Full text of "THE LEFT HAND OF THE ELECTRON - ENGLISH - ISAAC ASIMOV"

DEU J 47T7-T.25 THE LEFT HAND OF THE ELECTRON DOUBLEDAY A COMPANY, INC. CAMDEN Cmr, NEW YORK CONTENTS INTRODUCTION A — The Problem of Left and Right 1— ODDS AND EVENS 2— THE LEFT HAND OF THE ELECTRON 3— SEEING DOUBLE 4— THE 3-D MOLECULE 5— THE ASYMMETRY OF LD7E B — The Problem of Oceans 6 — THE THALASSOGENS 7— HOT WATER 8— COLD WATER C — The Problem of Numbers and Lines 9— PRIME QUALITY 10— EUCLID’S FIFTH 11— THE PLANE TRUTH D — The Problem of the Platypus 12— HOLES IN THE HEAD Vlll CONTENTS E — The Problem of History 13— THE EUREKA PHENOMENON 159 14— POMPEY AND CIRCUMSTANCE 172 15— BILL AND I 186 F — The Problem of Population 16 — STOP! 201 17 BUT HOW? 214 THE LEFT HAND OF THE ELECTRON A — The Problem of Left and Right 1 ODDS AND EVENS I have just gone through a rather unsettling experience. Ordinarily it is not veiy difficult to think up a topic for these chapters. Some interesting point will occur to me, which will quickly lead my mind to a particular line of development, beginning in one place and ending in another. Then, I get stalled. Today, however, having determined to deal with asymmetry (in more than one chapter, veiy likely) and to end with life and antilife, I found that two possible stalling points occurred to me. Ordinarily, when this happens, one stalling point see ms so much superior to me that 1 choose it over the other with a minimum of hesitation. This time, however, the question was whether to stall with even numbers or with double refraction, and the arguments raging within my head for each case were so equally balanced that 1 couldn't make up my mind. For two hours I sat at my desk, pon- dering first one and then the other and growing steadily un- happier. Indeed, I became uncomfortably aware of the resemblance of my case to that of "Buridan's ass." The reference, here, is to a fourteenth-century French philoso- pher, Jean Buridan, who was supposed to have stated the follow- ing: "If a hungry ass were placed exactly between two haystacks in every respect equal, it would starve to death, because there would be no motive why it should go to one rather than to the other." Actually, of course, there's a fallacy here, since the statement does not recognize the existence of the random factor. The ass, no logician, is bound to turn his head randomly so that one hay- stack comes into better view, shuffle his feet randomly so that one 4 THE PROBLEM OF LEFT AND RIGHT haystack comes to be closer; and he would end at the haystack better seen or more closely approached. Which haystack that would be, one could not tell in advance. If one had a thousand asses placed exactly between a thousand sets of haystack pairs, one could confidently expect that about half would turn to the right and half to the left. The individual ass, however, would remain unpredictable. In the same way, it is impossible to predict whether an honest coin, honestly thrown, will come down heads or tails in any one particular case, but we can confidently predict that a very large number of coins tossed simultaneously (or one coin tossed a very large number of times) will show heads just about half the time and tails the other half. And so it happens that although the chance of the fall of heads or tails is exactly even, just fifty-fifty, you can nevertheless call upon the aid of randomness to help you make a decision by tossing one coin once. At this point, I snapped out of my reverie and did what a lesser mind would have done two hours before. I tossed a coin. Shall we start with even numbers. Gentle Readers? I suspect that some prehistoric philosopher must have decided that there were two kinds of numbers: peaceful ones and warlike ones. The peaceful numbers were those of the type 2, 4, 6, 8, while the numbers in between were warlike. If there were 8 stone axes and two individuals possessing equal claim, it would be easy to hand 4 to each and make peace. If there were 7, however, you would have to give 3 to each and then either toss away the 1 remaining (a clear loss of a valuable object) or let the two disputants fight over it. The fact that the original property that marked out the signifi- cance of what we now call even and odd numbers was something like this is indicated by the very names we give them. The word "even" means fundamentally, "flat, smooth, without unusual depressions or elevations." We use the word in this sense ODDS AND EVENS 5 when we say that a person says something "in an even tone of voice." An even number of identical coins, for instance, can be divided into two piles of exactly the same height. The two piles are even in height and hence the number is called even. The even number is the one with the property of "equal shares." "Odd," on the other hand, is from an old Norse word meaning "point" or "tip." If an odd number of coins is divided into two piles as nearly equal as possible, one pile is higher by one coin and therefore rears a point or tip into the ah', as compared with the other. The odd number possesses the property of "unequal shares," and it is no accident that the expression "odds" in betting implies the wagering of unequal amounts of money by the two participants. Since even numbers possess the property of equal shares, they were said to have "parity," from a Latin word meaning "equal." Originally, this word applied (as logic demanded) to even num- bers only, but mathematicians found it convenient to say that if two numbers were both even or both odd, they were, in each case "of the same parity." An even number and an odd number, grouped together, were "of different parity." To see the convenience of this convention, consider the fol- lowing: If two even numbers are added, the sum is invariably even. (This can be expressed mathematically by saying that two even numbers can be expressed as z,m and zn where m and n are whole numbers and that the sum, zm + zn, is still clearly divisible by two. However, we are friends, you and I, and I'm sure we can dis- pense with mathematical reasoning and that I will find you willing to accept my word of honor as a gentleman in such matters. Be- sides, you are welcome to search for two even numbers whose sum isn't even.) If two odd numbers are added, the sum is also invariably even. If an odd number and an even number are added, however, the sum is invariably odd. 6 THE PROBLEM OF LEFT AND RIGHT We can express this more succinctly in symbols, with E standing for even and O standing for odd: E + E = E 0 + 0 = E E + 0 = 0 0 + E = 0 Or, if we are dealing with pail's of numbers only, the concept of parity enables us to say it in two statements, rather than four: 1) Same parities add to even. 2) Different parities add to odd. A veiy similar state of affairs exists with reference to multipli- cation, if we divide numbers into two classes: positive numbers (+)• and negative numbers ( — ). The product of two positive num- bers is invariably positive. The product of two negative numbers is invariably positive. The product of a positive and a negative number is invariably negative. Using symbols: + x+ = + -X- = + + x- = - -x + = - Or, if we consider all positive numbers as having one kind of parity and all negative numbers as another, we can say, in con- nection with the multiplication of two numbers: 1) Same parities multiply to positive. 2) Different parities multiply to negative. The concept of parity — that is, the assignment of all objects of a particular class to one of two subclasses and then finding two opposing results when objects of the same or of different sub- classes are manipulated — can be applied to physical phenomena. For instance, all electrically charged particles can be divided into two classes: positively charged and negatively charged. Again, ODDS AND EVENS 7 all magnets possess two points of concentrated magnetism of opposite properties: a north pole and a south pole. Let's symbolize these as +, — , N and S. It turns out that: + and + or N and N = repulsion — and — or S and S = repulsion + and — or N and S = attraction — and + or S and N = attraction Again, we can make two statements: 1) Like electric charges, or magnetic poles, repel each other. 2) Opposite electric charges, or magnetic poles, attract each other. The similarity in foim to the situation with respect to the sum- ming of odd and even, or the multiplying of positive and negative, is obvious. When, in any situation, same parities always yield one result and different parities always yield the opposite result, we say that "parity is conserved." If two even numbers sometimes added up to an odd number; or if a positive number multiplied by a nega- tive one sometimes yielded a positive product; or if two positively charged objects sometimes attracted each other; or if a north magnetic pole sometimes repelled a south magnetic pole, we would say that, "The law of conservation of parity is violated." Certainly in connection with numbers and with electromagne- tic phenomena, no one has ever observed the law of conservation of parity to have been violated, and no one seriously expects to observe a case in the future. What about other cases? Well, electromagnetism involves a field. That is, any electrically charged particle, or any magnet, is surrounded by a volume of space within which its properties are made manifest on other objects of the same sort. The other objects are also surrounded by a volume of space within which their properties are made mani- fest on the original object. One speaks, therefore, of an "electro- 8 THE PROBLEM OF LEFT AND RIGHT magnetic interaction" involving pairs of objects carrying electric charge or magnetic poles. Up through the first years of the twentieth century, the only other kind of interaction known was the gravitational. At first blush, there seems no easy way of involving gravitation with parity. There is no way of dividing objects into two groups, one with one kind of gravitational property and the other with the opposite kind. All objects of a given mass possess the same intensity of gravi- tational interaction of the same sort. Any two objects with mass attract each other. There seems no such thing as "gravitational repulsion" (and, according to Einstein's General Theory of Rela- tivity there can't be such a thing). It is as though, in gravity, we can say only that E + E = Eor + X + = -k To be sure, there is a chance that in the field of subatomic physics there might be some objects with mass that possess the usual gravitational properties and other objects with mass that possess gravitational properties of the opposite kind ("antigrav- ity"). In that case, the chances are that it would turn out that two antigravitational objects attract each other just as two gravi- tational objects do; but that an antigravitational and a gravita- tional object would repel each other. The situation with respect to the gravitational interaction would be the reverse of the elec- tromagnetic one (like gravities would attract and unlike gravities would repel) but, allowing for that reversal, parity would still be conserved. The trouble is, though, that the gravitational interaction is so much more feeble than the electromagnetic interaction that gravi- tational interactions of subatomic particles are as yet impossible to measure and a sub-tiny attraction can't be differentiated from a sub-tiny repulsion. — So the question of parity and the gravita- tional field remains in abeyance. As the twentieth century wore on, it came to be recognized that the gravitational and electromagnetic interactions were not the only ones that existed. Subatomic particles involved something ODDS AND EVENS 9 else. To be sure, electrons had negative charges and protons had positive charges and with respect to this, they behaved in accord- ance with the rules of electromagnetic interaction. There were other events in the subatomic world, however, that had nothing to do with electromagnetism. There was, for instance, some sort of interaction involving particles, whether with or without electric charge, that showed itself only in the super-close quarters to be found within the atomic nucleus. Did this "nuclear interaction" involve parity? Every subatomic particle has a certain quantum-mechanical property which can be expressed in a form involving three quanti- ties, x, y, and z. In some cases, it is possible to change the sign of all three quantities from positive to negative