientific community overnight. Rather scientists need a good
deal of persuading before they will invest belief in a new
theory ... . This process of persuasion must be backed up
by hard experimental evidence, preferably from new experiments
designed to test the predictions of the new theory. Only when
a large cross-section of the scientific community believes
in the new theory is it accepted as 'true'."
I am indebted to Professor Anthony Bell for
originally bringing the 1992 edition of Mills' book to my
attention and to Professor Lawrence Ruby and Mr. Thomas Stolper
for helpful advice.
Reinhart Engelmann - Professor of Electrical Engineering
Oregon Graduate Institute of Science and Technology,
Portland, OR 97291-1000
References:
[1] Jim Baggott, The Meaning of Quantum Theory,
Oxford University Press, 1992
[2] Abraham Pais, 'Subtle is the Lord...'
The Science and the Life of Albert Einstein, Oxford University
Press, 1982
[3] H.A Haus, "On the radiation from
point charges," Am. J. Phys. 54 (12), 1126 (December
1986)
[4] M. Fleischmann and S. Pons, "Electrochemically
induced nuclear fusion of deuterium," J. Electroanal.
Chem. 261, 301 (1989)
[5] David Z. Albert, "Bohm's Alternative
to Quantum Mechanics," Scientific American, May 1994,
p.58
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