When we talk about a particle's lifetime we always mean its average lifetime. A particle that is not absolutely stable has, at every moment of its life, the same chance of decaying. Some particles live longer than others, but the average lifetime is a characteristic of any particle species.

One can also use the concept of ‘half-life’. If we have a large number of identical particles, the half-life is the time it takes for one-half of all the particles to decay. The half-life is 0.693 times the average lifetime.

One glance at Table 1 shows that some particles have a much longer average lifetime than others. The lifetimes differ enormously. A neutron, for example, lives 1013 times longer than a sigma-plus, and the sigma-plus has more than 109 times as long a lifetime as the sigma-zero. But if you observe that the ‘natural’ time scale for an elementary particle (which is the time it takes for their quantum mechanical state, or wave function, to evolve or oscillate) is somewhere around 10−24 seconds, you can safely state that all these particles are pretty stable. In our professional jargon, they are all called ‘stable particles’.

How is a particle's lifetime determined? Particles with long lifetimes, such as the neutron and the muon, have to be captured, preferably in great numbers, after which one registers the decays electronically. Particles with lifetimes around 10−10 to 10−8 seconds used to be registered in a bubble chamber; nowadays this happens more often in a spark chamber.

Twentieth century physics began exactly in the year 1900 when the German physicist Max Planck proposed a possible solution to a problem that had been haunting physicists for years. The problem concerned the light emitted by any object that is heated to a certain temperature, and also the softer infrared radiation emitted, with less intensity, by colder objects.

It had become well accepted that all this radiation had an electromagnetic origin, and the laws of Nature for these electromagnetic waves were already known. Also known were the laws for heat and cold, so-called ‘thermodynamics’. Or so it seemed. But if we use thermodynamic laws to compute the intensity of the radiation in question, the outcome does not make any sense at all. Such a calculation would tell us that an infinite amount of radiation should be emitted in the very far ultraviolet. Of course, this is not what happens. What does happen is that the intensity of the radiation shows a peak at a certain characteristic wavelength, and diminishes both at wavelengths longer and shorter than this. This characteristic wavelength is inversely proportional to the absolute temperature of the radiating object (absolute temperature is defined by a temperature scale that begins at 273°C below zero or 459.6 OF below zero). At 1000°C or 1800°F an object is ‘red hot’; at this point the object is radiating in the visible light region.

We must now go back to 1954, to a time when the big successes of the theory for the electromagnetic forces between the particles were still fresh. Not yet discouraged by the discoveries of numerous particle species that were yet to come, scientists were still searching for simple, elegant and universal principles in physics.

All aspects of the electromagnetic forces between particles can be deduced from the equations that are obeyed by the electric and the magnetic fields. These fields are vector fields. A ‘vector’ is a quantity that is not only characterized by its strength but also by its direction, and several numbers (typically three) are needed its description. ‘Field’ means that these numbers may have different values at different points in space and time. The wind velocity in the atmosphere could be called a vector field. For the wind, you first indicate how much air is moving northwards (if it moves southwards you give this number a minus sign); secondly, you determine the east—west movement; and finally you give a number corresponding to the vertical component.

Taken all together the electromagnetic field has six components. But these cannot be chosen at will. These numbers are hanging together via ‘field equations’, just like the wind velocity components are related to the air pressure distribution in the neighborhood. If you know the air pressure, you can calculate the wind speed in all directions.

For the particles discovered so far, we now had a pretty detailed map of the weak, the electromagnetic and the strong interactions. Only one thing was not quite right in the picture presented so-far: on average, three out of every thousand KLong mesons decay into just two pions, and thus they violate conservation of PC symmetry, as I described in Chapter 7. Which force is responsible for this phenomenon?

