What is the origin of mass? You would think physicists long ago figured out the answer to so straightforward a question. After all, they have deduced what the Universe was like in its first split-second of its existence - and that must have be an incomparably harder nut to crack. Appearances, however, can be deceptive. The embarrassing truth is that, at the beginning of the 21st century, one of nature's best kept secrets remains the origin of mass. Remarkably, nobody knows why it is difficult to budge a loaded fridge or pick up a heavy bag of shopping.

Not only is the question of the origin of mass hard to answer, it is also open to interpretation. Just as US President Clinton said "I did not have sex with that woman" and qualified it with "it all depends on what you mean by sex", physicists ask "What is the origin of mass?" and qualify it with "it depends what you mean by mass". Several distinct characteristics are in fact commonly associated with mass - two familiar and everyday, and one a little more esoteric.

The three types of masses

The most obvious characteristic of massive bodies is that it takes an effort to get them moving. Think how hard it is to get a broken-down car rolling. Part of the reason is of course the need to overcome the friction between the tyres and the road. But, even if there were no such force - say, the car was standing on a perfectly shiny ice rink - it would still take an effort to get the car moving.

As Galileo first realised, all bodies have a curious in-built resistance to having their motion changed in any way. Bodies which are stationary want to stay stationary; bodies which are moving want to remain moving. On Earth this is not at all obvious because frictional forces always act to slow a body down. A car whose engine cuts out, for instance, travels only a short distance before grinding to a halt. In the empty vacuum of space, however, the tendency of moving bodies to keep on moving is very apparent. Newton distilled this idea into his first law of motion, which states: "A body remains in a state of rest or uniform motion in a straight line unless acted upon by an external force."

This stubborn opposition of mass to any attempt to change its motion is attributed to a property called "inertia". Every time we try to budge a fridge and it stubbornly opposes our efforts, physicists say we are encountering the fridge's inertia. This kind of mass - "inertial mass" - is the most familiar of all forms of mass.

In addition to inertia, however, there is another familiar characteristic which people associate with mass: "weight". The weight of a bag of shopping, for instance, is actually the "force" of gravity acting on it. In everyday life we tend to use the terms weight and mass interchangeably (much to the dismay of physicists). This is possible because the force of gravity is the same everywhere on the Earth's surface so that, if one body has twice the weight of another - as shown by, say, a set of bathroom scales - we can be sure it also has twice the mass.

The fact that weight is not the same as mass but also depends on the strength of gravity was obvious to the Apollo astronauts as they bobbed about on the Moon. Although their mass was the same as on Earth, in the weaker lunar gravity their weight plummeted to a sixth of its terrestrial value.

The mass that responds to gravity is referred to by physicists as "gravitational mass". And there is something very peculiar about it, first noted by Galileo and others, though it took Einstein to recognise its true significance for penetrating the mystery of gravity. The peculiar thing is that the force of gravity experienced by a body goes up exactly in step with its inertial mass. In other words, a body with double the inertial mass of another experiences twice the force of gravity; a body with ten times the inertial mass tens times the gravity; and so on. Recall, however, that a body's resistance to being moved also goes up exactly in step with its inertial mass. Because of this, a body that is twice as hard to move as another experiences a force of gravity twice as strong; one that is ten times as hard to move a force ten times as great. By some weird cosmic conspiracy, the effect of inertia and the effect of gravity compensate for each other perfectly. Consequently, all bodies falling under gravity pick up speed at exactly the same rate, no matter what their mass.

Galileo is said to have demonstrated this striking property of falling bodies by dropping different masses from the top of the Leaning Tower of Pisa and seeing them hit the ground simultaneously. However, it was shown beyond a doubt in 1972 when Dave Scott, commander of the Apollo 15 spacecraft, dropped a hammer and a feather together in the air-resistance-free environment of the Moon. Two simultaneous puffs of dust on the fuzzy black-and-white TV pictures were indisputable evidence that the hammer and the feather had struck the lunar surface at the same time.

