52 Symmetry in Physical Laws 52-1 Symmetry operations The subject of this chapter is what we may call symmetry in physical laws. 52-1 Symmetry operations We have already discussed certain features of symmetry in physical laws in con- 52-2 Symmetry in space and time nection with vector analysis(Chapter 11),the theory of relativity (Chapter 16),and rotation (Chapter 20). 52-3 Symmetry and conservation Why should we be concerned with symmetry?In the first place,symmetry is laws fascinating to the human mind,and everyone likes objects or patterns that are in 524 Mirror reflections some way symmetrical.It is an interesting fact that nature often exhibits certain kinds of symmetry in the objects we find in the world around us.Perhaps the 52-5 Polar and axial vectors most symmetrical object imaginable is a sphere,and nature is full of spheres- stars,planets,water droplets in clouds.The crystals found in rocks exhibit many 52-6 Which hand is right? different kinds of symmetry,the study of which tells us some important things about 52-7 Parity is not conserved! the structure of solids.Even the animal and vegetable worlds show some degree of 52-8 Antimatter symmetry,although the symmetry of a flower or of a bee is not as perfect or as fundamental as is that of a crystal. 52-9 Broken symmetries But our main concern here is not with the fact that the objects of nature are often symmetrical.Rather,we wish to examine some of the even more remarkable symmetries of the universe-the symmetries that exist in the basic laws themselves which govern the operation of the physical world. First,what is symmetry?How can a physical law be“symmetrical'"?The problem of defining symmetry is an interesting one and we have already noted that Weyl gave a good definition,the substance of which is that a thing is symmetrical if there is something we can do to it so that after we have done it,it looks the same as it did before.For example,a symmetrical vase is of such a kind that if we reflect or turn it,it will look the same as it did before.The question we wish to consider here is what we can do to physical phenomena,or to a physical situation in an experiment,and yet leave the result the same.A list of the known operations under which various physical phenomena remain invariant is shown in Table 52-1. Table 52-1 52-2 Symmetry in space and time Symmetry Operations The first thing we might try to do,for example,is to translate the phenomenon in space.If we do an experiment in a certain region,and then build another ap- Translation in space paratus at another place in space (or move the original one over)then,whatever Translation in time went on in one apparatus,in a certain order in time,will occur in the same way if Rotation through a fixed angle we have arranged the same condition,with all due attention to the restrictions that Uniform velocity in a straight we mentioned before:that all of those features of the environment which make it line (Lorentz transformation) not behave the same way have also been moved over-we talked about how to Reversal of time define how much we should include in those circumstances,and we shall not go into those details again. Reflection of space In the same way,we also believe today that displacement in time will have no Interchange of identical atoms effect on physical laws.(That is,as far as we know today-—all of these things are or identical particles as far as we know today!)That means that if we build a certain apparatus and start Quantum-mechanical phase it at a certain time,say on Thursday at 10:00 a.m.,and then build the same appara- Matter-antimatter (charge conjugation) tus and start it,say,three days later in the same condition,the two apparatuses will go through the same motions in exactly the same way as a function of time no matter what the starting time,provided again,of course,that the relevant features of the environment are also modified appropriately in time.That symmetry means, 52-1
of course, that if one bought General Motors stock three months ago, the same thing would happen to it if he bought it now! We have to watch out for geographical differences too, for there course, variations in the characteristics of the earth's surface. So, for example if we measure the magnetic field in a certain region and move the apparatus to some other region, it may not work in precisely the same way because the magnet field is different, but we say that is because the magnetic field is associated with the earth. We can imagine that if we move the whole earth and the equipment, it would make no diference in the operation of the apparat nother thing that we discussed in considerable detail was rotation in space if we turn an apparatus at an angle it works just as well, provided we turn every thing else that is relevant along with it. In fact, we discussed the problem of sym metry under rotation in space in some detail in Chapter 11, and we invented a mathematical system called vector analysis to handle it as neatly as possible On a more advanced level we had another symmetry-the symmetry under uniform velocity in a straight line. That is to say-a rather remarkable effect-that if we have a piece of apparatus working a certain way and then take the same ap- paratus