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(Sourced from Jan Noring)
Article 328 of alt.sci.physics.new-theories:
Path: merlin.hgc.edu!psinntp!rpi!usc!apple!netcomsv!mork!noring
From: noring@netcom.com (Jon Noring)
Newsgroups: alt.sci.physics.new-theories
Subject: Dr. Puthoff: Speculations on Energy Production From the
Vacuum (LONG)
Summary: Paper originally published in Speculations in Science and
Technology Date: 24 Mar 92 18:57:38 GMT
Organization: Netcom - Online Communication Services
(408 241-9760 guest)
Lines: 541
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
Page 1
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
Page 2
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)
Page 3
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
Page 4
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-
Page 5
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
Page 6
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.
Page 7
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.
Page 8
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
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fact necessary for the formal consistency of the theory*." The
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underlying fluctuation-dissipation theorem.
3. Casimir, H.B.G., Proc. K. Ned. Akad. Wet., volume 51, p. 793,
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Page 9
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10. Milonni, P.W., Cook, R.J. and Goggin, M.E. Phys. Rev. A,
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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,
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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
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volume 21, p. 2137, 1980.
27. Sakharov, A.D. Dokl. Akad. Nauk. SSSR [Sov. Phys. - Dokl.,
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and Wheeler, J.A. Gravitation, pp. 426-428, Freeman, San
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28. Forward, R.L. Phys. Rev. B, volume 30, p. 1700, 1984.
Page 10
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
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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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