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Reproduced below, with the permission of the author, is a paper written by Dr.
Harold E. Puthoff, a respected physicist in quantum electrodynamics (QED) and
in the relatively new field of stochastic electrodynamics (SED). This paper
originally appeared in Speculations in Science and Technology, vol. 13, no. 4,
pp. 247-257, 1990. The reader is encouraged to obtain a copy of the original
paper since the figures could not be reproduced here in ASCII.
This paper speculates, using current theories, that *net* energy MIGHT (and
only might) be extractable from the vacuum of space. Such a possibility does
not necessarily violate current thermodynamic laws since all we need to do is
to redraw our thermodynamic boundaries to include the vacuum energy of the
universe and its attributes. Dr. Puthoff is currently pursuing experimental
studies to ascertain whether or not there is tappable "excess" energy in the
vacuum (theoretical considerations cannot ascertain the answer to this although
there are several possible reasons why it could exist). Since the publication
of this paper, some preliminary experimental results by Dr. Puthoff and his
associates using a "condensed charge technology device" indicate that the
vacuum indeed has significant "excess" energy that is tappable; further work
to make sure of their results (to avoid the problems that plagued the cold
fusion controversy), and eventual publication will be done. A patent has
already been granted on this device: Patent Number 5,018,180, "Energy
Conversion Using High Charge Density..."
As an interesting aside, in my conversation with Dr. Puthoff recently, he
believed that anomalous heat generation observed in several "cold fusion"
experiments was not fusion, rather it was vacuum energy extraction (either net
energy extraction from vacuum energy "excess", or vacuum energy charging and
later extraction similar to a battery). This could explain why any anomalous
heat generation was not accompanied by a neutron and radiation signature
indicating nuclear fusion. Thus, I'm cross-posting this to the fusion energy
newsgroup for their comment.
The reader is also referred to four other related papers by Dr. Puthoff which
appeared in the literature (three appeared in Physical Review):
"Ground State of Hydrogen as a Zero-Point-Fluctuation-Determined State",
Physical Review D, vol. 35, no. 10, pp. 3266-3269, 15 May 1987.
"Gravity as a Zero-Point-Fluctuation Force", Physical Review A, vol. 39, no. 5,
pp. 2333-2342, 1 March 1989.
"Source of Vacuum Electromagnetic Zero-Point Energy", Physical Review A, vol.
40, no. 9, pp. 4857-4862, 1 November 1989. See also his replies to comments in
Physical Review A, vol. 44, no. 5, page 3382 and 3385-3386, and an Erratum in
Physical Review A, vol. 41, no. 5, page 2902.
"Everything for Nothing", New Scientist, pp. 52-55, 28 July 1990.
*************************************************************************
-Beginning of Paper-
THE ENERGETIC VACUUM: IMPLICATIONS FOR ENERGY RESEARCH
H.E. Puthoff
Institute for Advanced Studies at Austin
1301 Capital of Texas Highway S., Suite A-232
Austin, TX 78746
(512) 346-9947
"The existence of an actual vacuum was a subject of debate among scientists
from Aristotle into the twentieth century. Since light, magnetic fields and
heat all travel through a vacuum, something must be there. Borrowing a word
from Aristotle, scientists described various kinds of 'aethers' that exist in
even the hardest vacuum and that pervade space. Maxwell's theory of electro-
magnetism reduced these different types to just one, called the ether. Various
experiments were developed to detect this ether, of which the most famous was
the Michelson-Morley experiment, which failed to find it. Finally, in 1905,
Einstein banished the ether by means of special relativity and allowed the true
vacuum to exist.
"But not for long. The Heisenberg uncertainty principle of 1927 led particle
physicists to predict that particles would arise spontaneously from the vacuum,
so long as they disappeared before violating the uncertainty principle. The
quantum vacuum is a very active place, with all sorts of particles appearing
and disappearing. Careful experiments have demonstrated that the quantum
theorists are correct in this interpretation of the vacuum... Furthermore,
starting in 1980 with the theory of the inflationary universe, particle
physicists have told us that the entire universe was created as a 'false
vacuum', a quantum vacuum that has more energy in its nothingness than it
should. The decay of that particular vacuum to an ordinary quantum vacuum
produced all the mass in the universe and started the Big Bang."