and put it in a car, and move the whole car, plus all the relevant surround ngs,at a uniform velocity in a straight line, then so far as the phenomena inside the car are concerned there is no difference: all the laws of physics appear the same We even know how to express this more technically, and that is that the mathe- matical equations of the physical laws must be unchanged under a Lorentz trans formation. As a matter of fact, it was a study of the relativity problem that concen trated physicists'attention most sharply on symmetry in physical laws Now the above-mentioned symmetries have all been of a geometrical nature time and space being more or less the same, but there are other symmetries of a different kind. For example, there is a symmetry which describes the fact that we can replace one atom by another of the same kind to put it differently, there atoms of the same kind. It is possible to find groups of atoms such that if we change a pair around, it makes no difference-the atoms are identical. Whatever one atom of oxygen of a certain type will do, another atom of oxygen of that type will do. One may say, That is ridiculous, that is the definition of equal types!"That may be merely the definition, but then we still do not know whether there are any atoms of the same type"; the fact is that there are many, many atoms of the same type. Thus it does mean something to say that it makes no difference if we replace one atom by another of the same type. The so-called elementary particles of which the atoms are made are also identical particles in the above sense-all electrons are the same; all protons are the same; all positive pions are the same; and After such a long list of things that can be done without changing the phe nomena, one might think we could do practically anything; so let us give some examples to the contrary, just to see the difference. Suppose that we ask: "Are the physical laws symmetrical under a change of scale? Suppose we build a certain piece of apparatus, and then build another apparatus five times bigger in every part, will it work exactly the same way? The answer is, in this case, no The wavelength of light emitted, for example, by the atoms inside one box of sodium atoms and the wavelength of light emitted by a gas of sodium atoms five times in volume is not five times longer, but is in fact exactly the same as the other So the ratio of the wavelength to the size of the emitter will change Another example: we see in the newspaper, every once in a while pictures of a great cathedral made with little matchsticks-a tremendous work of art by some retired fellow who keeps gluing matchsticks together. It is much more elaborate and wonderful than any real cathedral. If we imagine that this wooden cathedral were actually built on the scale of a real cathedral, we see where the trouble is it would not last-the whole thing would collapse because of the fact that scaled-up matchsticks are just not strong enough. "Yes, " one might say, "but we also know that when there is an influence from the outside, it also must be changed in pro- portion! We are talking about the ability of the object to withstand gravitation So what we should do is first to take the model cathedral of real matchsticks and 52-2
e real earth, and then we know it is stable. Then we should take the larger cathe- dral and take a bigger earth. But then it is even worse, because the gravitation is increased still more Today, of course, we understand the fact that phenomena depend on the scale on the grounds that matter is atomic in nature, and certainly if we built an appara tus that was so small there were only five atoms in it, it would clearly be something we could not scale up and down arbitrarily. The scale of an individual atom is not at all arbitrary-it is quite definite. The fact that the laws of physics are not unchanged under a change of scale was discovered by Galileo. He realized that the strengths of materials were not in exactly the right proportion to their sizes, and he illustrated this property that we were just discussing, about the cathedral of matchsticks, by drawing two bones the bone of one dog, in the right proportion for holding up his weight, and the maginary bone of a"super dog"that would be, say, ten or a hundred times bigger-that bone was a big, solid thing with quite different proportions. We do not know whether he ever carried the argument quite to the conclusion that the laws of nature must have a definite scale, but he was so impressed with this dis motion, because he published them both in the same volume, called"On Two New Sciences Another example in which the laws are not symmetrical, that we know quite well, is this: a system in rotation at a uniform angular velocity does not give the same apparent laws as one that is not rotating. If we make an experiment and hen put everything in a space ship and have the space ship spinning in empty space, all alone at a constant angular velocity, the apparatus will not work the same way because, as we know, things inside the equipment will be thrown to the outside, and so on, by the centrifugal or coriolis forces, etc. In fact, we can tell that the earth is rotating by using a so-called Foucault pendulum, without