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The goal of theoretical

Paul Dirac, who discovered the equation which describes the behaviour of the electron. He has pointed out that this equation is the basis of 'most of physics and all of chemistry'.

75 the end in sight for theoretical of the century it was believed that physics ?'This was the question posed could be understood in by in his inaugural terms of continuum . All lecture * as incumbent of the presti­ that was needed was to measure a gious Lucasian Chair of certain number of coefficients of in the University of Cambridge. elasticity, , conductivity etc. Among his many other accomplish­ This hope was shattered by the dis­ ments, Hawking has successfully covery of atomic structure and quan­ brought together ideas from particle tum mechanics. Again, in the late physics, from and 1920s told a group of from (see October visiting Gottingen that 1977 edition, page 334) which have 'Physics, as we know it, will be over greatly influenced thinking on the in six months.' This was shortly after origin of the . the discovery by of the We are publishing the text of the equation which governs the behav­ lecture in two parts, the first dealing iour of the electron. It was expected with the motivations for constructing that a similar equation would govern unified in physics, and going the proton, the only other sup­ on to describe current efforts to unify posedly known the electroweak picture with that of at that . However, the discovery quark . As an influential phy­ of the neutron and of nuclear forces sicist not directly involved with parti­ disappointed these hopes. We now cle research, Hawking s views on par­ know that neither the proton nor the ticle make interesting reading. neutron are elementary but that they In the second part, to be published in are made up of smaller particles. our March issue, Hawking goes on to Nevertheless, we have made a lot of cover the subject of , where his in recent years and there statistical methods and abandon any pronouncements always provide sub­ are some grounds for cautious pretence of solving the equations stantial food for thought. optimism that we may soon see a exactly. Although in principle we complete theory. know the equations that govern the Even if we do achieve a complete whole of biology, we have not been unified theory, we shall not be able to able to reduce the study of make detailed predictions in any but behaviour to a branch of applied the simplest situations. For example, mathematics. 'I want to discuss the possibility that we already know the physical laws What would we mean by a com­ the goal of might that govern everything that we plete and unified theory of physics? be achieved in the not too distant in everyday life: as Dirac Our attempts at modelling physical future, say, by the end of the century. pointed out, his equation was the normally consist of two By this I mean that we might have a basis of 'most of physics and all of parts: complete, consistent and unified chemistry'. However we have been 1. A of local laws that are obeyed theory of the physical interactions able to solve the equation only for by the various physical quantities. which would describe all possible the very simplest system, the These are usually formulated in observations. hydrogen consisting of one terms of differential equations. Of course one has to be very proton and one electron. For more 2. Sets of boundary conditions that cautious about making such predic­ complicated with more elec­ tell us the state of some regions of tions : we have thought that we were trons, let alone for with the Universe at a certain time and on the brink of the final synthesis at more than one nucleus, we have to what effects propagate into it sub­ least twice before. At the beginning resort to approximations and intui­ sequently from the rest of the Uni­ tive guesses of doubtful validity. For verse. * 'Is the end in sight for theoretical physics?' macroscopic systems consisting of by Stephen Hawking, published by Cam­ Many people would claim that the 23 bridge University Press. 1 0 particles or so, we have to use role of was confined to the