Nobody knows why "gravitational mass" - which determines the gravitational force a body experiences - is the same as the inertial mass - which determines a body's resistance to being moved. Nevertheless, in 1915, Einstein was able to use this "equivalence" of gravitational mass and inertial mass as the cornerstone of his theory of gravity, the general theory of relativity .

But, in addition to gravitational mass and inertial mass, there is a third, less familiar, type of mass. This is the one physicists believe they have made the most progress in understanding. It stems from a more esoteric characteristic of matter. As well as responding to gravity and resisting attempts to change its motion, mass also behaves as a super-concentrated "knot" of "energy".

Energy is actually a slippery concept to define but it comes in many forms - for instance, heat energy, sound energy and energy of motion. If you doubt that is energy associated with motion, step into the path of a speeding bicycle - or, better still, just imagine it!. As pointed out before, one of the central characteristics of energy - first appreciated by 19th-century scientists and enshrined in the law of conservation of energy - is that energy can never be created or destroyed, merely changed from one form into another.

In 1905, Einstein surprised pretty much everyone by identifying an entirely new form of energy - the energy associated with mass. Of all the forms of energy, mass-energy is by far the most concentrated. A single gram of matter contains as much energy as is liberated by the detonation of about 10 tonnes of dynamite. (The precise amount of energy, E, locked inside a chunk of matter of mass, m, is given by the most famous equation in the whole of science: E = mc², where c is the speed of light) This fact would be of little consequence if the energy in matter was locked away irretrievably. However, it is not. Because one form of energy can be transformed into another, mass-energy can be converted into other forms of energy, ultimately heat energy. The awful reality of this was demonstrated in August 1945 with the exploding of atomic bombs above the Japanese cities of Hiroshima and Nagasaki .

One of the key question in physics is: Why does matter have the mass-energy it does? The question can be made more precise by relating it to the fundamental building blocks of all matter. These appear to be six particles called quarks and six particle called leptons, with only two types of quark and two types of leptons involved in the construction of all normal matter, including you and me . The crucial question physicists want to answer is therefore: Why do the fundamental particles have the masses they do? For instance, why does a top-quark have about a million times the mass-energy of an electron?

The origin of mass-energy

The fundamental particles of matter are believed to be "glued" together by just four fundamental forces. These are the electromagnetic force, which binds together the atoms in our bodies; the weak nuclear force and strong nuclear force, which hold sway in the ultra-tiny domain of the atomic "nucleus"; and the gravitational force, which governs the large-scale Universe of planets and stars and galaxies. All these forces are believed to arise from the exchange of "force-carrier" particles, which shuttle back and forth between the fundamental particles like microscopic tennis balls between tennis players. In the case of the electromagnetic force, for instance, the force-carrier is the photon, the humble particle of light; in the case of the strong nuclear force it is the "gluon", which comes not in one [type] but eight different types.

Having four different fundamental forces, transmitted by a legion of force-carrying particles, may appear a bit on the complicated side. And this is the consensus view of physicists. They are convinced that things were very much simpler once upon a time. What encourages them in this belief is nature's peculiar obsession with symmetry. All the fundamental laws of nature seem to be mere manifestations of deep underlying symmetries of the world - properties which remain the same when our viewpoint is changed, either in some concrete or in some abstract way . Admittedly, in today's world, some of nature's symmetries are flawed, or broken. Nevertheless, physicists believe that, in the blistering hot fireball of the big bang, symmetry reigned supreme.

The evidence for this belief rests on the observation that systems become simpler - which is synonymous with more symmetric - at higher temperatures. Ice, for instance, is not the same throughout - often it contains bubbles and flaws and fissures. However, if ice is heated until it becomes water, the non-uniformities vanish. It looks the same at every place, which is the same as saying it is more symmetric.

Similarly, physicists believe that, when the Universe was a lot hotter - as it was in the first moments of the big bang - it was a lot simpler, a lot more symmetric. Instead of the four fundamental forces, there was a single "superforce". The fundamental forces we observe in today's Universe turn out to be mere facets of this "unified" force.

