The most famous of all equations must
surely be E=mc^{2}. In popular culture that relation between
energy and mass is virtually synonymous with relativity, and Einstein,
its originator, has become a symbol of modern physics. The usual
interpretation of the equation is that one kind of fundamental physical
thing, mass (m in the equation), can be converted into a quite different
kind of fundamental physical thing, energy (E in the equation), and vice
versa; the two quantities are inextricably intertwined, related by the
factor c^{2}, the square of the velocity of light. The energy of
the sun, for instance, comes from nuclear fusion, in which the nuclei of
hydrogen atoms fuse together to become the nuclei of helium atoms. In
the prevailing view, mass is lost in the fusion reaction, and as one
popular astronomy textbook puts it, "The small fraction of mass that
disappears in the process is converted into energy according to the
formula E=mc^{2}."
Recent work by us and others now appears to offer a radically
different insight into the relation E=mc^{2}, as well as into
the very idea of mass itself. To put it simply, the concept of mass may
be neither fundamental nor necessary in physics. In the view we will
present, Einstein's formula is even more significant than physicists
have realized. It is actually a statement about how much energy is
required to give the appearance of a certain amount of mass, rather than
about the conversion of one fundamental thing, energy, into another
fundamental thing, mass.
Indeed, if that view is correct, there is no such thing as massonly
electric charge and energy, which together create the illusion of mass.
The physical universe is made up of massless electric charges immersed
in a vast, energetic, allpervasive electromagnetic field. It is the
interaction of those charges and the electromagnetic field that creates
the appearance of mass. In other words, the magazine you now hold in
your hands is massless; properly understood, it is physically nothing
more than a collection of electric charges embedded in a universal
energetic electromagnetic field and acted on by the field in such a way
as to make you think the magazine has the property of mass. Its apparent
weight and solidity arise from the interactions of charges and field.
Besides recasting the prevailing view of mass, this idea would
address one of the most profound problems of physics, the riddle of how
gravity can be unified with the other three fundamental forces of nature.
The electromagnetic force and the weak force, which is responsible for
nuclear decay, have been shown to be two manifestations of a single
force, appropriately called the electroweak force. There are tantalizing
hints that the strong force, which binds nuclei together, will someday
be unified with the electroweak force. But until now gravity has
resisted all attempts at unification. If the new view is correct,
however, gravity would not need to be separately unified. Just as mass
would arise from the electromagnetic force, so would gravity.
What is mass? Two key properties define the concept of the mass of a
given amount of matter, namely, its inertia and the gravitation to which
the matter gives rise. Inertia was defined by Galileo as the property of
matter that keeps an object in uniform motion once given an impetus,
until the object is acted upon by some further impetus. Galileo's idea
was generalized and quantified by Newton in his Principia. The tendency
of an object to remain in uniform motion, and the tendency of the motion
to change when impetus is applied, Newton expressed in one compact
equation. The equation states that the acceleration a, or change of
velocity, is proportional to the force F applied, where the constant of
proportionality is the inertial mass m of the object in question: thus,
F=ma.
In other words, inertial mass is the resistance an object offers to
being accelerated when it is subjected to a force. In Newton's equation
of motion, when the application of a force ceases, the acceleration goes
to zero, and the object remains in uniform motion. Objects are assumed
to resist acceleration, because that resistance is an innate property of
matter.
But try as he might, Newton could not explain the origin of inertia.
Imagine, he suggested, that the universe is empty except for a bucket
partly filled with water. Furthermore, imagine the shape of the surface
of the water: Is it flat? Then the water must be at rest. Is it curved,
shaped in cross section like a parabolic reflector? Then the water must
be rotating. But rotating with respect to what? That was the profound
dilemma that Newton identified. If the universe were truly empty, as his
thought experiment required, there would be no background against which
the rotation could be measured. But because the shape of the water
surface signals whether a rotation is taking place, Newton concluded
that there is a fundamental spatial frame of reference, an "absolute
space."
Some 200 years later the nineteenthcentury Austrian physicist and
philosopher Ernst Mach took a contrary view. To Mach, Newton's thought
experiment demonstrated the absurdity of the idea of absolute space. The
shape of the water in a rotating bucket, Mach held, was conferred,
somehow, through the presence of all the other matter in the universe.
Thus Mach agreed with Newton that the property of inertia creates the
need for a reference frame; he simply disagreed that such a reference
frame could exist as a distinct, absolute entity. Distant matter,
however, could define the reference frame. Unfortunately, his conjecture,
which has come to be known as Mach's principle, remains more of a
philosophical statement than a testable scientific proposition.