looking outside Next we mention a very interesting symmetry which is obviously false, i.e. reversibility in time. The physical laws apparently cannot be reversible in time because, as we know, all obvious phenomena are irreversible on a large scale he moving finger writes, and having writ, moves on. So far as we can tell, irreversibility is due to the very large number of particles involved, and if we could see the individual molecules, we would not be able to discern whether the machinery was working forward or backwards. To make it more precise: we build a small apparatus in which we know what all the atoms are doing, in which we can watch them jiggling. Now we build another apparatus but which starts its motion in the final condition of the other one, with all the velocities precisely reversed It will then go through the same motions, but exactly in reverse. Putting it another way: if we take a motion picture, with sufficient detail, of all the inner works of a piece of material and shine it on a screen and run it backwards, no physicist will be able to say, That is against the laws of physics, that is doing something wrong! If we do not see all the details, of course the situation will be perfectly clear, If we see the egg splattering on the sidewalk and the shell cracking open, and so on then we will surely say, " That is irreversible, because if we run the moving picture backwards the egg will all collect together and the shell will go back together, and that is obviously ridiculous! But if we look at the individual atoms themselves the laws look completely reversible. This is, of course, a much harder discovery to have made, but apparently it is true that the fundamental physical laws, on a microscopic and fundamental level, are completely reversible in time 52-3 Symmetry and conservation laws The symmetries of the physical laws are very interesting at this level, but they turn out, in the end, to be even more interesting and exciting when we come to quantum mechanics. For a reason which we cannot make clear at the level of the present discussion-a fact that most physicists still find somewhat staggering, a most profound and beautiful thing, is that, in quantum mechanics, for each of the rules of symmetry there is a corresponding conservation law; there is a definite
connection between the laws of conservation and the symmetries of physical laws We can only state this at present, without any attempt at explanation The fact, for aple, that the lav when we add the principles of quantum mechanics, turns out to mean that mo- mentum is conserved That the laws are symmetrical under translation in time means, in quantum mechanics, that energy is conserved Invariance under rotation through a fixed angle in space corresponds to the conservation of angular momentum. These connections are very interesting and beautiful things, among the most beautiful and profound things in physics. Incidentally, there are a number of symmetries which appear in quantum mechanics which have no classical analog, which have no method of description in classical physics. One of these is as follows: If y is the amplitude for some process or other, we know that the absolute square of y is the probability that the process will occur. Now if someone else were to make his calculations, not with this 4, but with a y which differs merely by a change in phase (let a be some constant, and multiply e times the old y), the absolute square of y, which is the probability of he event, is then equal to the absolute square of y W2=W2 (521) Therefore the physical laws are unchanged if the phase of the wave function is shifted by an arbitrary constant, That is another symmetry. Physical laws must be of such a nature that a shift in the quantum-mechanical phase makes no differ- ence. As we have just mentioned, in quantum mechanics there is a conservation law for every symmetry. The conservation law which is connected with the quar um-mechanical phase seems to be the conservation of electrical charge. This is altogether a very interesting business 524 Mirror reflections Now the next question, which is going to concern us for most of the rest of his chapter, is the question of symmetry under reflection in space. The problem is this: Are the physical laws symmetrical under reflection We may put it this way: Suppose we build a piece of equipment, let us say a clock, with lots of wheels and hands and numbers; it ticks, it works, and it has things wound up inside We look at the clock in the mirror. How it looks in the mirror is not the question But let us actually build another clock which is exactly the same as the first clock looks in the mirror-every time there is a screw with a right-hand thread in one we use a screw with a left-hand thread in the corresponding place of the other where one is marked“2” on the face, we mark a“s” on the face of the other; each coiled spring is twisted one way in one clock and the other way in the mir image clock; when we are all finished, we have two clocks, both physical, which bear to each other the relation of an object and its mirror image, although they are both actual, material objects, we emphasize. Now the question is: If the two clocks are started in the same