In fact, this belief is more than a qualitative, hand-waving one. As pointed out before, in the mid-1980s, at CERN, the European centre for particle research near Geneva, physicists slammed together subatomic particles with such violence that they were able to recreate for a split-second the ultra-high temperatures which existed in the fireball of the big bang. Sure enough, they observed the electromagnetic and weak forces merge together into a single, electroweak, force. Theorists have also devised "Grand unified theories", or GUTs, which predict that, at the far higher temperatures that existed at even earlier times in the big bang, all the non-gravitational forces of nature - not just the electromagnetic and weak forces - were fused together into a single force.

All this is well and good. However, there is a rather serious snag with GUTs and their prediction of the unification of the forces. The unification could have happened only if the fundamental particles had no mass!

Clearly, today's fundamental particles are not massless. Consequently, a vital jigsaw piece is missing from our picture of reality. Specifically, there must exist a mechanism by which nature bestows masses on the massless particles. Such a mechanism was in fact fleshed out in the mid-1960s by the Scots physicist Peter Higgs.

The Higgs mechanism employs the "Higgs field", a subtle and previously unsuspected feature of the vacuum. Physicists often visualise it as a kind of invisible cosmic treacle which fills all of space and sticks to particles. Since the Higgs field contains energy - which has a mass equivalent - the more treacle a particle accrues, the more massive it is. "The picture of particles accumulating some treacle is crude - but not totally misleading," says Nobel-prizewinner Frank Wilczek of the Massachusetts Institute of Technology .

The mass the Higgs field bestows on a particle is called its "rest mass". This is the mass it possesses when it is standing still and it is intrinsic to the particle. It is important to recognise this because a particle may also possess a mass by virtue of being in motion. This is apparent from Einstein's E=mc² formula, which can equally well be read from left to right as right to left. Not only is mass a form of energy - mass-energy - but energy has an equivalent mass. Since one form of energy is energy of motion, a particle has a greater mass when it is moving than when it is not.

Fields like the Higgs field, which fill all of space like a vast sea, are actually considered by physicists to be the most fundamental things in nature - even more fundamental than particles. In the modern view, the particles are nothing more than localised "excitations" - vortices if you like - in that sea. The vortex of the Higgs field not surprisingly called the Higgs particle. In fact, there may be several different types of Higgs particle, the [precise] number depends on precisely how nature has chosen to implement the Higgs mechanism.

Particle physicists are desperate to find the Higgs particle, which is widely regarded as a missing piece of their "Standard Model" of fundamental particles and forces. Currently, all their hopes are pinned on CERN's "Large Hadron Collider" which, when completed in 2008, will be the world's most energetic particle accelerator. If the LHC finds the Higgs, the relief among physicists will be palpable. Almost certainly they will declare to every newspaper and TV station that they have found the elusive origin of mass. However, according to Wilczek, this will be an exaggeration of the truth. "You have to be very clear about exactly what the Higgs mechanism does and does not explain," he says.

The Higgs mechanism does not in any sense "explain" the actual values of the masses of the fundamental particles. For instance, it does not explain why the top-quark has roughly a million times the mass of the electron. In the Higgs theory, the value of the mass of a particular particle depends on how well the Higgs "treacle" sticks to it. The stickiness is encapsulated in a number called a "coupling constant", which is different for each particle and, worst still, must be inserted into the theory by hand simply to make the masses come out right.

Far from shedding light on the origin of mass, the Higgs mechanism appears merely to substitute one mystery for another. Instead of having to explain the different masses of the fundamental particles, physicists must explain their different coupling constants. "I guess whether or not you call the Higgs mechanism an explanation of mass is a matter of taste," says Wilczek. "I would be inclined to say no, since it doesn't simplify the description of mass, nor suggest testable new properties of mass."