In the early twentieth century a number of investigators, including
Max Abraham, Hendrik Antoon Lorentz and Henri Poincare, suggested that
inertial mass might arise from an effect called electrostatic selfenergy.
Any charged particlethe electron, for instancepossesses a certain
quantity of electric charge. The charge is the source of an electric
field, which carries energythe electrostatic selfenergy. It was
proposed that the electrostatic selfenergy might correspond to the
inertial mass of the charged particle, through the equation E=mc^{2}.
But the theoretical mass of the electrostatic electron derived from the
equation is many orders of magnitude larger than the actual observed
mass of the electron, and the selfrepulsion of the electrostatic forces
would quickly disperse the electrostatic electron. Hence the theory
fails.
Our work suggests inertia is a property arising out of the vast, allpervasive
electromagnetic field we mentioned earlier, which is called the zeropoint
field (ZPF). The name comes from the fact that the field is held to
exist in a vacuumwhat is commonly thought of as "empty" spaceeven at
the temperature of absolute zero, at which all thermal radiation is
absent. The background energy of the vacuum serves as the reference, or
zero point, for all processes. To understand how the ZPF might give rise
to inertia, one must understand something about the nature of the field
itself.
Theoretical considerations indicate that the ZPF should be a
background sea of electromagnetic radiation that is both uniform and
isotropic (the same in all directions). The reader may already be
familiar with a somewhat similar concept: the remnant radiation from the
big bang. According to big bang cosmology, the universe began with a
titanic explosion, which gave rise to hot, energetic radiation
distributed throughout the infant universe. As the universe expanded and
cooled, the radiation became much less energetic, but it still pervades
space as a faint and nearly isotropic background of microwave radiation.
Like the cosmic microwave background, the ZPF is a sea of radiation
that fills the entire universe. There is a major difference, however.
The cosmic microwave background has a rather feeble spectrum identical
with the spectrum of an object in thermal equilibrium at a temperature
of only 2.76 degrees Celsius above absolute zero. In contrast, the ZPF
is a highly energetic emission whose predicted radiation spectrum
departs radically from the spectrum of an object in thermal equilibrium.
Instead of trailing off at high frequencies, the energy of the ZPF
continues to rise sharply with the frequency of the radiation.
Quantitatively, the energy density is proportional to the cube of the
frequency; double the frequency, and the energy increases by a factor of
eight. At what frequency the ZPF spectrum finally cuts off or loses its
ability to interact with matter are important and still unresolved
issues.
A more profound difference between the cosmic microwave background
and the ZPF is a result of the origin of the two emissions. When you
switch on a lightbulb, the source of the light emission is clear; it is
the heat produced by an electric current in the filament. The source of
the cosmic microwave background can also be traced to known physical
phenomena, namely, the heat radiation associated with the big bang, as
modified by the later expansion and cooling of the universe. The origin
of the ZPF is more esoteric. In fact, two distinct views about it exist
today.
The conventional view traces the ZPF to the laws of quantum mechanics,
the theory forged early in the present century to describe the atom. Any
electromagnetic field is characterized by the frequency, polarization
and direction of propagation of its radiation. A set of values for those
three quantities defines a single socalled mode of the field. Every
possible mode can be populated by an arbitrary number of photons, the
fundamental quanta of electromagnetic radiation. But according to the
probabilities calculated in quantum mechanics, even at its minimum
energy, each mode will contain one photon half the time and no photons
the other half the time. In a field of zero energy each mode would, with
certainty, contain no photons, but that is impossible because of the
equal probability that each mode also contains one photon. Thus every
mode acts, on average, as if it were populated with at least onehalf
photon (in addition to whatever other natural or manmade radiation
happens to be present).
All such modes add up quickly. Since the energy density of the ZPF
increases as the cube of the frequency, the amount of energy making up
the ZPF is enormous. That energy, in the conventional view, is simply
forced into existence by the laws of quantum mechanics. Not surprisingly,
it is regarded in quantum fashion as sometimes real and sometimes
virtual, depending on the problem at hand.
The competing theory for the origin of the ZPF comes from what has
heretofore been an obscure discipline within physics known as stochastic
electrodynamics, a modern version of much earlier twentiethcentury
investigations by Einstein, Max Planck, Walther Nernst, Ludwig Hopf and
Otto Stern. Stochastic electrodynamics postulates that the ZPF is as
real as any other radiation field. In such a view the existence of a
real ZPF is as fundamental as the existence of the universe itself. The
only difference between stochastic electrodynamics and ordinary
classical physics is the single assumption of the presence of this allpervasive,
real ZPF, which happens to be an intrinsic part of the universe.
