[CARILLON PLAYING "FAR ABOVE CAYUGA'S WATERS"] [CARILLON ENDS]
RICHARD FEYNMAN: Symmetry seems to be absolutely fascinating to the human mind. We like to look at symmetrical things in nature, such as balls, which are perfectly symmetrical, spheres, like planets and the sun, and so on, or symmetrical crystals in snowflakes, flowers, which are nearly symmetrical, and so on. But it's not the objects in nature-- the symmetry of the objects in nature-- that I want to talk about tonight. It's rather the symmetry of the physical laws themselves.
Now how can a physical law have a symmetry? It's easy to understand how an object has a symmetry. Of course, it can't. But physicists delight themselves by using ordinary words for something else.
And so, in this case, they have a thing about the physical laws, which is very close to symmetry of objects. And they call it the "symmetry of the laws." And that's what I'm going to talk about. To show how close it is, I asked for a definition of "symmetrical." What is a symmetry?
If you look at me, I'm symmetrical, right and left-- apparently, at least. A vase can be symmetrical that particular way, or in other ways. How can you define it? Well, Professor Weil, a mathematician, gave an excellent definition of symmetry. It's this.
As I am left-and-right symmetric, that means that if you put everything that's on this side on this side, and vice versa-- if you just exchange the two sides-- it'll look exactly the same. Or, for instance, a square has a symmetry-- a special kind. If I turn it around to 90 degrees, it still looks exactly the same. So, Weil said, a thing is symmetrical if there's something that you can do to it so that after you finish doing it, it looks the same as it did before.
And then that is the sense in which we say that the laws of physics are symmetrical. That there are things that we can do to the physical laws, or to our way of representing the physical laws, which make no difference and leave everything unchanged in its effect. And this aspect of physical laws are what's going to concern us tonight. And we'll take a number of examples.
The simplest example of all of a kind of symmetry-- as you'll see, it's not the same as you would have thought-- left-and-right symmetric, or anything like that. There's a symmetry called "translation in space." That has the following meaning. If you build any kind of apparatus or do any kind of experiment with some things, and then go and build the same apparatus or do the same kind of experiment with similar things but put them here instead of there-- merely translate it from one place to the other in space-- then the same thing will happen in the translated thing that would have happened in the original thing. It's not really true, actually.
If I actually built such an apparatus and then displaced 20 feet in that direction, it would get into the wall, and there would be difficulties. It's necessary, in defining this idea, to mean to take into account everything that might affect the situation. So that when you move the thing, you move everything. For example, if the system involved a pendulum, and I moved it 20,000 miles to the right, it wouldn't work right anymore, because the pendulum involves the attraction of the earth. But if I imagine I move the earth and the equipment, then it will behave the same way.
So the situation is that you must translate everything which may have any influence on the situation. Now that sounds a little dopey, because it sounds like, well, just translate it. And if it doesn't work, then you didn't translate enough stuff. And--
--you're bound to win. Actually, not. You see, it's not self-evident that you're bound to win. The remarkable thing about nature is that it is possible to translate enough stuff so that it does behave the same way. That's a positive statement.
Now I would like to illustrate that such a thing is true from the statement of the law of gravitation, for example, which said that the forces between objects was inversely as a square of the distance between them. And I remind you that a thing responds to force by changing its velocity, as time goes on, in a direction of the force.
Now if I move something from here to here-- a pair of objects, like a planet going around a sun-- and move the whole pair over, then the distance between the objects, of course, doesn't change. And so the forces don't change. And further, if they use, when they moved over a situation, the same speed, and all the change that will remain in proportion. Everything go around in two systems exactly the same way. So because the law said the distance between the objects, rather than some absolute distance from the central eye of the universe, but it talked about distance between the objects, then it means that the laws are translatable in space.
I give another example of symmetry-- that first symmetry is translation of space. The next one could be called "translation in time," if you like. But better just to say a delay in time makes no difference. If we start a planet going around a sun in a certain direction, as it goes aroun, then if we started all over again, two hours later-- or, say, two years later-- with another beginning, starting the planet and the sun going in the same way, it'll behave in exactly the same way. Because, again, the law of gravitation as stated talks about the velocity and never talks about absolute time and when you were supposed to start measuring things.
In this particular example, we are really not sure. And when we discussed gravitation, we talked about the possibility that the force of the gravity changed with time. Now this would mean that the translation in time was not a valid proposition, because if the constant of gravitation is weaker, a billion years hence than now, then it isn't true that the motion will be exactly the same for an experimental sun and planet a million years, a billion years from now as it is now.
But as far as we know, today-- I've discussed only the laws as we know them today. I wish I could discuss the laws as we will know them tomorrow, but I cannot. But as far as we know, a delay in time makes no difference.
Actually, we know that isn't really true. That's true for what we now call "physical laws." But one of the facts of the world which is very different-- well, which is maybe very different, and maybe not different than a physical law-- is the fact that it looks like the universe had a definite time of beginning-- that everything is exploding apart.
Now that you might call a condition of geography, analogous to the situation that if I say I translate, I don't translate everything. I mean, I have to move that wall, if it's going to make any difference. And in the same sense, you would say, oh, I see. He means the laws are the same. The universe expanded, and everything else.
