Yearbook University of Amsterdam, 1993

Towards a Theory of Nothing: about Hypothetical Particles and Empty Space

Sander Bais

Institute for Theoretical Physics
Faculty of Physics and Astronomy
University of Amsterdam

    Physics bridges the differences between microscopic and macroscopic, gaseous and solid, applied and fundamental, but at the same time appreciates a distinction between experimental and theoretical research. There has always been a dynamic interaction - even a healthy rivalry - between these different areas of physics research. Often, experiments lead the way, as demonstrated recently by such spectacular discoveries as high temperature superconductivity or the quantum Hall effect, in which, to a certain extent, the facts precede the theory. On the other hand, theory may anticipate experimental facts: abstract reasoning can reveal new links by connecting apparently unrelated pieces of data through new concepts. Think of a milestone such as the successful "standard model" of the fundamental interactions. This model gives a unified description of (a) the strong interaction which is ultimately responsible for the great diversity of stable nuclei; (b) the weak interaction which leads to the instability of various nuclei through radioactive decay; (c) the familiar electromagnetic force, with it's overwhelming variety of applications which tends to dominate our present way of life, at least at the everyday level. This standard model, which describes the properties of the most fundamental forms of matter successfully at least to the extent that we have been able to verify this experimentally, is based upon three central dogmas of contemporary physics: Einstein's theory of relativity, the postulates of quantum mechanics, and an important symmetry principle called gauge invariance. Experimental investigation of the smallest ingredients such as quarks, electrons, light particles (photons) and "heavy" particles (such as W- and Z-bosons) requires gigantic "microscopes" known as particle accelerators. These cost a fortune and are therefore found in only a few places throughout the world. Therefore this field has reached an advanced state of "internationalization", which is not restricted solely to communication or "exchange" of ideas, but implies the total integration of experimental work. However, despite this advanced "task distribution and concentration", which guarantees an unusually economical approach, this fundamental area of research has come under pressure because it is so expensive.

    Everyone is familiar a magnet, most electrical devices contain at least one. The earth itself is a somewhat larger magnet. A bar magnet has a north and a south pole. If we break the magnet in two pieces, what we have left is not a separate north and south pole, but rather two smaller magnets, each of which has its own north and south pole. We may continue this process all the way down to a microscopic scale, without ever being able to isolate a north or south pole. Apparently there are no particles occurring in nature with a magnetic (north or south) charge, in contrast with the case of electrical charges. In the end all magnetic phenomena we know of are a caused by currents - i.e. the motion of electric charges. A magnet is made up of microscopic magnetic dipoles which are nothing more than minuscule electrical current loops on a molecular or atomic scale. There is no such thing as a magnetic monopole, full stop. That is, unless...

    Back in 1931, Dirac published a famous argument which accounted for the crucial experimental fact that electrical charge only occurs in whole multiples of the electron charge, based on the existence of a magnetic monopole. His article concluded with the statement that "One would be surprised if nature would not have made use of this possibility". The hunt for the monopole was on. However, nothing was found...
    Despite the lack of encouragement from the experimental side, numerous great minds continued the stubborn pursuit of this hypothetical particle. The following episode illustrates the unpredictability of the fundamental (im)possibilities in physics. In 1974 Gerard 't Hooft and the Russian theoretician Sasha Polyakov (now at the Institute for Advanced Studies in Princeton) discovered that further unification of different interactions, in accordance with the successful principle of symmetry (gauge invariance) which forms the basis of the weel established standard model, necessarily implied the existence of magnetic monopoles. Good Heavens! The hunting season reopened, with an extended toolkit which included accelerators, and even satellites to collect moon rocks. Sure enough, the discovery of the particle was claimed twice ofcourse leading great commotion. But alas, both claims turned out to be false.