From "The Timetables of Science", Simon and Schuster, 1988
INTRODUCTION
Modern physical theory, specifically quantum electrodynamics (QED), tells us
that the vacuum can no longer be considered a void. This is due to the fact
that, even in the absence of matter, the vacuum is neither truly particle nor
field free, but is the seat of virtual particle-pair (e.g. electron-positron)
creation and annihilation processes, as well as zero-point-fluctuation (ZPF) of
such fields as the vacuum electromagnetic field, which will be the focus of our
study here.
Formally, the energy density associated with the vacuum electromagnetic ZPF
background is considered to be infinite. With appropriate high-frequency
cutoffs the ZPF energy density is still conservatively estimated to be on the
order of nuclear energy densities or greater.[1] The enormity of the figures
describing the vacuum electromagnetic zero-point energy raises the question as
to whether these numbers should be taken seriously, whether they are due to
some defect or misinterpretation of the theory, whether the ZPF fields ought to
be considered as 'virtual' or 'real'.[2] There is, however, no question but
that the ZPF fields lead to real, measurable physical consequences. One
example is the very real Casimir force,[3-6] an experimentally-verified [7-9]
ZPF-induced attractive quantum force between closely-spaced metal or dielectric
plates. An elegant analysis by Milonni, et al., at Los Alamos National
Laboratory shows that the Casimir force is due to radiation pressure from the
background electromagnetic zero-point energy which has become unbalanced due to
the presence of the plates, and which results in the plates being pushed
together.[10] (We will discuss this effect in more detail later when we
address the possibility of ZPF energy extraction.) Other effects which can be
traced back to interactions involving the ZPF fields in a fundamental way
include the Lamb shift (the slight perturbation of the emission lines seen from
transitions between atomic states),[11-13] the van der Waals chemical binding
forces,[14] the stabilization of atomic structure against radiative collapse,
[15-16] quantum field mechanisms underlying the gravitational interaction,[17]
and spontaneous emission.[18]
ZERO-POINT ENERGY
To understand just what the significance of zero-point energy is, let us begin
with a simple harmonic oscillator as shown in Figure 1. According to classical
theory, such a harmonic oscillator, once excited but with excitation removed,
will come to rest (because of friction losses) as shown in Figure 1(a). In
quantum theory, however, this is not the case. Instead, such an oscillator
will always retain a finite amount of 'jiggle', as shown in Figure 1(b). The
average energy (kinetic plus potential) associated with this residuum of
motion, the so-called zero-point energy, is given by: <E>= hw/2, where 'h' is
Planck's constant (h= 1.054e-34 joule/sec) and 'w' [really 'omega'] is the
frequency of oscillation. The meaning of the adjective 'zero-point' is that
such motion exists even at a temperature of absolute zero where no thermal
agitation effects remain. Similarly, if a cavity electromagnetic mode is
excited and then left to decay, as shown in Figure 2, the field energy dies
away, again to a minimum value <E>= hw/2 (half a photon's worth), indicating
that fields as well as mechanical systems are subject to zero-point
fluctuations. It is the presence of such ZPF 'noise' that can never be gotten
rid of, no matter how perfect the technology, that sets a lower limit on the
detectability of electromagnetic signals.
If we now consider the universe as a whole as constituting a giant cavity, then
we approach a continuum of possible modes (frequencies, directions) of
propagation of electromagnetic waves. Again, even in the absence of overt
excitation, quantum theory has us assign an <E>= hw/2 to each mode.
Multiplication of this energy by a density of modes factor [19] then yields
an expression for the spectral energy density that characterizes the vacuum
electromagnetic zero-point energy
rho(w)dw = [w^2/pi^2*c^3]/[hw/2]dw
= (hw^3)/(2*pi^2*c^3)dw joules/m^3 (eqn. 1)
There are a number of properties of the zero-point energy distribution given in
equation 1 that are worthy of note. First, the frequency behavior is seen to
diverge as w^3. In the absence of a high-frequency cutoff this would imply an
infinite energy density. (This is the source of such statements regarding a
purely formal theory.) As discussed by Feynman and Hibbs, however, we have no
evidence that QED remains valid at asymptotically high frequencies (vanishingly
small wavelengths).[1] Therefore, we are justified in assuming a high-
frequency cutoff, and arguments based on the requirements of general relativity
place this cutoff near the Planck frequency (~10^-33 cm).[17] Even with this
cutoff the mass-density equivalent of the vacuum ZPF fields is still on the
order of 10^94 g/cm^3. This caused Wheeler to remark that "elementary
particles represent a percentage-wise almost completely negligible change in
the locally violent conditions that characterize the vacuum...In other words,
elementary particles do not form a really basic starting point for the
description of nature. Instead, they represent a first-order correction to
vacuum physics."[20] As high as this value is, one might think that the vacuum
energy would be easy to observe. Although this is true in a certain sense (it
is the source of quantum noise), by and large the homogeneity and isotropy
(uniformity) of the ZPF distribution prevent naive observation, and only
departures from uniformity yield overtly observable effects.
