Rueda - Electromagnetic Zero Point Field as Active Energy Source in the Intergalactic Medium (1999), Energy from the ...

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Electromagnetic Zero Point Field as Active Energy Source
in the Intergalactic Medium
Alfonso Rueda and Hiroki Sunahata
California State University, Long Beach, CA 90840
E-mail: arueda@csulb.edu
Bernhard Haisch
Solar & Astrophysics Laboratory, Lockheed Martin
3251 Hanover St., Palo Alto, CA 94304
E-mail: haisch@starspot.com
Revised version of invited presentation at
35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit
20{24 June 1999, Los Angeles, CA
AIAA paper 99-2145
ABSTRACT
For over twenty years the possibility that the electromagnetic zero point eld (ZPF) may actively
accelerate electromagnetically interacting particles in regions of extremely low particle density (as those
extant in intergalactic space (IGS) with n 1 particle m
3
) has been studied and analyzed. This energizing
phenomenon has been one of the few contenders for acceleration of cosmic rays (CR), particularly at ultrahigh
energies. The recent nding by the AGASA collaboration (Phys. Rev. Lett., 81, 1163, 1998) that the CR
energy spectrum does not display any signs of the Greisen-Zatsepin-Kuzmin cut-o (that should be present
if these CR particles were indeed generated in localized ultrahigh energies CR sources, as e.g., quasars and
other highly active galactic nuclei), may indicate the need for an acceleration mechanism that is distributed
throughout IGS as is the case with the ZPF. Other unexplained phenomena that receive an explanation from
this mechanism are the generation of X-ray and gamma-ray backgrounds and the existence of Cosmic Voids.
However recently, a statistical mechanics kind of challenge to the classical (not the quantum) version of the
zero-point acceleration mechanism has been posed (de la Pena and Cetto, The Quantum Dice, 1996). Here
we briey examine the consequences of this challenge and a prospective resolution.
INTRODUCTION
The idea that the vacuum may play a fundamental role in the early development and future evolution of
the universe has been \in the air" for a long time [1]. Both the Steady State and the old (pre-ination model)
Big Bang cosmological scenarios needed to invoke this idea in one way or another [2]. The Steady State
proposed the perennial creation of particles (protons and electrons, presumably from the Dirac vacuum
of particle-antiparticle pairs) throughout the universe. The old Big Bang model postulated a localized
and instantaneous generation of all the matter and energy of the universe together with the subsequent
gradual generation of space-time which sprang from literally nothing. And the new Big Bang with its more
sophisticated Inationary Cosmological Model started from the postulation of an unstable vacuum (the false
vacuum) that collapsed, giving rise to the simultaneous creation of matter-energy and space-time followed
by an ination which produces a rapid expansion of space-time [3, 4, 5]. This ination [5] was brief but
extremely dynamic, and, as new space was actually being created, the process gave the illusion of being
superluminal. Once this stage terminated, the universe entered its much slower current Hubble expansion
[1, 5, 6], the era in which we now are and have been for the last 12 20 10
9
years or so.
Copyright
c
1999 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
1
If the vacuum played such an active role in the initial stages of the universe, a valid question would be
whether it is still playing some active role in the present expansion of the universe. Recent observational
ndings by two dierent teams of astronomers point in this direction [7, 8]. It has been discovered that
instead of a decreasing rate of expansion by cosmological gravitational attraction, as was assumed for many
years, the universe actually experiences an accelerated rate of expansion. This accelerated rate of expansion
may be physically explainable in terms of an ongoing involvement of the vacuum in energizing the expansion.
ACCELERATED EXPANSION AND COSMIC VOIDS
There is a paucity of known mechanisms by which the vacuum might yield some of its energy to steadily
contribute to an accelerated expansion of the universe. Recently however within a dierent astrophysical
context a mechanism that could accomplish this was proposed [9, 10, 11]. Rueda, Haisch and Cole [11]
investigated a mechanism that could account for the phenomenon of Cosmic Voids [12]. It is now known
that the structure of the universe presents a peculiar distribution of matter in which clusters and superclusters
of galaxies are found in \sheets" that surround \voids", i.e., large regions of space of typical diameters around
100 Megaparsecs, which are practically devoid of matter and where no galaxies are found [1]. The whole
structure may be represented by a soap-foam-like model where the particles and magnetic elds are mainly
found on the sheets along with galactic clusters and superclusters, surrounding enormous spaces in between
in which much lower particle densities and much smaller concomitant magnetic eld intensities prevail.