without changing the sign of the expression as a whole. Particles in which this is true are said to have "even parity." In other cases, changing the signs of the three quantities does change the sign of the entire expres- sion and a particle of which this is true is said to have "odd parity." Why even and odd? Well, an even-parity particle can break up into two even-parity particles or two odd-parity particles, but never into one even-parity plus one odd-parity. An odd-parity particle, on the other hand, can break up into an odd-parity particle plus an even-parity one, but never into two odd-parity particles or two even-parity particles. This is analogous to the way in which an even number can be the sum of two even numbers or of two odd number's, but never the sum of an even number and an odd num- ber, while an odd number can be the sum of an even number and an odd number, but can never be the sum of two even numbers or of two odd numbers. But then a particle called the "K-meson" was discovered. It was unstable and quickly broke down into "pi-mesons." Some K-mesons gave olf two pi-mesons in breaking down and some gave df three pi-mesons and that was instantly disturbing. If a K-meson did one, it ought not to be able to do the other. Thus an even number can be the sum of two odd numbers (10= 3 + 7) and an odd number can be the sum of three odd numbers (11 = 3 + 7 + 1), but no number can be the sum of two odd IO THE PROBLEM OF LEFT AND RIGHT numbers in one case and three odd numbers in another. It would be like expecting a number to be both odd and even. It would, in short, represent a violation of the law of conservation of parity. Physicists therefore reasoned there must be two kinds of K-meson; an even-parity variety ("theta-meson") that broke down to two pi-mesons, and an odd-parity variety ("tau-meson") that broke down to three pi-mesons. This did not turn out to be an altogether satisfactory solution, since there seemed to be no possible distinction one could make between the theta-meson and the tau-meson except for the num- ber of pi-mesons it broke down into. To invent a difference in parity for two particles identical in every other respect seemed poor practice. By 1956, a few physicists had begun to wonder if it weren't pos- sible that the law of conservation of parity might not be broken in some cases. If that were so, maybe it wouldn't be necessary to try to make a distinction between the theta-meson and the tau-meson. The suggestion roused the interest of two young Chinese- American physicists at Columbia, Chen Ning Yang and Tsung Dao Lee, who took into consideration the following — There is, as a matter of fact, not one nuclear interaction, but two. The one that holds protons and neutrons together within the nucleus is an extremely strong one, about 130 times as strong as the electromagnetic interaction, so it is called the "strong nu- clear interaction." There is a second, "weak nuclear interaction" which is only about a hundred-trillionth the intensity of the strong nuclear in- teraction (but still some trillion-trillion times as intense as the unimaginably weak gravitational interaction). This meant that there were four types of interaction in the universe (and there is some theoretical reason for arguing that a fifth of any sort cannot exist, but I would hate to commit myself to that): 1) strong nuclear, 2) electromagnetic, 3) weak nuclear, and 4) gravitational. We can forget about the gravitational interaction for reasons ODDS AND EVENS 11 I mentioned earlier in the article. Of the other three, it had been well established by 1956 that parity was conserved in the strong nuclear interaction and in the electromagnetic interaction. Nu- merous cases of such conservation were known and the matter was considered settled. No one, however, had ever systematically checked the weak nu- clear interaction with respect to parity, and the breakdown of the K-meson involved a weak nuclear interaction. To be sure, all physi- cists assumed that parity was conserved in the weak nuclear in- teraction but that was only an assumption. Yang and Lee published a paper pointing this out — and sug- gested experiments that might be performed to check whether the weak nuclear interactions conserved parity or not. Those experi- ments were quickly earned out and the Yang-Lee suspicion that parity would not be conserved was shown to be correct. There was very little delay in awarding them shares in the Nobel prize in physics in 1957, at which time Yang was thirty-four and Lee, thirty-one. You might ask, of course, why parity should be conserved in some interactions and not in others — and might not be satisfied with the answer "Because that's the way the universe is." Indeed, by concentrating too hard on those cases where parity is conserved, you might get the notion that it is impossible, in- conceivable, unthinkable to deal with a case where it isn't con- served. If the conservation of parity is then shown not to hold in some cases, the notion arises that this is a tremendous revolution that throws the entire structure of science into a state of collapse. None of that is so. Parity is not so essential a pari of everything that exists that it must be conserved in all places, at all times, and under all con- ditions. Why shouldn't there be conditions where it isn't con- served or, as in the case of gravitational interaction, where it might not even apply? It is also important to understand that the discovery of the fact that parity was not conserved in weak nuclear interactions 12 THE PROBLEM OF LEFT AND RIGHT did not "overthrow" the law of conservation of parity, even though that was certainly the way in which it was presented in the news- papers and even by scientists themselves. The law of conservation of parity, in those cases in which its validity had been tested by experiment, remained and is still as much in force as ever. It was only in connection with the weak nuclear interactions, where the validity of the law of conservation of parity had never- been tested prior to 1956 and where it had merely been rather carelessly assumed that it applied, that there came the change. The final experiment merely showed that physicists had made an as- sumption they had no real right to make and the law of conserva- tion of parity was "overthrown" only where it had never been shown to exist in the first place. It might help if we look at some familiar, everyday case where a law of conservation of parity holds, and then on another where it is merely assumed to hold by analogy, but doesn't really. We can then see what happened in physics, and why an overthrow of something that really isn't there to begin with, improves the struc- ture of science and does not damage it. Human beings can be divided into two classes: male (M) and female (F). Neither two males by themselves nor two females by themselves can have children (no C). A male and a female together, however, can have children (C). So we can write: MandM = noC FandF =noC M and F = C FandM = C There is thus the fami li ar parity situation: 1) Like sexes cannot have children 2) Opposite sexes can have children. To be sure, there are sexually immature individuals, barren fe- males, sterile or impotent men, and so on, but these matters are details that don't affect the broad situation. As far as the sexes ODDS AND EVENS 13 and children are concerned, we can say that the human species (and, indeed, many other species) conserves parity. Because the human species conserves sexual parity with respect to childbirth, it is easy to assume it conserves it with respect to love and affection as well, so that the feeling arises that sexual love ought to exist only between men and women. The fact is, though, that parity is not conserved in that respect and that both male homosexuality and female homosexuality do exist and have always existed. The assumption that parity ought to be conserved where, in actual fact, it isn't, has caused many people to find homo- sexuality immoral, perverse, abhorrent, and has created oceans of woe throughout history. Again, in Judeo-Christian culture, the institution of marriage is closely associated with childbirth and therefore strictly observes the law of conservation of parity that holds for childbirth. A mar- riage can take place only between one man and one woman be- cause, ideally, that is the simplest system that makes childbirth possible. Now, however, there is an increasing understanding that parity, which is rigidly conserved with respect to childbirth, is not neces- sarily conserved with respect to sexual relations. Increasingly, homosexuality is treated not as a sin or a crime, but as, at most, a misfortune (if that). There is the further attitude, slowly growing in our society, that there is no need to force the institution of marriage into the tight grip of parity conservation. We hear, more and more fre- quently, of homosexual marriages and of group marriages. (The old-fashioned institution of polygamy is an example of one kind of marriage, enjoyed by many of the esteemed men of the Old Testa- ment, in which sexual parity was not conserved.) In the next chapter, then, we'll go on with the nature of the experiment that established the non-conservation of parity in the weak nuclear interaction and consider what happened afterward. 2 THE LEFT HAND OF THE ELECTRON I received a letter yesterday which criticized my writing style. It complained, "you avoid the poetic to the extent that when a cryp- tic, glowing, 'charged' phrase occurs to you. I'd be willing to bet that you deliberately put it aside and opt for a clearer but more pedestrian one." All I can say to that is that you bet your sweet life I do. As all who read my volumes of science essays must surely be aware, 1 have a dislike for the mystical approach to the universe, whether in the name of science, philosophy, or religion. 1 also have a dislike for the mystical approach to literature. I dare say it is possible to evoke an emotional reaction through a "cryptic, glowing, 'charged' phrase" but you show me a ciyptic phrase and I'll show you any number of readers who, not knowing what it means but afraid to admit their ignorance, will say, "My, isn't that poetic and emotionally effective." Maybe it is, and maybe it isn't; but a vast number of literary incompetents get by on the intellectual insecurity of their readers, and a vast number of hacks write a vast quantity of bad "poetry" and make a living at it. For myself, 1 manage to retain a certain amount of intellectual security. When 1 read a book that is intended (presumably) for the general public and find that I can make neither head nor tail of it, it never occurs to me that this is because 1 am lacking in intelligence. Rather, 1 reach the calmly assured opinion that the author is either a poor writer, a confused thinker, or, most likely, both. Holding these views, it is not surprising that 1 "opt for a clearer but more pedestrian" style in my own writing. For one thing, my business and my passion (even in my fiction THE LEFT HAND OF THE ELECTRON 15 writing) is to explain. Partly it is the missionary instinct that makes me yearn to make my readers see and understand the uni- verse as I see and understand it, so that they may enjoy it as I do. Partly, also, I do it because the effort to put things on paper clearly enough to make the reader understand, makes it possible for me to understand, too. I try to teach because whether or not I succeed in teaching others, I invariably succeed in teaching myself. Yet I must admit that sometimes this self-imposed task of mine is harder than other times. Continuing the exposition on parity and related topics begun in Chapter 1 is one of the harder times, but then no one ever promised me a rose garden, so let's continue — The conservation laws are the basic generalizations of physics and of the physics aspects of all other sciences. In general, a con- servation law says that some particular overall measured property of a closed system (one that is not interacting with any other part of the universe) remains constant regardless of any changes taking place within the system. For instance, the total quantity of energy within a closed system is always the same regardless of changes within the system and this is called "the law of con- servation of energy." The law of conservation of energy is a great convenience to physicists and is probably the most important