CERN Courier, January/February 1981 3 first of these and that theoretical that stars' would never have been makes it very difficult to hold an physics will have achieved its goal formed by gravitational condensa­ anthropocentric view or to believe when we have obtained a complete tion. that the structure of the Universe set of local physical laws. They Some people have gone so far as is determined by anything so would regard the question of the to elevate these restrictions on the peripheral as some complicated initial conditions for the Universe as initial conditions and the parameters molecular structures on a minor pla­ belonging to the realm of metaphy­ to the status of a principle, the net orbiting a very average star in the sics or . In a way this attitude , which can be outer suburbs of a fairly typical spiral is similar to that of those who in paraphrased as 'Things are as they galaxy. earlier centuries discouraged scien­ are because we are'. According to If we are not going to appeal to the tific investigation by saying that all one version of the principle there is a Anthropic Principle, we need some natural phenomena were the work of very large number of different sepa­ unifying theory to account for the God and should not be inquired into. rate with different values initial conditions of the Universe and I think that the initial conditions of of the physical parameters and dif­ the values of the various physical the Universe are as suitable a sub­ ferent initial conditions. Most of parameters. However, it is too diffi­ ject for scientific study and theory as these universes will not provide the cult to think up a complete theory of are the local physical laws. We shall right conditions for the development everything all at one go (though this not have a complete theory until we of the complicated structures does not seem to stop some people; can do more than merely say that needed for intelligent life. Only in a I get two or three unified theories in 'Things are as they are because they small number, with conditions and the mail each week). What we do were as they were.' parameters like our own universe, instead is to look for partial theories The question of the uniqueness of will it be possible for intelligent life to that will describe situations in which the initial conditions is closely develop and to ask the question certain interactions can be ignored related to that of the arbitrariness of 'Why is the Universe as we observe or approximated in a simple manner. the local physical laws: one would it ?' The answer is, of course, that if it We first divide the material content not regard a theory as complete if it were otherwise there would not be of the Universe into two parts, 'mat­ contained a number of adjustable anyone to ask the question. ter' particles such as quarks, elec­ parameters such as or cou­ The Anthropic Principle does pro­ trons, muons etc., and 'interactions' pling constants which could be given vide some sort of explanation of such as gravity, any values one liked. In fact it seems many of the remarkable numerical etc. that neither the initial conditions nor relations that are observed between The particles are described the values of the parameters in the the values of different physical para­ by fields of half-integer spin and theory are arbitrary but that they are meters. However, it is not com­ obey the Pauli Exclusion Principle somehow chosen or picked out very pletely satisfactory: one cannot help which prevents more than one parti­ carefully. For example, if the proton- feeling that there is some deeper cle of a given kind from being in any neutron difference were not explanation. Also, it cannot account state. This is the reason that we can about twice the mass of the electron, for all the regions of the Universe. have bodies that do not col­ one would not obtain the couple of For example, our solar system is lapse to a point or radiate away to hundred or so stable nuclides that certainly a prerequisite for our exis­ infinity. The matter particles are div­ make up the elements and are the tence as is an earlier generation of ided into two groups, the hadrons, basis of chemistry and biology. Sim­ nearby stars in which heavy ele­ which are composed of quarks, and ilarly if the gravitational mass of the ments could have been formed by the leptons, which comprise the proton were significantly different, nuclear synthesis. It might even be remainder. one would not have had stars in that the whole of our galaxy was The interactions are divided phe- which these nuclides could have required. But there does not seem nomenologically into four catego­ been built up and if the initial expan­ any necessity for other galaxies to ries. In order of strength they are: the sion of the Universe had been exist, let alone the million million or strong nuclear forces which interact slightly smaller or greater, the Uni­ so of them that we see, distributed only with hadrons, electromagne­ verse would either have collapsed roughly uniformly throughout the tism which interacts with charged before such stars could have evolved observable Universe. This large- hadrons and leptons, the weak or would have expanded so rapidly scale of the Universe nuclear forces which interact with all

4 CERN Courier, January/February 1981 Murray Gell-Mann seen here lecturing at CERN on the 'Grand Unification' of the different forces in physics. In the audience is (top left) Stephen Hawking, whose own ideas on the subject are stimulating.

(Photo CERN 263.3.79)