Contributing to the lack of direct observability is a second feature of the ZPF
spectrum; namely, its Lorentz invariance. Whereas motion through all other
radiation fields, random or otherwise, can be detected by Doppler-shift
phenomena, the ZPF spectrum with its cubic frequency dependence is unique in
that detailed cancellation of Doppler shifts with velocity changes leaves the
spectrum unchanged. (Indeed, one can derive the ZPF spectrum to within a scale
factor by simply postulating a Lorentz-invariant random radiation field.
[21,22]) Thus, although any particular component may Doppler shift as a result
of motion, another component Doppler shifts to take its place. It is also the
case, again unique to the ZPF cubic-frequency-dependent spectrum, that Doppler
shifts due to other phenomena (e.g., cosmological expansion, gravitation) also
do not alter the spectrum. [23] This stands in contrast to, for example, the
3 K blackbody (thermal) microwave background left over from the Big Bang which
cools with cosmological expansion.
Yet another feature of the ZPF spectrum, related to its Lorentz invariance and
again unique in comparison with all other competitors, is the complete lack of
a drag force on a charged particle passing through it. This is because such a
drag forced (the so-called Einstein-Hopf drag [24]) is proportional to the
factor [rho(w) - (w/3)*(d rho/dw)], and this vanishes identically for
rho(w) ~= w^3.
On the other hand, accelerated motion through the vacuum can in principle
reveal the presence of the ZPF energy density directly. Unlike uniform motion
in which delicate cancellations of Doppler shifts leave the motion undetected,
in accelerated motion the Doppler-shift cancellations are no longer sustained.
As a result, the Lorentz-invariant spectrum which holds in uniform motion is
augmented by additional terms. One factor yields a thermal (Planck) spectrum
of temperature T= h*a/2*pi*c*k, where 'a' is acceleration, 'k' is Boltzmann's
constant and 'T' is temperature. This is known as the Davies-Unruh effect.
[25,26] Yet another factor which shows up in the ZPF spectrum of an
accelerated observer is found, via the equivalence principle, to reveal a deep
connection between zero-point energy and gravity along lines originally
proposed by Sakharov [27] (that gravity could be understood as an induced
effect brought about by changes in the quantum fluctuation energy of the vacuum
due to the presence of matter [17]).
Thus we see that, with its roots in relativity theory which banished the ether,
QED has in some sense come full circle to provide us with a model of an
energetic vacuum that once again constitutes a plenum rather than a void.
SOURCE OF ZERO-POINT ENERGY
The fact that the vacuum constitutes an energy reservoir leads naturally to the
question as to where the zero-point energy comes from, specifically, the vacuum
electromagnetic zero-point energy under discussion here. (This is an
especially important issue if one considers the possibility of extracting such
energy for use.) Nature provides us with but two alternatives: existence by
fiat as part of the boundary conditions of the present universe (like, for
example, the 3 K cosmic background radiation left over from the Big Bang), or
generation by the (quantum fluctuation) motion of charged particles that
constitute matter. This latter possibility was explored in a recent paper by
the author, with positive results.[23]
The argument goes as follows. Given charged particles in quantum zero-point
motion throughout the universe, a 1/r^2 dependence of the radiation from such
motion, and an average volume distribution of such particles in spherical
shells about any given point that is proportional to the area of the shell
(that is,proportional to r^2), one could reasonably expect to find at any given
point a sum of contributions from the surrounding shells that yielded a high-
density radiation field. (Recall a similar argument in astronomy associated
with Olbers' paradox.) The high-density ZPF fields would appear to be just
such a field.
The details of the calculations examine the possibility that ZPF fields drive
particle motion, and that the sum of particle motions throughout the universe
in turn generates the ZPF fields, in the form of a self-regenerating
cosmological feedback cycle not unlike a cat chasing its own tail. This self-
consistent field approach, carried out assuming inflationary cosmology, is
found to yield the correct frequency distribution and the correct order of
magnitude to match the known ZPF distribution, thus supporting the hypothesis
that the ZPF fields are dynamically generated.