single conservation law, and therefore the most important single law of any kind in all of science. Yet it does not seem to carry a note of overwhelm- ing necessity about it. Why should energy be conserved? Why shouldn't the energy of a closed system increase now and then, or decrease? Actually, we can't think of a reason, if we think of energy only. We simply have to accept the law as fitting observation. The conservation laws, however, seem to be connected with symmetries in the universe. It can be shown, for instance, that if one assumes time to be symmetrical, one must expect energy to be conserved. That time is symmetrical means that any portion of 16 THE PROBLEM OF LEFT AND RIGHT it is like any other and that the laws of nature therefore display "invariance with time" and are the same at any time. In a rough and ready way, this has always been assumed by man kin d — for closed systems. If a certain procedure lights a fire or smelts copper ore or raises bread dough on one day, the same procedure should also work the next day or the next year under similar conditions. If it doesn't, the assumption is that you no longer have a closed system. There may be interference from the outside in the form (mystics would say) of a malicious witch or an evil spirit, or in the form (rationalists would say) of unex- pected moisture in the wood, impurities in the ore, or coolness in the oven. If we avoid complications by considering the simplest possible for ms of matter — subatomic particles moving in response to the various fields produced by themselves and their neighbors — we readily assume that they will obey the same laws at any moment in time. If a system of subatomic particles were to be transferred by some time machine to a point in time a century ago or a million years ago, or a million years in the future, the change in time could not be detected by studying the behavior of the sub- atomic particles only. And if that is true, the law of conservation of energy is true. Of course, invariance with time is just as much an assumption as the conservation of energy is, and assumptions may not square with observation. Thus, some theoretical physicists have specu- lated that the gravitational interaction may be weakening in intensity very slowly with time. In that case, you could tell an abrupt change in time by noting (in theory) an abrupt change in the strength of the gravitational field produced by the particles being studied. Such a change in gravitational intensity with time has not yet been actually demonstrated, but if it existed, the law of conservation of energy would be not quite true. Putting that possibility to one side, we end with two equiv- alent assumptions: 1) energy is conserved in a closed system, and 2) the laws of nature are invariant with time. Either both statements are correct or both are incorrect, but it THE LEFT HAND OF THE ELECTRON 17 is the second, it seems to me, that seems more intuitively neces- sary to us. We might not be bothered by having a little energy created or destroyed now and then, but we would somehow feel very uncomfortable with a universe in which the laws of nature changed from day to day. Consider, next, the law of conservation of momentum. The total momentum (mass times velocity) of a closed system does not vary with changes within the system. It is the conservation of momentum that allows billiard sharps to work with mathematical precision. (There is also an independent law of conservation of angular momentum, where circular movement about some point or line is considered.) Both conservation laws, that of momentum and that of angular momentum, depend on the fact that the laws of nature are in- variant with position in space. In other words, if a group of sub- atomic particles is instantaneously shifted from here to the neighborhood of Mars, or of a distant galaxy, you could not tell by observing the subatomic particles alone that such a shift had taken place. (Actually, the gravitational intensity due to neighbor- ing masses of matter would very likely be different, but we are dealing with the ideal situation of fields originating only with the particles within the closed system, so we ignore outside gravita- tion.) Again, the necessity of invariance with space is more easily ac- cepted than the necessity of the conservation of momentum or of angular momentum. Most other conservation laws also involve invariances of this sort, but not of anything that can be reduced to such easily in- tuitive concepts as the symmetry of space and time. — Parity is an exception. In 1927, the Hungarian physicist Eugene P. Wigner showed that conservation of parity is equivalent to right-left symmetry. This means that for parity to be conserved there must be no reason to prefer the right direction to the left or vice versa in 18 THE PROBLEM OF LEFT AND RIGHT considering the laws of nature. If one billiard ball hits another to the right of center and bounces off to the right, it will bounce off to the left in just the same way if it hits the other ball to the left of center. If a ball bouncing off to the right is reflected in a mirror that is held parallel to the original line of travel, the moving ball in the mirror seems to bounce off to the left. If you were shown diagrams of the movement of the real ball and of the movement of the nrirror-image ball, you could not tell from the diagrams alone, which was real and which the image. Both would be following the laws of nature perfectly well. If a billiard ball is itself perfectly spherical and unmarked it would show left-right symmetry. That is, its image would also be perfectly spherical and unmarked, and if you were shown a photo- graph of both the ball itself and the image, you couldn't tell which was which from the appearance alone. Of course, if the billiard ball had some asymmetric marking on it, like the number 7, you could tell which was real and which was the image, because the number 7 would be "backward" on the image. The trickiness of the nrirror-image business is confused because we ourselves are asymmetric. Not only are certain inner organs (the liver, stomach, spleen, and pancreas) to one side or the other of the central plane, but some perfectly visible parts (the part in the hair, as an example, or certain skin markings) are also. This means we can easily tell whether a picture of ourselves (or some other familiar individual) is of us as we are or of a mirror image by noting that the part in the hair is on the "wrong side," for instance. This gives us the illusion that telling left from right is an easy thing, when actually it isn't. Suppose you had to identify left and right to some stranger where the human body could not be used as reference, to a Martian who couldn't see you, for instance. You might do it by reference to the Earth itself, if the Martian could make out its surface, for the continental configurations are asym- metric, but what if you were talking with someone far out near Alpha Centauri. THE LEFT HAND OF THE ELECTRON lO The situation is more straightforward if we consider subatomic particles and assume them (barring information to the contrary) to be left-right symmetric, like perfectly spherical unmarked bil- liard balls. In that case if you took a photograph of the particle and of its mirror image, you could not tell from the appearance alone which was particle and which mirror image. If the particle were doing something toward our left, then the mirror image would be doing the equivalent toward our right. If, however, both the leftward act and the rightward act were equally possible by the laws of nature, you still couldn't tell which was particle and which was mirror image. — And that is precisely the situation that prevails when the law of conservation of parity holds true. But what if the law of conservation of parity is not true under certain conditions. Under those conditions, then, the particle is asymmetric or is working asymmetrically; that is, doing something leftward which can't be done rightward, or vice versa. In that case, you can say, "This is the particle and this is the image. I can tell because the image is backward (or because the image is doing something which is impossible)." This is equivalent to recognizing that a representation of a friend of ours is actually a mirror image because his hair part is on the wrong side or because he seems to be writing fluently with his left hand when you know he is actually right-handed. When Lee and Yang (see Chapter 1) suggested that the law of conservation of parity didn't hold in weak nuclear interactions, that meant one ought to be able to differentiate between a weak nuclear event and its mirror image. — And one common weak nuclear event is the emission of an electron by an atomic nucleus. The atomic nucleus can be considered as a spinning particle, which is symmetrical east and west and also north and south (just as the Earth is). If we take the mirror image of the particle (the "image-particle"), it seems to be spinning in the "wrong direc- tion," but are you sure? If you turn the image-particle upside down, it is then spinning in the right direction and it still looks 20 THE PROBLEM OF LEFT AND RIGHT just like the particle. You can't differentiate between the particle and the image-particle by the direction of its spin because you can't tell whether the particle or the image-particle is right side up or upside down. As far as spin is concerned, an upside-down image-particle looks just like a right-side-up particle. Of course, a spinning particle has two poles, a north pole and a south pole, and to all appearances we can tell which is which. By lining the particle up with a strong magnetic field we can com- pare the direction of the particle's axis of rotation with that of the Earth and identify the north and south pole. In that way we could tell whether the particle was right side up or upside down. Ah, but we are using the Earth as a reference here and the Earth is asymmetric thanks to the position and shape of the con- tinents. If we didn't use the Earth as reference (and we shouldn't because we ought to be able to work out the behavior of sub- atomic particles in deep space far from the Earth) there would be no way of telling north pole from south pole. Whether we con- sidered spin or poles, we couldn't tell a symmetrical particle from its mirror image. But suppose the particle gives off an electron. Such an electron tends to fly off from one of the poles, but from which? Suppose it could fly off from either pole with equal ease. In that case, if we were dealing with a trillion nuclei giving off a trillion electrons, half would fly off one pole and half off the other. We could not distinguish one pole from the other and we still couldn't distin- guish the particle from the image-particle. On the other hand, if the electrons tended to come off from one pole more often than from the other, we would have a marker for one of the poles. We could say, "Viewing the particle from a point above the pole that gives off the electrons, it rotates counter- clockwise. That means that this other particle is actually an image- particle, because viewed in that manner it rotates clockwise." This is exactly what should be true if the law of conservation of parity does not hold in the case of electron emission by nuclei. But is it true? When atomic nuclei (trillions of them) are shooting off electrons, the electrons come off in every direction THE LEFT HAND OF THE ELECTRON 21 equally — but that is only because the nuclear poles are facing in every direction, in which case electrons would shoot off in all ways alike whether they were coming from one pole only or from both poles equally. In order to check whether the electrons are coming from both poles or from one pole only, the nuclei must be lined up so that all the north poles are pointing in the same direction. To do this, the nuclei must be lined up by a powerful magnetic field and must be cooled to nearly absolute zero so that they have no energy that will vibrate them out of line. After Lee and Yang made their suggestion, Madame Chien- Shiung Wu, a fellow physics professor at Columbia University, performed exactly this experiment. Cobalt-6o nuclei, lined up ap- propriately, shot electrons off the south pole, not the north pole. In this way, it was proven that the law of conservation of parity did not hold for weak nuclear interactions. This meant one could distinguish between left and right in such cases, and the electron, when involved in weak nuclear interactions, tended to act left- ward rather than rightward, so that it can be said to be "left- handed.” The electron, which carries a unit negative electric charge, has another kind of "image." There is a particle exactly like the elec- tron, but with a unit positive electric charge. It is the "positron." Indeed every charged particle has a twin with an opposite charge, an "antiparticle." There is a mathematical operation which converts the expression that describes a particle into one that de- scribes the equivalent antiparticle (or vice versa). This operation is called "charge conjugation." As it happens, if a particle is left-handed, its antiparticle is right-handed, and vice versa. Observe then, that if an electron is doing something left- handedly, its mirror image would seem to be an electron doing it right-handedly, which is impossible — and the impossibility would serve to distinguish the image from the particle. On the other hand, if you employed the charge conjugation 22 THE PROBLEM OF LEFT AND RIGHT operation, you would change a left-handed electron into a left- handed positron. The latter is also impossible and this impos- sibility would serve to distinguish the image fiom the particle. In weak nuclear interactions, then, not only does the law of conservation of parity break down, but also the law of conserva- tion of charge conjugation.