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,:S lSYMMETRY CONCEPTS IN
MODERN PHYSIC~
/ '6 ( .Iqbal Memorial Lectureij
By
?-- '. ABDUS \SALAM M. A. (Pb.), Ph.D. (Cantab.), D. Sc. (Pb.), F. R. S., S. Pk.
Professor of Theoretical Physics . . Imperial College of Science & Technology, London (England).
ATOMIC ENERGY CENTRE, LAHORE. -=t· 1 9 6 6 EDITORS' NOTE
This book is essentially the Iqbal Memorial Lectures delivered by Professor Abdus Salam on Radio Pakistan in March, 1965. Some diagrams FAYYAZUDDIN and tables have been added. As Professor Salam has not read these lectures in the final M. A. RASHID form, we are responsible for all the errors.
Fayyazuddin Muneer Ahmad Rashid
Published by the Atomic Energy Centre, Lahore (Pakistan), 1966
PRINTED BY A, HAMllllD KHAN AT FllROZSONS LIMITED, LAHORll.
v During March 1965, I was privileged to deliver the first Iqbal Memorial lectures at the invita tion of Radio Pakistan. This is a reprint of the lectures where I took as my theme Symmetry Concepts in Modern Physics. Iqbal was our greatest poet, our deepest thinker. I take pride in the association of his name with these lectures for two reasons. Firstly, as a true philosopher Iqbal fully recog nized that there is no finality in philosophical thinking and that the progress of all philoso phical thought must depend on new discoveries in the field of science. Again and again in his lectures on the reconstruction of Religious Thought, he points towards the possibility of breakthroughs still to come in the field of physics which may give a new outlook to philo sophy. This, indeed, is just what has happened since Iqbal's death twenty-seven years ago, and an account of these newer concepts will be the theme of my lectures. Even though Iqbal did not live to see the fulfilment of his own prediction, I am glad that Radio Pakistan has decided to dedicate these lectures to his memory which lives for ever. My second reason for welcoming Iqbal's association with these lectures is this. I believe that the rise of a great poet or a great writer or a great humanist in any civilization is not an isolated incident-that it is always accompanied by an equally significant emergence of men as great in sciences and philosophy. To give . . one example, it is good to recall that at the last zenith of Islamic civilization, in the early part of the eleventh century, the Shahnama of Firdusi preceded the Encyclopaedic Qanun of Ibn-Sina and the equally Encyclopaedic Tanjim of Al Biruni by no more than twenty years. I am absolutely certain that Iqbal's greatness in poetry
vii ------
and philosophy will not go unmatched so far as • the present Muslim renaissance in science is con cerned. I believe that, now that the nation has begun once again to aspire to higher things, the age of Iqbal, just like the age of Firdusi eight From the dawn of all civilization man has hundred years ago, will produce in Pakistan its wondered and asked questions-questions about great scientists who will rival the brilliance of the colour of the sunset, about the brilliance of Firdusi's contemporaries like lbn-Sina and the stars, about rainfall and cloud-burst, about Al-Biruni. the trajectory of a bullet and a space satellite, These lectures are an account of man's search and eventually, about life itself. But in all this for unity in the understanding of the physical questioning there has occurred one recurring universe and the ultimate nature of matter. theme. Man has always believed that the During these lectures I would like to show how answers to these questions, when they come, rewarding the faith in the eventual unity, the must follow from just a very few general prin eventual harmony, the eventual beauty of the ciples. Man has always held to an unreasoning basic laws of nature has proved in unravelling faith in an eventual unity, an eventual simplicity, some of the deeper insights we have achieved. an eventual symmetry in any basic laws which Some of these concepts are extremely deep. may govern the Universe. The history of I can only hope I have not relapsed into a misty science is the history of a search for such all profundity which is quite often in science a cloak embracing, such unifying concepts. Within for one's own ignorance. the compass of inanimate matter we shall discuss what we believe today to be the ultimate ABDUS SALAM constituents of all matter, and what we think are the fundamental principles which govern its behaviour. Perhaps the first people in the history of mankind who made a systematic search for a unified and a rational explanation of "'the universe were the Greeks. The Greeks sought the ultimate principles governing nature to lie in four elements of which they believed all matter was made. These, in their view, were the ele ments of air, water, fire and earth. Greek thought permeated also early Islamic thinking and this classification of elements remained as the basis of mediaeval science. The real quantitative breakthrough, however, came in the nineteenth century as a result of thousands of painstaking and accurate laboratory experiments accom ... panied by the deepest analytical thinking. The viii nineteenth century chemist could show that in the last analysis all matter in the Universe, living or dead, and of whatever form absolutely everything-was made up of just 92 different types of elements, and that every element could be subdivided into tiny units the so-called atoms. These are the atoms of -, hydrogen, helium, lithium and beryllium, and so on. The science of chemistry is more or less summarized in the so-called periodic table of atoms (Table l); this is a chart, invented first by the Russian chemist Mandeleev, which orders the atoms in the manner we have described: hydrogen, helium, lithium, the table ending with the ninety-second entry uranium. The nineteenth century chemist believed that the atoms were indivisible, immutable entities, that they could not be divided any further. One found that the atoms attracted one another when they were a short distance apart; this was the chemical force responsible for building from atoms the complex forms in which matter mani fests itself. One also found that one could not push atoms too close together; they repelled each other on being squeezed too closely. This repulsion-this resistance to squeezing clearly meant that atoms could be pictured as objects with a definite size-as little hard balls. To get an idea of atomic sizes one may remember this. If a cricket ball is magnified to the size of the earth, then each atom in it will look as large as the original ball itself. The discovery that absolutely everything is made up of 92 types of atoms was something tremendous. The discovery made the nine M teenth century scientists absolutely dizzy with excitement. The atoms were the "elementary Fig. 1 particles"; the chemical force was the "elemen Electrons in hydrogen, helium, lithium and 11eo11 atoms whirling around tary force". In 1891 Lord Kelvin, addressing the the nucleus in different orbits. Electron forming the beginning of British Association for Advancement of Science, .. a new shell is indicated with a circle around it. 3 went so far as to say, "We have discovered in physical . sciences all that can be discovered. The rest IS more and more refined measurement". But by one of those curious accidents that seem so frequent in the history of science, this same Periodic Table ol the Elements year was destined to bring in a new revolution - ~n physics. This was the year that J. J. Thomson, KEY · ~ Atomic Mass(Weight) _ 12.0111 5 Ill the Cavendish Laboratory at Cambridge, .2 +2 _ common Oxidation States +4 VllA first demonstrated that atoms were after all not l IA Symbol _ -4 0 l .)01't7 ., t~19) • 1 4,0020 0 indivisible- that all atoms could be split into ~ c Atomic Number _ _Covalent Atomic Radius( A) GROUPS still ~ma il er uni ts . After some tbi rly years of 1 Electron Configuration _ 6 0.77- H 2-4 0.)0 He H 0.9'J o.:io feve nsh experimentation at Ca mbridge by two llA lllA IVA VA VIA I ' _, 't I0,111 •J 1101111 .1 t4 0067 ,, ·l ~ . t'l984- 10.11) 0 of the greatest men of this century, Sir J.J. 6.Ht •I t OtU • l ., ., 13 '""" Thomson and Lord Rutherford, there •l 2 -· ·• B N" I 0 F Ne emerged a synthesis still deeper than any the Be 0.1T 070 1 0.$6 0.64 IO Li t,\) c 1.,J Transition f le men ts • ... • •,_ , ,., >-l ,... ~ • 2•1' • ' . ' >·• '" chemist had proposed. One could now show JJ1"98 ,, Z4.tl2"' ., 26.~llj •3 Ul.OM ,, )0.9'1l •! H .06• ., U .•H ., J9.9ollll 0 . ~ ., that all atoms-all 92 of them-were divisible; v 'I ..., .._, 3 GROUPS VIII -· p·· that they were made of just three fundamental A Al Si er· o.CJP Ar Na 1. 0 1.11 ,, s 1.,. ... 1.0.5 .Mg VllB ... l6 'o~ J•l •I ; . 1· 2 1118 IV8 VB VIB r 18 118 l 8 •J 'l'l 4. 1 6·.5 '·'° J · I 6 2·&·1 l·I g units. These fundamental units are very tiny " " ,, " " 19. '19Z •I <(1 .04 ·2 44.li$6 •• ci-1.90 •2 so.•o- •2 51 .996 .1 h .uao •J. ,5,847 • l U.9lJ7 • l !I 11 • 1 0).i4 .. 6J H •l &9. 71 ~ 1 n .s9 .2 7".9216 .. 11 .'6 19 OOf ti 10 ., .i ., ,,·' • chunks of matter, each weighing less than 10-27 .••. ,,+I .. " • l · 2 .. .. _, grams. These three fundamental units are 4 Sc " Cr Mn:; Fe Co Ni Cu Zn Ga Ge,,,, As'' Se'' Kr Br\.14 Ca I.)) l ,JJ 1.11 Ti 1.2' 1.24 "28 ilO K v J,H 1,16 32 ,, 1·21 ,, •9 l.ll •o l.97 r.oo ti 1,d t1 1.11 ,. 1.7' ,. 21 \I 1.09 2'1·1'· 2 .. •• called protons, neutrons and electrons. All t·e·1 ·1 1·8 8·1 ":t 1 · 9·~ "2•110 •2 , · 8·11·2 ,. .. ,,., 2"·•·n·1 2· 8 ·i.·2 "l"8H •J "t · 1 ·;•·1 1•118·2 2' 8·11·• 1·6 ·1e·+ 2·8 li·S' ?·I 18·6 2·• 11•7 7·&·rl·S U.'41 • I 17, 6) ·2 U .905 ·> 91 .u +A 9J: .,06 • J ,, 94 J (Vf) •4 101.01 • I *02.90,