    Further theoretical research brought numerous exotic properties of these monopoles to light. One of these was discovered by the young Russian theoretician Valery Rubakov. He demonstrated that monopoles should produce a dramatic instability of protons and neutrons, implying an instability of all common forms of matter. Monopoles would devour matter at an unimaginable rate, and the corresponding energy would be spewed in the form of extremely light particles. I remember one summer afternoon at that time, when we sat with a number of driven but peace-loving researchers on the terrace of the CERN laboratory in Geneva. On the table in front of us lay the first, rough draft of the preprint of Rubakov's work, which someone had got hold of through his contacts, in which this sensational claim was made public. It was a virtuoso article, containing impressive calculations, carried out with - by Russian standards - remarkable clarity. Absolutely convincing, in fact. We realised that here, not for the first time, in a world full of far-reaching abstractions, a new, gigantic - albeit extremely hypothetical - source of energy was revealed. Carried away by this speculative discovery, we amused ourselves with "Gedanken Experiments" and "back of envelope" calculations. If these monopoles really existed, where are they? Nobody has detected them, after all. Are they too rare perhaps? Or too heavy? The theory predicts an immense mass of 0.01 milligrams per particle, which is gigantic compared to the mass of a hydrogen atom, which weighs just 0.000 000 000 000 000 001 milligrams. An elementary particle with a mass comparable to that of a microbe is too heavy to be created in even the most costly accelerator. Are monopoles perhaps hidden in ordinary matter? Or do they form very strongly bound, magnetically neutral pairs with antipoles? Suppose that they fly freely through space, could we attract them with a gigantic magnet? Suppose we manage to "catch" one and lock it up in a magnetic cage, together with a substantial heap of rubbish: Would it indeed swallow the garbage and could this provide the ultimate solution to our pollution problem? Or were we on the verge of giving birth to a new, even more destructive type of BOMB, in view of the unimaginable amount of energy released when matter decays through a monopole? Could it be a possible explanation for the Bermuda Triangle? It looked as though a new horizon was opening up for what insiders would call "curiosity-driven technology". At this point I should probably fulfil an important moral duty, and raise my finger warning for the dangers conceivably hidden in what is supposed to be pure and innocent research into magnetic monopoles. Today's sweet dreams may well become tomorrow's nightmares. While a great social debate about the would be "blessings" of physics to society flourished, backstage new doors for science were opening up. "The world has not yet come to an end, but we are working on it", quipped Wim Kan. Indeed, in a God-fearing nation like ours, "value-free" physics is perceived as the Devil's henchman. People who devote their lives to the question of how nature works, whether they do so using high-tech instruments, laptop computers or pencil and paper, run the risk of being typecast as power-hungry Dr. Strangeloves, preferably seated in a wheelchair, who want to bend the universe to their will. But I digress...

    Well, I think I have made it clear that the theory made steady progress, but unfortunately not on the basis of facts. Or not yet, at any rate. People delved diligently into other aspects of the monopole question. At one point, convincing arguments from Moscow and Harvard claimed that these (anti)monopoles would be created in huge quantities at a very early stage of the universe's existence. Because of its rapid expansion, these extremely massive particles would "not have had the time" to find and annihilate each other. In short, monopoles, even if they are not the most predominant form of matter in our universe (food for those in search of dark matter, perhaps), would still completely disrupt extremely successful cosmological calculations such as the computation of the abundance of helium in the universe. It appeared that we could not have it both ways; we would have to throw either the successful Big Bang theory of the universe or the successful unification theories of elementary particles overboard. It was a meeting of extremes. Were the smallest particles going to be in charge of the cosmos, or had the lessons from the universe killed off a central paradigm of particle physics? As these things tend to, the situation cooled down a little; the extremes got together, and a thrilling new idea was born. While it was difficult to escape from the accursed monopoles within the standard Big Bang scenario, further study of their creation made it clear that the universe might have gone through a phase of exponential expansion in a very early stage. This "inflationary" phase lasted for a very short time according to our present-day timescales, but at that time it was very long: many times longer than the lifespan of the universe. According to this view, the number of monopoles per unit volume was reduced exponentially to a number of the order of one in our universe. Acceptable, thus. `Have these scientists really nothing better to do than to kill one fiction with another ?' I hear you asking in amazement. Compared with this, Don Quixote looks like a first class pragmatist. Actually an interesting footnote to the development described above is that the idea of inflation went on to live a life of its own - independent of the monopole question. In particular, Alan Guth showed that the proposed inflation itself eliminated a number of long-standing, relatively annoying shortcomings of the standard Big Bang model. In fact, it enriched the model, bringing it considerably closer in line with certain experimental facts.