* However, suppose you not only alter the right-left of the elec- tron by imagining its mirror image, but also imagine that at the same time you have altered the charge from negative to positive. You have effected both a parity change and a charge conjugation change. The result of this double shift would be the conversion of a left-handed electron into a right-handed positron. Since left- handed electrons and right-handed positrons are both possible, you cannot tell by simply looking at a diagram of each, which is the original particle and which the image. In other words, although neither parity nor charge conjugation is conserved in weak nuclear interactions, the combination of the two is conserved. Using abbreviations we say that there is neither P conservation nor C conservation in weak nuclear interactions, but there is, however, CP conservation. It may not be clear to you how it is possible for two items to be individually not conserved, yet to be conserved together. Or (to put it in equivalent fashion) you may not see how two objects, each easily distinguishable from its mirror image, are no longer so distinguishable if taken together. Well, then, consider — The letter b, reflected in the m ir ror is d. The letter d, reflected in the minor is b. Thus, both b and d are easily distinguished from their mirror images. On the other hand, if the combination bd is reflected in a mirror, the image is also bd. Both b and d are individually in- verted and the order in which they occur is inverted, too. All the * Both conservation laws are true in strong nuclear interactions, however. In strong nuclear interactions, not only are leftward and rightward equally natural at all times, but anything a charged particle can do. the oppositely charged antiparticle can also do. THE LEFT HAND OF THE ELECTRON 23 inversions cancel and the net result is that although b and d are altered by reflection, the combination bd is not. (Try it yourself with printed lower-case letters and a mirror.) Let's point out one more thing about left-right reflection. Sup- pose the solar system were reflected in a m ir ror. If we observed the image, we would see that all the planets were circling the Sun the "wrong way" and that the Moon was circling the Barth the "wrong way," and that the Sun and all the planets were rotating on their axes the "wrong way." If you ignored the asymmetry of the surface structure of the planets, and just considered each world in the solar system to be a featureless sphere, then you could not tell the image from the real thing from their motions alone. The fact that everything was turning the "wrong way" means nothing, for if you observe the image while standing on your - head, then everything is turning the "right way" again, and in outer space there is no way of dis- tinguishing between standing "upright" and standing "on your head." And certainly the gravitational interaction, which is the pre- dominant factor in the solar' system's working, is unaffected by the reversal of right and left. If all the revolutions and rotations in the solar' system were suddenly reversed, gravitational interac- tions would account for the reversed motions as adequately and as neatly as for the originals. But consider this — Suppose that we didn't use a m ir ror at all. Imagine, instead, that the direction of time reversed itself. The result would be like that of running a movie film backward. With time reversed, the Earth would seem to be going "backward" about the Sun. All the planets would seem to be going "backward" about the Sun, and the Moon to be going "backward" about the Earth. All the bodies of the solar system would be spinning "backward" about their axis. But notice that the "backward" that takes place on reversing time, is just the same as the "wrong way" that takes place in the 24 THE PROBLEM OF LEFT AND EIGHT mirror image. Reversing the direction of time flow and mirror- imaging space produce the same effect. And there is no way of telling from observing the motions of the solar system alone whether time is flowing forward or backward. This inability to tell the direction of time flow is also true in the case of sub- atomic reactions (T conservation).* Or consider this — An electron moving through a magnetic field pointing in a par- ticular direction will veer to the right. The positron, with an op- posite charge, would, when moving in the same direction through the same magnetic field, veer to the left. The two motions are mirror images, so that in this case the shift from a charge to its opposite also produces the same effect as a left-right shift. Or suppose we reverse the direction of time flow. An electron moving through a magnetic field may veer to its right, but if a picture is taken of the motion and the film is reversed and pro- jected, the electron will seem to be moving backward and, in doing so, will veer to its left. Again, time flow and left-right sym- metry are connected. It would seem then that charge conjugation (C), parity (P), and time reversal (T) are all rather closely related and all some- how connected with left-right symmetry. If, then, left-right sym- metry breaks down in weak nuclear interaction with respect to one of these, the symmetry can be restored with one or both others. If a particle is doing something leftward, and its image is doing something rightward, which is impossible (so that the image can be spotted through a breakdown in P conservation), you can re- verse the charge on the image-particle and convert the action into a possibility. If the action is impossible even with the reversed charge (so that the image can be spotted through a breakdown in CP conservation), you can reverse the direction of time flow, * We can tell the direction of time flow under ordinary conditions easily enough because of entropy-change effects. This produces the equivalent of an asymmetry in time. Where entropy change is zero, however, as in plane- tary motions and subatomic events, T is conseived. THE LEFT HAND OF THE ELECTRON 2$ and then you will find the action is possible. In other words, there is "CPT conservation" in the weak nuclear interaction.* The result is that the universe is symmetrical, as it has always been thought to be, with respect to strong nuclear interactions, electromagnetic interactions and gravitational interactions. Only weak nuclear interactions have been in question and there the failure of the law of conservation of parity seemed to intro- duce a basic asymmetry to the universe. The broadening of the concept to CPT conservation restored the symmetry — but only in theory. Does CPT conservation actually present us with a symmetrical universe in practice? As far as P (parity) is concerned, there is an equal supply of Tightness and leftness in the universe. As far as T (time reversal) is concerned, there is also an equal supply of pastness and futureness. But where C (charge conjugation) is concerned, symmetry in practice breaks down. The most common subatomic particles to be involved in weak nuclear interactions are the electron and the neutrino. For sym- metry to exist in practice, then, there should be equal supplies of electrons and positrons and equal supplies of neutrinos and anti- neutrinos. This, however, is not so. Certainly on Earth, almost certainly throughout our Galaxy, and, for anything we know to the contrary, throughout the entire universe, there are vast numbers of electrons and neutrinos, and hardly any positrons and antineutrinos. The universe then — at least our universe — or at the very least our section of our universe — is electronically left-handed and that may have had an interesting effect on the development of life. In order to explain that, I must change the subject radically, however, and make a new start. That I will do in the next chapter. * Actually, there was some indication in recent years that CPT is not invariably conserved in weak nuclear interactions and physicists have been examining the possible consequences in rather perturbed fashion. However, all the returns don't seem to be in Here- and we'll have to wait and see. 3 SEEING DOUBLE I currently do my writing in a two-room suite in a hotel, and about a month ago I became aware of someone banging loudly against the wall in the corridor outside. Naturally, I was furious. Did whoever it was not realize that within my rooms the most delicate work of artistic creation was going on? I stepped into the corridor and there, on a ladder, at the ele- vators, was an honest workingman banging a hole into the wall for some arcane purpose of his own. "Sir," I said, with frowning courtesy, "how long do you intend to make the world hideous with your banging at that hole?" And the horny-handed son of toil turned his sweat-streaked face in my direction and answered jauntily, "How long did it take Michelangelo to do the ceiling in the Sistine Chapel?" What could I do? I burst out laughing, went back to my cell, and worked cheerfully along to the tune of banging which I no longer resented since it was produced by an artist who knew his own worth. Things take as long as they take, in other words. And even Michelangelo's long stint on his back, painting that fresco, pales into insignificance in comparison to the length of the intervals it took to build some corner or other of the majestic structure of science. In the seventeenth century, for instance, a question arose about light which wasn't answered for 148 years, despite the fact that, till it was answered, no theory as to the nature of light could pos- sibly hold water. The story begins with Isaac Newton, who, in 1666, passed a beam of sunlight through a prism and found that the beam was SEEING DOUBLE 2J spread out into a rainhow lik e band which he called a "spectrum." ' • Newton felt that since light traveled in a straight path, it must be made up of a stream of veiy fine particles, moving at an enor- mous speed. These particles differed among themselves in some way so that they produced the sensations of different cold's. In sunlight, all the different particles were mixed evenly and the effect was to impress our eye as white light. In passing obhquely into glass, however, the light particles bent sharply in their path; that is, they were "refracted." Particles dif- fering in their color nature were refracted by different amounts so that the cold's in white light were separated within the glass. In an ordinary sheet of glass, with two parallel faces, the effect was reversed when the light emerged once more from the other side, so that the cold's were again merged into white light. In a prism, it was different. The light particles bent sharply when they entered one side of the triangular' piece of glass, and then bent a second time in the same direction on emerging through a second, non-parallel side. The colors, separated on en- tering the prism, were even farther separated on emerging. All this made excellent sense, and Newton backed it up with careful experimentation