It has been proposed [10, 11] that the ZPF of traditional quantum electrodynamics (QED), via a well-
known mechanism (discussed below), is responsible for the eect. This mechanism seems also to be involved
in contributing to other astrophysical phenomena: the X-ray and gamma-ray backgrounds [13] and the
acceleration of cosmic rays (CR), particularly at very high energies, E 10
17
eV (see [9] for an extensive
review). It is important to emphasize that when the ZPF is applied as an energizing entity to produce
the expansion associated with the Cosmic Voids, automatically an expansion of the universe itself must
necessarily be produced.
The ZPF acceleration mechanism expands the Voids by creating a pressure imbalance, transferring
energy to, and thereby increasing the pressure in, those regions where matter densities happen to be com-
paratively lower in the IGS plasma [10, 11]. As a consequence the low-density regions tend to expand and
to expel the trapped magnetic elds. It is well known in astrophysics that space plasma regions of higher
densities are colder, while regions of lower density are almost exclusively occupied by a highly energetic
(hot) plasma of electrons and ionized nuclei, mainly protons [15]. This temperature-density anticorrelation
is what occurs in the Voids and it is also what is happening in many places throughout IGS. Moreover, such
a distribution would be a natural outcome of the ZPF acceleration mechanism when combined with ordinary
radiative collisional cooling [9].
THE ZERO-POINT FIELD ACCELERATION MECHANISM
The origins of this mechanism go back to the early work of Einstein and his immediate collaborators [16,
17]. Einstein realized that when a gas of electromagnetically interacting particles
a
is submitted to the action
of a random electromagnetic background (e.g., the case of thermal radiation) two simultaneous phenomena
take place. Due to the action of the random electromagnetic medium, electromagnetically interacting parti-
cles become energized, steadily increasing their translational kinetic energy. They perform a random walk
in velocity space that takes them, on average, systematically away from the origin. Simultaneously however,
as their velocities increase the particles nd themselves submerged in a random electromagnetic medium
that is viewed by each of them as Doppler-shifted and thereby has lost its isotropy. This causes the random
electromagnetic background to appear distorted and thereby to produce a drag force on the particle that is
of a frictional character because it is exactly proportional to the velocity v,
a
Einstein restricted his considertion to polarizable particles. However it can be shown that in the case
of monopolar particles the mechanism is even more eective [9, 18]
2
F = A
(!;T)
1
3
!
@(!;T)
@!
v
c
;
(1)
where A is a positive constant. In a Hohlraum, at equilibrium temperature T; (!;T) represents the
volumetric spectral energy density of the radiation:
(!;T)d! =
h!
3
2
2
c
3
Coth
h!
2kT
d! =
h!
3
2
2
c
3
1
exp(h!=kT) 1
+
1
2
d! :
(2)
The rst term in the last parenthesis represents the thermal part: a Planck distribution at temperature T.
It disappears at zero temperature (T ! 0), leaving the last part,
(!; 0)d! =
0
(!)d! =
h!
3
2
2
c
3
d!
(3)
This is the spectral energy density of the ZPF. It originates in quantum theory from the harmonic oscillator
behavior of the individual cavity modes. At T = 0, each individual cavity mode behaves as a quantized
harmonic oscillator with minimum, or zero-point, ground state energy h!=2. When the energy in each
oscillator is multiplied by the density of modes per unit volume (!
2
=
2
c
3
), one obtains the ZPF spectral
energy density above.
It can be shown that such ZPF is also present in free space, and cogent arguments can be given for its
reality [19, 20]. Observe however, that when the temperature is set to zero (or close to zero) (!;T)d! !
0
(!)d! and because of the !
