Haisch - Zero-Point Field and the NASA Challenge to Create the Space Drive (1997).pdf

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(Invited Presentation at NASA Breakthrough Propulsion Physics Workshop, NASA Lewis Res. Ctr., Aug. 12{14, 1997)
For more recent papers on this topic see <http://www.calphysics.org/sci_articles.html>
The Zero-Point Field and the NASA Challenge to Create the Space Drive
Bernard Haisch
Solar and Astrophysics Laboratory, Lockheed Martin
3251 Hanover St., Palo Alto, CA 94304
Alfonso Rueda
Dept. of Electrical Engineering & Dept. of Physics, California State Univ.
Long Beach, CA 90840
ABSTRACT:
This NASA Breakthrough Propulsion Physics Workshop seeks to explore concepts that could someday enable
interstellar travel. The e®ective superluminal motion proposed by Alcubierre (1994) to be a possibility
owing to theoretically allowed space-time metric distortions within general relativity has since been shown
by Pfenning and Ford (1997) to be physically unattainable. A number of other hypothetical possibilities
have been summarized by Millis (1997). We present herein an overview of a concept that has implications
for radically new propulsion possibilities and has a basis in theoretical physics: the hypothesis that the
inertia and gravitation of matter originate in electromagetic interactions between the zero-point ¯eld (ZPF)
and the quarks and electrons constituting atoms. A new derivation of the connection between the ZPF and
inertia has been carried through that is properly co-variant, yielding the relativistic equation of motion from
Maxwell's equations. This opens new possibilites, but also rules out the basis of one hypothetical propulsion
mechanism: Bondi's \negative inertial mass," appears to be an impossibility.
INTRODUCTION:
The objective of this NASA Breakthrough Propulsion Physics Workshop is to explore ideas ranging from
extrapolations of known technologies to hypothetical new physics which could someday lead to means for
interstellar travel. One concept that has generated interest is the proposal by Alcubierre (1994) that e®ec-
tively superluminal motion should be a possibility owing to theoretically allowed space-time metric distortions
within general relativity. In this model, motion between two locations could take place at e®ectively hy-
perlight speed without violating special relativity because the motion is not through space at v > c, but
rather within a space-time distortion: somewhat like the \stretching of space" itself implied by the Hub-
ble expansion. Alcubierre's concept would indeed be a \warp drive." Unfortunately Pfenning and Ford
(1997) demonstrated that, while the theory may be correct in principle, the necessary conditions are physi-
cally unattainable. In \The Challenge to Create the Space Drive" Millis (1997) has summarized a number
of other possibilities for radically new propulsion methods that could someday lead to interstellar travel
if various hypothetical physics concepts should prove to be true. Seven di®erent propulsion concepts were
presented therein: three involved hypothetical collision sails and four were based on hypothetical ¯eld drives.
The purpose of this paper is to discuss a new physics concept that no longer falls in the category of \purely
hypothetical," but rather has a theoretical foundation and is relevant to radically new propulsion schemes:
the zero-point ¯eld (ZPF) as the basis of inertia and gravitation. On the basis of this concept we can de¯ni-
tively rule out one of the hypothesized propulsion mechanisms since the existence of negative inertial mass
is conclusively shown to be an impossibility. On the other hand a di®erential space sail becomes a distinct
possiblity. More importantly, though, the door is theoretically open to the possibility of manipulation of
inertia and gravitation of matter since both properties are shown to stem at least in part from electrody-
namics. This raises the stakes considerably as Arthur C. Clarke (1997) writes in his novel, 3001 referring to
the ZPF-inertia concept of Haisch, Rueda and Putho® (1994; hereafter HRP):
An \inertialess drive," which would act exactly like a controllable gravity ¯eld, had never been
discussed seriously outside the pages of science ¯ction until very recently. But in 1994 three
American physicists did exactly this, developing some ideas of the great Russian physicist
Andrei Sakharov.
1
(Invited Presentation at NASA Breakthrough Propulsion Physics Workshop, NASA Lewis Res. Ctr., Aug. 12{14, 1997)
THE ZERO-POINT FIELD FROM PLANCK'S WORK:
In the year 1900 there were two main clouds on the horizon of classical physics: the failure to measure the
motion of the earth relative to the ether and the inability to explain blackbody radiation. The ¯rst problem
was resolved in 1905 with the publication of Einstein's \Zur Elektrodynamik bewegter Korper" in the journal
Annalen der Physik, proposing what has come to be known as the special theory of relativity. It is usually
stated that the latter problem, known as the \ultraviolet catastrophe," was resolved in 1901 when Planck, in
\ Uber das Gesetz der Energieverteilung im Normalspektrum" in the same journal, derived a mathematical
expression that ¯t the measured spectral distribution of thermal radiation by hypothesizing a quantization
of the average energy per mode of oscillation, ² = hº.