and reasoning. And yet exactly what was different about the particles that gave rise to the various colors, Newton couldn't say. His contemporary the Dutch physicist Christiaan Huygens sug- gested in 1678 that light was a wave phenomenon. This made it possible to explain the different color's easily. A light wave would have to have some particular' length, and light of different wave- lengths might well impress the eyes as of different color's (just as sound of different wavelengths impresses the ears as of different pitch). Still, waves had their own problems. All man's experience with waves (water waves, for instance, and sound waves) made it clear' that waves curved around obstructions. Light on the other hand traveled in a straight line past obstructions and cast sharp shadows. Huygens tried to explain that away by presenting a mathemati- 28 THE PROBLEM OF LEFT AND RIGHT cal line of reasoning that showed that the ability to curve about an obstruction depended on the length of the wave. If light waves were much shorter than sound waves or water waves, they would then not bend, detectably, about ordinary obstructions. Newton recognized the convenience of the wave theory, but could not go along with the suggestion of waves so tiny they would cast sharp shadows. He stuck to particles and such was his eventual prestige that scientists, by and large, went along with the particle theory of light in order not to place themselves in dis- agreement with Newton. But in 1669, a Danish physician, Erasmus Bartholinus — a thoroughly obscure individual — made an observation which as- sured him a place in the history of science, for it raised a question the giants could not answer. Bartholinus had received a transparent crystal which had been obtained in Iceland, so that it became known as "Iceland spar," where "spar" is an old-fashioned term for a non-metallic mineral.* The crystal was shaped like a rhombohedron (a kind of slanted cube), with six flat faces, each one parallel to the one on the op- posite side. Bartholinus was studying the properties of this crystal and I presume he placed it on a piece of paper with writing or printing on it, on one occasion. When he picked it up, he noticed that the writing or printing was double when viewed through the crystal. In fact, when one looked through the crystal, it turned out one was seeing double. Apparently each beam of light entering the crystal was refracted, but not all to the same extent. Part of the light was refracted a certain amount and the remainder another and greater amount, so that though one beam entered the crystal, two beams emerged. The phenomenon was called "double re- fraction." Any theory of light had to explain double refraction, and neither Huygens nor Newton could do so. Apparently, the waves, or particles, of light must fall into two sharply defined classes so * Actually, Iceland spar is a transparent variety of calcium carbonate, if that helps any. SEEING DOUBLE 29 that one class can behave in one way and the other class in an- other. The two-way difference can have nothing to do with color, for all colors of light were equally double-refracted by Iceland spar. Huygens' view of light waves was that they were "longitudinal waves"; that is, similar to sound waves in structure (though much shorter in length) and that they represented a series of compres- sions and rarefactions in the ether they passed through. Huygens did not see how such longitudinal waves could fall into two sharply different classes. Nor could Newton see how light particles could be divided into two sharp classes. He speculated, rather vaguely, that the particles might differ among themselves in some fashion analogous to the two opposed poles of a magnet, but he didn't follow that up, since he was at a loss for any way of finding evidence for the suggestion. Physicists were forced to back away. Bartholinus' observation didn't fit either of the current theories of light, so, as far as pos- sible, it was to be ignored. This was not wickedness on the part of scientists; nor the ob- tuse workings of a conspiratorial "establishment." On the con- trary, it makes sense. Suppose a piece doesn't seem to fit a jigsaw puzzle. If you stop everything and start worrying exclusively about that troublesome piece, you may never get anywhere. If, however, you ignore the piece and continue working at other parts of the jigsaw, using whatever system seems convenient, you may eventually reach a point where, through the other work, new understandings are reached, and suddenly the old piece that was once so troublesome fits into place with no trouble at all. Double refraction was not forgotten altogether, of course. Even as late as 1808, it was still sticking in the scientific gizzard, and the Paris Academy offered a prize for the best mathematical treat- ment of the subject. A twenty-three-year-old French army engi- neer, named Etienne Louis Malus (who accepted Newton's particle theory) decided to see what he could do in that direction. 30 THE PROBLEM OF LEFT AND RIGHT He got some doubly refracting crystals and began to experiment with them. As it happened, he did not win the prize, but he made an interesting observation and coined a phrase that entered the scientific vocabulary. From his room he could see out on the Luxembourg Palace and, at one time, sunlight was reflected from a window of that palace into his room. Idly, Malus pointed a doubly refracting crys- tal in that direction, expecting to look through it and see two windows. He did not! He saw only one window. Apparently what happened was that the window, in reflecting the sunlight, reflected only one of the two classes of light particles. Malus remembered that Newton had said that the light particle varieties might be analogous to the opposing poles of a magnet. Thinking along those lines, he felt that only one pole of light had been reflected, and that the beam shining into his room contained only particles with that one pole. Malus therefore spoke of the light beam that entered his room as consisting of "polarized light." The phrase stands to this day, even though it is based on a false speculation, and even though the notion of poles of light was, in actual fact, being killed dead even before Malus had made his observation. In 1801, you see, an English physician, Thomas Young, began a series of experiments in which he showed that one beam of light could somehow cancel another intermittently, so that the two would not combine to give a smooth field of light, but rather a series of bands, alternately light and dark. If light consisted of particles, such "interference" was extremely difficult to explain. How could one particle cancel another? If light consisted of waves, however, interference was childishly easy to explain. If light consisted of alternate rarefactions and compressions, for instance, then if two light beams fitted together so that the compressed area in one beam fell on the rarefied area in the other and vice versa, the two lights would indeed cancel out into darkness. Young was able to explain every characteristic of his interfer- ence pattern by Huygens' wave theory. To be sure, many physi- SEEING DOUBLE 31 cists (especially English physicists) tried to object, in the name of Newton. However, not even the most glorious name can long resist observations that anyone can confirm and explanations that explain perfectly. — So the wave theory won out. Yet Young could not explain double refraction any better than Huygens had. But then, in 1817, a French physicist, Augustin Jean Fresnel, suggested that perhaps the light waves were not longitudinal after the fashion of sound waves, and did not represent alter- nate compressions and rarefactions in the ether. Perhaps, instead, they were "transverse waves," like those on water surfaces; waves which moved up and down at right angles to the line of propaga- tion of the wave. Transverse waves could explain interference just as well as longi- tudinal waves did. If two light beams merged, and one was waving up where the other was waving down, and vice versa, the two would cancel, and two lights would make darkness. Water waves, which serve as a model for light waves, can only move up and down at right angles to the two-dimensional water surface. A ray of light, however, has greater freedom. Imagine such a ray moving toward you. It could wave up and down, or right and left, or anything in between and always be waving at right angles to the direction in which it was moving. (You can see what this means concretely, if you tie one end of a long rope to a post and make waves in it, up and down, right and left, or obliquely.) Once such transverse waves were proposed, they were accepted with remarkably little trouble, for through them, the phenome- non of double refraction could finally be explained, 148 years after the problem had arisen. To see that, consider that the light waves in an ordinary beam of light could be waving in all possible directions at right angles to the direction of travel — up and down, left and right, and all de- grees of in-betweenness. That would represent ordinary or "un- polarized" light 32 THE PROBLEM OF LEFT AND RIGHT Suppose, though, there were some way of dividing the light into two varieties, one in which all the waves move up and down, and the other in which all the waves move left and right. For each wave in unpolarized light which vibrates obliquely, there would be a division into two waves, of lesser energy, of the permitted classes. If a particular wave were just at forty-five degrees to the vertical, just halfway between the up and down and the left and right, it would be divided into two waves, one up and down and the other left and right, each with half the energy of the original. If the oblique wave were nearer horizontal than vertical, then it would be broken up into two waves, with the left and right having the greater supply of energy. If it were nearer the vertical, then the up and down would end with the greater supply of energy. It is easy to show, in fact, that a beam of unpolarized light can be divided into two beams of equal energy, in one of which all the transverse waves are in one direction, while in the other all the transverse waves are in a plane at right angles to the first. Since in each case all the waves move in a single plane, the un- polarized beam of light can be viewed as broken up into two mutually perpendicular "plane -polarized" beams. But what causes light to break up into plane -polarized beams? Certain crystals do. Crystals are made up of serried ranks and files of atoms arranged in very orderly array. Light, in passing through, is sometimes compelled to take up waves in certain planes only. (You can see a crude analogy of this if you pass a rope through a picket fence and tie it to a pole somewhere on the other side. If you make up-and-down waves in the rope, they will pass through the opening between the pickets, so that the rope on the other side of the fence also waves. If you make waves left and right, the pickets on either side of the opening stop those waves and the rope on the other side of the pickets does not wave. If you make the rope wave in every which way, only those waves which will fit between the pickets at least partly will get through, and on the other side of the fence, whatever you do, there will only SEEING DOUBLE 33 be up-and-down waves. The picket fence polarizes the "rope waves.") Crystals such as Iceland spar will permit only two planes of vibration, one perpendicular to the other. Unpolarized light en- tering Iceland spar' breaks up into two mutually perpendicular plane-polarized beams within. The two beams of polarized light interact differently with the atoms, travel at different velocities and the slower beam is refracted through a greater angle. The two bea ms take separate paths within the crystal and emerge in different places. It is for that reason that looking through Iceland spar causes you to see double, and Bartholinus' puzzle is solved. Plane polarization can also take place on reflection. If an unpolarized beam strikes a reflecting surface at an angle, it often happens that those particular' waves which occupy a certain plane are more efficiently reflected than those in other planes. The re- flected beam is then heavily or even entirely plane-polarized and Malus' puzzle is solved. In 1828, a Scottish physicist, William Nicol, introduced