As it turns out, there is an additional bonus from the calculations. A derived
expression relating the zero-point energy density to such factors as the mass
density and size of the universe also yields a precise expression for an
observed 'cosmological coincidence' often discussed in the context of Dirac's
large-numbers hypothesis: namely, that the electromagnetic-to-gravitational
force ratio between an electron and proton is equal to the ratio of the Hubble
distance to the size of the classical electron. According to the relevant
calculations such a cosmological coincidence is seen to be a consequence of the
cosmologically-based ZPF-generation mechanism under consideration that serves
to link cosmological and atomic parameters.
The overall picture that emerges, then, is that the electromagnetic ZPF
spectrum is generated by the motion of charged particles throughout the
universe which are themselves undergoing ZPF-induced motion, in a kind of self-
regenerating grand ground state of the universe. In contrast to other
particle-field interactions, the ZPF interaction constitutes an underlying,
stable 'bottom-rung' vacuum state that decays no further but reproduces itself
on a dynamic-generation basis. In such terms it is possible to explicate on a
rational basis the observed presence of vacuum zero-point energy.
VACUUM ENERGY EXTRACTION?
As we have seen, the vacuum constitutes an extremely energetic physical state.
Nonetheless, it is a giant step to consider the possibility that vacuum energy
can be 'mined' for practical use. To begin, without careful thought as to the
role that the vacuum plays in particle-vacuum interactions, it would only be
natural to assume that any attempt to extract energy from the vacuum might
somehow violate energy conservation laws or thermodynamic constraints (as in
misguided attempts to extract energy from a heat bath under equilibrium
conditions). As we shall see, however, this is not quite the case.
The premier example for considering the possibility of extracting energy from
the vacuum has already appeared in the literature in a paper by R.L. Forward
entitled "Extraction of Electrical Energy From the Vacuum..."[28]; it is the
Casimir effect. Let us examine carefully this ZPF-driven phenomenon.
With parallel, non-charged conducting plates set a distance D apart, only those
(electromagnetic) modes which satisfy the plate boundary conditions (vanishing
tangential electric field) are permitted to exist. In the interior space this
constrains the modes to a discrete set of wavelengths for which an integer
number of half-wavelengths just spans the distance D (see Figure 3). In
particular, no mode for which a half-wavelength is greater than D can fit; as
a result, all longer-wavelength modes are excluded, since for these wavelengths
the pair of plates constitutes a cavity below cutoff. The constraints for
modes exterior to the plates, on the other hand, are much less restrictive due
to the larger spaces involved. Therefore, the number of viable modes exterior
is greater than that interior. Since such modes, even in vacuum state, carry
energy and momentum, the radiation pressure inward overbalances that outward,
and detailed calculation shows that the plates are pushed together with a force
that varies as 1/D^4, viz,[10]
F/A = -(pi^2/240)(h*c/D^4) newtons/m^2 (eqn. 2)
The associated attractive potential energy (Casimir energy) varies as 1/D^3,
U/A = -(pi^2/720)/(h*c/D^3) joules/m^2 (eqn. 3)
As is always the case, bodies in an attractive potential, free to move, will do
so, and in this case the plates will move toward each other. The conservation
of energy dictates that in this process potential energy is converted to some
other form, in this case the kinetic energy of motion. When the plates finally
collide, the kinetic energy is then transformed into heat. (The overall
process is essentially identical to the conversion of gravitational potential
energy into heat by an object that falls to the ground.) Since in this case
the Casimir energy derives from the vacuum, the process constitutes the
conversion of vacuum energy into heat, and is no more mysterious than in the
analogous gravitational case.
In such fashion we see that the conversion of vacuum energy into heat, rather
than violating the conservation of energy, is in fact required by it. And this
conversion can be traced microjoule by microjoule as modes (and their
corresponding zero-point energies) are eliminated by the shrinking separation
of the plates. What takes getting used to conceptually is that the vacuum
state does not have a fixed energy value, but changes with boundary conditions.