But what force is it that makes the electrons keep orbiting around the central nucleus? This was a new, a mysterious force, the so-called electrical force. Experiment showed that a proton and an electron attract one an thcr when close together; two electr ns or two pro tons, however, repel. A convenient description for this attraction r repul ion is t ascribe to the elecLr n or the proton an electrical charge by convention a negative charge to the electron, a positive charge to the proton. We expres the facts of repulsion or attraction by p tulat ing a law: like charges repel, unlike charges attract. I sometimes marvel at bow easily human mind can delude itself and feel com placent that an explanation has been achieved, when all that one really has done is to express the same idea in a different manner. It is some how more comforting to say electrons and protons ca~ry equal and opposite electrical charges; one feels one has gone deeper into heart of things, that more bas been said than just the bald statement that two electrons repel and a proton and an electron attract each other with a certain mysterious force. Perhaps this capacity to delude ourselves, to feel comforted, is a necessary price one must pay for the great gift of language, of speech, of ~'JI.) and 01=1. To return however, to the electrical force this then was the primeval force which keeps an atom together. And later still one was to discover that the chemical force which links atoms s together to make molecules (Fig. 2) and stacks molecules to form crystals (Fig. 3) and living cells was also nothing but a manifestation of the basic electrical forces of attraction and repulsion. The deeper that one went the more it became clear that the electrical force was the key to the I I 0 0 .. understanding of structure of matter. For I I example, one can now understand why metals 0 0 differ from semi-conducting transistors. Some II ~~~ !: 0 -s'A -Q ~~~1i u o~ x 9~0 metals-copper and silver for example-have II /I lj'-...... the property that electrons contained in their 0 HO/ a 0 'oH atoms are somewhat loosely bound; these I I RIBOSE RIBO~li electrons can drift freely and course throughout SUC.AR o-A1 B-Q SUtoAR I I the crystal lattice of copper or silver. Not so O~o Vo for a transistor; there the electrons are not so /~ 1"-.._ loosly bound; they cannot flow as easily; the HO/ O O OH transistor is only semi-conducting. In biology I I ~L8c?~~ 0-A :e-Q ~:Pc.o~: one understood, for example, that our bodies I I resemble a modern electrified city. In a human 0~9 9/0 body, just as in a modern city, there is a vast /~ ~'- electrical network of nerve fibres connected i:io/ a o 'oH I I centrally to the brain. It is the electrical impulses uJ which the brain sends out that control phy 0 ~u~c.°i: 0-o: c- Q ~m.~: )( siological processes. For example, a muscle g 0 I I o 0 ~9 9~ contracts when an electrical impulse shoots out z charged molecules-the ions of acetylcholine 0 HO/...... ~0 o~" OH co I I at its end. Physiology, biology, chemistry ~ R.\SOSE RIBOSE .., SU<:.AR 0-t•D-a SUC!IAR all science in principle-could be understood-in I I 0 0 terms of the electrons and the protons and the one I I fundamental-electrical force-between them. (a. ) No wonder in 1928 the great physicist Dirac Fig. 2 successor of Newton in the Lucasian Chair of Mathematics at Cambridge-could say with Molecular structure of carbon dioxide (one of the simplest molecule) justifiable elan, "With protons and electrons we arid of DNA (desoxyribose nucleic acid). DNA i~· the key substance which. is passed f n m one cell to another and carries the blue print as to can explain the whole of chemistry and most of ho":' to make the enzymes. The DNA. molecule is a pair of chains physics". twisted upon each other. The backbone of each of these chains is a Dirac was obviously right about chemistry; series of sugar and phosphate groups as shown in (a). was he also right about "most of physics"? Fig. 2 (a) In 1928 it seemed likely that he was. For Reproduced lrom the Feynman Lectures on Physics, Vol. I, by R.P. Feynman et al by special permission of the publishers Addison-Wesley Publishing Company. earlier, Faraday and Maxwell had made another
6 7 remarkable discovery. An electron or a proton when accelerated could emit electrical waves just as a stick moving up and down in a pool of water sets up water waves in the pool, so an accelerating electrical charge could set up electromagnetic waves in space. And Maxwell and Faraday discovered that these waves could be picked up by other electrons in a receiving set, just as the waves in a water pool set up by the moving stick i would make a cork floating in the pool bob up { and down in rhythm with the moving stick. An .• example of the waves Maxwell and Faraday spoke about are the radio waves on which voice is transmitted; the electrons in the cathode ray tubes or transistors of receiving set move in harmony with the electrons in the transmitter. If the wave length of the radio waves is shortened an accelerating electron or a proton would set up what we call infra-red radiation. The human z frame is not attuned to receive radio-waves but we-or rather our skins are excellent receivers for the shorter infra-red wave length; we call such waves "heat radiation". The sun is con tinuously beeming out infra-red radiation; we receive them in exactly the same manner as a radio set receives the radio signals. Still shorter electrical waves can be received by the nerve cells of the retina of our eyes. We call th~e waves "light radiation"-ordinary visible light. Still shorter waves are X-rays, still shorter waves are called gamma-rays. The crucial point is all phenomena of radio waves of heat and light and X-rays are basically the same {Table II). All y these are electrical radiations, produced when x electrons or protons in a transmitter oscillate. The waves are received by other electrons and Fig. 3 protons in the receivers' radio tubes, in its transistors, in the retinal membranes, in the An i/lu!tration of three-dimensional structure of common salt (!odium sensitive nerve cells of the human skin or by chloride). Dot (•) and circle (0) represent sodium and chlorine atom! respectively. electrons and protons contained in the silver
8 9 TABLE II The Electromagnetic Spectrum II
Frequency in Name In the first lecture we gave the picture of Oscillations/Sec. physical sciences which obtained in 1930. With just three fundamental particles, electrons, protons and neutrons, and just one type offorce 102 Electrical Disturbance the electrical force-one seemed to have synthesized most science. There were, however, ~x 105-108 Radio Broadcast yawning gaps in our knowledge. The nuclear core of every atom contains about equal numbers 10s FM-TV of protons and neutrons. A neutron is a chunk of matter as heavy as a proton but with no lQlO Radar electrical charge, and therefore no electrical attraction or repulsion. What is the neutron's Sx lQl'-1016 Light role in the scheme of things? What holds a nucleus together? 101s X-Rays Since 1930, physics, and since 1945, most of humanity, has been occupied with the nuclear 1021 Y-Rays, Nuclear problem. The world of the nucleus revealed a 24 new-a completely unexpected-richness. 10 Y-Rays, "Artificial" Since 1930 one has discovered that though all known stable forms of matter we had encoun 1027 Y-Rays, in Cosmic Rays tered so far in nature consisted of just the three
Reproduced from the Feynman Lectures on Physics, Vol. I, by R. P. fundamental particles mentioned before, there Feynman et al by special permission of the publishers Addison Wesley Publl1hln1 Company. do exist other companion particles-companions to the protons, to the neutrons, and to the ele.c trons-as fundamental, as elementary, as these atoms of a sensitive photographic plate. God three. It is the story of these newer entities and said, Let there be light; to make light, and to the domain of phenomena they have revealed that perceive it, He made protons and electrons will be our major concern henceforth. the two fundamental particles of physics. We have called these newer particles com panions to the known ones. It is important to realize that the new particles were not discovered by the classical procedure of sub-division of protons, neutrons or electrons. The principle of divisibility which took us from ordinary bulk matter to atoms and then from atoms to protons, does not seem to function any more. With