The actual story is somewhat more complex (cf. Kuhn 1978). Since the objective is to calculate an elec-
tromagnetic spectrum one has to represent the electromagnetic ¯eld in some fashion. Well-known theorems
of Weyl allow for an expansion in countably many in¯nite electromagnetic modes (e.g. Kurokawa 1958).
Every electromagnetic ¯eld mode behaves exactly as a linear harmonic oscillator. The Hamiltonian of a
one-dimensional oscillator has two terms, one for the kinetic energy and one for the potential energy:
H =
2m + Kx 2
:
(1)
2
The classical equipartition theorem states that each quadratic term in position or momentum contributes
kT =2 to the mean energy (e.g. Peebles 1992). The mean energy of each mode of the electromagnetic ¯eld
is then < E >= kT . The number of modes per unit volume is (8¼º 2 =c 3 )dº leading to the Rayleigh-Jeans
spectral energy density (8¼º 2 =c 3 )kT dº with its º 2 divergence (the ultraviolet catastrophe).
In his \¯rst theory" Planck actually did more than simply assume ² = hº. He considered the statistics of how
\P indistinguishable balls can be put into N distinguishable boxes." (Milonni 1994) So Planck anticipated
the importance of the fundamental indistinguishability of elementary particles. With those statistics, the
average energy of each oscillator becomes < E >= ²=(exp(²=kT ) ¡ 1). Assuming that ² = hº together
with the use of statistics appropriate to indistinguishable energy elements then led to the spectral energy
distribution consistent with measurements, now known as the Planck (or blackbody) function:
8¼º 2
c 3
µ
hº
e hº=kT ¡ 1
½(º; T )dº =
dº:
(2a)
Contrary to the cursory textbook history, Planck did not immediately regard his ² = hº assumption as a
new fundamental law of physical quantization; he viewed it rather as a largely ad hoc theory with unknown
implications for fundamental laws of physics. In 1912 he published his \second theory" which led to the
concept of zero-point energy. The average energy of a thermal oscillator treated in this fashion (cf. Milonni
1994 for details) turned out to be < E >= hº=(exp(hº=kT ) ¡ 1) + hº=2 leading to a spectral energy density:
8¼º 2
c 3
µ
e hº=kT ¡ 1 + hº
hº
½(º; T )dº =
dº:
(2b)
2
The signi¯cance of this additional term, hº=2, was unknown. While this appeared to result in a º 3 ultraviolet
catastrophe in the second term, in the context of present-day stochastic electrodynamics (SED; see below)
that is intepreted as not to be the case, because this component now refers not to measurable excess radiation
from a heated object, but rather to a uniform, isotropic background radiation ¯eld that cannot be directly
measured because of its homogeneity. Planck came to the conclusion that the zero-point energy would have
no experimental consequences. It could be thought of as analagous to an arbitrary additive constant for
potential energy. Nernst (1916), on the other hand, took it seriously and proposed that the Universe might
actually contain enormous amounts of zero-point energy.
Work on zero-point energy in the context of classical physics was essentially abandoned at this stage as the
development of quantum mechanics, and then quantum electrodynamics (QED), took center stage. However
the parallel concept of an electromagnetic quantum vacuum soon emerged.
2
p 2
177883266.001.png
(Invited Presentation at NASA Breakthrough Propulsion Physics Workshop, NASA Lewis Res. Ctr., Aug. 12{14, 1997)
THE ZERO-POINT FIELD FROM QUANTUM PHYSICS:
For a one-dimensional harmonic oscillator of unit mass the quantum-mechanical Hamiltonian analagous to
Eq. (1) may be written (cf. Loudon 1983)
H =
1
2 (p 2 + ! 2 q 2 );
(3)
where p and q are momentum and position operators respectively. Linear combination of the p and q result in
the ladder operators, also known as destruction (or lowering) and creation (or raising) operators respectively:
a = (2h!)
¡1=2 (!q + ip);
(4a)
a
y
= (2h!)