Even if the Higgs mechanism is accepted as an explanation of mass, it has an another, rather embarrassing, shortcoming. It can account for hardly any of the mass of ordinary matter - that is, of you and me!

Most of the mass of ordinary matter is tied up in particles called protons and neutrons, which are found in tight clumps at the heart of atoms. The protons and neutrons are, in turn, composed of up- and down-quarks. The Higgs mechanism can certainly account for the masses of these quarks. However, the quark masses are actually very small indeed. In fact, they contribute only a tiny fraction of the mass of protons and neutrons. So, even with the Higgs, the lion's share of their mass is still unaccounted for. It must arise in some totally different way.

In fact, the missing mass arises from the gluons, which transmit nature's strong, or "colour", force, and so glue together the quarks inside protons and neutrons. The bizarre thing is that gluons actually have no mass whatsoever! Nevertheless, the colour field possesses mass by virtue of the fact it contains energy, much as the magnetic field of a magnet contains energy - witness its ability to draw in metal filings. The mass of the magnetic field of even the strongest magnet is far too small to be measurable. However, the colour force is enormously stronger than any conceivable magnetic force. Consequently, the mass of the colour field is substantial. In fact, it can perfectly account for the missing mass of ordinary matter.

Bizarrely, then, most of mass of you and me does come not from the fundamental building blocks of our bodies. Instead, it comes from the glue that cements those building blocks together.

The inability of the Higgs mechanism to explain much of the mass of ordinary matter - or even predict the precise values of the masses of the fundamental particles - might be expected to dampen the enthusiasm of physicists. Not a bit of it, however. "A lot of hype is perpetrated about the Higgs mechanism and what it actually explains," admits Wilczek.

Without doubt, the Higgs mechanism provides a vivid and intuitive picture of how ordinary matter acquires a small portion of its mass by accumulating the cosmic treacle of the Higgs field. However, the kind of mass being talked about is, strictly speaking, the most esoteric type of all - a measure of the energy content of matter. Think of it as microscopic book keeping. If a particle at rest disintegrates, or "decays", into other particles, the total energy of these particles must always be equal to the mass-energy of the original particle .

But the energy content of mass is, of course, only one of its characteristics. Mass also opposes attempts to change its motion and reacts to gravity. Where do inertial mass and gravitational mass come from? Like most physicists, Wilczek thinks these types of mass come along, part and parcel, with mass-energy. In other words, the Higgs mechanism explains not just the energy content of mass but all aspects of mass. However, others disagree. "There is nothing in the Higgs' theory that explicitly says mass-energy should doggedly oppose all attempts to change its motion or that it should respond in any shape or form to gravity," says Bernard Haisch of the Calphysics Institute in Scotts Valley, California.

Haisch is perfectly prepared to believe that the rest mass of a particle - its mass-energy - is "explained" by the Higgs mechanism and that the rest mass is intrinsic to the particle. However, Haisch believes that the inertial mass and gravitational mass of a particle are not explained by the Higgs mechanism and are not intrinsic. If they are not intrinsic then there is only one other option. They must be "extrinsic". "In other words, they must somehow arise from the interaction between a particle and the environment through which it moves," says Haisch. "That environment can only be the 'quantum vacuum'."

The quantum vacuum

The quantum vacuum is an unavoidable consequence of two things, the first of which is the existence of fields of force. As pointed out, physicists view fundamental reality as a vast sea of such fields. In their picture, known as "quantum field theory", the fundamental particles are mere localised humps, or knots, in the underlying fields.

The best understood of all the fields, and the one with the greatest bearing on the everyday world because it glues together the atoms in our bodies - not to mention all other normal matter - is the electromagnetic field. The electromagnetic field can undulate in an infinite number of different ways, each oscillation "mode" corresponding to a wave with a different wavelength . Think of the waves at sea, which can range all the way from huge, rolling waves down to tiny ripples.