a new refinement to Iceland spar'. He sawed a crystal in half in a certain fashion* and cemented the halves together with Canadian balsam. When light enters the crystal, it splits up into two plane-polarized beams, which travel in slightly different directions and hit the Canadian balsam seam at slightly different angles. The one that hits it at the lesser angle to the perpendicular' passes through into the other half of the crystal and eventually emerges into open ah'. The one that hits it at the greater angle is reflected and never enters the other half of the crystal. In other words, a beam of unpolarized light enters the "Nicol prism" at one end and a single beam of plane-polarized light emerges at the other end. Now imagine two Nicol prisms lined up in such a way that a * I am tempted every once in a while to present diagrams, and on rare occasions I do. I am, however, primarily a word-man and I try not to lean on pictorial crutches. In this case, the exact manner of dividing the crystal doesn't affect the argument, so the heck with it. 34 THE PROBLEM OF LEFT AND RIGHT beam of light passing through one will continue on into the sec- ond. If the two Nicol prisms are lined up parallel, that is, with the atom arrangements oriented in identical fashion in both, the beam of polarized light emerging from the first passes also through the second without trouble. (It is like a rope passing through two picket fences in both of which the pickets are up and down. An up-and-down rope wave that passes between the pickets in the first fence will also pass between the pickets in the second.) But what if the two Nicol prisms are oriented perpendicularly to each other? The plane-polarized beam emerging from the first Nicol prism is refracted through a greater angle by the second one and is reflected from the Canadian balsam seam in it. No light at all emerges from the second prism. (If we go back to the picket fence analogy, and have the pickets in the second fence arranged horizontally, you will see that any up-and-down waves that get through the first fence will be stopped by the second. No rope waves of any kind can go through two fences in one of which the pickets are vertical and in the other horizontal.) Suppose, next, that you arrange to have the first Nicol prism fixed in place, but allow the second Nicol prism to be rotated freely. Arrange also an eyepiece through which you can look and see the light that passes through both Nicol prisms. Begin with the two Nicol prisms arranged in parallel fashion. You will see a bright light in the eyepiece. Slowly rotate the second prism, which is nearer your eye. Less and less of the light emerg- ing from the first prism can get through the second, since more and more of it is reflected at the second's Canadian balsam seam. The light you see becomes dimmer and dimmer as you rotate the second prism, until, when you have turned through ninety de- grees, you see no light at ah. The same thing happens whether you rotate the prism clockwise or counterclockwise. Using such a pan of Nicol prisms you can determine the plane of vibration of a beam of polarized light. Suppose such a beam emerges from the fixed Nicol prism, but you are not sure as to exactly how that prism is oriented. That means you don't know SEEING DOUBLE 35 the location of the plane of vibration of the light emerging. In that case, you need only turn the rotating Nicol prism until the beam of light you see through it is at its brightest.* At that point, the second prism is oriented parallel to the first and from the position of the second you know the plane of vibration of the polarized light. For this reason the first, fixed, Nicol prism is called the "polar- izer," and the second, rotating, one, the "analyzer." Now imagine an instrument in which there is a space between polarizer and analyzer into which a standard tube can be placed containing some liquid transparent to light. To make sure con- ditions are always the same, the temperature is kept at a fixed level, light of a single fixed wavelength is used, and so on. If the tube contains distilled water, nothing happens to the plane of polarized light emerging from the polarizer. The air, the glass, the water all may and do absorb a trifle of light, but the analyzer continues to mark the plane at the same point. If a salt solution is used in place of distilled water, the same thing is true. But place sugar solution in the tube, and something new hap- pens. The light you see through the analyzer is now greatly dimmed and this is not the result of absorption. Sugar solution doesn't absorb light significantly more than water itself does. Besides, if you rotate the analyzer, the light brightens again. You can eventually get it as bright as it was originally, provided you completely alter the orientation of the analyzer. What it amounts to is that the sugar solution has rotated the plane of polarized light. Anything which does this is said to display "opti- cal activity." The instrument used to detect optical activity and measure its extent is called a "polarimeter." A useful polarimeter was first devised in 1840 by the French physicist Jean Baptiste Biot. He had pioneered in the study of * It isn't so easy to tell when the light is brightest, but there is a device whereby the circle of light you see is divided into two half-circles and you turn the prism until the two half-circles are equally bright, something easy to determine. 36 THE PROBLEM OF LEFT AND RIGHT optical activity long before he devised the polaiimeter (to make his work easier and more precise) and even before Nicol had first constructed his prism. As early as 1813, for instance, Biot reported certain observations that were eventually interpreted according to the new transverse- wave theory. It turned out that a quartz crystal, correctly cut, ro- tated the plane of polarized light passing through it. What's more, the thicker the piece of quartz, the greater the angle through which the plane was rotated. And still further, some pieces of quartz ro- tated the plane clockwise and some rotated it counterclockwise. The usual way of reporting the clockwise rotation was to say that the plane of polarization had been rotated to the right. Ac- tually, this is a careless and ambiguous way of reporting it. If the plane is viewed as straight up and down, then the upper end of it is indeed rotated to the right when it is twisted clockwise, but the lower end is rotated to the left. Vice versa, in the case of counterclockwise rotation. However, once a phrase enters the literature it is har'd to change no matter how poor, inappropriate, or downright wrong it is. (Look at the phrase "polarized light" itself, for instance.) Conse- quently, something that rotates the plane of polarized light clockwise, is said to be "dextrorotatory" ("right-rotating") and something that rotates it counterclockwise is "levorotatory" ("left-rotating"). What Biot had shown was that there were two kinds of quartz crystals, dextrorotatory and levorotatory. Using initials, we can speak of d-quartz and Z-quartz. As it happens, quartz crystals are rather complicated in shape. In certain varieties of those crystals, just those varieties which show optical activity, it can be seen that there are certain small faces that occur on one side of the crystal, but not the other, in- troducing an asymmetry. What's more, there are two varieties of such crystals, one of which has the odd face on one side, the other of which has it on the other. The two asymmetric varieties of quartz crystals are minor SEEING DOUBLE 37 images. There is no way in which you can twist one variety through three-dimensional space in order to make it look like the other, any more than you can twist a right shoe so as to make it fit a left foot. And one of these varieties is dextrorotatory, while its mirror image is levorotatory. It was quite convincing to suppose that an asymmetric crystal will rotate the plane of polarized light. The asymmetry of the crys- tal must be such that the light beam, traveling through, must be constantly exposed to an asymmetric force, one which pulls, so to speak, more strongly in one direction than the other. So the plane twists and keeps on twisting at a steady rate the greater the distance it must pass through such a crystal. What's more, if a crystal twists the plane of light in one direction, it is inevitable that, all else being equal, the mirror-image crystal will twist the plane in the opposite direction. You might even argue further that any substance which will crystallize in either of two mirror-image forms will be optically active. Furthermore, if two mirror-image crystals are taken of the same substance and of the same thickness, and if all the circum- stances are equal (such as temperature and wavelength of light), then the two crystals will show optical activity to precisely the same extent — one clockwise, the other counterclockwise. And, indeed, all evidence ever gathered shows all of this to be perfectly correct. But then, Biot went on to spoil the whole thing by discover- ing that certain liquids, such as turpentine, and certain solutions, such as camphor in alcohol and sugar in water, are also optically active. This presents a problem. Optica] activity is tied in firmly with asymmetry in all work on crystals, but where is the asymmetry in the liquid state. None that any chemist could see in 1840. Once again, then, the solution of one problem in science served to raise another. (And thank heaven for that, or where would there be any interest in science?) Having solved Bartholinus' prob- lem and Malus' problem by establishing the existence of transverse 38 THE PROBLEM OF LEFT AND RIGHT light waves, science found itself with Biot's problem — how a liquid which seemed to have no asymmetry about it could produce an effect that seemed to be logically produced only by asymmetry. Which brings us to Louis Pasteur's first great adventure in sci- ence — next chapter. 4 THE 3-D MOLECULE In the days when I was actively teaching, full time, at a medical school, there was always the psychological difficulty of facing a sullen audience. The students had come to school to study medi- cine. They wanted white coats, a stethoscope, a tongue depressor, and a prescription pad. Instead, they found that for the first two years (at least, as it was in the days when I was actively teaching) they were subjected to the "basic sciences." That meant they had to listen to lectures veiy much in the style of those they had suffered through in col- lege. Some of those basic sciences had, at least, a clear' connection with what they recognized as the doctor business, especially anat- omy, where they had all the fun of slicing up cadavers. Of all the basic sciences, though, the one that seemed least immediately "rel- evant," farthest removed from the game of doctor-and-patient, most abstract, most collegiate, and most saturated with despised Ph.D.'s as professors was biochemistry. — And, of course, it was biochemistry that I taught. I tried various means of counteracting the natural contempt of medical student for biochemistry. The device which worked best (or, at least, gave me most pleasure) was to launch into a spirited account of "the greatest single discovery in all the history of medi- cine" — that is, the germ theory of disease. I can get very dramatic when pushed, and I would build up the discovery and its conse- quences to the loftiest possible pinnacle. And then I would say, "But, of course, as you probably all take for granted, no mere physician could so fundamentally revolution- ize medicine. The discoverer was Louis Pasteur, Ph.D., a bio- chemist." 