condition, the springs wound to corresponding tight- nesses, will the two clocks tick and go around forever after, as exact mirror images? (This is a physical question, not a philosophical question. Our intuition about the laws of physics would suggest that they would We would suspect that, at least in the case of these clocks, reflection in space is one of the symmetries of physical laws, that if we change everything from"right' to"left"and leave it otherwise erence, Let example, impossible to define a particular absolute velocity by a physical phe- nomenon. So it should be impossible, by any physical phenomenon, to define bsolutely what by‘ right” as opposed to"left may call "geography, "surely"right"can be desal.Forexample,using what Of course the world does not have to be symmetri d. For instance, we stand
in New Orleans and look at Chicago, and Florida is to our right(when our feet are on the ground: ) So we can define"right " and"left"by geography. Of course the actual situation in any system does not have to have the symmetry that we are talking about; it is a question of whether the laws are symmetrical--in other words hether it is against the physical laws to have a sphere like the earth with"left handed dirt"on it and a person like ourselves standing looking at a city like Chicago from a place like New Orleans, but with everything the other way around so Florida is on the other side. It clearly seems not impossible, not against the physical laws, to have everything changed left for right. Another point is that our definition of"right ""should not depend on history An easy way to distinguish right from left is to go to a machine shop and pick up a screw at random. The odds are it has a right-hand thread--not necessarily, but it is much more likely to have a right-hand thread than a left-hand one. This is a estion of history or convention, or the way things happen to be, and is again not a question of fundamental laws. As we can well appreciate, everyone could have started out making left-handed screws! So we must try to find some phenomenon in which"right hand"is involved fundamentally. The next possibility we discuss is the fact that polarized light rotates its plane of polarization as it goes through, say, sugar water in Chapter 33, it rotates, let us say, to the right in a certain sugar solution.That is a way of defining"right-hand, "because we may dissolve some sugar in the water and then the polarization goes to the right. But sugar has come from living things and if we try to make the sugar artificially then we discover that it does not rotate the plane of polarization! But if we then take that same sugar which is made artificially and which does not rotate the plane of polarization, and put bacteria in it ( they eat some of the sugar)and then filter out the bacteria, we find that we still have sugar left(almost half as much as we had before), and this time it does rotate the plane of polarization, but the other way! It seems very confusing, but is easily explained Fig. 52-1.(a)L-alanine(left), and(b) -alanine (right) Take another example: One of the substances which is common to all living creatures and that is fundamental to life is protein. Proteins consist of chains of amino acids. Figure 52-1 shows a model of an amino acid that comes out of a protein. This amino acid is called alanine, and the molecular arrangement would look like that in Fig. 52-1(a) if it came out of a protein of a real living thing. On the other hand, if we try to make alanine from carbon dioxide, ethane and am monia(and we can make it, it is not a complicated molecule), we discover that we re making equal amounts of this molecule and the one shown in Fig. 52-1(b) The first molecule, the one that comes from the living thing, is called L-alanine The other one, which is the same chemically, in that it has the same kinds of atoms and the same connections of the atoms, is a"right-hand"molecule, com pared with the"left-hand"L-alanine, and it is called D-alanine. The interesting thing is that when we make alanine at home in a laboratory from simple gases we get an equal mixture of both kinds. However, the only thing that life uses is L-alanine. (This is not exactly true. Here and there in living creatures there is a Now if we make both kinds, and we feed the mixture to some animal which hi special use for D-alanine, but it is very rare. All proteins use L-alanine exclusivel to"eat, or use up, alanine, it cannot use D-alanine, so it only uses the L-alanine; that is what happened to our sugar-after the bacteria eat the sugar that works