In this case vacuum-plus-plates-far-apart is a higher energy state than vacuum-
plus-plates-close-together, and the combined system will decay from the higher-
energy state to the lower, in the process creating kinetic energy, then heat,
to conserve overall energy. Similar vacuum-decay processes have been discussed
within the context of so-called charged vacuum states.[29]
With regard to extracting zero-point energy for use, in Forward's proposed
embodiment the two plates in a Casimir experiment are charged with the same-
sign charge (e.g., electrons). At sufficiently small spacings the Coulomb
repulsion between the plates (which goes in an inverse square law 1/D^2 or
less, depending on spacing and geometry) can always be overcome by the stronger
1/D^4 attractive Casimir force. The plates will therefore be drawn together in
a collapsing motion. This confines the charge distribution to a smaller and
smaller volume and results in an increased electric field strength in the
vicinity of the plates. In such fashion the zero-point energy (Casimir energy)
is transformed into stored Coulomb energy, which can then be extracted by a
variety of means.
Although demonstrating in principle the extraction of energy from the vacuum,
Forward's embodiment is admittedly impractical for significant, continuous
energy generation, for a number of reasons. First and foremost is the fact
that the generator is a 'one-shot' device. To recycle the generator one must
put as much energy into the device to return the plates to their original
separated positions as was obtained during the collapse phase, as would be
expected in any conservative potential. As a result, given the losses in any
real system, not even 'break-even' operation can be achieved, let alone net
energy gain.
Let us carry this one step further, however. If one could arrange to have an
inexhaustible supply of such devices, and if it took less energy to make each
device than was obtained from the Casimir-collapse process, and if the devices
were discarded after use rather than recycled, then one could envision the
conversion of vacuum energy to use with a net positive yield. Although almost
certainly not achievable in terms of mechanical devices, a possible candidate
for exploitation along such lines would be the generation of a cold, dense,
non-neutral (charged) plasma in which charge condensation takes place not on
the basis of charged plates being drawn together, but on the basis of a Casimir
pinch effect. (Casimir pinch effects have been explored in the literature, not
with regard to energy conversion, but in terms of semiclassical modelling of
charge confinement in elementary particles, hadron bag models, etc.[30]) Such
an approach would constitute a 'Casimir-fusion' process, which in its cycle of
operation would mimic the nuclear-fusion process. It would begin, like its
nuclear counterpart, with an initial energy input into a plasma to overcome a
Coulomb barrier, followed by a condensation of charged particles drawn together
by a strong, short-range attractive potential (in this case a Casimir rather
than a nuclear potential), and with an accompanying energy release. Should the
energy requirements for plasma formation, and electrical circuit and heat
losses be kept at a level below that required for break-even operation, then
net, useful energy could in principle be generated, as in the nuclear case.
Such a proposal is, of course, highly speculative at this point, and further
detailed analysis of the energetics involved may yet uncover some hidden flaw
in the concept. Nonetheless, known to this author are programs in the United
States, the Soviet Union and other countries to explore just such an approach
on an experimental basis.
The above provides just one example of the type of concept that can be explored
with regard to possible vacuum energy extraction. Other proposals for
extracting vacuum energy have been made as well,[31] covering the gamut from
the clearly unworkable to the intriguing. To this author's way of thinking,
however, there is as yet neither clear-cut evidence of experimental success nor
an absolutely unimpeachable theoretical construct. Nonetheless, it is only by
continued, careful consideration of such proposals that we can hope to resolve
the issue as to whether energy can be extracted from the vacuum, as part of a
generalized 'vacuum engineering' concept of the type suggested by Nobel
Laureate T.D. Lee.[32] As a caution along the way, the prudent scientist,
while generally keeping an open mind as to the possibility of vacuum energy
extraction, must of course approach any particular device claim or theoretical
proposal with the utmost rigor with regard to verification and validation.
Can the energy crisis be solved by harnessing the energies of the zero-point
sea? In the final analysis, given our relative ignorance at this point we must
of necessity fall back on a quote given by Podolny [33] when contemplating this
same issue. "It would be just as presumptuous to deny the feasibility of
useful application as it would be irresponsible to guarantee such application."
Only the future can reveal whether a program to extract energy from the vacuum
will meet with success.
ACKNOWLEDGEMENTS
I wish to express my appreciation to G.W. Church, Jr., for helpful discussion
in the exploration of the concepts developed here. I also wish to thank K.R.
Shoulders of Jupiter Technologies, Austin, Texas, and William L. Stoner, III,
of OmniTech International, Springdale, Virginia, for continuing impetus and
encouragement to explore these issues.