But we could have made another analysis, in which we start the universe later. But we don't start the universe. And we had no control on the situation. And we had no way to define that idea experimentally.
Therefore, as far as the science is concerned, there really is no way to tell. And the fact of the matter is that the conditions of the world are changing in time. As we know, apparently, at least, the galaxies are all separating from one another. So if you were to awake in some science-fiction story at an unknown time, by measuring the average distances to the galaxies, you could tell when it was. And that means that the world will not look the same if delayed in time.
Now it is conventional today to separate the physical laws, which tell how things will move if you start them in a given condition, from the statement of how the world actually began, because we know so little about that. And it is usually considered that astronomical history-- or "cosmological" history, or whatever you want-- is a little different than physical laws. But if put to a test of how would you define the difference, I would be hard-pressed.
The best characteristic of physical law is its universality. And if there's anything universal about the thing, it's the universal expansion of all the nebulae. So I have no way of defining that. But if I restrict myself to disregard that matter, then as far as the other physical laws are known, and the law that determines how a thing expands-- I mean, the cause of it, and so on, is not known-- if you take only the physical laws that are known, a delay in time makes no difference.
Now we take some other examples. And another is a rotation in space-- a fixed rotation. If I build a piece of equipment and do some experiment with a piece of equipment built here, and then take another one-- better translate it, so it doesn't get in the way-- here, but turn it, so that all the axes are a different direction, it'll work the same way. Again, we have to turn everything that's relevant. If the thing is a grandfather clock, and you turn it this way, well, the pendulum would just sit up against the wall of the can and won't work. But if you turn the earth, too, as it's going on all the time, it still keeps working all right.
The mathematical description of this possibility of turning is a rather interesting one, because to describe what goes on in this situation, we like to use numbers to tell where something is. They're called the "coordinates" of a point. And we use, for instance, sometimes, three numbers to do it-- how high it is about some plane, how far it is in front of me, say, and back is the negative numbers, and how far to the left?
Suppose I did that. And I'm not going to worry about up and down, because for rotations I just have to use two of these three. Let's call the distance this way x, in front of me, and y is how much to the left. And I can locate any body by telling how far it is in front, how far to the left. Those who come from New York City will know that the street numbers work that way very neatly.
Until they began to change the name of 6th Avenue.
Now the mathematical idea about the turning is this. That if I'm set at a somewhat different angle and make my calculations, then what's directly in front of me at distance x is a mixture. Let's say there's a man over here-- u-- who's standing this way and making his analysis, and me standing this way and making my analysis.
When I measure distance x, if I go straight out at x and don't change to the right or to the left, you'll see that that line is a mixture of some of your x-y business and some of the y. So that the connection-- the transformation is that x gets mixed into x and y, and y gets mixed into y and x, and that the laws of nature shall be so written that if you make such a mixture and resubstitute it in the equations, the equations will not change their form.
That's the mathematical way in which the symmetry appears. If you write in mathematical form, the symmetry appears this way. You write the equations with certain letters, then there's a way of changing the letters from x and y to a different x-- x prime-- and a different y-- y prime-- which is some formula, in terms of the old x and y. And the equations look the same, only you have primes all over them. That just means that the man will see the thing behaving in this apparatus the same way as I see it in mine, which is turned the other way.
I give another example. This example is very interesting. It's a question of uniform velocity in the straight line. It is believed that the laws of physics are unchanged under the symmetry under the operation of making a uniform velocity in a straight line. This is called the "principle of relativity."
If we have, for instance, a spaceship, and we do have equipment in it that is doing something, and we have another equipment, down here on the ground, and the spaceship is going along at a uniform speed, then, inside the spaceship, somebody watching what's going on can see nothing different than the man that's standing still in his apparatus in there. Because if he looks outside, or he bumps into an outside wall, or something like that, it's another matter. But insofar as he's moving in a uniform velocity in a straight line, the laws of physics look the same to him as it do to me who was not moving. Since that's the case, I cannot say who's moving.
Now I insist and emphasize, here, something, before we go any further, that in all of these transformations and all of these symmetries we are not talking about moving the whole universe. Just like the case of the time. I could imagine I moved all the times in the whole universe, but that doesn't make any difference. There'd be no content to the statement that if I took everything in the whole universe and moved it over it would all behave the same way.
The very remarkable thing is that if I take a piece of apparatus and move it over, then if I make sure about a lot of conditions and can include enough apparatus I can get a piece of the world and move it relative to the average of all the rest of the stars and it still doesn't make any difference. And in this case, it means that someone coasting at a uniform velocity in a straight line relative to the average of the rest of the nebulae-- seasonal effect-- it is impossible to determine by experiments inside a car without looking out, by any effects, that you're moving relative to all the stars, if you want.
This proposition was first stated by Newton. Let's take his law of gravitation, for instance. It said that the forces are inversely-- to the squares-- (MUTTERING) let's see. What else? Yes. (NORMAL VOICE) And that the force produces changes in velocity.
Now suppose that I watch a moving thing. For instance, I have worked out what happens when a planet goes around a fixed sun. And now I want to work out what happens when a planet's going around a drifting sun. Well, then, all of the velocities that I had in the first case are different than in the second case. I just add a constant velocity on.
