The most fundamental equation in physics is the relation between force, mass, and acceleration which Isaac Newton postulated over three centuries ago: F=ma. It defines the concept of inertia, the resistance that an object puts up to a change in motion. To make something move faster or slower, you need to apply a force, and the force you need to apply is greater for larger masses. This is such a simple, intuitive fact that it seems more foolish than profound to ask, Why is it true? Why do objects have inertia?

As fundamental as this question is, a convincing answer has eluded the likes of Albert Einstein and Richard Feynman. Ideas about inertia have fallen into two schools. Newton himself argued it is an intrinsic property of matter, capable of no further explanation. To tell whether an object possesses inertia, you do not have to measure its motion with respect to external reference points; you need only look for the telltale distortions that occur whenever a body that has inertia accelerates. Rotation, for example, is one form of acceleration. As Earth rotates, its equator bulges out — a dead giveaway that our planet possesses inertia.

Newton's idea of absolute acceleration, one that did not need external objects to define it, bothered many scientists — among them the 19th-century Austrian physicist and philosopher Ernst Mach, whose ideas helped to inspire Einstein's theories of relativity. Mach argued that all motion is relative. If Earth were all alone in a hypothetical universe devoid of other matter, how would it know whether it was rotating? And if Earth did not know whether it was rotating, how would its equator know whether to bulge out? Mach resolved this paradox by concluding that the solitary Earth could not have any inertia. Somehow, the Earth's inertia is generated by the presence of other matter in the universe.

But how? Einstein thought that his general theory of relativity would embody Mach's principle, but it turned out not to. The source of inertia remained a mystery until, we believe, 1994 — when, together with Harold Puthoff of the Institute for Advanced Studies in Austin, Texas, we proposed a radical theory: that inertia is an electromagnetic force that switches on whenever an object accelerates through space. It turns out that Mach was almost right. In our theory, inertia does depend on an external frame of reference, but this frame of reference is provided not by the other bodies in the universe, but by an electromagnetic field that pervades the cosmos. This field, in turn, arises because of quantum mechanical ferment in the vacuum — a subject shaping up as a major theme of 21st-century physics.

Last year, we realized that the vacuum also might explain another great mystery of modern science: how the universe, at the largest scales, came to look like a whiffle ball. The honeycombed arrangement of galaxy clusters may hold the key to understanding how inertia, gravity, and mass came to be.

Sponges and Swiss Cheese

Four years ago, the NASA Cosmic Background Explorer detected blemishes in the microwave afterglow of the Big Bang. Astronomers were relieved. It was the first evidence that the early universe was not perfectly smooth and uniform [see ``New Image of the Universe Soon After Creation,'' May/June 1992, p. 91]. Perfect uniformity would have left no way for cosmologists to explain how the lumpy present-day universe could arise from utterly homogeneous primordial stuff.

Yet the COBE discovery accounted for only the highest level of inhomogeneity, on scales of 1 to 2 billion light- years (see images on p. 13). The largest structures known today in the universe are 10 times smaller.

Those structures are the great voids and sheets. Astronomers have known for some time that galaxies are concentrated into enormous clusters, but in the past decade, observers have discovered that the clusters are themselves concentrated into vast sheets, or walls. In between the walls are giant voids almost free of galaxies (see diagram above). The size of the cosmic voids ranges from tens to hundreds of millions of light-years. On these scales, the universe looks like Swiss cheese or a sponge: more hole than substance [see ``Mapping the Universe,'' May/June 1990, p. 66].

How did this superstructure come about? Gravitation can explain the clumping if you assume the universe had just the right mixture of ordinary matter, cold dark matter, and hot dark matter. But this leaves astronomers a bit uneasy. After all, we do not know what the dark matter is or whether it could exist in the necessary amounts. The recent announcement that white dwarfs may comprise half the dark matter in our galaxy does not help, because the cosmological dark matter would have had to reside outside galaxies and consist of material entirely unlike ordinary atoms.

Under these circumstances, the prudent thing to do is to examine other possible explanations, to search for the dark horse in addition to the dark matter. Can we account for the structures without having to populate the universe with unknown kinds of matter?

Deep intergalactic space, where the large-scale structures began to form, is a cosmic desert. Out there, the density of gas is low, so low that gas particles are subject only to minute forces exerted by the vacuum that surrounds them. The word vacuum innocently implies "empty,'' but nothing in quantum mechanics is ever so straightforward. The vacuum of modern physics is far from empty — quite the opposite. It is a seething soup of subatomic particles and energy fields bubbling in and out of existence, a cauldron where the very notions of ``space'' and ``time'' may take on their meaning.