What makes this problem particularly difficult is that KLong is the only particle in which this peculiar force has manifested itself up till now. KLong is composed of two quarks, strange and down. Apparently, quarks exert forces on each other that are not quite PC symmetric. Where could such a force come from? Until now, our mathematical scheme has not included such a force; all our equations have automatically been PC symmetric. Several ways of repairing our model, by adding a PC violating force, such that the KLong decay could be explained, have been invented. In any case, more ‘auxiliary particles’ would be needed to transmit the new force.

It turns out not to be possible to repair our model by invoking yet another Yang–Mills field. The spin 1 particles always preserve PC symmetry (could this be why the violation of PC symmetry is so tenuous?)

The gravitational force is surely one of the most remarkable forces acting upon our elementary particles. You may remember that at the beginning of our journey towards the world of the small we observed that gravity is much less important for tiny creatures than it is for large ones. We used the example that, whereas a mouse can climb up a nearly straight wall, an elephant cannot. For atoms and molecules, and all the other particles we have discussed so far, gravity is practically a negligible phenomenon. But when we look at particles considerably smaller than the size of an atomic nucleus, we reach a turning point. Gravity acts upon the mass of the particles, whereas all other forces act on something we call ‘charge’. The difference is that charge depends only very slightly on the degree of magnification of our microscope, whereas mass is connected to energy, and if we try to localize a particle in a smaller volume then, according to the rules of quantum mechanics, there will be more motion; the energy of motion (called ‘kinetic energy’) increases. This is why smaller distances correspond to higher energies, and hence also larger masses. When distances are so small that the movements become relativistic (i.e. close to the speed of light) the effects of the gravitational force gradually begin to increase relative to the other forces; however, they are still incredibly weak, and so they have a long way to go before thay can compete in strength.

If superstrings will not yield the ultimate answers, then in which direction should we continue our research? Or did we throw ourselves so far into the world of the unknown and unintelligible that we are about to drown in nonsense? Are we burying ourselves beneath so many impossible questions that we should be considered lost for science? Does it make any sense at all to speculate about a Theory of Everything in this strange world of Planck numbers? Perhaps the title of this chapter makes you fear the worst.

Nothing excites our curiosity more than the unintelligible. What is so curious about the world at the Planck length is that no model at all can be found that gives a reasonably self-consistent description of particles that influence each other with such strong gravitational forces, while at the same time obeying the laws of quantum mechanics. So, even if we had been able to perform experiments with particles that hit each other with Planckian energies, we would not have known how to compare the results with a theory. There is work here to do for physicists: make a theory. We do not care too much how such a theory describes the gravitational force, but there are quite a few demands on our list that make the creation of a candidate theory extremely difficult. As I explained at the end of the preceding chapter, superstring theory came close to doing just this, but it may well fail to fulfil its promises.

It is difficult to venture into the world of the ultimately small, or even to talk about it, without a very good understanding of the laws of Nature that govern that world. The forces one finds there determine the way in which the tiny particles we wish to study move about, and also all their other properties. Whether, and how, we can actually observe them will also depend on these forces.

And this is not easy, because the laws of Nature are complicated. More and more experts in this field seek refuge in a kind of mathematical gibberish no ‘normal’ person can follow, unless he or she belongs to the in-crowd. To really appreciate the rock-solid logic of the laws of physics, one actually cannot avoid math. Nonetheless, we physicists feel the need to share the joy of all our beautiful discoveries with whoever wants to listen. We are advised then to avoid all math. This then is what I shall reluctantly do.

It is my intention to provide a narrative of twenty-five years of research on the very tiniest particles of matter. During those twenty-five years, I began to view Nature as an intelligence test to which humanity as a whole has been subjected, as a giant jigsaw puzzle given to us to play with. Time and again, we stumble upon new pieces, large or small, that fit beautifully with those we already have. I want to share with you the sense of triumph we feel at such moments.