But the law is stated in terms of changes in velocity. So that what happens is that the pull of this planet, where this changes this one's speed and, on the other case, changes its speed by the same amount. So anything that I started with-- any initial speed I started with-- just keeps on going. And all the changes are accumulated on top of that.
That's not very good description, but the net result of the mathematics is that if you add a constant speed, the laws will be exactly the same. So that we cannot, by studying the solar system and the way the planets go around the sun, figure out whether the sun is itself drifting through space. There is no effect of such a drift through space on the motion of the planets around the sun, according to Newton's law. So that Newton said "The motion of bodies among themselves is the same in a space, whether that space is itself at rest relative to the fixed stars or moving at a uniform velocity in a straight line."
Now it turns out that, as time went on, the new laws were discovered after Newton-- and those were the laws of electricity-- by Maxwell. And one of the consequences of the laws of electricity were that there should be waves-- electromagnetic waves-- light, in fact, is an example-- which should go at 186,000 miles a second, flat.
I mean by that 186,000 miles a second, come what may. So then it was easy to tell where rest was, because a law like "a light goes 186,000 miles a second" is certainly not one-- well, at first sight-- is certainly not one which is quite right-- which will permit one to move and get the same law.
Because it's evident, is it not, that if you're in a spaceship going 100,000 miles a second in that direction, I shoot-- I'm standing still-- and shoot a light beam at 186,000 miles a second, you look out the window-- or if I shoot the beam through a little hole through your ship, as it goes through your ship, since you're going 100,000, and the light's going 186,000, the light is only going to look like it's passing you at 86,000 miles a second. But if you do the experiment, it looks like it's going 186,000 miles past you and past me.
The facts of nature are not so easy to understand. And the fact of the experiment was so obviously counter to common sense that there are some people who still don't believe the result.
But experimentally, time after time, experiments indicated that the speed is 186,000 miles a second, no matter how fast you're moving. And now the question-- how could that be? Poincare proposed that one take as one of the principles of nature that Maxwell's equations are right and that the mathematical changes needed to compare a system moving and a system standing still that come in that case should be-- well, I'm making it sound too complicated. I'll come back and change the way of stating it.
Einstein realized-- and Poincare, too-- and it's hard to get the history right while you're trying to explain the idea at the same time-- that the only possible way in which a person moving and a person standing still could measure the speed to be the same was that their sense of time and their sense of space are not the same. That the clicking clocks inside the spaceship are ticking at a different speed than they are on the ground, and so forth.
Of course you say, yeah, but if the clock is ticking, I look at the clock in the spaceship and I see it's going slow. No, no. Your brain is going slow, too.
So by making sure that everything went just so, inside the spaceship, it was possible to cook up a system by which, in the spaceship, it would look like 186,000 spaceship miles per spaceship second, whereas it looks like 186,000 mind miles and mind seconds, the same thing. It's a very ingenious thing to be able to do. It turns out, remarkably enough, to be possible.
I mentioned already one of the consequences of this principle of relativity-- that you cannot tell how fast you're moving in a straight line-- in which we had two cars and there was an event. It happened at each end of this car. A man was standing in the middle of the car, and there was an event that happened at each end of this car at a certain instant, which this man claimed was the same time. Because, standing in the middle of the car, he saw the light from both of these things at the same time. Whereas a man in another car who happened to be moving this way with a velocity saw these same two events, not at the same time, but in fact saw the one here first, because the light reached him before the light of the vehicle, because he was moving forward.
So you see that one of the consequences of the principle of symmetry for a uniform velocity in a straight line-- that symmetry means you can't tell who's right-- is that when someone talks about something like-- when I talk about everything that's happening in the world now, that doesn't mean anything. If you're moving along at a uniform velocity in a straight line, everything that happens at now, simultaneous, is not the same events as my now, even though we're passing each other. And our instant here is the same, but somewhere else-- we cannot agree what "now" means at a distance.
So this means a profound transformation in our ideas of space and time, in order to maintain this principle that uniform velocity in a straight line cannot be detected. Actually, what's happening here is that a little bit-- that the time from one point of view, two things that are simultaneous seem, from another point of view, to be not at the same time, provided they're not at the same place-- that they're far apart in distance. That's very much like my x and y-- two things that seem to me to be at the same horizontal-- well, let's say the same distance in front-- zero distance in front-- will, from somebody this way-- he'll say "one of them is in front of me, and one is in back."
See, consider-- from my point of view-- they're both even with me. That wall and that wall is even with me. But if I stand and turn, like this, and look at the same pair of walls but from a different point of view, that one's in front of me, and that one's behind.
And so it is that two events which, from one point of view, seem to be at the same time, from the other point of view seem to be a different time, the generalization of the two-dimensional rotation that I'm talking about into space and time was made. So that the time was added to the space, to make a four-dimensional world. And it's not merely an artificial addition to say, well, we add time to space because, as you see in most of the popular books, you cannot only locate a point, but you have to say when. That's all true, but that doesn't make it real space. That just puts two things together.