The not-so-empty vacuum is a consequence of the fact — recognized by German physicist Werner Heisenberg in 1927 — that you can never remove all the energy from anything. Take an electromagnetic field. It consists of photons, individual packets of energy each in a state defined by its direction, frequency, and polarization. Try as you might, you could never remove all the photons from any given state. According to the principles of quantum mechanics, every state must have a minimum population of either zero or one photon, with equal probability. The average of zero and one is one-half. Therefore there must be, on average, the equivalent of at least half a photon in every possible state.

Half a Photon Here, Half a Photon There

Half a photon in each state is not much — a 100-watt light bulb puts out 100 billion billion photons every second — but there are countless possible states. The result is a vast sea of radiation underlying the universe. All those virtual photons constitute the electromagnetic zero-point field, so named because it is present even at a temperature of absolute zero. In the deepest reaches of intergalactic space, where particles are so widely spaced that their mutual interactions are weak, this irreducible radiation field comes into play.

In 1910, about halfway between the publication of special and general relativity, Einstein and his colleague Ludwig Hopf investigated how a thin gas would react when immersed in an electromagnetic radiation field. The radiation, they found, would have two counteracting effects on each gas particle. The particle would jiggle as photons bombarded it at random, but its motion would be opposed by a drag force due to the Doppler effect. The Doppler effect would stiffen the resistance of photons in the direction that the particle was trying to move. The particle would smack head-on into blueshifted photons, which, being more energetic than the photons from other directions, would push it back the way it came. This drag force would prevent the random jiggles of the gas particle from developing into net motion.

The Einstein-Hopf process would be an interesting, but irrelevant, curiosity were it not for one peculiarity that sets the electromagnetic quantum vacuum apart from other radiation fields: the shape of its spectrum. The shape is exactly proportional to the frequency cubed — precisely the right shape to be ``Lorentz invariant.'' A spectrum with this shape does not produce a Doppler effect. The photons that a gas particle meets head-on in the quantum vacuum are no more energetic than those that strike the particle from behind. Consequently, the photons can offer no concerted resistance to uniform motion. (The spectrum and directional distribution of photons, however, do change for particles that are accelerating; this is the origin of inertia in our theory, as discussed in the box on p. 15.)

This idiosyncrasy of the vacuum electromagnetic field throws the Einstein-Hopf process out of balance (see figure on p. 14). Once gas particles are set in motion by the random fluctuations of the electromagnetic field, nothing can stop them. Over millions of years they accelerate steadily, reaching velocities near to that of light and moving across astronomical distances.

Astrophysicists are no strangers to this mechanism. Twenty years ago, one of us proposed it as a possible source of the most energetic cosmic rays. Most cosmic rays consist of electrons, protons, and ions, but those of extremely high energy are missing the electrons. The Einstein-Hopf process would explain this, because it operates more efficiently on protons and ions than on electrons. What no one had considered was that this process could also segregate matter on a cosmological scale.

When we first looked into the matter, the Einstein-Hopf process sounded too good to be true. By transferring energy from virtual photons into real particles, would the process yield something for nothing? To check, we teamed up with IBM physicist Daniel Cole, an expert on the quantum vacuum. For over five years, Cole had been assessing whether theories of the vacuum violate any basic principles, such as the conservation of mass-energy or the second law of thermodynamics. He was able to find nothing amiss with the quantum Einstein-Hopf mechanism.

Emptiness Begets Emptiness

The Einstein-Hopf process works best in places where particles hardly ever collide with each other, since collisions prevent the particles from building up speed. The less matter there is, the more the matter wants to go someplace else. Thus the tendency is for regions of low density to empty out even more, and for regions of high density to become denser. This is exactly the sort of snowball effect that cosmologists have been looking for to explain how matter congregated to form sheets and walls.

At some point, the acceleration must have come to an end, or else all matter would have clumped into a single mega-galaxy. We believe that the end drew near when the agglomerating sheets developed appreciable magnetic fields. As the particles scurried into sheets, they dragged along their primordial magnetic fields. Those fields piled up, creating a magnetic pressure that ultimately balanced the Einstein-Hopf evacuation process. Gravity took over to form smaller structures, such as galaxies. The end result, we proposed last spring in The Astrophysical Journal, was the honeycombed structure of the universe.

The theory rests on many assumptions, and the one that worries us is the most fundamental: that the quantum vacuum produces a real electromagnetic field. Physicists normally treat the virtual photons as just that: virtual, hence unable to produce any far-reaching real effects. But numerous experiments indicate the field may indeed influence matter. The quantum vacuum creates an attraction between neutral parallel plates, as predicted by Dutch physicist Hendrick Casimir in 1948 and confirmed experimentally several years later. The interaction of the vacuum electromagnetic field with electrons causes a shift of hydrogen spectral lines, as discovered by American physicists Willis Lamb Jr. and Robert Retherford in 1947 and explained later that year by Hans Bethe. And the spontaneous emission of photons can be altered by changing the electromagnetic environment of atoms; this suggests that ``spontaneous'' emission is actually stimulated by the fluctuations of the vacuum.