¡1=2 (!q ¡ ip):
(4b)
The application of the destruction operator on the nth eigenstate of a quantum oscillator results in a lowering
of the state, and similarly the creation operator results in a raising of the state:
ajni = n 1=2 jn ¡ 1i;
(5a)
a
y jni = (n + 1) 1=2 jn + 1i;
(5b)
It can be seen that the number operator has the jni states as its eigenstates as
Njni = a
y
ajni = njni:
(5c)
The Hamiltonian or energy operator of Eq. (3) becomes
µ
N + 1
2
µ
a + 1
2
H = h!
y
= h!
a
:
(6)
The ground state energy of the quantum oscillator, j0i, is greater than zero, and indeed has the energy
2 h!,
Hj0i = E 0 j0i =
1
2 h!j0i;
(7)
and thus for excited states
µ
n + 1
2
E n =
h!:
(8)
Now let us turn to the case of classical electromagnetic waves. Plane electromagnetic waves propagating in
a direction k may be written in terms of a vector potential A k as
E k = i! k fA k exp(¡i! k t + ik ¢ r) ¡ A
¤
k exp(i! k t ¡ ik ¢ r)g;
(9a)
B k = ik£fA k exp(¡i! k t + ik ¢ r) ¡ A
k exp(i! k t ¡ ik ¢ r)g;
(9b)
Using generalized mode coordinates analogous to momentum (P k ) and position (Q k ) in the manner of Eqs.
(4ab) above one can write A k and A
k as
A k = (4² 0 V ! k )
¡ 2 (! k Q k + iP k )" k ;
(10a)
A
k = (4² 0 V ! k )
¡ 2 (! k Q k
¡ iP k )" k ;
(10b)
3
1
¤
¤
¤
(Invited Presentation at NASA Breakthrough Propulsion Physics Workshop, NASA Lewis Res. Ctr., Aug. 12{14, 1997)
where " k is the polarization unit vector and V the cavity volume. In terms of these variables, the single-mode
phase-averaged energy is
< E k >=
1
2 (P k + ! k Q k ):
(11)
Note the parallels between equations (10) and (4) and equations (11) and (3). Just as mechanical quantization
is done by replacing position, x, and momentum, p, by quantum operators x and p, so is the \second"
quantization of the electromagnetic ¯eld accomplished by replacing A with the quantum operator A, which
in turn converts E into the operator E, and B into B. In this way, the electromagnetic ¯eld is quantized
by associating each k-mode (frequency, direction and polarization) with a quantum-mechanical harmonic
oscillator. The ground-state of the quantized ¯eld has the energy
< E k;0 >=
1
2 (P k;0 + ! k Q k;0 ) 2 =
1
2 h! k
(12)
that originates in the non-commutative algebra of the creation and annihilation operators. It is as if there
were on average half a photon in each mode.
ZERO-POINT FIELD IN STOCHASTIC ELECTRODYNAMICS:
A common SED treatment (cf. Boyer 1975 and references therein; also the comprehensive review of SED
theory by de la Pena and Cetto 1996) has been to posit a zero-point ¯eld (ZPF) consisting of plane elec-
tromagnetic waves whose amplitude is exactly such as to result in a phase-averaged energy of h!=2 in each
mode (k,¾), where we now explicitly include the polarization, ¾. After passing to the continuum such that
summation over discrete modes of propagation becomes an integral (valid when space is unbounded or nearly
so) this can be written as:
X
2
Z
·
h! k
8¼ 3 ² 0
¸
1
2
E ZP (r; t) = Re
d 3 k" k;¾
exp(ik ¢ r ¡ i! k t + iµ k;¾ );
(13a)
¾=1
X
Z
·
h! k
8¼ 3 ² 0
¸
1
2
d 3 k(k £ " k;¾ )
B ZP (r; t) = Re
exp(ik ¢ r ¡ i! k t + iµ k;¾ );
(13b)
¾=1
, and this is represented by having
the µ k;¾ phase random variables independently and uniformly distributed between 0 and 2¼.
0
DAVIES-UNRUH EFFECT:
In connection with \Hawking radiation" from evaporating black holes, Davies (1975) and Unruh (1976)
determined that a Planck-like component of the ZPF will arise in a uniformly-accelerated cordinate system
with constant proper acceleration a (where jaj = a) having an e®ective temperature,
T a =
ha
2¼ck :
(14)
This temperature is negligible for most accelerations. Only in the extremely large gravitational ¯elds of
black holes or in high-energy particle collisions can this become signi¯cant. This e®ect has been studied
using both quantum ¯eld theory (Davies 1975, Unruh 1976) and in the SED formalism (Boyer 1980). For
the classical SED case it is found that the spectrum is quasi-Planckian in T a . Thus for the case of no true
external thermal radiation (T = 0) but including this acceleration e®ect (T a ), equation (2b) becomes
8¼º 2
c 3
·
³
a
2¼cº
´
2
¸ ·
hº
2
hº
e hº=kT a ¡ 1
¸
½(º; T a )dº =
1 +
+
dº;
(15)
4
2
where µ k;¾ is the phase of the waves. The stochasticity is entirely in the phase of each wave: There is no
correlation in phase between any two plane electromagnetic waves k and k
177883266.002.png
(Invited Presentation at NASA Breakthrough Propulsion Physics Workshop, NASA Lewis Res. Ctr., Aug. 12{14, 1997)
where the acceleration-dependent pseudo-Planckian component is placed after the hº=2 term to indicate
that except for extreme accelerations (e.g. particle collisions at high energies) this term is very small. While
these additional acceleration-dependent terms do not show any spatial asymmetry in the expression for the
ZPF spectral energy density, certain asymmetries do appear when the electromagnetic ¯eld interactions with
charged particles are analyzed, or when the momentum °ux of the ZPF is calculated. The ordinary plus a 2
radiation reaction terms in Eq. (12) of HRP mirror the two leading terms in Eq. (15).