Real space, in a sense, is a characteristic that looked at from a different-- that it's possible to look at it from a different point of view that it has an existence that's independent of the particular point of view. That there's a commonness-- a certain amount of time can get mixed up with a certain amount of space. So that space and time must be completely interlocked. And after this discovery, Minkowski said that "space of itself and time of itself shall sink into mere shadows, and only a kind of union of the two shall survive."
I bring this particular example up in such detail because it is really the beginning of the study of symmetries in physical laws. It was Poincare's suggestion to make this analysis of what you can do to the equations and leave them alone. It was Poincare's attitude to pay attention to the symmetries of physical laws. The symmetries of translation, space, delay in time, and so on were not very deep. But the symmetry of uniform velocity in a straight line is very interesting and has all kinds of consequences.
Furthermore, these consequences were extendable into laws that we did not know. By guessing that this principle is true with the disintegration of a mu meson-- we don't know why the mu meson disintegrates in the first place-- we can tell a lot about it by the proposition that we can't use mu mesons to tell how fast we're going in the spaceship, either. And that tells us something, at least about the mu meson disintegrations.
There are many other symmetries, some of them of different kinds. I just mention others. Another one is that you can replace one atom by another of the same kind, and it makes no difference to any phenomenon. You say, yeah, (CHUCKLING) what do you mean by 'the same kind'?" You mean, one way, you replace it by the other one, and it doesn't make any difference.
It looks like physicists are always talking nonsense, in a way, isn't it? Because there are many different kinds. And if you replace one by one of a different kind, it makes a difference, but if you replace one by the same kind, it doesn't make any difference. And that just seems like a circular definition.
But the meaning of the thing is that there are atoms of the same kind. That it is possible to find groups-- classes-- of atoms. That you can replace one by another of the same kind, and it doesn't make any difference. There are such things.
Since the number of atoms in any little, tiny piece of material is one followed by 23 naughts or so, it's very important that they're not all different kinds. And it's really very interesting that we can classify them into a limited number of a few hundred atoms. So that their statement that we can replace one atom by another of the same kind has a very great amount of content.
It has the greatest amount of content in quantum mechanics. And it is impossible for me to explain how, partly-- but only partly, because this is an audience that is mathematically untrained. It's quite subtle, anyhow.
But in quantum mechanics the proposition that you can replace one atom by the same kind has marvelous consequences. It produces peculiar phenomena in liquid helium-- a liquid that flows through pipes without any resistance-- just coasts on forever. It has all kinds of consequences.
In fact, it's the origin of the whole periodic table of the elements and the force that keeps me from going through the floor. But I can't go into that particular thing. But I want to emphasize the importance of looking at these principles.
By this time, you're probably convinced that all the laws of physics are symmetric under any kind of change whatsoever. So I have to give a few ones that don't work. First one, change of scale. It is not true that if you build an apparatus and then come over here and build one twice as big-- every part made exactly the same-- same kind of stuff, but twice as big-- that it will work exactly the same way.
You who are familiar with atoms are aware of this fact. Because if I made it 10 billion times smaller, I would only have five atoms in it. And I can't make a machine tool-- which this thing is, with screw threads and so on-- out of five atoms.
So it's perfectly obvious if we go far enough that we can't change the scale. But even before the complete awareness of the atomic picture was developed, it became apparent that this law isn't right. You've probably seen in the newspaper, from time to time, somebody who's made a cathedral with matchsticks. Several floors, and beautifully delicate, and everything. Just more Gothic than any Gothic cathedral has ever been. More delicate.
Why don't we build big ones like that, with great logs, with the same degree of ginger cake-- the same enormous degree of detail? The answer is if we did it would be so high and so heavy it would collapse.
You say, yeah, but you forgot, when you're comparing two things, you must change everything that's in the system. The little cathedral made with matchsticks is attracted to the earth. So to make the comparison, I should make the big cathedral attracted to an even bigger Earth. Too bad. A bigger Earth would attract it even more, and the sticks would break even more surely.
This fact, that the laws of physics were unchanged on the scale, was first discovered by Galileo. He argued, in discussing the strength of rods and bones, he argued that if you need a bone for a bigger animal-- say an animal that's twice as high, wide, and thick-- you need eight times the weight. So you need a bone that can hold the strength eight times. But what a bone can hold depends on its cross section. And if you made the bone twice as big, it would only have four times the cross section. It would only be able to support four times the weight.
And in Galileo's book called The Two New Sciences you'll see pictures of imaginary bones of enormous dogs, way out of proportion. Galileo felt that the discovery-- I suppose he felt; I don't know-- that the discovery of the fact that the laws of nature are not unchanged on the change of scale was as important as his laws of motion, because they're both put together in a tome called On Two New Sciences.
Now I'll go on to another example of something that is not a symmetry law. And that is it is not true that if you're spinning at a uniform, angular speed in a spaceship, you can't tell if you're going around. You can. Everything gets thrown to the walls. I was going to say you get dizzy, but that soon passes.