REFERENCES
1. Feynman, R.P. and Hibbs, A.R. *Quantum Mechanics and Path Integrals*,
page 245, McGraw-Hill, New York, 1965. See also Misner, C.W., Thorne,
K.S. and Wheeler, J.A. *Gravitation*, page 1202 ff. Freeman, San
Francisco, 1973.
2. See, for example, the Closing Remarks section in Boyer, T.H., Phys.
Rev. D, volume 29, p. 1089, 1984. It can be added that, although the
approach developed here involves treating the ZPF fields as real, an
alternative viewpoint can be taken in which the results of field-
particle interactions traditionally attributed to ZPF are expressed
instead in terms of the radiation reaction of the particles involved,
without explicit reference to the ZPF. For this viewpoint, see Milonni,
P.W., Phys. Rev. A, volume 25, p. 1315, 1982. Although it is sometimes
assumed that the radiation-reaction approach might imply that the ZPF
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in terms of either radiation reaction or the zero-point field, *both
fields are in fact necessary for the formal consistency of the theory*."
The interrelationship between these two approaches (ZPF, radiation
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fluctuation-dissipation theorem.
3. Casimir, H.B.G., Proc. K. Ned. Akad. Wet., volume 51, p. 793, 1948.
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15. Puthoff, H.E. Phys. Rev. D, volume 35, p. 3266, 1987. See also
New Scientist, volume 115, p. 26, 9 July 1987.
16. Cetto, A.M. and Pena, L. de la. Found. Phys., volume 19, p. 419, 1989.
17. See Puthoff, H.E. Phys. Rev. A, volume 39, p. 2333, 1989 and references
therein.
18. Milonni, P.W. Physica Scripta, volume T 21, p. 102, 1988.
19. See, for example, Pantell, R.H. and Puthoff, H.E. *Fundamentals of
Quantum Electronics*, pp. 179 ff., Wiley, New York, 1969.
20. Wheeler, J.A. *Geometrodynamics*, Academic Press, New York, 1962.
21. Marshall, T.W. Proc. Camb. Philos. Soc., vol. 61, p. 537, 1965.
22. Boyer, T.H. Phys. Rev., vol. 182, p. 1374, 1969.
23. Puthoff, H.E. Phys. Rev. A, volume 40, p. 4857, 1989. Errata in
Phys. Rev. A, volume 44, p. 3385, 1991. See also New Scientist,
volume 124, p. 36, 2 December 1989.
24. Milonni, P.W. Am. J. Phys., volume 49, p. 177, 1981.
25. Davies, P.C.W. J. Phys. A, volume 8, p. 609, 1975.
26. Unruh, W.G. Phys. Rev. D, volume 14, p. 870, 1976. For a semi-classical
derivation, see also Boyer, T.H. Phys. Rev. D, volume 21, p. 2137, 1980.
27. Sakharov, A.D. Dokl. Akad. Nauk. SSSR [Sov. Phys. - Dokl., volume 12,
p. 1040], 1968. See also Misner, C.W., Thorne, K.S. and Wheeler, J.A.
Gravitation, pp. 426-428, Freeman, San Francisco, 1973.
28. Forward, R.L. Phys. Rev. B, volume 30, p. 1700, 1984.
29. Rafelski, J., Fulcher, L.P. and Klein, A. Phys. Rep., volume 38, p. 227,
1978. See also "The Decay of the Vacuum", Scientific American, volume
241, p. 150, 1979.
30. For the original concept see Casimir, H.B.G., Physica, volume 19, p. 846,
1956. Early follow-on efforts include Boyer, T.H., Phys. Rev, volume 174,
p. 1764, 1968; Milton, K.A., Annals Phys., volume 127, p. 49, 1980;
DeRaad, L.L., Jr. and Milton, K.A., Annals Phys., vol. 136, p. 229, 1981;
Brevik, I., Annals Phys., volume 138, p. 36, 1982; Brevik, I. and
Kolbenstevdt, H., Annals Phys., volume 143, p. 179, 1982.
31. Booth, L.I. Speculat. Sci. Tech., volume 10, p. 201, 1987.
32. Lee, T.D. *Particle Physics and Introduction to Field Theory*, p. 826,
Harwood Academic Publ., London, 1988.
33. Podolny, R. *Something Called Nothing*, Mir Publ., Moscow 1986.
-End of Paper-
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