well for them, only the"wrong "kind is left! (Left-handed sugar tastes sweet, but gar. So it looks as though the phenomena of life permit a distinction between ight"and"left, "or chemistry permits a distinction, because the two molecules are chemically different. But no, it does not! So far as physical measurements can be made, such as of energy, the rates of chemical reactions, and so on, the two kinds work exactly the same way if we make everything else in a mirror image too One molecule will rotate light to the right, and the other will rotate it to the left in precisely th mount, through the ant of fluid. Thus, so far physics is concerned, these two amino acids are equally satisfactory. So far as we understand things today, the fundamentals of the Schrodinger equation have it that the two molecules should behave in exactly corresponding ways, so that one is to the right as the other is to the left. Nevertheless, in life it is all one way! It is presumed that the reason for this is the following. Let us suppose, for example, that life is somehow at one moment in a certain condition in which all the proteins in some creatures have left-handed amino acids, and all the enzymes are lopsided-every substance in the living creature is lopsided-it is not symmet rical. So when the digestive enzymes try to change the chemicals in the food from one kind to another, one kind of chemical"fits"into the enzyme, but the other kind does not (like Cinderella and the slipper, except that it is a"left foot that we are testing). So far as we know, in principle, we could build a frog, for example in which every molecule is reversed, everything is like the"left-hand"mirror image of a real frog; we have a left-hand frog. This left-hand frog would go on all right for a while, but he would find nothing to eat, because if he swallows a fly,his enzymes are not built to digest it. The fly has the wrong"kind"of amino acids (unless we give him a left-hand fly ). So as far as we know, the chemical and life processes would continue in the same manner if everything were reversed If life is entirely a physical and chemical phenomenon, then we can understand that the proteins are all made in the same corkscrew only from the idea that at the very beginning some living molecules, by accident, got started and a few won omewhere, once, one organic molecule was lopsided in a certain way, and from this particular thing the"right "happened to evolve in our particular geography a particular historical accident was one-sided, and ever since then the lopsidedness has propagated itself. Once having arrived at the state that it is in now, of course it will always continue--all the enzymes digest the right things, manufacture the right things: when the carbon dioxide and the water vapor, and so on, go in the plant leaves, the enzymes that make the sugars make them lopsided because the enzymes are lopsided. If any new kind of virus or living thing were to originate at a later time, it would survive only if it could"eat"the kind of living matter already present. Thus it, too, must be of the same kind There is no conservation of the number of right-handed molecules.Once started, we could keep increasing the number of right-handed molecules. So the presumption is, then, that the phenomena in the case of life do not show a lack of symmetry in physical laws, but do show, on the contrary, the universal nature and the commonness of ultimate origin of all creatures on earth, in the sense de- ibed ab 52-5 Polar and axial vectors where wa we go further. We observe that in physics there are a lot of other places where we have“ right”and“left” hand rules. As a matter of fact, when we learned about vector analysis we learned about the right-hand rules we have to use in order to get the angular momentum, torque, magnetic field, and so on, to come out right The force on a charg moving in a magnetic field, for example, is F= y X In a given situation, in which we know F, v, and B, isn't that equation enough to define right-handedness? As a matter of fact, if we go back and look at where the vectors came from, we know that the "right-hand rule"was merely a convention it was a trick. The original quantities, like the angular momenta and the angular velocities, and things of this kind, were not really vectors at all! They are all 52-6
somehow associated with a certain plane, and it is just because there are three dimensions in space that we can associate the quantity with a direction perpendicu lar to that plane. Of the two possible directions, we chose the"right-hand direction So if the laws of physics are symmetrical, we should find that if some demon were to sneak into all the physics laboratories and replace the word"right "for "left"in every book in which"right-hand rules"are given, and instead we were to se all "left-hand rules, "uniformly, then it should make no difference whatever Let us give an illustration. There are two kinds of vectors. There are"honest vectors, for example a step Ar in space. If in our apparatus there is a piece here and something else there, then in a mirror apparatus there will be the image piece and the image something else, and if we draw a vector from the piece"to the"some thing else, "one vector is the mirror image of the other(Fig. 52-2). The vector arrow changes its head, just as the whole space turns inside out; such a vector we call a But the other kind of vector, which has to do with rotations, is of a different nature. For example, suppose that in three dimensions something is rotating as shown in Fig. 52-3. Then if we look at it in a mirror, it will be rotating as indicated namely, as the mirror image of the original rotation. Now we have agreed to repre- mirror image, A step in space and its Fig.52-2 sent the mirror rotation by the same rule, it is a"vector"which, on reflection, does not change about as the polar vector does, but is reversed