There are a lot of effects, however. Things do get thrown to the walls from the centrifugal force, or however you wish to describe it. I hope that there's no teachers of freshman Physics here--
--to correct me. But it is possible to tell that the Earth is rotating by a pendulum or by a gyroscope. And you're probably aware-- in various observatories and museums and so on-- have the Foucault pendulums that prove the Earth is rotating, without looking at the stars. So it's possible to tell that we are going around at a uniform angular velocity on the earth, without looking outside, because the laws of physics are not unchanged by that.
Many people have proposed that really you're rotating relative to the galaxy, see? And if you would turn the galaxies too, it wouldn't make any difference. Well, I don't know what would happen if we would turn a whole universe. And we have, at the moment, no way to tell. Nor, at the moment--
--do we have a theory which describes the influence of a galaxy on things here so that it comes out of this theory in a straightforward way, and not by cheating or forcing or anything like that, but in a straightforward way, that the inertia for rotation-- that the effects of rotation-- the fact that a spinning bucket of water has a shape-- and a surface like this-- that this is the result of a force from the objects around. That's not known to be the case. That this should be the case was called "Mach's principle," but that it is the case has not yet been demonstrated.
But the real question is-- I mean, the more direct, experimental question is-- that if we're rotating at a uniform velocity relative to the nebulae, do we see an effect? The answer is yes. If we're moving in a spaceship at a uniform velocity, in a straight line, relative to the nebulae, do we see an effect? The answer is no. Two different things.
So don't say all motion is relative. That's not the content of relatively. Relativity says that uniform velocity in a straight line, relative to the nebulae, is undetectable.
Now the next symmetry law that I would like to discuss is an interesting one, because it has an interesting history, and that's the question of reflection in space. If I build a piece of apparatus-- say, a clock-- and then I come over here, and I build another clock exactly the same way, but like this one looks in a mirror-- I don't mean I look at this one in a mirror, only. I mean I build another clock which is exact built to be a Chinese copy of what the other looks like in a mirror.
In other words, I have the number 2 painted neatly on the dial here, then I paint the number 2 on the other way around, over here. I should have-- I've got an opportunity to make a drawing. 2 on one clock, 2 on the other clock.
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--which is wound one way in one clock is wound in the corresponding, opposite way in the other clock. They match each other like two gloves-- right and left.
Now we wind up the two clocks. We set them in corresponding position-- I was going to say "the same." But we set them to the mirrored positions, and we let them tick.
Question-- will they always agree with each other? Will all the machinery of the clock go in the mirror image of the other one? And I don't know what you would guess about that. But you'd probably guess it's true, and most people did guess it was true.
Of course, we're not talking about geography. We can distinguish right and left by geography. We can say if we stand in Florida and look at New York, the ocean is on the right. And that distinguishes right and left.
And if the clock involved the water of the sea and New York, and so on, then it wouldn't work if you'd built it the other way, because its tickler wouldn't get in the water. But what we have to imagine, of course, is that the geography of the earth is turned around, too, on the other clock. Anything that's involved must be turned around.
Nor are we interested in history. For example, if you pick up a screw in a machine shop, the chances are it's right-hand thread. And you might argue the other clock isn't going to be the same as this one because it's harder to get the screws. But that's just a question of what kind of things we make.
So that, all together, the first guess is that it doesn't make any difference. And it turns out that the laws of gravitation are such that it wouldn't make any difference if it worked by gravity. The laws of electricity and magnetism are such that if, in addition, it had electric and magnetic guts, currents and wires and whatnot, it would still-- the corresponding clock would run the same.
And if the clock involved nuclear reactions-- ordinary nuclear reactions-- to make it run, it wouldn't make any difference, either. But--
--it does make a little bit of difference. I'll come to what makes a difference in a minute.
But the first possibility that might suggest itself to you, if you know anything much, you may have heard that it's possible to measure the concentration of sugar in water by putting polarized light through the water. If you put the piece of Polaroid that lets light through in a certain access through the water, then you'll find, when you watch the light as it goes through deeper and deeper sugar water, you have to turn the Polaroid-- you have to have another piece of Polaroid, at the other end of the water-- more and more to the right, as the stuff goes through. Maybe it's to the left. I can't remember. But let's say to the right, as you through deeper and deeper solution.
And if you go make the light go the other way through the solution, it's still to the right. So there's a difference between right and left. So if we put sugar water in the clocks and light, then if we put, say, in one tank of water and make the light go through and turn and put the Polaroid so it can just get through, and make the corresponding image on the other side, hoping the light will turn this way, it won't. It'll turn the other way, and it won't go through right.
So, by using sugar water, our two clocks can be made different.
So it's a very remarkable fact. And it isn't true, therefore, at first, that the physical laws are symmetric for reflections. However, it's possible to make sugar in the laboratory. The sugar that we got that time might have been from sugar beets.
But sugar isn't a complicated molecule. And it's possible to make sugar in a laboratory out of carbon dioxide and water, and going through lots and lots of stages in between, and make artificial sugar. And when you put the artificial sugar in there, which is chemically-- and, measured every way, seems to be-- the same, it doesn't turn the light.
Then if you put bacteria in the water-- in the sugar water-- bacteria eat the sugar. And when you let the bacteria eat the sugar, and then try with what's left, it turns out first they only eat half the sugar. The artificial sugar.