3
dependence, the Einstein-Hopf drag disappears. This last fact, rst realized
by Boyer [21], is at the basis of the ZPF acceleration mechanism. So, under circumstances in which there
are negligible particle collisions and negligible ambient radiation elds other than the the ZPF, when the
temperature is low or negligible, particles are still translationally energized by the random background
ZPF radiation. But the Einstein-Hopf drag due to the ZPF is zero. In the original formulation of a ZPF
acceleration mechanism [21, 16], it was assumed for simplicity that the translational displacement of the
particle was restricted to a single dimension (say, the x-axis) and that the internal dipole vibrated along a
single direction (say the z-axis). These restrictions were removed by one of us when proposing this concept as
a mechanism for the actual acceleration of cosmic ray (CR) particles in IGS [14, 9]. Soon after it was realized
[18] that monopolar particles could also be accelerated by the ZPF, but in a much more eective manner
than polarizable particles. This conforms with the well-known observational constraint on CR acceleration
mechanisms that restricts the acceleration to fully ionized nuclei [9]. Another well-known constraint is that
electrons appear in CR only at the very low energies, E 10
12
eV, and not beyond. This could be explained
[22] by the ultrarelativistic Zitterbewegung that, because of a time dilation eect, decorrelates the actions
of the electric and of the magnetic elds in the Einstein-Hopf mechanism. This therefore prevents the
acceleration of electrons to ultrahigh CR energies. This decorrelation does not take place in the case of the
much more massive and sturdy protons that, if allowed, can be carried up to the highest CR energies beyond
10
20
The ZPF CR acceleration mechanism can be derived in a quantum way [23, 24]. It was found that it
occurs in a time-symmetric or Wheeler-Feynman version of QED. But acceleration does not occur in the
more ordinary time-unidirectional version of QED [24, 9]. However, as the time-symmetric QED version and
the time-unidirectional version are equivalent (as long as certain initial boundary conditions are assumed
for the radiation in space-time and as those conditions seem to hold in the original universe [25]) there is
no clear reason for taking one or the other versions of QED: no reason other than the fact that we are more
used to the time-unidirectional version.
It is moreover very interesting to mention that both the Wheeler-Feynman version of QED and the
classical stochastic theory give exactly the same nal form for the translational kinetic energy rate of growth
, namely
3
eV [9].
=
3
5
(!
0
)
2
h!
0
mc
2
(h!
0
) !
0
(4)
where is the Abraham-Lorentz parameter ( = 2e
2
=3mc
3
), with e the charge and m the mass of the
particle (proton). The frequency !
0
is a parameter that depends on other considerations, e.g., what entity
really performs the oscillations, whether the whole proton or some component (like quarks, proton vibration
modes, etc.) inside the proton. In the most simplistic case !
0
comes to be half the proton Compton frequency
(!
0
= mc
2
=2h), but this applies only under unrealistic strictly subrelativistic considerations. In practice !
0
is taken as a free-parameter to be phenomenologically tted by observation.
The ZPF acceleration mechanism could be found to satisfy all standard CR observational constraints
[26, 9], certainly at energies E 10
17
eV. But lower energies could not be immediately excluded, though
the situation there was somewhat less certain [9]. The least that we can say then is that the mechanism, up
to now, seems to be one of the strongest contenders for CR acceleration at ultrahigh E 10
17
eV energies.
CHALLENGE TO THE ZPF ACCELERATION CONCEPT
Recently in their 1996 textbook on the theory of Stochastic Electrodynamics (SED) and related theories,
de la Pena and Cetto [20] have challenged at least some aspects of the ZPF acceleration concept. In a lucid
reanalysis [27] of the Boyer derivation [21] of the translational kinetic energy growth, they argue that if
an arguably more realistic non-Markovian stochastic process is assumed for the phenomenon in its classical
form, no systematic translational kinetic energy growth takes place. This would then rather t, according to
de la Pena and Cetto, the time-unidirectional version of the QED acceleration mechanism that indeed yields
no systematic translational kinetic energy growth [24, 9]. We discuss the de la Pena and Cetto argument in
the Appendix.
Formally, of course, and once the non-Markovian behavior is assumed, the argument of de la Pena and
Cetto seems faultless. The situation however is far from clear. Time-symmetric QED [25] still gives the
acceleration and there is no certainty at all that even when a classical viewpoint is implemented, the process
has to be non-Markovian, i.e., having some memory. Moreover, recent work of Cole [28] strongly suggests the
thermodynamics soundness of the ZPF acceleration mechanism both in its physical and in its astrophysical
context. This step is important. Before this there remained a thermodynamic challenge to ZPF acceleration
[29]. Apparently, ZPF acceleration seemed to violate standard interpretations of the rst and of the second
laws of thermodynamics. It has been shown that this is indeed not the case [28].