relative to the polar rectors and to the geometry of the space; such a vector is called an axial vector. Now if the law of reflection symmetry is right in physics, then it must be true that the equations must be so designed that if we change what corresponds to reflection, nothing will happen. For instance, when we write a formula which says that the angular momentum is L =r X p, that equation is all right, because if ye change to a left-hand coordinate system, we change the sign of L, but p and r do not change; the cross-product sign is changed, since we must change from a right-hand rule to a left- hand rule. as another example, we know that the force mirror image. Nole a Fig. 52-3. A rotati right-to a left-handed system, since F and v are known to be polar vectors the sign direction vector"isthat on a charge moving in a magnetic field is F v xB, but if we change from a velocity vector"is not reversed in angular change required by the cross-product must be cancelled by a sign change in B, which means that B must be an axial vector. In other words . if we make such a reflection, B must go to-B. So if we change our coordinates from right to left, we must also change the poles of magnets from north to south Let us see how that works in an example. Suppose that we have two magnets as in Fig. 52-4. One is a magnet with the coils going around a certain way, and with current in a given direction. The other magnet looks like the reflection of the first magnet in a mirror--the coil will wind the other way, everything that happens inside the coil is exactly reversed, and the current goes as shown. Now, from the laws for the production of magnetic fields, which we do not know yet officially, but which we most likely learned in high school, it turns out that the magnetic field is as shown in the figure. In one case the pole is a south magnetic pole, while in the other magnet the current is going the other way and the magnetic field is reversed--it is a north magnetic pole. So we see that when we go from right Fig. 52-4 to left we must indeed change from north to south! net and its mirror Never mind changing north to south; these too are mere conventions. Let us talk about phenomena. St have an electron movin one field, going into the page. Then, if we use the formula for the force, B (remember the charge is minus), we find that the electron will deviate in the indi cated direction according to the physical law. So the phenomenon is that we have a coil with a current going in a specified sense and an electron curves in a certai way-that is the physics-never mind how we label everything Now let us do the same experiment with a mirror we send an electron through in a corresponding direction and now the force is reversed, if we calculate it from the same rule, and that is very good because the corresponding motions are then mirror images
52-6 Which hand is right? So the fact of the matter is that in studying any phenomenon there are always two right-hand rules, or an even number of them and the net result is that the phenomena always look symmetrical. In short, therefore, we cannot tell right from left if we also are not able to tell north from south. However it can tell the north pole of a magnet. The north pole of a compass needle, for ex- ample, is one that points to the north. But of course that is again a local property that has to do with geography of the earth; that is just like talking about in which direction is Chicago, so it does not count. If we have seen compass needles, we may have noticed that the north-seeking pole is a sort of bluish color. But that is just due to the man who painted the magnet. These are all local, conventional cre to have the property that if enough we would see small hairs growing on its north pole but not on its south pole, if that were the general rule, or if there were any unique way to distinguish ne north from the south pole of a magnet, then we could tell which of the two To illustrate the whole problem still more clearly, imagine that we were talking to a Martian, or someone very far away, by telephone. We are not allowed to send him any actual samples to inspect; for instance, if we could send light, we could send him right-hand circularly polarized light and say, "That is right-hand light just watch the way it is going. But we cannot give him anything, we can only talk to him. He is far away, or in some strange location, and he cannot see anything we can see. For instance, we cannot say, "Look at Ursa major; now see how those stars are arranged. What we mean by rightis.. "We are only allowed hone him Now we want to tell him all about us. Of course, first we start defining num- bers, and say, "Tick, tick, two, tick, tick, tick, three.. so that gradually he can understand a couple of words, and so on. After a while we may become very famil- iar with this fellow, and he says, " What do you guys look like? We start to de scribe ourselves, and say, " "Well, we are six feet tall. "He says, "Wait a minute what is six feet? "Is it possible to tell him what six feet is? Certainly! We say, You know about the diameter of hydrogen atoms-we are 17,000, 000,000 hydrogen atoms high!" That is possible because physical laws are not variant under change