Second, when you'll all done, it's turned to the left-- the stuff that's left. And now you find the explanation to all this is the following. A sugar is a complicated molecule-- a set of balls-- atoms-- in some complicated arrangement. If you make exactly the same arrangement, but left as right-- like if the arrangement is complicated like this, then you make one the same way.
Then every distance between every pair of atoms is the same in one as in the other. The energy of the molecules is exactly the same. And for all chemical phenomena not involving light, they're the same.
But living creatures find a difference. The bacteria eats one kind and not the other. The sugar that comes from sugar beets is only one kind-- all left-hand molecules. And so-- or right-handed-- whatever. And so it turns the light one way. The bacteria can only eat that kind of molecule. When we manufacture the sugar from substances which themselves are not asymmetrical-- simple gases-- we make all kinds in equal number.
Then, if we let the bacteria eat, they'll eat the kind they can eat, and the other is left. And that's why it comes out the other way. It's possible to separate the two by looking through magnifying glasses at the crystals and separating them, and so on, as Pasteur discovered, and so forth, so that we can definitely show that all this make sense. And even our artificial sugar, then, we can separate, ourselves. We don't have to wait for the bacteria.
But the interesting thing is that the bacteria can do this. Does that mean that the living processes don't obey the same laws, and so on? Apparently not. It seems that in the living creatures there are many, many complicated molecules, and they all have a kind of thread to them.
One of the most characteristic molecules in living creatures are proteins. And it takes a little while to explain the details, but let's put it very simply. They have a corkscrew property, and they go, let's say, to the right.
Now as far as we can tell chemically, if we make-- we could make this chemically the same thing to the left. It would not function biologically, because it wouldn't, when it met the other proteins, fit the same way. That is, a left-hand thread will fit a left-hand thread, but a left and right don't fit very well the same way.
So the bacteria having a left-hand thread in their chemical insides can distinguish the left and right sugar. How did they get that way? Physics and chemistry cannot distinguish the molecules. It can only make both kinds. But biology can.
It's easy to believe that the explanation is that, you know, long, long ago, when the light processes first began, some accidental molecule got started and propagated itself by reproducing itself, and so on, until, after many, many years, these funny-looking blobs with the prongs sticking out yak at each other--
But they are nothing but the offspring of the first few molecules. And then the accident of the first few molecules, that it happened to form one way instead of the other. It has to be one or the other. So the thing that reproduces itself is either left or right. And then it goes on and propagates this on and on. It's much like the screws in the machine shop use right-hand-thread screws to make new right-hand-thread screws, and so on.
So this is probably one of the deepest demonstrations of the-- the fact that the protein molecules are exactly the same, in all light-- they all have exactly the same kind of thread-- is probably one of the deepest demonstrations of the uniformity of the ancestry of light-- the common ancestry of all light from back, in fact, to the completely molecular level.
Now in order to test better this question about whether the laws of physics are same right and left, we can put the problem to ourselves this way. Suppose that we were in telephone conversation with a Martian, or an Arcturian, or something. We don't know where he is, and we would like to describe things to him. We want to tell him about things.
We say, well, how is he going to understand the words? Well, that's been studied very much by Prof. Morrison, here. And he has pointed out that one way would be to start out and say "Tick, tick, two. Tick, tick, tick, three," and so on. And pretty soon the guy'd catch on to the numbers.
And then, after he understands your number system, then you could write lots of numbers. And you could, for example, write a whole sequence of numbers that represents the weights-- the proportional weights-- of the different atoms in succession. And then say hydrogen, 1.00, [INAUDIBLE], so on and so on.
And he would, after he sat down with all those numbers and piddled around awhile, would discover that the mathematical ratios were the same as the ratios of the weights of the elements, and therefore those names must refer to elements. And so, gradually, you could, in talking to him, have a common language. In many ways common. There are many.
Now comes the problem. Suppose that he says "You fellas"-- after we get familiar with him-- he says "You're very nice. Now I'd like to know what you look like." And you start out, "Well, we're about 6 feet tall."
He says "6 feet? Well, how big is a foot?" "Well, it's very easy," you say. "A foot. 6 feet tall is 170,000 million hydrogen atoms high."
Well, it's not a joke. It's a possible way of describing 6 feet to someone that has no measure, assuming that we cannot send him any samples. Nor can we both look at the same object.
If we have to tell him how big we are, we can do it. That's because the laws of physics are not unchanged under a scale change. So we can use that fact-- use the properties of the scale-- I mean, you can use that fact to determine the scale.
Well, we describe ourselves. After telling we're 6 feet tall, and we're so-and-so bilateral on the outside, and we look like this. And there are these prongs sticking out, and all this. And he says "That's very interesting. What do you look like on the inside?"
So we describe the heart and so on. And we say "Now put the heart in on the left side." Now the question is, how can we tell him which side is the left side? By what possible-- you say, ah, you take beet sugar, see? And you put it--
And you put it in water, and it turns. Only trouble is he has no beets up there.
Well, we have no way of knowing whether the evolution-- if it was even corresponding to the same proteins on Mars as here-- whether the accidents of the evolution would have started with maybe the wrong-handed threads. There's no way to tell.