10 11 protons, electrons and the newer particles one gun or an arrow shot into space will g.o o~ ~oving seems to have reached the limits f divisibility. in a straight line if there was no air friction to We do n t know if this is becau e we have not stop their motion, or gravitational force to pull tried ha rd enough . We believe we have; it may them down. Perhaps this great law of classical well be that we have reached a level of something physics is completely obv!ous to you in .this completely new in human experience. If I liken satellite age. But it certamly was not obvious these particles to a brick t hrown against a wa ll , to Aristotle nor to Ibn-Sina. For it seemed it would seem not that the brick fragments into contrary to all common experience of mankind. still smaller piece . For the first time it appears Ifwe roll a ball on a table, one's normal experi as if we are receiving back five or six whole bricks, ence is that sooner or later it will come to a identicn lly alike to the first that was thrown. standstill. One might assume-and this is in fact If one has indeed reached the end of the line of what Aristotle did-that the natural tendency divisibility then one is at a level of comprehension of a moving object is to stop; that some force is quite different from any that has ever gone before. needed to keep things in motion. It took the But before we describe these particles, their genius of Galileo and Newton to contradict inter-relations and interactions and the concepts Aristotle. They asserted that just the contrary associated with them we would like to review is the case. If there is a natural tendency for a some of the basic concepts of modern physics, moving object it is to persist in its motion. One concepts which we shall need to refer to again should not look for an agency which keeps it and again. moving, one should rather look for an agency The first concepts we shall need are the classical which is likely to stop it. What a revolution in ones of momentum and energy. Momentum is thought this bold assertion of Newton and the amount of motion possessed by an object Galileo brought about! This intrinsic attribute when it is moving. In mathematical language of persistence of motion is called "inertia" it is simply the product of the velocity times the plain laziness if you like. The tendency to persist mass of the body. Similar to the concept of in moving in a straight line is called conservation momentum is another concept-perhaps still of momentum; the persistence to spin is called more crucial for my lectures-the concept of conservation of angular momentum. spin, or angular momentum. If an object is These conservation laws have been tested rotating around an axis, a spinning top or a millions of times under controlled conditions. spinning cricket ball, for example, we say it When we say controlled conditions all we mean possesses angular momentum. The faster an is that one has attempted to eliminate extraneous object rotates, the larger is the angular momen forces like friction very scrupulously. These tum carried by it. Now there is a very important laws represent an ultimate truth, the distillation law of classical physics which states that the of our physical experience. But is there some amount of momentum or angular momentum thing deep we can infer from these, or do we have remains constant unless there are external forces to accept them as obstinate facts which must be tending to stop the motion or the spin. A incorporated in any description of nature we spinning fly-wheel will go on spinning if there is make? It happens that for the conservation no friction of its bearings. A bullet fired from a laws of momentum and angular momentum
12 13 one can relate these to something deeper, some subjects in Physics which have aroused such thing more profound, something more basic. strong misconceptions. The reason is not By a process of mathematical reasoning which difficult to find. Relativity theory makes state we cannot go into, Dirac and the great Hungarian ments about time, within a context used by the Physicist Wigner, were able to show that the physicist. Since immemorial days however, tendency to persist in straight line motion the professional philosopher has always felt conservation of momentum-can be inferred as that "time" was a concept which was his ex a basic law of nature provided we assume that clusive preserve. The misconceptions arose the results of any physical experiment are inde when the philosopher started to interpret Ein pendent of where the experiment is performed. stein's work in his own mysterious language. Not many of us have ever stopped to ask our To most philosophers, the theory has been selves the question : Do a proton and an elec obvious, compelling, a priori-after its discovery. tron on the planet Mars attract each other with To me there is nothing a priori about relativity. the same force as they do on the planet Earth? Relativity is based on a remarkable, on a far Once the question is formulated most of us would reaching experiment, whose result one would instinctively say, yes; why should the force not never have conjectured at before it was perform be the same? It would be an intolerable compli ed. The experiment is this: if we take a candle cation in the scheme of nature if laws of physics and measure the velocity of light which it emits depended on one's location in the Universe. But we get a certain value. More precisely we dis what is the proof? Dirac and Wigner assert cover the velocity is one hundred and eighty six that if we can verify-with arbitrary precision thousand miles per second. Now move the that momentum is conserved, we can be sure candle as fast as you possibly can. Naively that the basic laws of physics are the same all one might imagine that the light velocity-deter over the Universe. Likewise if spin is conserved, mined by the time it takes for light to get to us we can be sure that space is rotation-invariant, should depend on whether the candle is moving that the results of an experiment-like the pitch or not. Not so, however, when the experiment of a whistle, or the rate of our respiration, will was actually performed by Michelson and not depend on whether we face East or West, Morley. The velocity of light is exactly the s~me here or on Mars. I have lived for about sixteen irrespective of whether the source of light moves years with this reasoning of Wigner and Dirac, towards or away from us with whatever speed. a reasoning which connects things so distinct, Not only that; it is also unchanged irrespective so disparate; which connects symmetry of the of what we may be doing: we may try running Universe with conservation of spin; a reasoning away from the candle with a speed even as fast at once so abstract and yet so concrete. I still as that of light itself. A normal sane person marvel at its boldness, its audacity and its might expect that in that case the light would sweep. It is one of the most powerful things never reach us. But astonishingly enough, one I know of. would be wrong again. Light will still reach us So much for classical physics. The second with the same velocity as before. Astounding, discipline we shall make frequent reference to unexpected! As we said, there was nothing a is Einstein's theory of relativity. There are few priori about the Michelson Morley experiment
14 15 nor its result. The results of the experiment just proton is some 2000 times as heavy as an had to be incorporated into physics. Einstein's electron. But both carry the same quantity profound analysis accomplished just that. of electric charge. All charges in nature exist Einstein expressed his analysis in some most as integer multiples of this one fundamental spectacular language-that the resolution of the unit. Take another example. I have spoken apparent paradox lay in the relative character of before of spin, of angular momentum. Recall time. Einstein's language was a translation, an that this is the amount of rotation possessed by expression of certain mathematical relations. a given object. One would never have believed We cannot here try to go deeper into this; for that one cannot impart an arbitrary amount of our pi.irposes the rucial content of reial'ivily spin, for example, to a cricket ball. Yet this is is the fo llowing. From lho c nsta n.cy of velocity precisely what quantum theory asserts. It is of light Einstein deduced lhat matter and energy impossible to find in nature a spinning object must be identica l. To illustrate Einstein a top, a cricket ball-whose spin is not half asserted, for examp le, that a Jump-shade which integer multiple of a basic unit discovered by absorbs the energy of light waves must get Planck. Tops can rotate with spin value equalling heavier, the absorbed light energy manifesting half of a Planck unit or one Planck unit, or two itself as increase in its matter content. The units, or two and a half units-but never, never, radio transmitters of Radio Paki lan, pouring with 1. 3 or 2. 7 or 20. 67 times Planck's basic electrical energy into space, are progressively value. For quantum theory integers, or at worst dimini hfog in their matter content. Luckily half-integers, are sacred, inviolate. Quite clearly these transmitters are replenished ; they receive if the theory did not have the sanction of precise energy also from the electrical main but one might experiments one would never have believed it. worry about the sun, for the sun is certainly getting lighter every day; it is losing mass which Take one more example: would one believe is continually converting to energy of heat and that the energy carried by a radio-wave or a light light. These statements can be, and have been, ray or heat radiation can exist only in multiples verified hundreds of times in the laboratory. of a certain basic unit in discrete chunks; that energy is quantized? Again, if we did not know So much for Relativity Theory. The third set that this was true by repeated experimentatron of concepts we shall have occasion to refer to are the concepts of quantum theory. Quantum one would hardly credit this. In the case of theory, like relativity, began in the early part of electrical radiation, we designate this basic unit a photon. A beam of light or a beam of X-rays this century with certain experiments whose in this quantum view then consists of nothing but results one would never have believed possible, so obstinately contrary are they to anything we a stream of photons, all photons travelling with had apprehended before. the velocity of light. The quantum statement is that there is no such thing as a quarter of a Quantum theory asserts that there are in nature photon. The statement that an oscillating certain fundamental units and that a number of electron emits electro-magnetic radiation in the physical quantities can exist only as integer quantum language reads: an electron or a multiples of these basic units. One simple proton emits or absorbs photons when it accele example is quantization of electric charge. A rates and oscillates. 