of scale, and therefore we can define an absolute length. and so we define the size of the body, and tell him what the general shape is-it has prongs with five bumps sticking out on the ends, and so on, and he follows us along, and we finish describing how we look on the outside, presumably without encountering any particular difficulties. He is even making a model of us as we go along. He says y, you are certainly very handsome fellows; now what is on the inside?" So we start to describe the various organs on the inside and we come to the heart, and we carefully describe the shape of it, and say, "Now put the heart on the left side He says, " Duhhh-the left side? Now our problem is to describe to him which side the heart goes on without his ever seeing anything that we see, and without our ever sending any sample to him of what we mean by"right"no standard right-handed object. Can we do it? 52-7 Parity is not conserved! It turns out that the laws of gravitation, the laws of electricity and magnetism nuclear forces, all satisfy the principle of reflection symmetry, so these laws, or anything derived from them, cannot be used. But associated with the many par ticles that are found in nature there is a phenomenon called beta decay, or weak decay. One of the examples of weak decay, in connection with a particle discovered in about 1954, posed a strange puzzle. There was a certain charged particle which disintegrated into three Mesons, as shown schematically in Fig.52 particle was called, for a while, a T-meson. Now in Fig. 52-5 we also see another particle which disintegrates into two mesons; one must be neutral, from the con
servation of charge. This particle was called a B-meson. So on the one hand we have a particle called a T, which disintegrates into three T-mesons, and aa, which disintegrates into two T-mesons. Now it was soon discovered that the T and the are almost equal in mass; in fact, within the experimental error, they are equal Next, the length of time it took for them to disintegrate into three T's and two T's was found to be almost exactly the same; they live the same length of time Next, whenever they were made, they were made in the same proportions, say 14 percent T's to 86 percent as Anyone in his right mind realizes immediately that they must be the same particle, that we merely produce an object which has two different ways of dis- integrating-not two different particles. This object that can disintegrate in two different ways has, therefore, the same lifetime and the same production ratio (because this is simply the ratio of the odds with which it disintegrates into these A schematic diagram However, it was possible to prove(and we cannot here explain at all how ),fromthe ation of a t+andaθ the principle of reflection symmetry in quantum mechanics, that it was impossible particle to have these both come from the same particle-the same particle could not disintegrate in both of these ways. The conservation law corresponding to the principle of reflection symmetry is something which has no classical analog, and so this kind of quantum-mechanical conservation was called the conservation of parity. So, it was a result of the conservation of parity or, more precisely, from the symmetry of the quantum-mechanical equations of the weak decays under reflec tion, that the same particle could not go into both, so it must be some kind of incidence of masses lifetimes and so on but the more it was studied the more remarkable the coincidence, and the suspicion gradually grew that possibly the deep law of the reflection symmetry of nature may be false. As a result of this apparent failure, the physicists Lee and Yang suggested that ther experiments be done in related decays to try to test whether the law was correct in other cases. The first such experiment was carried out by Miss wu fro Columbia, and was done as follows. Using a very strong magnet at a very low temperature, it turns out that a certain isotope of cobalt, which disintegrates by emitting an electron, is magnetic, and if the temperature is low enough that the thermal oscillations do not jiggle the atomic magnets about too much, they line up in the magnetic field. So the cobalt atoms will all line up in this strong field They then disintegrate, emitting an electron, and it was discovered that when the atoms were lined up in a field whose b vector points upward, most of the electrons were emitted in a downward direction If one is not really"hep"to the world, such a remark does not sound like anything of significance, but if one appreciates the problems and interesting things in the world, then he sees that it is a most dramatic discovery: when we put cobalt atoms in an extremely strong magnetic field more disintegration electrons go down than up. Therefore if we were to put it in a corresponding experiment in a"mirror, in which the cobalt atoms would be lined up in the opposite direction, they would spit their electrons up, not down; the action is unsymmetrical. The magnet has grown the electrons in a B integration tend to go away from it that distinguishes, in a physical way, the north pole from the south pole After this, a lot of other experiments were done: the disintegration of the T into u