So after much thought, you see, you can't do it. And so you conclude it's impossible. However, about five or six years ago certain experiments indicated that-- produced all kinds of puzzles. I won't go into the detail. We got into tighter and tighter difficulties. More and more paradoxical situations. Until somebody proposed-- Lee and Yang-- proposed maybe the principle that right and left symmetry-- that nature is the same for right and left is not right. And that would help to explain a number of mysteries.
And Lee and Yang proposed some more direct experiments to demonstrate this. And I'll just mention the most direct of all the experiments-- the easiest way to tell-- an experiment done-- well, there were several first experiments which were quite clear. But the one that's easiest to explain is this.
That when we have a radioactive disintegration in which an electron and a neutrino are emitted-- for example, this is one that we talked about before. Electron and antineutrino. This is a neutron disintegrating into a proton, an electron, and an antineutrino. Well, the corresponding thing can happen to a neutron and a nucleus.
Anyway, there are many radioactivities in which the charge of the nucleus increases by one and an electron comes out. The thing that's interesting is that if you measure the spin-- electrons are spinning, as they come out. If you measure the spin, you find out that they're spinning to the left. That has a definite significance-- that the electron, when it comes out of the disintegration, is turning this way. And that helical description is a left-hand thread.
It's as through, in the beta decay, the gun that was shooting out the electron were a rifled gun. And there's two ways to rifle a gun. Because there's a direction-- out-- and then there's a question. Do you turn it this way or that way as you go out?
And the experiment is that the electrons come from a rifled gun-- rifled, twisted to the left. And so, using this fact, we can call up the Martian and say "Listen. Take a radioactive stuff"-- (MUTTERING) and I ought to have prepared a particular example-- (NORMAL VOICE) "a neutron. And look at the electrons which come from such a beta decay. And then you define left by this screw thread, and-- let's see. You let"-- uh-- it'll take me some while to figure out how to do it in detail. Say "The electron's going up, and the direction of motion of the way it's spinning is into the body on the left side. And that's where the heart goes."
Something like that. I'd have to think a little bit more. But anyway, it is possible to tell right from left. And thus the law of this, that the world was symmetrical for left and right, has collapsed.
Every conservation law has-- well, the next thing I would like to talk about is the relationship of conservation laws to symmetry laws. We, last time, talked about conservation principles-- conservation of energy, momentum, angular momentum, and so on. Now we're talking about symmetry laws.
It's extremely interesting that there seems to be a deep connection between the conservation laws and the symmetry laws. This connection has its proper interpretation-- at least, as we understand it today-- only in the knowledge of quantum mechanics. Nevertheless, I will show you the following.
I will try to explain the following. That if we will assume that the laws of physics are describable by a minimum principle, that the paths are taken so that some quantity is least-- an idea I described once before. If we add that the laws of nature come from a minimum principle, then we can show that if the law is such that you can move all the equipment to one side-- in other words, if it's translatable in space-- then there must be conservation of momentum. That there's a deep connection between the symmetry principles and the conservation laws, but that that connection requires that the minimum principle be assumed.
You remember at one time we discussed one way of describing physical laws by saying that a particle goes from one place to another in a given length of time by trying different paths. And the actual path taken has this property. That there's a certain quantity-- which unfortunately happens to be called the "action," which is not be taken to signify anything, because it's got nothing to do with action.
Anyway, there's a certain quantity called the "action" which you calculate on this path. And if you will calculate it for any other path, the answer's bigger. It's least for the real path. And that one way of describing the laws of nature is to say that the action of a certain mathematical quantity is least for the actual path than for any other path.
Now another way of saying the thing is least is to say this. That if you move the path a little bit, at first it doesn't make any difference.
Suppose you were walking around in a wood-- in a mountain-- on hills-- but smooth hills, please-- smooth. The mathematical things that were involved here correspond to smooth hills. We're walking around on hills and valleys. And we come to a place where we're lowest.
Then I say if you take a small step forward you won't change your height. When you're at the lowest, or at the highest, point, a step doesn't make any difference in the altitude, in first approximation. Whereas if you're on a slope, you can walk down the slope with a step. And then, if you take the step in the opposite direction, you walk up.
And that's the key to the reason why, when you're at the lowest place, taking a step doesn't make much difference, because if you did make any difference, you could put the step in the opposite direction, you'd go down. I mean, if it went up one way, it would go down the other way. But since this is the lowest point, and you can't go down, in first approximation the step doesn't make any difference.
So we therefore know that if we move this path a little bit, in first approximation it doesn't make any difference to the action. Now I want you to consider the following possible other path. First, we jump immediately over to another place, here, nearby. Then we go along--
This sticks out too far to make the diagram clear. So if you'll permit me to just change the shape of the path. Then we move on exactly the corresponding path to another point, here-- which is displaced the same amount, of course, because it's the corresponding path-- to this sign.
Now we have just discovered that the laws of nature are such that the action-- the total amount of action going on this path is the same, in first approximation, to that path. That's from the minimum group, when it's the real motion.