There has existed a phenomenological theory for the weak force since 1958. That is to say, there existed formulae that correctly described the effects of the weak force for all particles, under all circumstances, that could be realized in the experiments of that time, with margins of error within a small percentage. The theory could never be a fundamental theory, because it was understood that the theory would break down in more violent collision experiments. But it was also known that it would take at least a decade for the experimentalists to reach such energies in a laboratory, and so it seemed that for the time being this ‘temporary’ theory would have to be sufficient.

For the strong force there were a hotchpotch of phenomenological theories. None of these were very accurate, and this situation was obviously very unsatisfactory. The only features of the strong interactions that were well understood were its various symmetry properties and the ensuing conservation laws. Strangeness, isospin and a few other quantities were very strictly conserved for this force.

This was in striking contrast to the situation with the electromagnetic force. This has the peculiarity that it can propagate over long distances, and so this force is also experienced in the everyday world. The British physicist James Clerk Maxwell had given the mathematical formulation of electrodynamics as early as 1873 (see Figure 6).

So here we are. Apart from just a few minor technical details, theoretical physics is finished. We have a model that encapsulates everything we wish to know about our physical world. What else do we want?

Well, the Standard Model is nearly, but not quite, perfect. First of all, we could begin to complain about those twenty uncalculable constants. But if this were the only complaint there would probably be little we could do about it. Of course, numerous ideas have been suggested to explain the origin of these numbers, and theories have been put forward that purportedly ‘predict’ their values. The problem with all these theories is that the arguments they give are never compelling. Why should Nature care about some magic formula if without such a formula no real contradictions arise? What we really need is some fundamental new principle, such as the relativity principle, but we do not want to abandon all the other principles that are already known; these, after all, have been so tremendously helpful in discovering the Standard Model! The best place to look for a new principle is where our present theory has other weak spots.

A universal rule in particle physics is that, when particles collide with greater and greater energies, the effects of the collisions are determined by tinier structures in space and time. Suppose we had at our disposal a particle accelerator in which particles can be given 1000 times the energy that can presently be reached.

There are two directions in which one can try to extend the presently known Standard Model, and these can essentially be characterized as follows:

(1) rare new particles and extremely weak new forces, and

(2) heavy new particles and new structures at very high energies.

Let us begin with the first. Particles could exist that are very difficult to produce and to detect, and, for that reason, they could have escaped our attention up till now. All particle types that exert strong forces on any of the known particles could never hide themselves from us. According to the forbidding laws of quantum particle theory, such particles would be frequently produced, either singly or in particle–antiparticle pairs – this would only not happen if their masses are too great, but that is covered by case (2). They would betray their presence by colliding against particles in a detector. The only light particles that can avoid our detection are ones that exert only very tiny forces upon most or all known species.

The first additional particle that springs to mind is a neutrino spinning to the right. Recall from Chapter 7 that neutrinos only rotate to the left (antineutrinos rotate to the right), if you take the axis of rotation parallel to the direction of movement. From a mathematical point of view, there is no objection to this, but it is somewhat unaesthetic.

While we began to understand how to construct renormalizable theories for the weak intractions, the strong interactions were still shrouded in mystery. They looked much less controllable. Investigators did learn how to cause various particles to collide with each other with increasing collision energies, using new and ever more powerful acceleration machines, resulting in a much better understanding of the curious internal structure of the hadrons. What was immediately obvious was that the list of resonances became longer and longer. A resonance could best be described as a particle that in all respects resembles one of the particles of Table 1, only its mass is bigger and often its spin is greater. The resonances came in series, with the heavier ones often having the highest spin. There are baryonic and mesonic resonances. Without changing the total of the quantum numbers S (strangeness) and I3 (isospin), these resonances can decay into lighter particles within some 10−23 seconds.

It was difficult to understand why the hadrons behaved in this way. But, without attempting to answer such questions, Gabriele Veneziano discovered a simple mathematical formula that represented, in a particularly elegant way, the effects of all these resonances when particles collide. The remarkable thing about his formula was that in it the effects of the strong force were described very realistically (that is, relatively well in agreement with what was known from experiments), whereas no single existing theory could explain the formula. Not yet. Veneziano's formula would playa very important role, and I will return to it later.