and v; u into an electron and two neutrinos; nowadays, the a into proton and T; disintegration of 2's; and many other disintegrations. In fact, in almost all cases where it could be expected, all have been found not to obey reflection symmetry! Fundamentally, the law of reflection symmetry, at this level in physics, incorrect In short, we can tell a martian where to put the heart: we say, " Listen, build yourself a magnet, and put the coils in, and put the current on, and then take some cobalt and lower the temperature. Arrange the experiment so the electrons go from foot to the head, then the direction in which the current goes through the coils is the direction that goes in on what we call the right and comes out on the left So it is possible to define right and left, now, by doing an experiment of this kind 52-9
There are a lot of other features that were predicted. For example, it turns that the spin, the angular momentum, of the cobalt nucleus before disintegration is 5 units of h, and after disintegration it is 4 units. The electron carries spin angular momentum, and there is also a neutrino involved. It is easy to see from this that the electron must carry its spin angular momentum aligned along its direction of motion, the neutrino likewise. So it looks as though the electron is spinning to the left, and that was also checked. In fact, it was checked right here at Caltech by Boehm and Wapstra, that the electrons spin mostly to the left. (There were some other experiments that gave the opposite answer, but they were wrong!) The next problem, of course, was to find the law of the failure of parity con- servation. What is the rule that tells us how strong the failure is going to be? The rule is this it occurs only in these very slow reactions, called weak decays, and when it occurs, the rule is that the particles which carry spin, like the electron neutrino,and so on, come out with a spin tending to the left. That is a lopsided ule;it connects a polar vector velocity and an axial vector angular momentum and says that the angular momentum is more likely to be opposite to the velocity than along it. Now that is the rule, but today we do not really understand the whys and wherefores of it. Why is this the right rule, what is the fundamental reason for it, and how is it connected to anything else? At the moment we have been so shocked by the fact that this thing is unsymmetrical that we have not been able to recover enough to understand what it means with regard to all the other rules. however the subject is interesting, modern, and still unsolved, so it seems appropriate that we discuss some of the questions associated with it 52-8 Antimatte The first thing to do when one of the symmetries is lost is to immediately go back over the list of known or assumed symmetries and ask whether any of the others are lost. Now we did not mention one operation on our list, which must necessarily be questioned and that is the relation between matter and antimatter Dirac predicted that in addition to electrons there must be another particle, called the positron(discovered at Caltech by Anderson), that is necessarily related to the electron. All the properties of these two particles obey certain rules of corre- spondence: the energies are equal; the masses are equal the charges are reversed but, more important than anything, the two of them, when they come together can annihilate each other and liberate their entire mass in the form of energy, say Y-rays. The positron is called an antiparticle to the electron, and these are the characteristics of a particle and its antiparticle. It was clear from Dirac's argument hat all the rest of the particles in the world should also have corresponding anti- particles. For instance, for the proton there should be an antiproton, which is now ymbolized by a p. The p would have a negative electrical charge and the same mass as a proton, and so on. The most important feature, however, is that a proton and an antiproton coming together can annihilate each other. The reason w emphasize this is that people do not understand it when we say there is a neutron and also an antineutron, because they say, "A neutron is neutral, so how can it have the opposite charge? "" The rule of the"anti""is not just that it has the opposite charge, it has a certain set of properties, the whole lot of which are opposite.The antineutron is distinguished from the neutron in this way: if we bring two neutrons together, they just stay as two neutrons, but if we bring a neutron and an anti neutron together, they annihilate each other with a great explosion of energy being liberated, with various T-mesons, y-rays, and whatnot ow if we have antineutrons, antiprotons, and antielectrons, we can make antiatoms, in principle. They have not been made yet, but it is possible in principle For instance, a hydrogen atom has a proton in the center with an electron going around outside Now imagine that somewhere we can make an antiproton with a positron going around, would it go around? Well, first of all, the antiproton is electrically negative and the antielectron is electrically positive so they attract each other in a corresponding manner-the masses are all the same; everything is the