One justification for making such an assumption is that by adding the
ZPF to classical physics many quantum phenomena can be derived without
invoking the usual laws or logic of quantum mechanics. It is premature
to claim that all quantum phenomena could be explained by stochastic
electrodynamics (that is, classical physics plus the ZPF), but that
claim may one day turn out to be the case. In that event, one would have
to make a choice. One could accept the laws of classical physics as only
partly true, with a wholly different set of quantum laws required to
complete the laws of physics; that is essentially what is done in
physics now. Or one could accept the laws of classical physics as the
only necessary laws, provided they are supplemented by the presence of
the ZPF.
Whether the ZPF arises from quantum laws or is simply an intrinsic
part of the universe, an important question remains: Why do people not
sense the presence of the radiation if indeed it is made up of real
electromagnetic waves spanning the spectrum of radio waves, light and X
rays? The idea that space could be filled with a vast sea of energy does
seem to contradict everyday experience. The answer to the question lies
in the utter uniformity and isotropy of the field. There is no way to
sense something that is absolutely the same everywhere, outside and
inside everything. To put the matter in everyday terms, if you lie
perfectly still in a tub of water at body temperature, you cannot feel
the heat of the water.
Motion through a medium almost always gives rise to asymmetries,
which then makes it possible to detect the medium. But in the case of
the ZPF, motion through space at a constant velocity does not make the
field detectable, because the field has the property of being "Lorentz
invariant." (Lorentz invariance is a critical difference between the
modern ZPF and nineteenthcentury concepts of an ether.) The field
becomes detectable only when a body is accelerated through space. In the
mid1970s the physicists Paul C. W. Davies, now at the University of
Adelaide in Australia, and William G. Unruh, now at the University of
British Columbia, showed that as a moving observer accelerates through
the ZPF, the ZPF spectrum becomes distorted, and the distortion
increases with increasing acceleration. Can the distortion be seen? Yes
indeed, but not with one's eyes, because the energies involved are
minute.
Although the distortion is small, it is extremely important: our
analysis shows that it is the origin of inertia. In an article published
last February in Physical Review A, we showed that when an
electromagnetically interacting particle is accelerated through the ZPF,
a force is exerted on the charge; the force is directly proportional to
the acceleration but acts in the direction opposite to it. In other
words, the charge experiences an electromagnetic force as resistance to
acceleration. We interpret the resistance associated with the charge as
the very inertia Newton regarded as an innate property of matter. Note
that we do not say, "associated with the mass of the particle." In our
formulation, the m in Newton's second law of motion, F=ma, becomes
nothing more than a coupling constant between acceleration and an
external electromagnetic force. Thus what we are proposing is that
Newton's second law can be derived from the laws of electrodynamics,
provided one assumes an underlying zeropoint field.
Our work suggests that the conventional Newtonian idea of mass must
be boldly reinterpreted. If we are correct, physical theory need no
longer suppose that there is something called mass having an innate
property, inertia, that resists acceleration; what is really happening,
instead, is that an electromagnetic force acts on the charge inside
matter to create the effect of inertia. Indeed, it appears that the more
parsimonious interpretation is not even that there is charge lurking
"inside matter," but that there is only charge. The presence of charge
and its interaction with the ZPF creates the forces we all experience
and attribute to the existence of matter. Our interpretation would apply
even to an electrically neutral particle such as the neutron, because
the neutron, at the most fundamental level, is thought to be made up of
smaller particles called quarks, which do carry electric charge.
We have had little to say so far about the second key property for
the concept of mass, the gravitation to which matter gives rise. But
experimental evidence shows that an object's inertial mass, or its
resistance to acceleration, is equivalent to the object's gravitational
mass, or its mass in a gravitational field. Einstein's general theory of
relativity is based on the assumption that inertial and gravitational
mass are equivalent and indistinguishablethe socalled principle of
equivalence. Hence it stands to reason that if the ZPF gives rise to the
phenomenon of inertia, it must also in some way generate the effect of
gravity. This audacious idea was proposed as early as 1968 by the
Russian physicist and dissident Andrei D. Sakharov, but he never fully
developed the concept into a scientific theory.