Naively, the vacuum of empty space would be expected to contain no electromagnetic waves whatsoever. And this would be true but for the small matter of the Heisenberg uncertainty principle. According to the principle, every conceivable oscillation of the electromagnetic field must contain at least a minimum amount of energy. This seemingly innocuous rule has dramatic and profound implications for the vacuum because it means that each of the infinite number of possible oscillation modes of the electromagnetic field must be jittering with the minimum energy dictated by the uncertainty principle. In other words, the existence of each mode is not simply a possibility, it is a certainty. Far from being empty, the "quantum vacuum" is a fantastically choppy sea of fluctuating fields .

These quivering fields, known as "quantum", or "zero-point", fluctuations, can manifest themselves in a truly remarkable way. Recall that fundamental particles are nothing more than localised hummocks in nature's underlying fields. Consequently, the choppy sea of the vacuum is continually conjuring particles into existence like microscopic rabbits out of hats. Known as "virtual particles", they have only a fleeting existence, popping into existence for far less than the blink of an eye before popping back out again.

Haisch began thinking about the intriguing possibility that the quantum vacuum might have something to do with inertial mass in February 1991. The trigger was a talk he attended by Alfonso Rueda of California State University in Long Beach. It was about "stochastic electrodynamics".

According to the idea, first devised in the 1960s, the quantum vacuum is absolutely central to the creation of the world. Ultimately, all the bizarre "quantum" behaviour of microscopic particles can be traced back to the relentless buffeting they receive from the ceaselessly churning quantum vacuum.

Sitting in the audience of Rueda's talk, Haisch had been pretty much letting it all waft over him when something Rueda said suddenly made him sit up and pay attention. Rueda mentioned an esoteric discovery made independently by two physicists in the 1970s. Paul Davies and Bill Unruh had been exploring Stephen Hawking's remarkable idea that black holes are not completely black. According to Hawking, the immense gravity close to a black hole distorts the quantum vacuum in such a way that the fleeting virtual particles can become real, fountaining out of the vacuum as permanent "Hawking radiation".

Understanding exactly how Hawking radiation arises requires knowing that, when virtual particles pop out of the vacuum, they pop out in pairs - typically an electron-positron pair. The positron is the "antiparticle" of the electron. Every subatomic particle has an associated antiparticle with opposite properties such as electrical charge. A particle and its antiparticle are always born together. Furthermore, when a particle and its antiparticle meet, they self-destruct, or "annihilate". Such creations and annihilations are the stuff of the quantum vacuum. All over space electron-positron pairs are continually winking into existence, lingering in the world for the merest of instants, then undergoing mutual annihilation and winking out again.

Close to a black hole, however, something else can happen. During the fleeting life of an electron-positron pair, one of the particles can find itself dragged through the black hole's "event horizon" - the point of no-return for in-falling matter. Since the particle outside the hole now has no partner with which to annihilate, it has no means of popping back out of existence. It has been elevated from the status of a transitory virtual particle to a real particle with a permanent existence.

All around the horizon of a black hole virtual particles from the quantum vacuum are continually being boosted to reality in this way, flying away from the hole as Hawking radiation. Of course, ultimately something must pay for their mass-energy and that something is the gravitational field of the black hole, which gradually weakens as it loses an equivalent amount of energy .

What Davies and Unruh were interested in was exactly what the Hawking radiation would look like. They concluded that an observer looking at the black hole would see radiation exactly like that which emerges from a hot furnace. In the case of a furnace, the radiation is known as "thermal" radiation and has a mix of colours determined solely by the temperature of the furnace. In the case of the black hole, the mix of colours is determined by the black hole's gravity. In some weird sense, then, a black hole's gravity gives it a "temperature." Black holes are hot!

From this unexpected discovery, Davies and Unruh made an intriguing extrapolation. Einstein had realised that gravity is indistinguishable from constant acceleration, at least in any small enough region of space. This he called "the happiest thought of my life" and made a cornerstone of his theory of gravity. The equivalence of gravity and acceleration enabled Davies and Unruh to extend their result about Hawking radiation. Just as someone near a black hole would see heat radiation coming from the hole's vicinity with a temperature dependent on its gravity, someone accelerating through space - that is, through the quantum vacuum - would see heat radiation coming from in front of them with a temperature dependent on their acceleration.