16 17 Let us recapitulate. On the basis of what the topological structure of space and time but we know, we believe that the Universe, the space we do not know. This again is perhaps a prob time we live in, is endowed with certain charac lem for the fortunate few of a hundred years teristics. We understand the origin of some of after. All we can do at present is to incorporate these characteristics. Others we are forced to these facts within the formalism we use. This accept as empirical facts and leave for our we have learnt to do. successors in the twenty-first and perhaps later centuries to find the deeper basis of. We know empirically that there are certain conservation laws-like conservation of momentum, of energy, of angular momentum. We believe we can find a deeper significance for these laws in the sense that we can correlate them with the properties of space and time. From conservation of momentum one may infer that space is location symmetric. From conservation of energy we may infer that the results of an experiment do not differ with the epochs of time at which the ex periment is performed, that an electron and proton will have the same attractive force to-day as they had yesterday and will have tomorrow. From conservation of spin, of rotation, we infer that space is rotation-symmetric. From relativity experiments we know that velocity of light has astonishing properties, that it is invariant unchanging, irrespective of the motion of the light source and any motion of the observer. Accept this as something which we must incorporate in our description of funda mental physics, we may then infe r that all energy possesses inertia and vice-versa. Experjment has forced us also to accept quantum theory. We know, fo r example, that we can never impart spin to an object which is not an integer or a half integer multiple of Planck's basic unit. We know that the energy of electromagnetic radiation can exist only in discrete quantum \lnits-the so-called photons. We find this utterly bewil dering, utterly astonishing. Why some physical quantities are quantized may be connected with 19 18 111
By 1930, the physicist believed that all matter in the Universe was composed of three particles -electrons, protons and neutrons. He also believed that all energy, whether it existed as heat or light, was basically electrical in character and that it manifested itself in discrete chunks, in discrete quanta-the so-called photons. All matter and all energy in his view was then composed of just four fundamental entities photons, electrons, protons and neutrons. The electrons and protons carry an electrical charge; when accelerating, these particles emit heat or light in the form of photons. The neutron is electrically neutral. Now these four particles are not just simple chunks of matter or energy. One other property they all seem to possess is that of intrinsic spin. An electron or a proton continually spins like a top around an axis fixed in the body (Fig. 4). And as we discussed in the second lecture, this R L spin motion, like all spin motions in the Universe is a half-integer multiple of the fundamental ~ -0- unit of Planck. ... (d) ( b> Why should elementary particles behave like MIRROR spinning tops? What gives them their intrinsic L spins? Why should the spin-values be just what they are? The answer to this last ques --®- tion was brilliantly given in 1928 by Dirac at . ·. Cambridge in a paper which is an epic of (C> modern physics. Let us recall the laws of Fig. 4 persistence-of persistence of inertia, of per sistence of spin. One could show that this Elect;on sp~nn~ng with respect to an axis indicated by the long arrow persistence was related to rotation symmetry (a) right ~pmmng ~/ectr~n, (b) l~ft . spbmlng electron, (c) left spinning of the Universe. Now Dirac demonstrated electron is the mirror image oj right spinning electron. that when one married together this notion of
20 21 rotation symmetry of the Universe, with the ideas of Einstein's relativity, one could demon strate that electrons or protons must spin and with the precise values found by experiment. Dirac's work is one of the monuments of modern physical theory. Not only did Dirac give a deeper meaning to the concept of intrinsic spin, he was also able to deduce from the same equation something even more im portant. He could show on general grounds that all particles in nature must exist in pairs (Fig. 5); that to every particle there must correspond an anti-particle of precisely the same mass, the same spin but of opposite elec
•I • trical charge. Thus the existence of the posi • I . ' · ' tively-charged proton must imply the possible ...... :- ---· · ·-i I • !' 1" ' existence of an anti-proton carrying a negative • -.-·-- .. w ~ \ ~-r-~ ,.,,. , electric charge; if the hydrogen atom exists, • ; I ."' • '°' • .; • ' ':'"·a6·. !t ·• f---"---- 4+. •- I--. · ~~". I ' ._J "'I', 1 • ·.\·• ·• •·-· • • • there can equally exist an atom of anti-hydrogen, I j .. ~ • • •I ,, a • '• ·~ ·i; - - - I ' • ~I -" .. \. perhaps in some distant corner of the Universe. Dirac could show that if a particle and an '-~ -~ .... " ' "\ . .. ··.· . ~ · .~--. .: ': anti-particle collide, both must disappear, their . , .. -:-1-- .. ,;· .. .'f·7·· ' energy, their momentum, their spin going into . \'. " ... ' ·, photons, into heat or light in other words, and .. ,·:I . .. .,,..,, .. \~ this is all that is left of the collision . · ·';'·· •. In Dirac's language anti-matter is "minus matter"; matter and anti-matter just cannot co-exist in the same part of the Universe without the ever-impending catastrophe of annihilation; and indeed some astronomers do believe that just this type of annihilation of galaxies and anti-galaxies is taking place at the sites of some Fig. 5 powerful X-ray sources in the heavens. 1/'a~~ creation by pltotons (Y-rays) When passing through a lead plate Dirac made his prediction of the existence ms! e a cloud chamber. The Y-ray enters the lead plate from above. of anti-matter in 1934; the anti-electron was bemg_ unch~rged leaves 110 track in the chamber. Four pairs of track; discovered in cosmic rays the same year; the startmg as n~verted V's in lead plate, can be seen. The cloud clurmbe;. 1 ~a~ pladd m. a strong magnetic field so that electrons curve to the discovery of the anti-proton (Fig. 6) had to ng t an positrons to the left forming im1erted V's as shown ; th wait longer till the completion of the giant 11 lower half of the chamber. e proton accelerating machine at Berkeley, California in the 1950's. In one stroke 22 23
------Dirac had doubled the number of elementary particles from four to eight. There is an apo cryphal story in Cambridge of how Dirac first conceived of the idea of anti-matter, of minus matter as one may call it. As a graduate student Dirac once attended a Problems' Drive so the story goes-organized by the Cambridge Under-graduate Mathematical Society, the Archimedians. One of the problems presented was the following. On a stormy night three fishermen go fishing and make a big haul. The storm forces them to seek refuge on a lonely island where they tie up their boats and go to 2 sleep. During the night one of the fishermen gets up; he would like to get away. Without waking up his friends he divides the catch into Jff- three equal parts. He finds one fish outstanding. This extra fish he throws into the sea. Taking his one-third portion of the catch he rows away. A short while later the second fisherman wakes up. He does not know that one of his friends is gone already. He too proceeds to divide the haul into three equal parts, finds one fish out ' standing, throws it into the sea and rows away 4 with his one-third. The same thing happens -I / a third time. The problem is, what is the mini ( 6 • mum number of fish-the minimum size of the 50µ ff~ •l' /}" catch-which can thus be sub-divided thi:ee 7 ~ - .. 5 times successively with one fish outstanding .. each time? The story goes that Dirac thought for a few seconds and then jotted down his Fig. 6 answer-minus two. You see, if you divide - minus two fish into three equal heaps, each heap Photomicrograph of an antiproton (p) interaction in emulsion. Jn will consist of minus one fish, with plus one this ii star, five 7r mesons (tracks 2 3, 5 7 and 8) were created in the annihilation process. The tracks labelled 1, 4, and 6 are due ro hedvy fish outstanding-minus three plus one equals particles, such as protons. The energy observed in charged partiales minus two (- 2 = - 1 -1-1+1). Throw the alo!ie totalled 1.4 M,,c~ (1300 MeV) which could result only from a outstanding plus one fish into the sea, take P·P annihilation. The remaining 0. 6 MvC~ was carried away by your minus one fish away; plus one and minus undetected neutral particles such as 7r mesons and neutrons. one equal zero, so that you are leaving behind Courtesy Lawrence Radiation Laboratory. on the island precisely minus two fish again,