40 THE PROBLEM OF LEFT AND RIGHT Pasteur's first great discovery, however, had nothing to do with medicine, but was a matter of straight chemistry. It involved the matter of optically active substances, a subject I discussed in the previous chapter. To see how he contributed, let's start at the be- ginning. In the wine-making process of the fermentation of grape juice, a sludgy substance separates and is called "tartar," a word of un- known origin. From this substance, the Swedish chemist Karl Wil- helm Scheele in 1769 isolated a compound which had acid properties and which he naturally called "tartaric acid." In itself this wasn't terribly important, but then in 1820, a Ger- man manufacturer of chemicals, Charles Kestner, prepared some- thing he felt ought to be tartaric acid and yet didn't seem to be. For one thing, it was distinctly less soluble than tartaric acid. A number of chemists obtained samples and studied it curiously. Eventually, the French chemist Joseph Louis Gay-Lussac named this substance "racemic acid" from the Latin word for a "cluster of grapes." The more closely racemic acid and tartaric acid were studied, the more puzzling were the differences in properties. Analysis showed that each acid had exactly the same proportion of exactly the same elements in their molecules. Using modern symbols, the formula for each compound was C |H f ,06. In the early nineteenth century, when the atomic theory had only been in existence for a quarter of a century or so, chemists had decided that every different molecule had a different atomic content, that it was, in fact, the difference of atomic content that was responsible for the difference of properties. Yet here were two substances, quite distinguishable, with molecules made up of the same proportions of the same elements. It was very disturbing, especially since this was not the first time such a thing had been reported. In 1830, the staunchly conservative Swedish chemist Jons Jakob Berzelius,* who didn't believe that molecules with equal structures * I have a tendency (as you may occasionally have noticed) to mention large numbers of scientists and to give the contribution of each whenever THE 3-D MOLECULE 41 but different properties were possible, examined both tartaric acid and racemic acid in detail. With considerable chagrin, he decided that even though he didn't believe it, it was nevertheless so. He bowed to the necessary, accepted the finding, and called such equal-structure-different-property compounds "isomers" from Greek words meaning "equal proportions" (of elements, that is). But how could isomers have the same atomic composition and yet be different substances? One possibility is that it is not just the number of atoms of each element that is distinctive, but their physical arrangement within the molecule. This thought, how- ever, was something chemists shuddered away from. The whole notion of atoms was a shaky one. Atoms were useful in explaining chemical properties but they could not be seen or detected in any way and they might very well be no more than convenient fictions. To start talking about actual arrangements within the molecules was to advance farther down the road of accepting atoms as real entities than most chemists cared to — or dared to. The phenomenon of isomerism was therefore left unaccounted for and kept suspended until such time as chemical advance might produce an explanation. One difference in properties between tartaric acid and racemic acid was particularly interesting. A solution of tartaric acid or of its salts (that is, compounds in which the acid hydrogen of the compound was replaced by an atom of such elements as sodium or potassium) was optically active. It rotated the plane of polar- ized light clockwise and was therefore dextrorotatory (see the previous chapter), so that the compound could well be called d-tartaric acid. A solution of racemic acid, on the other hand, was optically inactive. It did not rotate the plane of polarized light in either direction. This difference in properties was clearly demonstrated I get science-historical. This is not a matter of name-dropping. Every advance in science is the result of the co-operative labor of a number of people, and I like to demonstrate that. And I am careful to mention nationalities because it is also important to recognize the fact that science is international in scope. 42 THE PROBLEM OF LEFT AND RIGHT by the French chemist Jean Baptiste Biot, whom I mentioned in the previous chapter as a pioneer in the science of polarimetry. No one at the time knew why any substance should be optically active in solution, but they did know this — Those crystals known to be optically active had asymmetric structures. In that case, if one were to prepare crystals of tartaric acid and racemic acid or of their respective salts, it would surely turn out that those of the former were asymmetric and those of the latter, symmetric. In 1844, however, the German chemist Eilhardt Mitscherlich undertook this investigation. He formed crystals of the sodium ammonium salt of both tartaric acid and racemic acid, studied them carefully, and announced that the two substances had ab- solutely identical crystals. The basic findings of the budding science of polarimetry were blasted by this report and for the moment all was confusion. It was at this point that the young French chemist Louis Pas- teur entered the scene. He was only in his twenties and his scho- lastic record at school had been mediocre, yet he had the temerity to suspect it possible that Mitscherlich (a chemist of the first rank) might have been mistaken. After all, the crystals he studied were small and perhaps some tiny details were overlooked. Pasteur applied himself to the matter and began to produce the crystals and study them painstakingly under a hand lens. He finally decided that there was a definite asymmetry to the crystals of the sodium ammonium salt of tartaric acid. So far, so good. That, at least, was to be expected, since the substance was optically active. But was it possible now that the sodium ammonium salt of racemic acid yielded crystals of precisely the same sort, as Mitscherlich maintained? In that case, there would be asymmetric crystals of a substance which was not optically active, and that would be very unsettling. Pasteur produced and studied the crystals of the salt of racemic acid and found that they were indeed also asymmetric but that not all the crystals were identical. Some of the crystals were exactly like those of the sodium am- THE 3-D MOLECULE 43 monium salt of tartaric acid, but others were mir ror images of the first group and were asymmetric in the opposite sense. Could it be that racemic acid was half tartaric acid and half the mirror image of tartaric acid, and that the reason racemic acid was optically inactive was that it was made up of two parts, one pail of which neutralized the effect of the other pail? This had to be checked directly. Making use of his hand crystal and a pair of tweezers, Pasteur began to work over those tiny crystals of the racemic acid salt. All those which were right-handed he shoved to one side; all those which were left-handed, to the other. It took him a long time, for he wanted to make no mistake, but he was eventually done. He then dissolved each set of crystals in a separate sample of water and found both solutions to be optically active! One of the solutions was dextrorotatory, exactly as tartaric acid was. In fact, it was tartaric acid, in eveiy sense. The other was levorotatory, and differed from tartaric acid in rotating the plane of polarized light in the opposite direction. It was Z-tartaric acid. Pasteur's conclusion, announced in 1848, when he was only twenty-six, was that racemic acid was optically inactive only be- cause it consisted of equal quantities of d-tartaric acid and Z-tartaric acid. The announcement created a sensation and Biot, the grand old man of polarimetry, who was seventy-four year's old at the time, cautiously refused to accept Pasteur's finding. Pasteur there- fore undertook to demonstrate the matter to him in person. Biot gave the young man a sample of racemic acid which he had personally tested and which he knew to be optically inactive. Un- der Biot's shrewd, old eyes, alert for hanky-panky, Pasteur formed the salt, crystallized it, isolated the crystals, and separated them painstakingly by means of hand lens and tweezers. Biot then took over. He personally prepared the solutions from each set of crystals and placed them in the polarimeter. You guessed it. He found that both solutions were optically 44 THE PROBLEM OF LEFT AND RIGHT active, one in the opposite sense to the other. After that, with typical Gallic enthusiasm, he became fanatically pro-Pasteur. Actually, Pasteur had been most fortunate. When the sodium ammonium salt of racemic acid crystallizes, it doesn't have to form separate mirror-image crystals. It might also form combination crystals in each of which are equal numbers of molecules of d-tartaric acid and Z-tartaric acid. These combination crystals are symmetrical. Had Pasteur obtained these crystals he would still have noted their difference from those of the sodium ammonium salt of tar- taric acid and have refuted Mitscherlich. On the other hand, he would have missed the far greater discovery of the reason for the optical inactivity of racemic acid and he would also have missed having been the very first man to form optically active substances from an optically inactive start. As it happens, only symmetric-combination crystals are formed out of solutions above 28° C. (82° F.). It requires solutions of so- dium ammonium salt of racemic acid at temperatures below 28° C. to form separate sets of asymmetric crystals. Furthermore, the crystals formed are usually so tiny that they are far too small to separate with hand lens alone. It just happened that Pasteur was working at low temperatures and under conditions which pro- duced fairly good-sized crystals. Pasteur might be dismissed as an ordinary man who took ad- vantage of an unexpected good break, but (as I used to tell my biochemistry class) .he managed to take advantage of similarly unexpected good breaks every five years or so. After a while, you had to come to the conclusion that it was Pasteur who was re- markable and not the laws of chance. As Pasteur himself once said, "Chance favors the prepared mind." We all get our share of lucky breaks and the great man is he who is capable of recognizing a break when it comes, and of taking advantage of it. Pasteur continued to interest himself in the matter of the tar- taric acids. He found that if he heated d-tartaric acid for pro- THE 3-D MOLECULE 45 longed periods under certain conditions, some of the molecules would change to the Z-fonn and racemic acid would be produced. (Ever since, the ability to change optical activity to optical in- activity by heat or by some chemical process through forma- tion of some of the oppositely active form has been known as "racemization.") Pasteur also found a kind of tartaric acid which was optically inactive, which could not be separated into opposite forms under any conditions, and which possessed properties distinct from those of racemic acid. He called it meso-tartaric acid, from the Greek word for "intermediate," since it seemed intermediate between the d- and the Z-fomis of the acid. But all these facts could not explain the existence of optical activity in solutions. Granted that some crystals are symmetrical, while others are asymmetric in one sense or the other, still there are no crystals in solution. There are only molecules. Could not the molecules themselves retain the asymmetry of the crystals? Was not the asymmetry of the crystals but a reflec- tion of that of the molecules that composed them? Was not racemization a result of the heat-induced rearrangement of atoms within the molecule? Pasteur was sure of all this, but he could think of no way of proving it or of demonstrating what the ar- rangements must be. In the 1860's, to be sure, the German chemist Friedrich August Kekule worked out a system whereby a molecule was pictured not merely as a conglomeration of so many atoms of this element or that, but as a collection of atoms connected to one another in a definite arrangement (see Chapter 13). Little dashes were used between symbols of the elements to represent the "bonds" link- ing one atom to another, so that the molecule did get to look like a Tinker Toy. However, the Kekule structures were considered to be highly schematic and to be merely another useful tool for chemists who were working out organic structures and reactions. As in the case of atoms themselves, chemists were not prepared to say that the 46 THE PROBLEM OF LEFT AND RIGHT Kekule structures actually represented the true situation within the molecules. The Kekule structures did explain the existence of many isomer's, since they demonstrated gross differences in atomic arrangement even when the total numbers of atoms of each element present within the molecule were the same. The Kekule structures did not, however (as used originally), account for those "optical isomers" which differed only