would have to be smeared out with some probability distribution around the nucleus. In this state the electron could not radiate in the form of electromagnetic waves because there would be no lower energy state for it to go to. In the 1 920s and 1 930s wa#s applied with great success to systems such as atoms or molecules which have only a finite number of degrees of freedom. Diffi­ culties arose when people tried to hadrons and leptons and finally, the quantities which were continuously apply it to the electromagnetic weakest by far, gravity which inter­ variable and which could, in principle which has an infinite number of acts with everything. The interac­ at least, be measured to arbitrary degrees of freedom, roughly speak­ tions are represented by integer-spin accuracy. However a problem arose ing, two for each point of -time. fields which do not obey the Pauli when one tried to use such theories One can regard these degrees of Exclusion Principle. This means that to construct a model of the atom. It freedom as oscillators, each with its they can have many particles in the had been discovered that the atom own position and . The same state. consisted of a small positively oscillators cannot be at rest because In the case of electromagnetism charged nucleus surrounded by a then they would have exactly and gravity, the interactions are also cloud of negatively charged elec­ defined positions and momenta. long-range which means that the trons. The natural assumption was Instead each oscillator must have fields produced by a large number of that the electrons were in orbit some minimum amount of what are matter particles can all add up to around the nucleus like the is in called 'zero point fluctuations' and a give a field that can be detected on a orbit around the Sun. However the non-zero energy. The of the macroscopic scale. For these rea­ Classical Theory predicted that the zero point fluctuations of all the sons they were the first to have electrons would radiate electromag­ infinite number of degrees of free­ theories developed for them, gravity netic waves. These waves would dom would cause the apparent mass by Newton in the seventeenth cen­ carry away energy and would cause and charge of the electron to tury and electromagnetism by Max­ the electrons to spiral into the become infinite. well in the nineteenth century. How­ nucleus, producing a collapse of the In the late 1940s, a procedure ever these theories were basically atom. called renormalization was devel­ incompatible because the Newton­ This problem was overcome by oped to overcome this difficulty. It ian Theory was if the whole what is undoubtedly the greatest consisted of the rather arbitrary sub­ system was given any uniform ve­ achievement in theoretical physics traction of certain infinite quantities locity whereas the Maxwell Theory this century, the discovery of the to leave finite remainders. In the defined a preferred velocity, the Quantum Theory. The basic postu­ case of electrodynamics, it was speed of . In the end it turned out late of this is the Heisenberg 'Uncer­ necessary to make two such infinite to be the Newtonian Theory of Grav­ tainty Principle' which states that subtractions, one for the mass and ity which had to be modified to make certain pairs of quantities, such as the other for the charge of the elec­ it compatible with the invariance the position and momentum of a tron. This renormalization procedure properties of the Maxwell Theory. particle, cannot be measured simul­ has never been put on a very firm This was achieved by Einstein's taneously with arbitrary accuracy. In conceptual or mathematical basis, General which the case of the atom this meant that but it has worked quite well in prac­ was formulated in 191 5. in its lowest energy state the elec­ tice. Its great success was the pre­ The General Relativity Theory of tron could not be at rest in the diction of a small displacement, the Gravity and the Maxwell Theory of nucleus because, in that case, its Lamb Shift, in some lines in the Electrodynamics were what is called position and velocity would both be spectrum of atomic hydrogen. How­ Classical Theories — they involved defined exactly. Instead the electron ever it is not very satisfactory from

CERN Courier, January/February 1981 5 The cupola which roofs over the experimental area at the CERN SPS housing apparatus for the UA1 to study high energy collisions of protons and antiprotons. High on its agenda of priorities is a search for the intermediate bosons of weak interactions, long predicted but so far not seen.

(Photo CERN 387.11.80} the point of view of a complete theory because it does not make any predictions of the values of the finite remainders left after making infinite subtractions. Thus we would have to fall back on the Anthropic Principle to explain why the electron has the mass and charge that it does. During the 1950s and 1960s it was generally believed that the weak and strong nuclear forces were not renormalizable and would re­ quire an infinite number of infinite subtractions to make them finite. There would be an infinite number of finite remainders which were not determined by the theory. Such a theory would have no predictive power because one could never measure all the infinite number of parameters. However, in 1971 't Hooft showed that a unified model of the electromagnetic and weak interactions that had been earlier proposed by Salam and Weinberg was indeed renormalizable with only a finite number of infinite subtrac­ strong interactions. It was realized The strong interactions between tions. In the Salam-Weinberg theory fairly early on that the proton and the quarks are supposed to be car­ the photon, the spin-1 particle that other hadrons such as the pion could ried by spin-1 particles called gluons carries the electromagnetic interac­ not be truly elementary particles, but rather like the particles that carry the tion, is joined by three other spin-1 that they must be bound states of . The gluons also partners called W+, W~ and Z°. other particles called quarks. These carry colour and they and the quarks At very high energies these four seem to have the curious property obey a renormalizable theory called particles are all predicted to behave that, although they can move fairly or QCD in a similar manner. At lower ener­ freely within a hadron, it appears to for short. A consequence of the gies a phenomenon called 'sponta­ be impossible to obtain just one renormalization procedure is that neous breaking' is in­ quark on its own; they always come the effective coupling constant of voked to explain the fact that the either in groups of three (like the the theory depends on the energy at photon has zero rest mass whereas proton or neutron) or in pairs consist­ which it is measured and decreases the W+, W" and Z° are all very ing of a quark and antiquark (like the to zero at very high energies. This massive. The low energy predictions pion). To explain this, quarks were phenomenon is known as asymp­ of this theory have agreed remarka­ endowed with an attribute conve­ totic freedom. It means that quarks bly well with observation and this led niently called 'colour'. The idea is inside a hadron behave almost like the Swedish Academy in 1979 to that quarks come in three 'colours', free particles in high energy colli­ award the to Salam, red, green and blue, but that any sions so that their interactions can Weinberg and to Glashow, who had isolated bound state such as a be treated successfully by perturba­ also constructed similar unified hadron has to be 'colourless', either a tion theory. theories. combination of red, green and blue The predictions of perturbation The success of the Salam-Wein­ like the proton, or a mixture of red theory are in reasonable qualitative berg theory led to the search for a and antired, green and antigreen, agreement with observation but one similar renormalizable theory of the and blue and antiblue like the pion. cannot yet really claim that the the-