NEWTONIAN INERTIA FROM ZPF ELECTRODYNAMICS:
The HRP analysis resulted in the apparent derivation of Newton's equation of motion, F = ma, from
Maxwell-Lorentz electrodynamics as applied to the ZPF. In that analysis it appeared that the resistance to
acceleration known as inertia was in reality the electromagnetic Lorentz force stemming from interactions
between a charged particle (such as an electron or a quark) and the ZPF, i.e. it was found that the
stochastically-averaged expression < v osc £ B ZP > was proportional to and in the opposite direction to
the acceleration a. The velocity v osc represented the internal velocity of oscillation induced by the electric
component of the ZPF, E ZP , on the harmonic oscillator. For simplicity of calculation, this internal motion
was restricted to a plane orthogonal to the external direction of motion (acceleration) of the particle as a
whole. The Lorentz force was found using a perturbation technique; this approach followed the method of
Einstein and Hopf (1910a, b). Owing to its linear dependence on acceleration we interpreted this resulting
force as Newton's inertia reaction force on the particle.
The analysis can be summarized as follows. The simplest possible model of a structured particle (which,
borrowing Feynman's terminology, we referred to as a parton) is that of a harmonically-oscillating point
charge (\Planck oscillator"). Such a model would apply to electrons or to the quarks constituting protons and
neutrons for example. (Given the peculiar character of the strong interation that it increases in strength with
distance, to a ¯rst approximation it is reasonable in such an exploratory attempt to treat the three quarks in
a proton or neutron as independent oscillators.) This Planck oscillator is driven by the electric component
of the ZPF, E ZP , to harmonic motion, v osc , assumed for simplicity to be in a plane. The oscillator is then
forced by an external agent to undergo a constant acceleration, a, in a direction perpendicular to that plane
of oscillation, i.e. perpendicular to the v osc motions. New components of the ZPF will appear in the frame
of the accelerating particle having a similar origin to the terms in equation (15). The leading term of the
acceleration-dependent terms is taken; the electric and magnetic ¯elds are transformed into a constant proper
acceleration frame using well-known relations. The Lorentz force arising from the acceleration-dependent
part of the B ZP acting upon the Planck oscillator is calculated. This is found to be proportional to the
imposed acceleration. The constant of proportionality is interpreted as the inertial mass, m i , of the Planck
oscillator. The inertial mass, m i , is a function of the Abraham-Lorentz radiation damping constant of the
oscillator and of the interaction frequency with the ZPF,
m i =
2¼c 2 ;
(16)
where we have written º 0 to indicate that this may be a resonance rather than the cuto® assumed by HRP.
Since both ¡ and º o are unknown we can make no absolute prediction of mass values in this simple model.
Nevertheless, if correct, the HRP concept substitutes for Mach's principle a very speci¯c electromagnetic
e®ect acting between the ZPF and the charge inherent in matter. Inertia is an acceleration-dependent
electromagnetic (Lorentz) force. Newtonian mechanics would then be derivable in principle from Maxwell's
equations. Note that this coupling of the electric and magnetic components of the ZPF via the technique of
Einstein and Hopf is very similar to that found in ordinary electromagnetic radiation pressure.
THE RELATIVISTIC EQUATION OF MOTION AND ZPF ELECTRODYNAMICS:
The physical oversimpli¯cation of an idealized oscillator interacting with the ZPF as well as the mathematical
complexity of the HRP analysis are understandable sources of skepticism, as is the limitation to Newtonian
mechanics. A relativistic form of the equation of motion having standard covariant properties has been
obtained (Rueda and Haisch 1997a,b). To understand how this comes about, it is useful to back up to
fundamentals.
5
¡hº 0

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