DISCUSSION
Given the overwhelming astrophysical explanatory possibilities of the ZPF acceleration mechanism |
to mention a few, accelerated cosmic expansion, ultrahigh energies CR, part of the X-ray and the gamma-ray
backgrounds, Cosmic Voids, etc. | it is of paramount importance to clarify the situation and decide if the
de la Pena and Cetto challenge is or is not a surmountable diculty.
There are also other important possibilities for the ZPF acceleration mechanism. If valid, the mechanism
should eventually provide a means to transfer energy, back and forth, but most importantly forth [9], from
the vacuum electromagnetic ZPF into a suitable experimental apparatus. A more far-fetched but not triing
possibility is that a better understanding of the Einstein-Hopf process, that accompanies ZPF acceleration,
would lead to an understanding of the recently proposed ZPF contribution to inertia [30], also presumably
to some means for inuencing inertia, and by the Einstein Principle of Equivalence, also gravity. This has
very interesting prospective engineering applications.
ACKNOWLEDGEMENTS
BH and AR acknowledge partial support from NASA research contract NASW-5050. AR and BH
acknowledge interesting exchanges with Prof. Daniel C. Cole (Boston University).
4
APPENDIX: Possible suppression of the secular ZPF acceleration
De la Pena and Cetto [20] have reached the conclusion that the zero-point eld may not produce secular
acceleration. In this Appendix, the arguments leading to this conclusion are discussed.
1. Dipole Oscillator Model
The Boyer SED approach to the problem [21] is based upon the model originally developed by Einstein
and Hopf [16, 17]. In this model, that for simplicity we follow here, it is assumed that the internal particle
motion is in the x-direction and the oscillator dipole vibrates along the z-axis. (An extension to fully
three-dimensional motions was obtained in [14].)
During a time interval t, this oscillator experiences two forces due to electromagnetic radiation, namely
the impulse transferred to the dipole via the interaction with the uctuating eld, and the force of resistance
Rp due to the anisotropy of the eld as seen by the moving particle. Then, if at time t, the momentum of the
translational motion of the oscillator is p, after a short time t, its momentum becomes p+ Rpt. Since
in equilibrium the mean-square momentum has to be constant in time, we get the equilibrium condition,
p
2
=
(p + Rpt)
2
;
(A1)
R
where the impulse =
Fdt, and the drag coecient R are given respectively by
*
Z
t+t
dtez
@E
z
@x
!
2
+
4
4
c
4
5!
2
2
=
=
2
(!;T)t;
(A2)
t
and
R =
6
2
c
5m
1
3
!
@
@!
:
(A3)
Equation (A1) , when expanded and neglecting the term of second order in t yields
2
+ 2hpi 2R
p
2
t 2Rhpit = 0:
(A4)
At T = 0, however, there is no drag force since
0
is Lorentz-invariant, so that the above equation yields
2
0
+ 2hpi
= 0:
(A5)
0
6= 0 due to the presence of the zero-point eld, the momentum p and the
uctuation have to be correlated, contrary to the assumption hpi = 0 correctly made by Einstein and
his coworkers, but only for the case of pure thermal radiation. It is here where de la Pena and Cetto disagree
with Boyer [21] who assumed even when the ZPF is present that hpi = 0 always. So, de la Pena and Cetto
sensibly claim that the uctuation at a given time is not independent of past ones, i.e., the process p = p p
is not Markovian and the system acquires a certain degree of memory in its interactions with the ZPF.
0
0
(which is justied because
the thermal component of the eld is not expected to contribute signicantly to the correlation hpi
Now let us combine (A4) with (A5) using the approximation hpihpi
0
) to
yield
2
2
0
= 2R
p
2
tR
2
0
t:
(A6)
It can be shown and is well-known to experts dealing with the model of Einstein and Hopf in SED that the
stochastic average of the square of the uctuating impulse h
2
i
0
is of order t. Thus, the last term is of
order (t)
2
and can be neglected. Hence the equation simplies to
5
This suggests that since h
2
i
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