in the way in which they twisted the plane of polarized light. We next come to the Dutch chemist Jacobus Hendricus van't Hoff, who took up the problem in 1874, when he was only twenty- two. The following represents what may have been his line of rea- soning. According to the Kekule system, a carrion atom is represented by the letter C with four little bonds attached to it. Usually, these little bonds are shown pointing to the comers of an imaginary square, thus, j C I , so that the angle between any two adjacent bonds is ninety degrees. A carrion atom will combine with four hydrogen atoms to form the substance methane, which will then look like this: / \ Are the four - bonds identical? If each is different from the rest, somehow, then what would happen if one of the hydrogen atoms is replaced by a chlorine atom to form "methyl chloride"? Surely, there would then be four - different methyl chlorides, depend- ing on which of the four different bonds the chlorine atom hap- pened to attach itself to. But there aren't. There is only one methyl chloride and no more. This indicates that the four' carrion bonds are equivalent and, indeed, if the four' are drawn to the comers of a square, that THE 3-D MOLECULE 47 is what should be expected. One comer of the square should be no different from any other. Consider the situation, though, if two chlorine atoms replace hydrogen atoms to form "methylene chloride." Then, if we still deal with bonds pointing to the cornel's of a square, there ought to be two different methylene chlorides, depending on whether the two chlorine atoms are placed at adjacent comers of the square or at opposite comers, thus: H Cl H Cl V (R V h a ci h But there aren't. There is only one methylene chloride and no more, which shows that the Kekule structures can't possibly cor- respond to reality (and, of course, no one claimed that they did). One way in which they were almost certain not to correspond to reality was that all were drawn, for convenience' sake, in two dimensions — that is, in a plane — and surely it was unlikely that all molecules would be strictly planar in nature. The foui' bonds of the carbon atoms were almost certainly dis- tributed in three dimensions and it was only necessary to choose some 3-D arrangement in which each bond was equally adjacent to all three remaining bonds. Only then would there be only a single methylene chloride. The simplest way of arranging this was to have the four bonds pointing toward the apices of a tetrahedron.* The carbon atom then looks as though it were resting on three bonds forming a squat tripod while the fourth bond is pointing straight up. It doesn't matter which bond you point upward, the other three al- ways form the squat tripod. The carbon atom can thus stand in each of four different positions and look the same each time. * A tetrahedron is a solid bounded by four equilateral triangles. It can best be understood if it is inspected in the form of a three-dimensional model. Failing that, you are probably familiar with the shape of the Egyptian pyra- mids — a square base, with each wall slanting inward from one side of that base toward an apex on the top. Well, if you imagine a triangular base in- stead, you have a tetrahedron. SIMHBH AA HMH1 48 THE PROBLEM OF LEFT AND RIGHT What's more, any one bond is equally far from each of the other three. The angle between any two bonds is 109%°. If we deal with such a "tetrahedral carbon," then as long as two of the bonds are attached to identical atoms (or groups of atoms), it doesn't matter what atoms, or groups of atoms, are attached to the other two; in every case all possible arrangements are equiv- alent and only one molecule is formed. Thus, if attached to the four' bonds of a carbon atom are aaaa, or aaab, or aabb, or aabc, then it doesn't matter to which bond which atom is attached. If you attach them so as to form what seem to be two different arrangements, then by twisting the first arrangement so that some different bond faces upward, you can make it identical with the second. Not so when you have four different atoms or groups of atoms attached to the four bonds: abed. In that case, it turns out there are two different and distinct arrangements possible, one of which is the mir ror image of the other. No amount of twisting and turn- ing can then make one arrangement look like the other. A carbon atom to which four' different atoms or groups of atoms are attached is an "asymmetric carbon." It turns out that optically active organic substances invariably have asymmetric molecules if the Van't Hoff system is used. Al- most always there is at least one asymmetric carbon present. (Sometimes there is an asymmetric atom other than carbon pres- ent and sometimes the molecule as a whole is asymmetric even though none of the carbon atoms are.) In tartaric acid there are present two asymmetric carbon atoms. Either can be present in a certain configuration or in its mirror image. Let's refer to these arbitrarily as p and q (since q is the mir ror image of p ). If the two carbon atoms are pp, then we have d-tariaric acid and if qq, Z-tartaric acid. If the two halves of the molecule, each with one asymmetric carbon, were not identical, we would have two other optically ac- tive forms, pq and qp. In the case of tartaric acid, however, the two halves are identical in structure, so that pq and qp are identi- cal and, in each case, the optical activity of one half balances the THE 3-D MOLECULE 49 optical activity of the other. The net result is optical inactivity, and we have meso-tartaric acid. It is not easy to see all this without careful structural formulas, which I will not plague you with. The crucial point to remember is that from 1874 right down to the present day, all questions of optical activity, no matter how involved, have been satisfactorily explained by a careful consideration of the tetrahedral carbon atom together with similar structures for other atoms. Although our knowledge of atomic structure has enormously expanded and grown vastly more subtle in the century since, Van't Hoffs ge- ometrical picture remains as useful as ever. Van't Hoffs paper dealing with the tetrahedral atom appeared in a Dutch journal in September 1874. Two months later, a some- what similar paper appeared in a French journal. The author was a French chemist, Joseph Achille Le Bel, who was twenty-seven at the time. The two young men worked it out independently, so that both are given equal credit and one usually speaks of the Van't Hoff-Le Bel theory. The tetrahedral atom did not at once meet with the approval of all chemists. After all, there was still no direct evidence that atoms existed at all (and nothing direct enough to be convincing was to come for another generation). To some of the older and more conservative chemists, therefore, the new view, placing atom bonds just so, smacked of mysticism. In 1877, the German chemist Hermann Kolbe, then fifty-nine years old and full of renown, published a strong criticism of Van't Hoff and his views. It was quite within Kolbe's right to criticize, for it could be argued that the new view went beyond the foun- dations of chemistry as they then existed. In fact, an essential part of the practical working of the sci- entific method is that new ideas be subjected to searching criti- cism. They must be jumped at and hammered down in fair and sporting fashion, for one of the tests of the value of the new idea is its ability to survive hard knocks. 50 THE PROBLEM OF LEFT AND RIGHT Kolbe, however, was neither fair nor sporting. He characterized Van't Hoff as a "practically unknown chemist," which had noth- ing to do with the case. Even more unforgivably, he sneered at him for holding a position at the Veterinary School of Utrecht, managing to refer to it three times in a short space, thus exhibit- ing a rather unlovely professorial snobbeiy. Nevertheless, to those who think that the scientific "establish- ment" has the power to quash useful advances permanently at the simple behest of conservatism and snobbeiy, let it be stated that the tetrahedral atom was adopted with reasonable speed. It worked so well that not all of Kolbe's sour fulminations could stop it and Van't HofFs career went on untouched. (In fact, Van't Hoff rapidly became one of the leading physical chemists in the world and in 1901, when the Nobel prizes were established, the first award in chemistry went to him.) Kolbe is today best known, perhaps, not for his own veiy real contributions to chemistry, but for his diatribe against Van't Hoff — which is reprinted to amuse the audience.* And again a new advance meant new problems. Once the struc- ture of the carbon atom and its bonds had been worked out, and the details of molecules described in 3-D, a curious asymmetry turned out to exist in living tissue. That will be the subject of the next chapter. * I was recently challenged to give my views on a book of far-out theory by someone who said he wanted my views especially if unfavorable, as he was making a collection which would someday, in hindsight, make very amusing reading. The book of far-out theory seemed like nonsense to me but I was aware of Kolbe's misfortune and I hesitated. But then I decided that I was not going to duck the issue out of fear for posterity's views. I thought the theories were worthless and I said so. However, I was polite about it. That much costs nothing. 5 THE ASYMMETRY OF LIFE Only yesterday (as I write this) I was on a Dayton, Ohio, talk show, by telephone, one of those talk shows where the listeners are encouraged to call in questions. A young lady called in and said, "Dr. Asimov, who, in your opinion, did the most to improve modern science fiction?" I answered, after the barest hesitation, "John W. Campbell, Jr."* Whereupon she said, "Good! I'm Leslyn, his daughter." I carried on, of course, but inside I had a momentary dizzy spell. The reason for my second's hesitation in answering was that I had had to make a quick choice between two alternatives. I could have answered honestly and said, "Campbell!" as I did; or I could have played it for laughs, as I so often do, and said, "Me!" If I had had a visible audience and could have relied on hearing the laugh, I would undoubtedly have opted for the joke. As it was, with no possibility of a tangible reaction, I played it, thank goodness, straight — and avoided what would have been a terrible embarrass- ment. Well, it sometimes happens, in science, that a person has a choice of two alternatives and has to face the possibility that his choice, whichever it is, will stamp itself indelibly on the field. If he guesses wrong, that wrongness may be impossible to remove and will be a source of endless posthumous embarrassment. Thus Benjamin Franklin once decided that there were two types of electric fluid and that one of them was mobile and one sta- * John Campbell, who died on July 11, 1971, was, in my opinion (and that of many others) the outstanding personality of all time in the field of science fiction. I owe a personal debt to him past all calculation. I have said this elsewhere. I wish to say so here. 52 THE PROBLEM OF LEFT AND RIGHT tionary. Thus some substances, when nibbed, gained an excess •(+) of the mobile fluid, while others lost some of the mobile fluid and suffered a deficit ( — ). The one with the deficit showed the effect of the excess of the other, stationary fluid, so we could say that the two substances, (+) and ( — ), would show opposite electrical effects. And so they do. An amber rod and a glass rod show opposite electrical effects when rubbed. (They attract each other, once charged, instead of repelling each other as like charges — two glass rods, for instance — would.) The question was: Which had the ex- cess of the movable fluid and which the deficit; which was (+) and which was ( — -)? There was absolutely no way of telling and Fran kli n was forced to guess. He guessed the amber had the excess, assigned it (+) and the glass he assigned ( — ). That set the standard. All other charges were traced back to Franklin's decision on amber vs. glass and to the present day it is usually assumed in electrical engineer- ing that the current flows from the positive terminal to the nega- tive. By Franklin's standard the first two fundamental subatomic particles of ordinary matter were assigned their charge, too. The electron which tends to move toward the positive terminal is as- 