6 CERN Courier, January/February 1981 Setting the scene for the hunting of the elusive intermediate bosons of weak interactions, which according to current theory should soon be within reach. This underground cavern at the CERN SPS will shortly house several of the being prepared to exploit high energy proton- antiproton colliding beams.

(Photo CERN 189.12.80)

beyond the scope of any laboratory experiment: the present generation of particle accelerators can produce centre-of-mass energies of about 10 GeV and the next generation will produce energies of 100 GeV or so. This will be sufficient to investigate the energy range in which the elec­ tromagnetic forces should become unified with the weak forces accord­ ing to the Salam-Weinberg theory but not the enormously high energy at which the weak and electromag­ netic interactions would be pre­ dicted to become unified with the strong interactions. Nevertheless there can be low energy predictions of the Grand Unified Theories that might be testable in the laboratory. For example, the theories predict that the proton should not be com­ pletely stable but should decay with a lifetime of order 1031 years. The present experimental lower limit on the lifetime is about 1030 years and it should be possible to improve this. ory has been experimentally verified. be a significant step toward a com­ Another observable prediction At low energies the effective cou­ plete unified theory. The basic idea is concerns the ratio of baryons to pling constant becomes very large that the effective coupling constant photons in the Universe. The laws of and perturbation theory breaks of the strong interactions, which is physics seem to be the same for down. It is hoped that this 'infrared large at low energies, gradually particles and antiparticles. More pre­ ' will explain why quarks are decreases at high energies because cisely, they are the same if particles always confined in colourless bound of asymptotic freedom. are replaced by antiparticles, right- states but so far no-one has been On the other hand, the effective handed is replaced by left-handed able to demonstrate this really con­ coupling constant of the Salam- and the velocities of all particles are vincingly. Weinberg theory, which is small at reversed. This is known as the CPT Having obtained one renormaliza- low energies, gradually increases at and it is a consequence of ble theory for the strong interactions high energies because this theory is basic assumptions that should hold and another one for the weak and not asymptotically free. If one extra­ in any reasonable theory. Yet the electromagnetic interactions, it was polates the low energy rate of Earth and indeed the whole solar natural to look for a theory which increase and decrease of the cou­ system is made up of protons and combined the two. Such theories are pling constants, one finds that the neutrons without any antiprotons or given the rather exaggerated title of two coupling constants become antineutrons. Indeed such an imbal­ 'Grand Unified Theories' or GUTsfor equal at an energy of about ance between particles and antipar­ short. This is rather misleading 1015 GeV. The theories propose that ticles is yet another a priori condition because they are neither all that above this energy the strong interac­ for our ; for if the solar grand, nor fully unified, nor complete tions are unified with the weak and system were composed of an equal theories in that they have a number electromagnetic interactions but mixture of particles and antiparti­ of undetermined renormalization pa­ that at lower energies there is spon­ cles, they would all annihilate each rameters such as coupling constants taneous symmetry breaking. other and leave just radiation. and masses. Nevertheless they may An energy of 1015 GeV is way From the observed absence of

CERN Courier, January/February 1981 7