24 25 ready for exactly the same sub-division as before. no larger than the Quaid-e-Azam's mausoleum. Dirac of course, did not then worry what a This compactness, this tight binding must come catch of minus fish may signify. Nor does the from some force inside the nucleus-we may story relate if he got the under-graduate Prize call it the nuclear force-and this force must be that night. But when faced with minus electrons at least a thousand times stronger than the two years later as a consequence of his rela electrical force which keeps an atom together. tivistic equation, he just had to find a meaning The neutron may not carry an electrical charge for these anti-objects. Thus, goes the story, but it must carry a nuclear charge, and so was the brilliant notion of anti-particles born indeed must the proton since protons too exist and with it the uncovering of one more pro within the nucleus. found symmetry of the Universe we live in The tremendous strength of the nuclear force the symmetry of matter and anti-matter. explains why a nuclear bomb-size for size Before we go further let us recapitulate once must be a million times more potent than a again. In the 1930's view of nature all matter chemical bomb; why nuclear fuel in a nuclear and all energy could be considered made up reactor must deliver a million times more power from four elementary particles or their anti than chemical fuel. One had always puzzled particles; eight entities in all. Further, every about the tremendous output of energy from particle possesses a specified value of spin. the stars. With the knowledge of the nuclear Now so far we have mainly concentrated our force, and nuclear reactions, one knew at long attention to protons and electrons, both these last what makes the stars shine; and how the particles carry an electrical charge. We have sun can pour such vast amounts of energy. The neglected the "neutron"-a particle as massive hydrogen in the sun is continually converted by as the proton, without, however, its electrical nuclear fusion to helium; star-dust if you like charge. The neutron was discovered in 1930 is nothing but high-grade nuclear fuel. I at the Cavendish Laboratory at Cambridge. always fondly recall the story of Professor Immediately after its discovery the question Hans Bethe the night when he first realized arose: if the neutron is electrically neutral one that this outpouring of luminous energy from could not expect it to attract the charged protons. the stars was basically the energy of nucle.ar We had, however, earlier learnt that neutrons reactions-the continual nuclear conversion of and protons together make up the central core hydrogen to helium, (Fig. 7). Bethe and his the central nuclei -of all atoms. What is the wife were standing gazing on the Californian force that keeps the nucleus bound together if it desert sky when Mrs. Bethe said: "How beauti is not the electrical force? Why do protons and fully do the stars shine tonight". Professor neutrons inside the nucleus not fly apart? The Bethe turned slowly towards her: "Would you dilemma appears deeper still when one reflects believe it", he said, "but right now I am the that even the lightest nucleus is incomparably only human being in the Universe who knows more compact, more tightly bound than any what makes them shine at all." atom we know of. To compare sizes, if a We have spoken of the nuclear force quali hydrogen atom is blown up to the size of the tatively so far. Since 1935, the major problem city of Karachi, the hydrogen nucleus would be in physics has been to find its quantitative
26 27 REAC.TIOH RlAC.TI°" Tl Ml
P + ctt-N''+ '1 1o'yr
N'"-c"+ a++ v 10 rnin
14 '+ cP-N +Y 2•105yr
P + N1<'- o's+ .,, 15 o's- N + e•+ 11 2tnift 4 I'+ Nf5-t11+ H•4 10 yr I MET llE'-tTIOH I 4 PROTOllS-Kt+£HEllf>-., 4 4p - H• + !NEllC.Y Fig. 7 b Fig. 7 a Two chain$ of nuclear reactions which satisfactorily account for the. release of energy by the sun. The first series of reaction is the corbo11- 11 itroge11 cycle (a). The second series is the proton proton chain (b). The C-N cycle and the p-p chain are similar in that they effectively synthesize from four hydrogen nuclei, one helium nucleus plus about 26MeV ill thermal energy. Reproduced from Nuclear Physics and Fundamental particles by Heckman and Starrlnc, Copyright 1963, by special permission of the publishers Holt, Rinehart and Winston Inc. 28 29 aspects. It is these aspects which shall engage In 1935 Yukawa knew this classical theory us now. First two ectures are wholly con of the electrical force. In 1935 the nuclear cerned with the electrical force-the force force, however, was still very much of a mystery. which keeps atoms together; which binds an Yukawa asked himself the question: what is electron to a proton. One had known from the corresponding quantum, the rugger ball, the work of Planck and Einstein that photons the carrier of the nuclear force? What do the particles of heat and light-are the quanta protons and neutrons exchange? of the electrical force. The first question which Yukawa relates that he used to keep near his one asked regarding nuclear force was: what bedside a notebook; during the nights he would are its quanta? scribble his speculations in the dark. Every The first man to ponder on these questions morning he would eagerly look at what he jotted was the great Japanese physicist, Yukawa. down in the sleeping-wakefulness of the night Yukawa's thinking, in 1935, went something before. One morning he discovered he had like this. An electron or a proton when ac solved the problem of what the carrier of the celerated emits or absorbs photons. One can nuclear force must be. Yukawa had speculated understand the attractive electrical force between that there must exist three new elementary a proton and an electron in terms of an exchange particles, one charged positively, one negatively of photons. Think of two rugger players who and the third neutral, with masses intermediate make passes to each other. One throws the between those of the proton and the electron ball over, the other catches it; then throws it which must play the role of the nuclear rugger back and so on. The passes, the exchange of balls, continually exchanged between protons the rugger ball is impossible to continue unless and neutrons. Yukawa called these hypothe the players remain within a specified distance tical particles the mesons. The triumph of of each other, unless they move in consonance. this speculation made in 1935 came full twelve A spectator who watches them from a great years later. In 1947, Powell at Bristol dis distance and who perhaps cannot see the ball covered precisely these three particles. Their will notice only one thing; there are these two signatures were inscribed as tracks on a photo men, always close to each other. If the specta graphic plate (Fig. 8), when the plate was tor is a physicist used to expressing all physical exposed to a shower of cosmic rays. In the phenomena as resulting from forces, he will next lecture we shall speak more of these mesons say, there is an attractive force between these and the nuclear force. men. Take the analogy of the two players over to an electron and a proton. The photon is the ruggar ball; the proton emits the photon, '· the electron absorbs it; re-emits it a short while after, passing it back to the proton. This con tinual exchange of the rugger ball, the photon, forces the proton and the electron to remain forever in consonance, to move together. The photon is the carrier of the electrical force. 30 31 IV In this lecture we return to the theme of symmetries-in particular the symmetries of the nuclear force. We ended the last lecture with the two nuclear particles, protons and neutrons, each of which carries a nuclear charge. We 'f also mentioned Yukawa's prediction that if the nuclear force exists, there must also exist three particles, three carriers of this force-the so called mesons. And we ended by speaking of the experimental discovery among cosmic rays of just the three particles-the three mesons • Yukawa had speculated about. This was 1947 . With the discovery of the mesons, the number of elementary particles had increased to a total of seven. One felt some-how that enough was enough; one felt one had all the ingredients to make complete theories of the two basic forces of nature-the electrical force as well as the nuclear force. Unfortunately, when one actually tried to consider the theories quantitatively, even though one succeeded admirably with the electrical force, one met with miserable failure in the case of the nuclear force. And this in spite of the fact that in the meanwhile"' the physicist had learnt to unlock the force itself in all manner of nuclear devices. Clearly some thing was still missing. Just the total of seven elementary particles was not enough. Fig. 8 Now, this something missing started coming 71'-meson. Wf!S discovered experimentally by Powell by observing the in from 1947 onwards-first in small measure characteristic 7T' -µ, decay in photographic emulsion. The figure among the cosmic ray showers, thel,l in torrents shows four examples of the process from. the newly-constructed proton-synchrotons 71'+ ·-+ µ.