Now I'll show you something else. That the action on this path is the same as the action from this little cross to that little cross, if the world is the same when you move everything over. Because the difference of these two is only that you moved everything over. So if this symmetry principle of translation in space is right-- if that's right-- then the total action between the crosses is the same as between the dots. But for the true motion-- the total action on this cockeyed path, here-- is very closely the same as for the original one. So subtracting equals from equals, and so on, and so on.
Anyway, you could probably see, therefore, that the contribution from this little section and from this little section are equal. But in making this little motion, we're going this way. And making this one, we're going the other way.
So if we make a new-- the contribution of this taken as the effect of moving that way, and the contribution of this, thinking of it as an effect of moving that way but taking it the other sign, because it's the other way. We see that there is a quantity here which has to match the quantity here, to cancel out, which is the effect on the action of a little, tiny step in the x direction.
So there is that quantity-- the effect on the action of a small step in the x direction is the same at the beginning as at the end. There is a quantity, therefore, that doesn't change as time goes on, provided the minimum principle works and symmetry principle of displacement in space is right. Now this quantity, which doesn't change, is in fact exactly the momentum-- the momentum we discussed last time.
A corresponding argument for the displacement in time-- the delay in time-- comes out as the conservation of energy. The case that we could-- if we rotate in space, doesn't make any difference. Comes out as the conservation of angular momentum, and so on. That we can reflect it, and it makes no difference doesn't come out to be anything simple in the classical sense. And it hasn't, therefore, got a simple, classical interpretation.
And people have called it the "parity." And they have a conservation law called the "conservation of parity," but those are just complicated words, in the case of the quantum mechanics. All we're saying is that the right and left symmetry law is not valid.
But I have to mention that "conservation of parity," because you may have read it in the papers. But the law of conservation of parity has been proved wrong. It should have been written, because it's much easier to understand. The principle that you can't distinguish right and left has been proved wrong.
Now I would like to say, as we go on, about other symmetries, that there are a few problems-- new problems. For instance, for every particle, like an electron, there's an antiparticle-- a positron. For a proton, there's an antiproton. And we can make, in principle, what we call "antimatter," in which every atom has its corresponding anti pieces put together.
For example, a hydrogen atom has a proton and an electron. If we take an antiproton-- which is electrically negative-- and a positron and put them together, they will also make a kind of hydrogen atom-- an antihydrogen atom-- in principle. It's never been made, in fact, but this is figured out that we could make this.
And so we could make all kinds of antimatter, in the same manner. Now the question is whether the matter works the same as the antimatter. And as far as we know, it does. And one of the laws of symmetry is that if we make stuff out of antimatter, it'll behave the same way as we make the corresponding stuff out of matter. Of course, if they come together they annihilate, there are big sparks, and everything else.
And it was believed that this is true-- that matter and antimatter have the same laws. Now the next question is this. Once it's found that the left and right is wrong-- the left and right symmetry is wrong-- an important question comes.
If I look at this disintegration, but with antimatter-- an antineutron goes into an antiproton plus an antielectron-- (MUTTERING) well, that's an elec-- positron-- plus a neutrino, the question is, does the antimatter behave like the matter, in the sense that it comes out left-hand thread, or does it behave the other way? And it turns out, we think, up until a few months ago, that it behaves the opposite way and that the antimatter behaves like-- uh-- it goes to the right where matter goes to the left.
And so there was another principle. And, in fact, we really can't tell the Martian which is right and left, because if he happens to be made out of antimatter, he'd get the thing the other way. Because when he does his experiment, his positrons are coming out-- puts the heart on the wrong side. And so you can see that if you telephone the Martian, and explain how to make a man-- and suppose he makes one, and it works.
Well, let's take it-- and uh-- and you explain to him, also, all our social conventions, and so on, then, when we go, finally, to meet this man-- after he tells us how to build a sufficiently good spaceship. We go to meet this man, and you walk up to him. And if you put out your right hand to shake hands, if he puts out his right hand, OK. But if he puts out his left hand, watch out, because the two of you--
The two of you will annihilate with each other.
These are all the symmetries that I have time to tell you about. I wish I could tell you about a few more, but they become more difficult technically to explain. But there are some very remarkable things which are the near symmetries. The remarkable feature of this effect, that we can distinguish right and left, is that we can distinguish right and left only with a very weak effect, with this beta disintegration.
What it means-- that nature is 99.99 indistinguishable, right from left, but that there's just one little piece-- one little characteristic phenomenon-- which is completely different, in the sense that it's absolutely lopsided-- is a mystery that no one has the slightest idea about yet. Thank you.
[CARILLON PLAYING "FAR ABOVE CAYUGA'S WATERS"]
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In these Messenger Lectures on "The Character of Physical Law," originally delivered at Cornell University Nov. 9-19, 1964, physicist Richard Feynman offers an overview of selected physical laws and gathers their common features into one broad principle of invariance. He maintains at the outset that the importance of a physical law is not "how clever we are to have found it out, but...how clever nature is to pay attention to it," and tends his discussions toward a final exposition of the elegance and simplicity of all scientific laws.
From 1945 to 1950, Feynman taught theoretical physics at Cornell. He went on to accept a professorship at Caltech and was named co-winner of the 1965 Nobel Prize in physics for his contribution to the renormalization of quantum electrodynamics.