The virtual particles popping in and out of existence in the quantum vacuum actually have a remarkable property. If an observer flies through the vacuum at constant speed - and it does not matter what that speed is, as long as it is constant - the view they see of virtual particles popping in and out of existence is the same behind them as in front of them. This means that the quantum vacuum is completely compatible with Einstein's special theory of relativity, which recognises that all observers travelling through space at uniform speed see the world in exactly the same way.

Because the vacuum looks the same to an observer flying through it at constant speed, it effectively behaves as if it is not there. Just like the air in which we live, it has no discernible effect on us. However, Davies and Unruh's discovery that someone who accelerates through the quantum vacuum will find themselves bathed in heat shows that accelerated motion is fundamentally different from motion at constant speed. From the point of view of an accelerated observer, the vacuum is transformed into a real, detectable thing, capable of affecting them.

To Haisch, listening to Rueda's talk, this prompted an intriguing thought. "If an accelerated body sees heat coming at it from in front, that heat might apply a force which slows the body," says Haisch. "I'm an astrophysicist, you see. I'm used to the idea that heat radiation - for instance, sunlight - can exert a force on bodies such as the tiny dust particles that make up the tail of a comet."

After the talk, Haisch told Rueda his idea and Rueda said he would do some calculations. For a few months nothing happened. Then, one morning, Haisch arrived at his office at Lockheed Martin's Solar and Astrophysics Laboratory in Palo Alto to find his answer machine light flashing. "Alfonso had left a message at 3 am!" says Haisch. "He was so tremendously excited by the result of a mammoth calculation he had been doing that couldn't wait to tell me. 'I think I can explain Newton's second law of motion!' he said."

Newton's second law, postulated in 1687, is conventionally written as F = ma, where F is the force experienced by a body of mass, m, and a is the acceleration that results. The law is in fact no more than a definition of inertial mass, which is defined as the ratio of the force applied to a body to the acceleration produced.

Rueda had examined in detai the electric and magnetic components of the electromagnetic radiation experienced by a body as it accelerates through the vacuum. A magnetic field has long been known to exert a force on a moving electric charge. In fact, this is the basis of the electric motor. When an electric current - a flow of charged electrons - passes through a coil of wire placed in a magnetic field, the coil rotates on its spindle. Rueda discovered that there would be a similar force between the magnetic field experienced by an accelerating body and the moving electric charges in the atoms of the body. "And when he calculated the force he found it was exactly as required by Newton's second law," says Haisch. "A retarding force which depended on the body's acceleration. After three centuries, someone had at last explained inertia."

According to Rueda, inertial mass is not intrinsic to a body at all. It is extrinsic, bestowed on a body from outside. Specifically, it arises from the interaction between the basic building blocks of matter and the great roiling ferment of virtual particles that make up the quantum vacuum .

Haisch says he is not surprised by the idea that inertial mass is not intrinsic to a material body - that it is not a fundamental thing. He points to the fact the inertial mass is impossible to measure directly. Instead, people infer it. They take two measurable quantities - the force applied to a body and the acceleration it produces - and deduce the mass of the body from the ratio. The lot of inertial mass, Haisch believes, is to go the same way as space and time. In the wake of Einstein's special theory of relativity, both ceded their fundamental status to the speed of light. "Inertial mass is not a fundamental thing," says Haisch. "The really fundamental thing turns out to be the quantum vacuum."

If mass is not a fundamental thing, it may explain why it appears to come in so many different kinds - inertial mass, gravitational mass and rest mass, the mass associated with energy. "It simply reveals a different face depending on how it is measured," says Haisch.

So, what of the Higgs mechanism? Haisch sees no incompatibility between this and the electromagnetic interaction between a particle and the vacuum. "The Higgs mechanism explains the rest mass of subatomic particles while the vacuum interaction explains their inertial mass," he says.