Certainly in the world of living creatures scale does create important differences. In many respects, a mouse's anatomy is a carbon copy of that of an elephant, but, whereas a mouse can climb up a nearly vertical piece of rock without much difficulty (and even if it fell from a height many times its own size, it would not greatly injure itself), an elephant would not be able to perform such a feat. Quite generally, the effects of gravity are less important as we study smaller and smaller objects (be they living or inanimate).

Arriving at unicellular creatures, we see that for them there is no distinction at all between up and down. For them, the surface tension of water is a far more important force than gravity. For example, just observe that surface tension is the force that gives a drop of water its shape. Compared with the size of unicellular creatures, drops of water are very big; evidently, surface tension is very important at this scale.

Surface tension is a consequence of the fact that all molecules and atoms attract each other with a force that we call the Van der Waals force. This Van der Waals force has only a very short range. To be precise, the strength of this force over a distance r is roughly proportional to 1/r7. This means that if you reduce the distance between two atoms by one-half, the Van der Waals force with which they attract each other becomes 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128 times stronger.

We return to the next-to-last bus stop on the super-highway, called ‘supergravity’. Supergravity theory worked well, but not well enough. At some points the mathematical construction did not work perfectly. Also, not all particle types seemed to fit together in such a model, and not all infinities cancelled. In courageous perseverence, researchers next tried the same theories in spaces with many more dimensions than ours.

A two-dimensional space can be compared with the surface of a piece of paper, such as the pages you are reading now. Suppose you tear one page out now and roll it up to obtain a cylinder. For a little red spider that happened to be walking on your paper, this makes little difference. It takes a long time for the spider to walk one full circle around the cylinder. It probably would not even notice that it came back to where it started from. We say that its world is still two-dimensional. But, seen from some distance, the pipe is rather like a stick, having only one dimension. In the same vein, the world of the very tiniest particles could have more than three (space-like) dimensions. These tiny particles could be like our little red spider. They would not notice that some of their dimensions are ‘rolled up’. For us, these rolled-up dimensions have become invisible. This idea had already been suggested by Theodor Kaluza in 1919, and was further elaborated upon by Oskar Klein, in Stockholm, Sweden.

Let us begin our journey to the world of the tiny by beginning with what we can see with the naked eye, and with those laws of physics that we are all accustomed to. Take a large piece of paper and fold it into an airplane. You may decide to cut the paper in half to make two smaller airplanes. You could even cut the smaller pieces again to make even smaller planes. The properties of the paper, and the rules for folding it into an airplane, will hardly be different, except that the airplanes will become smaller and smaller. Gradually, however, as you continue to cut the paper into smaller and smaller pieces, you will find it harder to make planes, and eventually you will only have little shreds of what once was usable pieces of paper. The property ‘foldable into an airplane’ has been lost.

We have a similar situation when we start off with a bucket of water and pour the water into smaller buckets. The physical properties of water such as ‘flows from high to low’ remain the same, until finally we have less than one drop left. You cannot pour drops from high to low; you have to shake them off.

Every child who plays with toy cars or dolls knows that one can imitate the world of the large at a smaller scale. The writer Jonathan Swift based his famous stories on this.

The problem of permanent quark confinement became more and more intriguing to me during 1973 and 1974. What we knew was only that the color forces on the naked quarks at small distances are relatively small compared with the forces between dressed quarks at larger distances from each other. This was the ‘negative screening effect’ I mentioned in the previous chapter. It seems plausible that if this is extrapolated to larger distances, the color forces among quarks will continue to increase. The forces could easily become so strong that they keep the quarks permanently together. But is this really what happens? The essential difficulty was that because the forces are so great, calculations are nearly impossible. The only thing we are good at is performing calculations on particles that move in approximately straight lines. This is certainly not what quarks do when the forces are so strong. So the question became: is there a fundamental reason why quarks will remain invisible forever? Why do the field lines in a color theory form sausages, as in Figure 14, without spreading apart as in ‘ordinary’ electric and magnetic fields? If this could be explained, perhaps a calculational scheme could be devised to explain the properties of hadrons. I tried all sorts of things to find an answer.