In 1989 the idea was taken up by one of us (Puthoff) and formulated
within the framework of stochastic electrodynamics into a preliminary
but quantifiable, nonrelativistic representation of Newtonian
gravitation. The underlying principle is remarkably intuitive. If a
charged particle is subjected to ZPF interactions, it will be forced to
fluctuate in response to the random jostlings of the electromagnetic
waves of the ZPF. Moreover, since the ZPF is allpervasive, charged
particles everywhere in the universe will be forced to fluctuate. Now a
basic result from classical electrodynamics is that a fluctuating
electric charge emits an electromagnetic radiation field. The result is
that all charges in the universe will emit secondary electromagnetic
fields in response to their interactions with the primary field, the ZPF.
The secondary electromagnetic fields turn out to have a remarkable
property. Between any two particles they give rise to an attractive
force. The force is much weaker than the ordinary attractive or
repulsive forces between two stationary electric charges, and it is
always attractive, whether the charges are positive or negative. The
result is that the secondary fields give rise to an attractive force we
propose may be identified with gravity.
It is important to note that the fluctuations are relativisticthat
is, the charges move at velocities at or close to the speed of light.
The energy associated with the fluctuationswhich for historical reasons
is given the German name zitterbewegung, or trembling movementis
interpreted as the energy equivalent of gravitational rest mass. Since
the gravitational force is caused by the trembling motion, there is no
need to speak any longer of a gravitational mass as the source of
gravitation. The source of gravitation is the driven motion of a charge,
not the attractive power of the thing physicists are used to thinking of
as mass. To interpret Einstein's equation E=mc^{2}, we would say
that mass is not equivalent to energy. Mass is energy.
Naturally there are a host of objections that have been or can be
raised to our radical interpretation of mass. One important objection is
that for gravity our model so far is nonrelativistic, whereas the
zitterbewegung motions are relativistic. Another possible objection
is that we treat the ZPF as real, not virtual, as conventional quantum
theory doeseven though real, measurable forces can be attributed to it.
One such force is the socalled Casimir force between two parallel
plates.
It is also claimed that if the ZPF really exists, it would be such an
enormous source of gravitational force that the radius of curvature of
the universe would be several orders of magnitude smaller than the
nucleus of an atom. Of course, such a conclusion directly conflicts with
everyday experience. The fallacy in the argument is that in the SakharovPuthoff
model the ZPF as a whole would not itself gravitate. The gravitational
force results from perturbations of the ZPF in the presence of matter.
In the SakharovPuthoff model, then, the uniform ZPF is not a
gravitational source and hence would not contribute to curving the
universe.
A third large question also remains to be answered. How can our
theory of Newtonianlike gravity be reconciled with twentiethcentury
measurements of effects predicted only from general relativity? How, for
example, can our theory account for the gravitational deflection of
light, the measurement of which in 1919 served as the first proof of
general relativity? On that point we can only conjecture. Sakharov
suggested accounting for the effects of general relativity by
introducing the concept of an "elasticity of space," analogous to the
wellknown curvature of spacetime. The answer could also lie in the
proper treatment of the socalled Dirac sea of particleantiparticle
pairs. The question of general relativistic effects, however, is a valid
concern that legitimately challenges the interrelated ZPF concepts of
gravity and inertia.
Serious as the objection appears to be, we propose that it is prudent
to suspend judgment. A great deal of work lies ahead to test and refine
our concepts. We and others will continue to study the problem, and in
due course the theoretical foundations of those proposals will either be
verified or be shown to contain some irreparable flaw. As controversial
as the ideas and their implications might be, however, we are encouraged
that we are on the right track because of a second analysis now being
carried out by one of us (Rueda). In the new analysis it appears that
you obtain the same electromagnetic relation between force and
acceleration as you get in the original analysis, yet the approach is
entirely different. We also submit that a theory that offers new
insights with elegance and simplicity is a compelling approach to
reality, and we suggest that our view of inertial and gravitational mass
has a certain elegance and simplicity.
If our ideas prove to be correct, they will point to revisions in the
understanding of physics at the most fundamental level. Even if our
approach based on stochastic electrodynamics turns out to be flawed, the
idea that the vacuum is involved in the creation of inertia is bound to
stay. Perhaps even bolder than the concepts themselves are their
implications. If inertia and gravity are like other manifestations of
electromagnetic phenomena, it might someday be possible to manipulate
them by advanced engineering techniques. That possibility, however
remote, makes a compelling case for pressing on with the work.
Bernhard Haisch is a
staff scientist at the Lockheed Martin Solar and Astrophysics Laboratory
in California and a regular visiting fellow at the MaxPlanckInstitut
fuer extraterrestrische Physik in Garching, Germany.
Alfonso Rueda is a professor of electrical engineering at California
State University in Long Beach.
H. E. Puthoff is director of the Institute for Advanced Studies at
Austin, Texas.
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