Rueda agrees. "The Higgs field deposits energy, and hence rest mass, around structures we call elementary particles," he says, "The claim that this accumulated energy behaves in some way that gives such elementary particles the property of inertia is a mere hope. You need something else for that - and we think we've found it."

As pointed out, the force carrier of the electromagnetic field is the photon. At a microscopic level, therefore, the interaction between the constituent particles of matter and the quantum vacuum involves photons being exchanged between the virtual particles of the vacuum and the quarks and electrons in matter.

An electron is considered by physicists to be a truly fundamental and indivisible particle - a point-like concentration of electric charge. However, in order to obtain his F = ma result, Rueda had to assume that such an electron jitters back and forth within a characteristic volume of space . This may seem a bit of an arbitrary - not to say peculiar - assumption. However, it revives an old idea proposed by Louis de Broglie and Erwin Schrodinger, two of the pioneers of quantum theory.

De Broglie and Schrodinger were puzzled that, in experiments in which photons rebound, or "scatter", off electrons, the electrons behave exactly as if they have a particular size called the "Compton wavelength". To make sense of this, the two physicists proposed that an electron is in fact a point-like charge which jitters about randomly within a sphere of diameter the Compton wavelength. They called this trembling motion "zitterbewegung". "Alfonso and I believe De Broglie and Schrodinger were onto something with their zitterbewegung," says Haisch. "Their mistake, however, was in thinking that the motion was intrinsic to an electron. In fact, it is extrinsic - due to the random battering the point-charge receives from the jittery vacuum. In effect, this smears out the electron, making it appear as big as the Compton wavelength."

According to Haisch, it is always possible that this jittering motion could explain more than inertial mass. "A massless particle may pick up energy from the zitterbewegung, hence acquiring what we think of as rest mass," he says. "It would be a neat, tidy package. It might be possible to dispense with the Higgs mechanism altogether. It strikes me as far more elegant than an undetected Higgs field."

Piling speculation on speculation, Haisch and Rueda suspect that the interaction that produces inertia occurs preferentially at a special, "resonant", frequency. This is a frequency at which energy is most efficiently transferred from one body to another. Think of someone pushing a swing. Everyone knows there is a particular frequency - perhaps one once every 10 seconds - at which the energy in the push is most effectively transferred to the child on the swing, making it go higher and higher. This frequency of once every 10 seconds is an everyday example of a resonant frequency. Well, when Haisch and Rueda speculate that the interaction that produces inertia occurs preferentially at a resonant frequency, they speculate further that this resonant frequency is the zitterbewegung, or Compton, frequency. "If we knew what caused this resonance, we would probably be able to explain the ratio of the various quarks rest masses to the electron rest mass," says Haisch.

If, as Haisch and Rueda believe, inertial mass is a consequence of an electromagnetic interaction with the vacuum, this still cannot explain the small mass claimed for a particle such as the "neutrino" . This is because it interacts via the weak nuclear force and not the electromagnetic force. "The origin of neutrino mass must be in its interaction not with the electromagnetic zero-point fields of the vacuum but with the zero-point weak fields," says Haisch.

Gravitational mass

If inertial mass does indeed have its origin in the interaction between matter and the quantum vacuum, what of gravitational mass? Well, inertial and gravitational mass are of exactly the same magnitude, an observation which is a cornerstone of general relativity. This equivalence can logically have only a limited number of possible explanations.

One is that inertial mass has a gravitational origin. This was the hope of the 19th-century Austrian philosopher Ernst Mach. He postulated that inertia of a body was the result of the combined gravity of all the objects in the Universe. The reason there is resistance when you try to stop a moving body or start a stationary body, Mach maintained, is because the stars and galaxies Universe are pulling against you!

Mach's idea appealed enormously to Einstein. He hoped that it would emerge as a natural consequence of his own theory of gravity. However, he was to be disappointed. Like everyone else, Einstein was reduced to assuming, without any understanding or proof, that matter has inertia.