Gulliver boldly continues his journey. When protons and neutrons are magnified 1000 times, the Standard Model tells him what details as small as 1/1000 of their diameter will look like. What comes after that, at even greater magnifications, is uncertain. We are now entering the world of very heavy particles, carriers of forces over ultra-short distances. We will concentrate on structures at distance scales between 1/1000 and 1/10000000000000000000 (that is, 10−19) times the proton diameter.

This seemingly absurd figure implies that the territory we are entering now covers some sixteen orders of magnitude (sixteen more zeros). This is about as much as the difference in size between a house and an atomic nucleus.

Surely this new world could be just as complicated as the previous one, the one described in the preceding nineteen chapters. But it could also be quite a bit simpler, in the sense that it might be possible to extrapolate all of the laws of physics over the whole area. It certainly seems as if the rules which I described in Chapter 11 will remain irreplaceable. Perhaps we will continue to find other particles and other fields, but no matter how I adjust the magnification of my imaginary microscope, I will see the same ground rules for objects with spin 1, spin ½ and spin 0 (as long as the gravitational force may be neglected, but more about that later).

When in 1931 Paul Dirac concluded from his equation for the electron that there should exist an antiparticle with opposite electric charge, he felt very embarrassed. Such a particle had not yet been discovered, and he really did not want to disturb the scientific community with such a revolutionary proposition. ‘Maybe this strange positively charged particle is simply the proton,’ he suggested. When shortly after that the real antiparticle of the electron (the positron) was identified, he was so surprised that he exclaimed: ‘My equation is smarter than its inventor!’

Nowadays, physicists no longer suffer from such modesty. High energy physicists are now accused of arrogance, and not fully without reason: when the new gauge theory for the weak force became popular, Weinberg and Salam had no trouble at all advertising it as a ‘unification’ of the weak force with the electromagnetic force; and to avoid any misunderstanding: ‘the most important unification since Sir James Clerk Maxwell unified electricity with magnetism’.

I have always maintained that the Weinberg-Salam model does not fully deserve such laudable comment. Did the new theory not start off with two different gauge fields, which we indicate by the mathematical terms ‘SU(2)’ and ‘U(l)’? That is not unification. On the other hand, however, you could emphasize that both force systems are based on exactly the same mathematical principles, and furthermore they are intimately mixed to produce the phenomena that are now explained. And, as in any meaningful theory, numerous new predictions emerged that could be vindicated by experiment. It was much less the case with the previous formalisms, so in this sense one could talk of unification.

Supersymmetry has beautiful mathematics, and so the professional literature is full of it. As we experienced earlier, for instance when the Yang–Mills theory was proposed, we have a brilliant mathematical scheme, which we do not yet know how to fit into the system of existing laws of Nature. It does not make sense, as yet, but we may hope that it will do some time in the future.

There is another scenario, actually much more appealing to our imagination. We have seen that atoms consist of smaller constituents, the protons, neutrons and electrons. And then we discovered that these constituents, in tum, have a further substructure: they are built from quarks and gluons. Why, as you might already have thought earlier, do not things go on like that? Perhaps these quarks and gluons, and also the electrons and all other particles still called ‘elementary’ in the Standard Model, are in tum built out of yet smaller grains of matter?

You would not be the first to have this idea. I have already reported how Jonathan Swift pictured the world of the small as a carbon copy of the world of larger things. Big fleas carry little fleas on their skins, and so on, ad infinitum. Well, just as biologists would try to explain to you that the kingdom of the fleas has to be looked upon somewhat differently, I must also state that the picture of an infinite repetition of building blocks cannot be correct as such.