If the zero-point field is real, it should be possible to reproduce the Einstein-Hopf process in the laboratory. The main obstacle would be achieving densities comparable to those in the cosmic voids: less than one particle per cubic meter. But if we could even approximate this, the effect might be measurable. One possibility would be to create an extremely low temperature magnetic trap and inject anti-protons into it. If the Einstein-Hopf process ejected the anti-protons, the experimenter should see them annihilate with protons in the matter surrounding the trap.

The idea that the zero-point field might really exist dates to the early 20th century, when there was not yet a clear division between classical and quantum physics. Quantum mechanics emerged from a radical, and unsupported, assumption that German physicist Max Planck made in 1900: that the energy of a system can only take on certain discrete, or quantized, values. From this hypothesis, he was able to explain the blackbody spectrum of the light that stars and other glowing bodies give off. Planck searched for something to explain the quantization, and one possibility he considered was that space is filled with unseen energy, a proposal also made by Walther Nernst in 1916.

During the 1920s, quantum mechanics proved so successful that physicists abandoned the search for an underlying cause of quantization. Quantization, like inertia, came to be regarded as just a given, a new law of nature. But in a series of papers beginning in 1969, Timothy Boyer appears to have vindicated Planck by deriving the blackbody spectrum directly from classical physics, without quantization — by positing a background zero- point field. This reopens the questions that concerned Planck.

Is it possible that quantum mechanics is classical physics done in the presence of a zero-point field? Could the counterintuitive laws of quantum physics someday go the way of Ptolemaic epicycles? Quantum mechanics is certainly successful in terms of predicting observations, but so was Ptolemaic astronomy. In fact, the Ptolemaic system predicted planetary positions much better than Nicolaus Copernicus's initial theory. If astronomers had simply rejected the Copernican model, rather than worked to fix its shortcomings, we would still think Earth is the center of the universe.

As Planck did when he first derived the blackbody spectrum, we have taken a pragmatic approach: suppose that the quantum vacuum does produce real effects and consider the implications. Many new theories are ad hoc, conjured up to explain one thing and unable to explain anything else. The fact that the zero-point field might account for inertia, gravity, quantization, and, now, cosmic voids indicates that it is worth investigating.

BERNARD HAISCH is an astrophysicist at the Lockheed Martin Solar and Astrophysics Laboratory in Palo Alto, Calif. He is a scientific editor of The Astrophysical Journal and the managing editor of the Journal of Scientific Exploration. When he is not rethinking scientific paradigms, Haisch, writing under the name of Bernie Sims, is a songwriter and producer. His and his wife's first commercially released song on a major label, Common Ground, will be on the forthcoming album by new Nashville artist Paul Jefferson. Haisch's email address is haisch@sag.space.lockheed.com.

ALFONSO RUEDA is a professor of electrical engineering at California State University in Long Beach. His email address is arueda@csulb.edu. For more information on the zero-point field theory, see the authors' article "Beyond E=mc²'' in the November/December 1994 issue of The Sciences. Their technical papers appeared in Physical Review A, volume 49, p. 678 and The Astrophysical Journal, volume 445, p. 7.

Illustration captions

An astrophysical Genesis. More precisely, this is a map of the cosmic microwave background radiation, which reflects the distribution of matter shortly after the Big Bang. Darker areas had a higher density, brighter areas a lower density. NASA released a similar map in 1992, but it was based on preliminary measurements, which were so prone to noise that scientists could not be certain what was real. This latest map, released in January, contains more signal than noise. Even the smallest feature on the map is far larger than the largest structure astronomers see in the universe today. Images courtesy of Charles L. Bennett, NASA Goddard Space Flight Center.

Holes. The universe is full of holes. The regions shown on this diagram, which depicts a cube 500 million light-years on a side, are all but empty of luminous matter. These voids interconnect like the holes in your kitchen sponge. This diagram is based on an early-1990s redshift survey of infrared galaxies by Queen Mary College, the University of Durham, Oxford University, and the University of Toronto. Our Milky Way is at the center. Diagram courtesy of Carlos S. Frenk.