++v - f~om Brookhaven, Berkeley, Dubna and Geneva. - µ. + ·--+- et + v + v __ v, v being uncharged leave no track in the emulsion. Between 1947 and 1962, something like thirty Courtesy Professor C. F. Powell. new particles · {Table III) were discovered, each 32 33 seemingly as elementary, each seemingly as fundamental as the proton and the meson. The techniques used to isolate these particles experimentally form a saga of modern experi mental physics. We shall not discuss these ex perimental methods but the theoretical concepts one had to develop to understand their correla tions, their interactions-the concepts to comprehend the very reasons for their existence, shall form the theme of this chapter. The ideas, the concepts, are not easy; they are still in a stage of development and flux. TABLE III Briefly the experiments showed this. As dis cussed before, the nuclear particles, the protons ~ A'llllUllVOlll UllVONS ll'1'0!1S All'!Lt n1111S IDSOln and neutrons, are spin !- particles. Between 1947 and 1954 one discovered a total of six +1 _, A" _,_w' a-.;r I new spin 1- particles (Fig. 9), all closely resembl 0 0 ¥f !2i=:• Ji->:" 2l. ing protons and neutrons. There was, in nature, I - - then a multiplet of eight nuclear objects, all with 0 0 I "" I .5- spin !, all as basic to the nuclear force, as a familiar neutron or the proton. Likewise, the -I +I i. ~ J1 !. t OOOMEI/ ' I number of Yukawa mesons increased, once I -1 +1 £ !."1~ again from three to eight. There were, in I - Yukawa's language, not just three but eight I " carriers of nuclear force. And as if this was 0 0 I .!!...- ±· f'I+ I I not bad enough, in addition to these two families IA+ 1£. I I I OOM!:V of mesons and nucleons two other families of I I I I particles were discovered, each family consis~ng I I 1 MEV of nine particles. These large numbers of .- ,I _ -•• I I particles-34 in all-were bewildering. Even :! I ~ .! OMEV I I more bewildering appeared in the 1950's their I _, I CHAH& _, 0 ., 1-t 0 +1 -1 0: Q ;1 0 +I 0 mutual interactions. As a rule all nuclear SPIN 1/1 0 1/2 1/2. I 1/2. particles can emit or absorb mesons-but the a I +I 0 0 0 '0 question arose: which ones? What was the c -·0 0 I -1 0 0 I i· basic law governing the behaviour of these new Thirty e~ementary particles are re.[Jrese11ted /11 this table (mass labelling objects? The situation was confused for a s~hemat1c, ~ot to scale). Unstable particles are identified by wavy number of years but then around 1960 a definite Imes. Particles and antiparticles have opposite electric charge (Q) pattern began to emerge. And the pattern was ~~d hyp er - cha~ge ( Y). Hyper-charge is not defined for leptons. the following. What we have called the F1om the relat1on Q= l a+ Y/2, the isotopic charge (Ia) can be de duced for baryons and bosons. nuclear charge, consists really of two distinct 35 34 varieties. These varieties have been named as isotopic charge (1 3) and hyper-charge (Y). The names of the charges are not important. All that is important is that nuclear charge exists in two forms. What one discovered was that in a multiplet of eight particles, some will carry hyper-charge, others will carry isotopic charge, some others will carry both. The type of meson a nuclear particle emits or absorbs depends on the type of charge it carries. Together with electric charge, the two nuclear charges make a total of three. One could then classify all newly-discovered particles in terms of just what charge each one could carry. Let us summarize at this stage once again. A new era opened up in physics during the years 1947-1960. As a result of feverish experi mentation with the giant accelerators, a new and perhaps somewhat embarrassing rich ness was discovered among the set of nuclear particles and among mesons. It is not im portant to remember the names of the particles or their different correlations; all that is neces sary is to remember that there were in early 1964 a total of eight particles constituting a nuclear multiplet of spin -L nine other nuclear particles constituting a multiplet of spin 3/2; eight Yukawa mesons forming a multiplet of spin 0, and another nine mesons of spin 1. Notice the recurrences of the magic numbers-eight and nine. The particles in a multiplet could be distinguished by giving either their electric charge or hyper-charge or isotopic Fig. 9 charge. These facts which we have summarized The. ~lassie example ~! ~he production of /\ 0 and K0 particles in 7f p took years of patient experimentation, long collzswn. At (l) an mc1dent 7T- meson collides with a proton (in a and lonely vigils among the snows of Jung hydrogen J!ubble chamber). A /\ 0 and a K 0 are produced in the re fraufoch, or involved working with capricious 0 0 0 action 7f +P -- K + /\ • The K decays at (2) into 7r + and 7T-. 0 multi-million volt accelerators. These results The /\ decays into a proton and 7T-meson at 3. were not arrived at in a day, they had to be Courtesy Lawrence Radiation Laboratory. .. deduced painstakingly from data which was 36 37 often inadequate, and almost always cluttered with inconsequential secondary details. Pro fessor P. T. Matthews at Imperial College, r\ p London, once gave a brilliant description of how . . hampered the experimental physicist in our , / subject is. The only tool an experimental worker I / .. ·. has is a beam of protons accelerated by a syn I \ lo + :I: E •• E:. chroton or in a cosmic ray burst. One directs . ._/\o / this beam on to a lump of copper or aluminium . ·. .. / . / From the number and variety of particles which / . / fly off at a given angle to the original beam ' {d.) Eo direction, one is required to reconstruct and - deduce the spins and the charges and the types of forces which exist among the fundamental particles. The analogy which Matthews gave *o N·- N was that of a beautiful marble statue in a darken ed room, on which one is playing a jet of water / I / from a hose. One cannot see the statue but / ...... / / one can collect the amounts of water splashed from each square inch of the statue. Suppose v•-...... / ··("o I you were set the task of reconstructing how the statue itself looks-the Jines and the figure and I / the shape and the only information supplied .. .;, . -*o :!: --- -1---411 = was this splashing spray, I am sure you would .. I begin to sympathize with the modern experi mental physicist. ' . I .. Returning to our multiplets of eights and nines, the very first question which arose was this: Here are eight or nine (Fig. 10) objects cb> all essentially similar; can we in some approxi Fig. 10 mation treat these particles as manifestations of one single entity? Is there some unity in this Plot of hyper-charge Y against isotopic charge I~. The dots on thick multiplicity? Is there some single symmetry horizontal lines in (a) represent the eight spin f particles and those principle in terms of which one may comprehend in (b) represent nine spi11 3/2 1u1rticles. Eight p articles i11 (a) f orm the complexity presented by the particles? a hexagonal pattern and they can be regarded as manifestations of one single entity provided dots can be comzected obliquely as shown by We earlier had an example of this essential unit, dotted and dashed lines. Such a connection is supplied by SU (3). in the particles and anti-particles of Dirac. !11 order to complete the triangular pattern in (b) particle with hyper One can speak of a particle and its anti-particle charge ( - 2) shown as a circle must exist. This particle called o -a proton and an anti-proton-as a two-fold was discovered experimentally in Brookhaven N ational Laboratory multiplet. But we also know that the two are in Feb. 1964. 39 38 intimately related; the proton is the minus 60 degrees. The symmetry principle provides the particle of the anti-proton. The two are the unifying principle for the six-fold multiplet. The facets of the same reality, two opposite sides of pattern itself is a manifestation of the symmetry. the same coin. There is a unity in the multi The problem in nuclear physics then was, what plicity. Or to put it another way, Dirac's is the symmetry principle underlying its three postulate of particle anti-particle symmetry in charges and its multiplets of the eights and the the Universe makes it possible conceptually to nines 7 What is the secret of the carpet pattern speak of particles alone. One need never speak of the Universe? of the two-fold multiplet. One need never speak of the anti-particles. It is the symmetry Now, about one hundred years ago, one CYf the f principle which is of paramount importance, greatest mathematicians of the world, Sophus 'f the existence of a two-fold multiplet (particle Lie, had tabulated all conceivable abstract sym and anti-particle) is something which follows metries. He had classified all symmetries, or as a consequence. Take another example. symmetry groups, as he called them, in terms You may recall when I spoke about spin I of the number of key directions. Recall that said a spin ! particle can exist in two states. It to make a hexagon there was just one key can either spin in a clock wise direction relative direction-the 60 degree rotation. Recall that to its direction of motion, or in an anti-clock· for particle anti-particle symmetry there was wise direction (Fig. 4). One could think of spin! just one key direction; change plus with protons as two distinct particles, one spinning minus. Recall that for spin ! there was just clock-wise, the other spinning anti-clock wise, one key direction, flip over a left screw with a one behaving like a left screw, the other behaving right screw; a right spin with a left spin. To like a right screw. A completely equivalent des realize this physically you can look in a mirror. cription would be to say, there is just one entity, A mirror reflects a left hand to a right hand. the spinning proton, but there is additionally a The problem Sophus Lie solved was this: given symmetry principle which permits one to infer the number and type of the key directions, he from the existence of left-spinning proton the could then say unambiguously how many existence also of a right-spinning one. Take flowers-how many particles-the pattern, the one more example. If one has a Persian carpet multiplet, could contain. For the case of the or an embroidered bed cover, with a pattern carpet · pattern, even a child can work out the on it, one can describe the pattern in many answer. Given the key element, the key direc different ways. Take as an example a hexagonal tion I mentioned before, rotate through 60 pattern, six flowers arranged as a hexagon. To degrees-one must get six flowers all lying on someone wishing to weave a similar carpet one the corners of a hexagon. Suppose, however, may either give the positions of all the six flowers < t • the key directions are more complicated; sup individually or simply describe just one typical pose there are in fact three direciions (Fig. 11), flower and ask him to make a hexagon. of like three symmetries, like flipping electric charge flowers, To describe what a hexagon is one would with hyper-charge and hyper-charge with isotopic say, rotate the first flower-through 60 degrees. charge. How shall one work out the detailed The symmetry principle then is the rotation of pattern 7 Sophus Lie gave the following method. 