    Apart from a theory of non-existent particles (`to be or not to be' remains the question), the monopoles also appear to turn up in the theory of "nothing", i.e. the description of empty space, or the vacuum. In physics (quantum mechanics) this term is used to refer to the state of lowest energy - the ground state. One would imagine that in a theory of particles the lowest state would always correspond with a state in which no particles are present. However, this is not entirely correct; sometimes it may be that a certain type of particle "condenses" in order to lower the energy still further. Water forms a vapour at high temperature and normal pressure, but when the temperature is lowered below boiling point it will spontaneously condense to a fluid state with much greater density. This illustrates how the ground state, the state of minimal (free) energy, can change as a function of the temperature. If we're talking about empty space, "fish" for example would probably refer to a situation without fish or plants, but not one without water. A powerful statement about the nature of a vacuum was made by John Archibald Wheeler: "No point is more central than this, that empty space is not empty. It is the seat of the most violent physics." When monopoles failed to show up in our detectors, the monopole freaks had to ask themselves whether they might be hidden in the ground state. One sector of the standard model in particular, which describes the strong interactions, became the target of their activity. In this sector, dubbed "quantum chromodynamics", another sort of fairly elusive particles, known as quarks, play a leading role. Their status is also somewhat dubious, since they do not occur as free particles, but are permanently confined within what are called hadrons, such as the protons and neutrons which make up all our atomic nuclei. What we see are thus protons, and from the properties of these protons we can indirectly deduce that in fact they contain three quarks. Why do quarks always assemble in threes (or with an antiquark) in a hadron? Because of a law against assemblies of less than three quarks. This remarkable property can be blamed on the "repressive tolerance" of the surrounding vacuum, which is described by people like Nambu, Mandelstam and 't Hooft as follows: the quarks have what is known as a certain "colour" electric charge. The vacuum is a superfluid made up of "colour" monopoles and antimonopoles, a magnetic superconductor in which the monopoles can move without resistance. Moving magnetic charges create electrical fields. When we put a quark charge in the vacuum, the colour electrical fields are cancelled out by the coherent movement of monopoles, to the extent this is possible. The total electrical field produced by the quark charge is squeezed into a narrow tube, and that tube can end only with an antiquark. A single quark would drag an endlessly long cylinder of field energy behind it, which would mean that the corresponding physical state would have infinite energy. Such states are not found in nature. This also applies to every state which a colour combination of quarks contains which is not neutral (white) in colour. The result, if we pull a quark-antiquark pair apart, is reminiscent of the story of the magnet. At some point, a new quark-antiquark pair will be spontaneously created, and the fluxtube which bound the original pair will break in two. Thus, whenever we try to break the hadron into quark pieces, the end product will once again be a number of hadrons. Hence there appears to be a natural limit to our urge to isolate increasingly smaller building-blocks of matter. The enigmatic monopole vacuum forms a connecting link between the quarks and their hadronic manifestation.

    With this brief "case history", I have tried to illustrate the fact that developments in basic science can be capricious and unpredictable. They are constantly exciting for those involved in the field, who find themselves unexpectedly confronted with unimaginable vistas while maybe standing at the edge of an abyss. Managers and policy-makers want to be able to plan things properly: to set concrete goals and hold interim evaluations; they want flow charts and rock-hard criteria; advisory committees, panel discussions, councils; visits, accurate reports, strategy meetings at windy seaside resorts or in nature reserves. No cost or effort is saved to divide the limited resources fairly. Science acts as a main job supplier to the bureaucracy. However it remains pretty much true that Mother Nature does not strip herself bare for a halfpenny, and she appears to be immune to both political instinct and managerial enthusiasm. She rather responds to patience and persistence, of which basic science is after all the cultural expression. As for those monopoles, maybe we are on the wrong track, but perhaps.....

F.A. Bais