Nowadays, Mach's idea has fallen out of favour, principally because it requires the Universe to react instantaneously to the acceleration of a body on Earth. However, we are pretty sure that the cosmic speed limit is set by the speed of light and that no influence, not even gravity, can act without any time delay.

A second logical possibility for the equivalence of inertial and gravitational mass is that gravitational mass has an inertial origin. In fact, this is what Einstein showed in general relativity. There is in fact no "force" of gravity. Bodies actually move under their own inertia along straight lines. The straight lines, or "geodesics", are actually in a higher, 4-dimensional, space-time and so appear to us as curves. However, even though general relativity shows that gravitational mass has an inertial origin, the theory still leaves unanswered: what is the origin of inertial mass? "Trying to coax inertia out of gravity or gravity out of inertia, you wind up with an inevitable circularity," says Haisch.

The final logical explanation for the equivalence of inertial and gravitational mass is that they share a common origin. And this is what Haisch and Rueda think. Both kinds of mass, they claim, arise from interactions of the electric charges of matter with the quantum vacuum. But, whereas Haisch and Rueda's idea of the origin of inertial mass is well developed, their idea of the origin of gravitational mass is far more speculative.

Basically, the two physicists believe, charges in a chunk of matter distort, or "polarise", the quantum vacuum in their immediate vicinity. In other words, they attract virtual particles with opposite electrical charges and repel virtual particles with similar electrical charges. This distortion of the vacuum in turn interacts with the charges in another chunk of matter. By this roundabout means, a force of attraction arises between the two chunks. "The mechanism is so tortuous it might explain why gravity is so much weaker than the other fundamental forces of nature," says Haisch. "One mass does not pull directly on another mass but only through the intermediary of the quantum vacuum."

Haisch and Rueda's description may appear puzzling if you know anything about Einstein's theory of gravity. After all, general relativity "explains" gravity perfectly in terms of the warpage of higher dimensional space-time by matter. At first glance, this "geometrical" picture does not appear to be at all compatible with the picture of Haisch and Rueda.

However, Haisch points out that the warpage of space described by Einstein's theory is actually not directly measurable. Instead, astronomers infer it from the bending of the paths of light rays passing through space. If the light from a distant star passes close to the Sun on its way to the Earth, for instance, its path is bent by the warped space close to the Sun. "If matter distorts, or 'polarises', the quantum vacuum, this changes its ability to bend light, or its 'refractive index'," says Haisch. "The vacuum then bends the path of light just like a piece of glass does."

Haisch conjectures that the change of refractive index of the vacuum caused by the presence of matter has exactly the same effect on the paths of light rays as the warpage of space which in Einstein's theory is caused by the presence of matter. In this way, all the mathematics of general relativity remains intact since space-time, though unwarped, looks exactly as if it is warped! "I strongly suspect that the vacuum-inertia theory can be made consistent with general relativity and the warping of space-time," says Rueda. "But it is still too early to be certain."

In their latest work, Rueda and Haisch even explain why inertial mass and gravitational mass are the same. And it turns out to be remarkably straightforward. If you accelerate through the quantum vacuum, the vacuum resists your motion, which is why you have inertia. However, if you are held fixed in a gravitational field, it is the quantum vacuum that accelerates past you. "But this immediately shows that the 'mass' associated with inertia and the 'mass' associated with weight must be equal because the two situations are the same," says Haisch. "Accelerating through the quantum vacuum or having the quantum vacuum accelerate past you are the same process. Hence Einstein's principle of equivalence is neatly explained."

Perhaps the most mind-blowing consequence of gravitational and inertial mass owing their existence to the vacuum is the possibility of modifying both through modifying the vacuum. If a way could be found to change the vacuum in the right way, it might be possible to nullify mass, making an inertia-less drive that could accelerate a spaceship from a standstill to the speed of light - the cosmic speed limit - in the blink of an eye!