The Einstein-Hopf process. In a near-vacuum, collisions between gas particles are rare; collisions between particles and photons are more important. The photons are part of whatever electromagnetic field the particles happen to be immersed in. These photons are always hitting each particle from all sides, but not with equal strength. Those that hit a moving particle head- on are more energetic than those striking from behind, because of the Doppler effect. This imbalance automatically keeps the particle velocities in check (top). There is one exception: If the dominant electromagnetic field is the zero-point field, the spectrum of the field cancels out the Doppler effect, so that photons striking head-on are no more energetic than any other photons (bottom). As a result, the particles are free to move without restraint. Diagrams by Bernhard M. Haisch.

The Illusion of Mass

Maybe there is no such thing as "mass'' — only charge, which gives the illusion of mass when it is immersed in the quantum vacuum. It is an audacious idea, but one that would unify gravitation with the other fundamental forces of nature.

Physicists universally accept the reality of the quantum vacuum, a sea of virtual particles and photons that wink in and out of existence too fast to be seen. But physicists are less confident that the virtual photons could create a real electromagnetic field. For starters, this zero-point field would raise problems with general relativity.

Einstein's theory states that energy produces gravity in the same way that matter does. Just as a planet attracts other bodies gravitationally, an electromagnetic field attracts bodies gravitationally. A uniform zero-point field that filled the universe would be an enormous source of gravitation — so enormous that it should reduce the universe to microscopic size. This is clearly not the case.

Two linked theories have been proposed to resolve this paradox. If correct, they would constitute a paradigm shift in our view of matter itself. The first theory grew out of a suggestion made by the Russian physicist Andrei Sakharov in 1968 that gravity could originate in the quantum vacuum. Harold Puthoff published a quantitative, albeit preliminary, development of this idea in 1989. According to his theory, the zero-point field would cause charged particles, such as the electron or the quarks inside protons and neutrons, to oscillate. Whenever a charged particle oscillates, it emits electromagnetic waves of its own. These secondary fields would attract other charged particles.

If true, this theory would unify gravity with electromagnetism — an unexpected resolution to the long search for a unified theory. It would neatly answer the general relativity paradox. In this view, gravitation is caused by secondary fields induced by the zero-point field; the zero-point field, in and of itself, cannot produce gravitation.

The second theory is our proposed mechanism for inertia. Einstein's principle of equivalence tells us that inertial and gravitational mass are the same. If gravitation is electromagnetic, inertia must be, too. This implies a complete rethinking of what matter really is.

The zero-point field is completely uniform for observers in uniform motion. But it is asymmetric for observers in accelerated motion. In 1994, we and Puthoff examined a phenomenon no one had thought to investigate before: how the magnetic component of the zero-point field interacts with matter during acceleration. The result was surprising, to say the least. The magnetic Lorentz force opposed acceleration with a strength that varied in direct proportion to the magnitude of the acceleration (see figure). It looked like a derivation of Newton's second law, F=ma, heretofore considered an underivable postulate.

What we feel and interpret as "mass'' is, in this theory, an electromagnetic resistance arising out of the zero-point field. If it is true that mass is a consequence of charge, rather than an inherent property of matter, it might be possible (in the distant future) to build anti-gravity devices that would switch off the inertia of objects.

Are there objections to this theory? Certainly. We propose it not as a done-deal, but as a new approach to long-standing, unresolved fundamental problems. There are two major reservations. First, we treated the quantum vacuum as if it were a perfectly real electromagnetic field. The available evidence on this issue is ambiguous, and more experiments need to be done — ranging from laboratory measurements of the Casimir force to astronomical observations of large-scale structure in the universe.

Second, even our simple model demanded a complex mathematical analysis, which is difficult to verify. For instance, we ignored non-electromagnetic vacuum fields, such as those associated with the gluon particles that bind quarks together. We are now completing a different approach that avoids this and other problems, and the preliminary results have confirmed the first approach. We hope that more researchers will look into these problems, drawn by the appeal of unsuspected deep connections.

Illustration caption

The origin of inertia? Quantum mechanics predicts that photons are constantly flitting on and off the stage of existence. These photons are "virtual'' in that each survives so short a time that the rest of us hardly notice. Collectively, however, they have observable effects, one of which was predicted by physicists Paul Davies and William Unruh in the mid-1970s and studied in detail by the authors. To a particle sitting still or moving uniformly, the field of virtual photons looks the same in all directions (top left). But as the particle begins to accelerate, the field ceases to look the same in the fore and aft directions (top center). For faster accelerations, the asymmetry worsens (top right). Physicists had thought the Davies-Unruh effect was an esoteric curiosity significant only near black holes. But the authors have found that the asymmetry creates a force similar to the radiation pressure that pushes cometary dust tails away from the Sun. This force always opposes the acceleration (bottom). Voilà, inertia. Diagrams by Bernhard M. Haisch.