40 41 Consider a triangle-an equilateral triangle with corners representing the three types of charges, and now attempt to make all conceivable patterns by a juxtaposition of such triangles in a specified manner. What are the patterns one arrives at? One of the first one gets is a hexagon again, but with two extra elements at the centre, making a total of eight corners; of eight elements, of eight particles if you like. The numbers 8 and 3 are inter-related. From the symmetry of the three charges, of electric, isotopic and hyper, one may infer that multiplets of nuclear particles-the manifestations of this symmetry-must exist in multiplets of eight and this is precisely what one had experimentally discovered. Lie's theory is in fact one of the profoundest, one of the most beautiful mathematical con structs. Sophus Lie was the Michelangelo of classical mathematics. Even though we may have failed to convey its depth, we do hope the basic idea itself is clear, which let us repeat again: In the quest for symmetry of nuclear law, one had found a deep correlation between the number of charges, electric, hyper and isotopic and the numbers of elementary particles in a nuclear multiplet. The multiplets themselve; are scarcely important after the symmetry is discovered. However the fact that the eight particles in a multiplet have the same nuclear Fig. 11 properties implies that the three charges them Three key directions are shown as AB, AC, and AD. These are the selves are similar, are mutually interchangeable; the three charges are but a manifestation of one lines m2=constant, Q = y'fm - m2=constant and Q=v'3m +m = 1 1 2 single charge or they are the different aspects of constant respectively where v3ln, = 13 and 2m 2= Y. These direc tions form an equilateral triangle and vertices of this triangle give a single entity. Technically the symmetry is possible states. As is olear from the figure ive get either a hexagonal known as the SU (3) symmetry-three for the pattern or a triangular pattern. For example, the red dots represent three types of charges we started from, " U " a multiplet of eight particles and blue dots represent a multiplet of for Unitary. ten particles. 42 43 K+ (2) I \ \ \ Ko' \ \ \ .,,.- n (4) (3) Fig. 12 First observation of O and one of its decays. On page 44 is given schematic representation of the decay. Courtesy Brookhaven National Laboratory. 44 i 45 I The Unitary symmetry appeared in early 1964 scanned. These precious two are in fact just to be the symmetry of nuclear physics. This the only two Omega minus's in the Universe was encouraging-tantalising. But there seemed that we know of. Their discovery completely one serious difficulty. On the basis of SU (3) vindicated the SU (3) Unitary symmetry. The one could understand multiplets-patterns possibility that such a symmetry might exist consisting of eight particles. What about the was first conjectured by Japanese physicists, patterns-consisting of nine particles which had led by Professor Sakata, in 1959. It was elabo been found experimentally 7 In Lie's mathe rated in the present form in 1961 by one of my matical classification one could easily check pupils in London, Y. Ne'eman, and indepen that the only possible patterns of spin 1 or spin dently by Professor M. Gell-Mann at the 3/2 which could at all exist must consist of either California Institule of Technology. The 8, or 10, or 27 particles-but never of nine. SU (3) symmetry scheme represented a deep Recall that in early 1964 one knew of only nine synthesis in nuclear physics. The validity of nuclear particles of spin 3/2. If Lie's ideas were the symmetry was established in February 1964. right, there must exist a tenth particle, otherwise The same year, however, SU (3) was no longer the whole edifice would collapse. Those of you new. A deeper still synthesis came in Septem who may be familiar with the philosophy of ber 1964 and a still, still deeper one in January Pythagoras may recall the famous emblem 1965. From its somewhat measured growth which Pythagoreans displayed in their secret the physics of eleme ntary particles has acquired meetings. This was a figure made from equila in the last six months a hectic, a breath-taking teral triangles with exactly ten corners. In pace. We shall deal with these very, very Lie's language this was one of the allowed recent developments in the next lecture. SU (3) patterns. In 1964 one knew of nine spin 3/2 nuclear particles, filling all the corners of the Pythagorean figure except the apex. The crucial tenth was missing. The characteris tics of this particle-named Omega minus could almost exactly be predicted from the existence of the remaining nine. One could assert that the particle must carry an electric charge of - 1 unit, a hyper-charge of-2 units and no isotopic charge. One could predict its mass-it must be nearly twice as heavy as a proton; its spin must of course be 3/2. The search was on and in February 1964 this elusive object was finally discovered (Fig. 12). A team consisting of 32 experimental physicists· at the Brookhaven National Laboratory in the United States finally tracked two Omega minus's among literally the millions of other particles that were 46 47 .. like spin. Spin is called external because it has its deeper roots in the structure of something v external to all of us-in the structure of space and time. It had always been a recurrent dream in physics that some day one may be able to In this last lecture we wish to discuss two find a deeper unification between these two things. First, we wish to discuss the most .... types of properties, that internal and external recent synthesis achieved in rt::spect of the properties might merge in one single whole. symmetries of the nuclear force. Second, we This would be the ultimate synthesis, and it is would like to speak of two other forces of nature the story of this synthesis achieved in the last -the gravitational force and the so-called weak few months that we wish to describe during force. With this our survey of all known forces the first part of this lecture. of nature will be complete. We shall finally Before we go on to discuss the new symmetry make some remarks about the general outlook itself, let us briefly go over the concept of spin in the subject. once again. In terms of Sophus Lie's ideas, We ended the last lecture by mentioning the intrinsic spin symmetry may be called the SU(2) SU (3) symmetry group as the basic underlying symmetry. This is because, as we learnt in the symmetry of the nuclear force. Recall that the fourth lecture, a spin t particle can be pictured summetry takes its name from three types of as an object rotating either clockwise or anti charges, electric, hyper and isotopic. The clockwise relative to its direction of motion; symmetry lies in treating all these three charges in terms of multiplets, these two left and right as if they were manifestations of just one unitary spinning objects form a two-fold multiplet. characteristic. It is perhaps good to remind In Sophus Lie's language, just as three varieties once again-when we use the words "manifesta of charge give rise to an SU (3) summetry, tion of a single unitary characteristic", we do two varieties of spin give rise to SU(2). Just not wish to load the phrase with philosophical as SU (3) multiplets consist of8, 10 or 27 particles or mystical connotations. The word "mani one can show that higher spin multiplets can festation" is used in the precise mathematical contain 2 or 3 or 4 different spinning ob.i,rcts. sense of Sophus Lie. Let us never forget that To take a concrete example-in nature we have mathematics is the language of physics. We 8 particles of spin t and 10 of spin 3/2. In further said that using Sophus Lie's ideas had the making these counts we made no distinction of further corollary that nucleons and mesons must left spin from right spin. If we do make this be found in nature in multiplets of 8 or 10 or distinction the multiplets really consist of 27. And this seems confirmed by experiment. .,, 8X2=16 and 10 x4=40 distinguishable entities . . Now throughout these lectures we.have noticed making up a total of 56. that the elementary particles and elementary Now as a first part of the programme to marry, phenomena have been characterized . by two to synthesize, spin with charge, let us assume types of properties. First are the so-called that the right and left spins can be treated on a internal properties, like emtric charge or hyper basis completely analogous to the three types charge; second are the external properties of charges. This is to say, consider a total of 49. six types of charges, electric charges spinning with spin in 1964 was the same as the one Dirac clockwi e, electric charges spinning ·anti-clock faced in 1928. At that time one knew of spin, wise; hyper-charges spi nning clockwise, hyper but it seemed to have no relevance to relativity. charges spinning anti-clockwise, and so on. Dirac bad the audacity to put relativity first. These six charges will give rise to a new Lie He did not consciously look for spi n ; a synthesis group, the group SU (6). Now the mathematics of relativity with quantum theory led him -the group theory-of the SU (6) structure has automatically to the concept of intrinsic spin. its own volition. One can either look up Lie's What we wanted was a similar miracle to happen works or work out oneself diagrammatically for the case of the nuclear particles. One would the structure of the SU (6) multiplets. The first like to marry relativity into the structure of the result one discovers to one's astonishment is three charges, electric, hyper and isotopic. One that the lowest nucleon multiplet of SU (6) must wanted for the proton the analogue of Dirac's contain precisely 56 quantities. We said equation for the electron. And this was "astonishment" because 56 is just the number precisely what was done in January of this year. of distinguishable nucleons which we know One found it was necessary to generalize SU(2) exist in nature. This 56-fold multiplet of SU(6) once again to SU(4). Combining this with the now contains both the familiar protons and SU(3) the final symmetry turns out to be SU(I2) ne utrons (of spin D as well as t11e exotic Omega -the largest yet in respect ofthe symmetries of mi nus (with spi n 3/2) of wh ich just two specimens nuclear force. The multiplets extend once again, are known in the Universe. A still deeper from 56 to 364 particles; what is much more nucleons' synthcsi has been achieved; spin l and important, one has at long last the beginning of spin 3/2 are no longer distinct; 56 of them the dynamics of nuclear physics. One can form one single entity; spin is nothing but a new perhaps now write down a quantitative measure fo rm of charge; one bas married internal sym of the nuclear force, the dream of Yukawa in metries of charge with the external symmetries 1935, the problem which has eluded physics for of space and time. the last 30 years. A fair part of this work was The basic idea of marrying spin with charge done by Pakistani physicists notably at the was first conjectured essentially 27 years ago by International Centre of Theoretical Physics at the great Hungarian physicist Wigner. In its Trieste. Some of the names concerned in the present form it was worked out in September 1964 development are those of Mirza Baqi Beg, Dr.M. by Professor Feza Gursey-the great Turkish A. Rashid, Dr. Riazuddin and Dr. Fayyazuddin. physicist, by Professor L. Radicati-from Italy This concludes what we wanted to say about and by Professor B. Sakita-a young physicist nuclear force. Let us take stock of the situation from Japan. and make a survey of fundamental physics. We Now the SU(6) symmetry was profound, but have so far discussed two forces, the electric and it was not profound enough. It had one serious the nuclear. These give us a complete compre flaw. When speaking of space-time, and of its hension of the world of the atom and the world marriage, of its synthesis with charge, one must of the nucleus. There are in addition, however, make sure that the space-time concepts one uses to these two forces two more. One is the ever accord with the relativity theory. The situation present classical force of gravitation-the first 50 SI Universal force to be discovered; the force .. unfortunately, we do not know. Because of which holds us all captive to the surface of the the tenuous weakness of the gravitational force, earth. Every particle in nature carries what one it would be very hard to detect these carriers may call a gravitational charge. The astonishing the so-called "gravitons". This surely is one of thing about gravitational charge is that, unlike the things which perhaps 21st century physicists all other charges, there is only one type of gra will have more to worry about. vitational charge. There are no positives or In addition to gravity, there is one more force negatives among them. Put it another way; of nature-the so-called weak force. It is every particle in nature attracts every other something very peculiar; its very existence was particle-there is no gravitational force of re unknown until the neutron was discovered in pulsion. A second remarkable fact about 1930. It is a force which seems to have just one gravitation is its extreme weakness. Relative purpose; to make all elementary particles decay. to the electrical force the gravitational force is a Whereas a free proton or a free electron left to billion, billion, billion times weaker. To give itself lives on for ever, this is not the case for a you an idea of the orders of magnitude involved, free neutron. Left to itself a free neutron let us take a comparison. The gravitational disappears in about ten minutes; it decays into force produced on the surface of the earth is the a proton, an electron and a new and rather result of all the matter contained within the earth mysterious particle called the neutrino. It was itself. An ordinary electro-magnet used for as if the neutron was really a time-bomb; its lifting material, about a centimetre or so in length, fuse-rate being determined by the so-called weak however, can produce an electro-magnetic force force. The neutrino, the signature of this as strong as earth's gravitation-the small electro weak force, is a particle of spin ! , it carries no magnet can counteract gravity. Size for size charge, and it travels with the velocity of light. a tiny electrical system is as potent as the pull And it has one more extraordinary peculiarity. of the whole earth. But if the gravitational Whereas left-spinning neutrinos exist, there are force is so weak, why is it so persistent while the no right-spinning neutrinos. The neutrino electrical force is not? We are all made up of does not obey the mirror symmetry principle. electrons and protons, we are electrical systems, Like Hoffmann in Offenbach's opera, a neutrino but none of us exerts an electrical force on anyone reflected in a mirror sees no shadow of itself. else even though the electrical forces are so very Why this is so, we do not know. much more powerful. The reason is the one we Summarizing once again, we have four forces: have already mentioned; electrical charge is of the strongest is the nuclear. The next in order two types-positive and negative-while the of strength is electrical, 100 times weaker than gravitational charge is of only one sign. The the nuclear force. The next is the weak force, electric force cancels itself out, the gravitational a million times weaker, and the still next the force never does. Another question which gravitational force, which is a billion, billion, arises with the gravitational force is: are there billion times weaker still. All particles can be carriers of gravitational force just like the considered manifestations of these forces. The carriers of the electric and the nuclear forces? nuclear force seems to obey the SU(l2) symmetry Theoretically, there should be, Experimentally, law. The multiplets consist of 364 or more 52 53 particles; the photon is the signature of the elect with two rival theories for the same set of pheno ric force. The electric and the nuclear forces mena one has always fou nd that a theory more seem to be fairly well understood, and so is the aesthetically satisfying i also the correct one. gravitational force, since the days of Newton The Holy Book in has and Einstein. The weak force is completely mysterious. Still more mysterious, however, is proclaimed the faith of the true scientist the fact of why all these forces are divided in this somewhat arbitrary manner; why do they possess such different symmetry properties? Why do their strengths vary so very much? Physics can never rest till this final synthesis comes; the synthesis which, for example, must include not only electric and the nuclear charges, but also the gravitational. We have certainly not solved the whole of physics. In Oppen heimer's phrase: "The future will be only more radical and not less, only more strange and not more familiar, and it will have its own new insights for the inqu.iring mind". The same thought was expressed in an eloquent line by Paiz Ahmad Faiz. (Thou see t not in lhe creation of the All-merciful any imperfection. Return thy gaze; sccst thou any fissure? Then return thy gaze again, and again, and thy gaze comes back to thee dazzled, aweary). For my final words in all humility I wish t,o If there is one hallmark of true science, if there conclude with a prayer is one perception that scientific knowledge heightens, it is this spirit of jl The deeper that one goes, the more profound ones insight, the more i one's sense of wonder increased. If we have done anything we hope to have shown that allied with the wonder of God's creation, alJ explanation we have ever found i based on symmetry concepts. Whenever faced SS 54