[CHURCH BELLS] SPEAKER 1: The distinction of past and future.
RICHARD FEYNMAN: Now, it's obvious to everybody that the phenomena of the world are evidently irreversible. By that I mean, things happen that don't happen the other way. You drop a cup and it breaks, and you can sit there a long time waiting for the pieces to come together and come back into your hand.
If you watch the waves breaking at the sea, you stand there and wait for the great moment when the foam collects together, rises up out of the sea, and falls back further out from the shore. Would be very pretty.
As a matter of fact, the demonstration of this in such lectures is usually made by having a section of moving picture in which you take a number of phenomena and running the thing backwards, and then see all the laughter. The laughter just means this ain't gonna happen in the real world.
But actually, that's a kind of a weak way to put something which is so obvious and deep as the difference between the past and the future. Because even without an experiment, our very experiences inside are completely different for past and future. We remember the past. We don't remember the future. We have a different kind of awareness about what might happen than we have of what most likely has happened.
The past and future look completely different psychologically, and so forth. And the questions of memory, of apparent freedom of will, in the sense that we feel that we can do something to affect the future but none of us-- or very few of us-- believe that there's anything you can do to affect the past. And remorse and regret and hope and so forth are all words which distinguish, perfectly obviously, the past and the future.
Now, if the world of nature is made of atoms, and we too are made of atoms and obey physical laws, this obvious distinction between what happened in the past and the future and this obviously irreversibility of all phenomena, you would think, would most likely-- and obviously, it's interpretation in that some laws, some of the motion laws of the atoms, are going one way. That the atom laws are not such that they can go either way. That there's somewhere in the works some kind of a principle that uxles only make wuxles and never vice versa. And so the world is turning from uxley character to wuxley character all the time. And that this one-way business of the interactions of things is the thing that makes the whole phenomena of the world seem to go one way.
And yet we haven't found it yet. That is, in all the laws of physics that we've found so far, there doesn't seem to be any distinction of the past and the future. That the moving picture should work the same way going both ways, and the physicist who looks at it should not laugh. Details now be explained.
Let us take the law of gravitation as our standard example. If I have a sun and a planet that I started off in some direction going around to here, and then take a moving picture of this. Say it gets to here. Now, take a moving picture of this backwards. Take a moving picture of it, excuse me, and run the movie backward and look at it. What happens?
Planet goes around the sun in an ellipse-- this way, of course. Starts here, goes to here, keeps on going around. Goes in an ellipse. The speed of the planet is such that the area swept out by the radius is always the same in equal time. Just does exactly the way it ought to do, perfectly satisfactory. It cannot be distinguished from the one going the other way.
So the law of gravitation is of such a kind that it doesn't make any difference if you show any phenomenon involving just gravitation running backwards on a film, it'll look perfectly satisfactory. Put it precisely more this way-- if, in a given instant, the particle moving this way-- if all the particles in a more complicated situation would have every one of their speeds reversed, suddenly, then the thing will just unwind through all the things that it wound up into. That is, if you have a lot of particles doing this, then you suddenly reverse the speeds, they will completely undo what they did before.
Now this is in the laws of gravitation, which say the velocity changes as a result of the forces, and so on. If I reverse the time, the forces are not changed. And so the changes in velocity are not altered at corresponding distances. And so each velocity then has its succession of alterations made in exactly the reverse way that they were made when it went out before. And it's easy to prove that the law of gravitation is time reversible.
And the law of electricity and magnetism? Time reversible. The laws of nuclear interaction? Time reversible, as far as we can tell. The laws of beta decay that we talked about at a previous time? Also time reversible. The difficulty of the experiments of a few months ago, which indicate that there's something the matter with some unknown about the law, suggests the possibility that, in fact, it may not be also time reversible. But we shall see.
But at least the following is true-- this beta decay that we're talking about-- which may not be time reversible, but I don't know-- is a very unimportant phenomena for most ordinary circumstances. The possibility of my talking to you does not depend on that happening. It does depend on chemical interactions. It depends on electrical forces. It doesn't actually depend much on nuclear forces at the moment. But it depends also on gravitation.
But I am one sided. I speak, and the voice goes out into the air and doesn't come sucking back into my mouth when I open it. And this irreversibility cannot be hung on the phenomena of beta decay. In other words, we believe that there are, in the world, most of the ordinary phenomenal, which are produced by atomic motions, which are according to laws which could be completely reversed.
So we have to look some more to find the explanation. If we look at this more carefully, at planets moving around the sun more carefully, your soon find that it isn't quite right. For example, the Earth's rotation on its axis is slightly slowing down. And it's due to tidal friction. And you see that friction is something which is obviously irreversible. If I took a heavy weight on the floor here and pushed it, it would slide and stop. If I stand and wait for it, it doesn't suddenly start up and speed up and come into my hand.
So a frictional effect seems to be irreversible. But a frictional effect, as we discussed at another time, is the result of the enormous complexity of the interactions of the block with the wood, that the jiggling of atoms inside at the organized motion of the block has changed into disorganized, irregular, wiggle-waggles of atoms in the wood. So that therefore, we should look at the thing more closely. And as a matter of fact, we have here the clue to the apparent irreversibility.
I take a simple example. For example, if we have blue water-- say, ink-- and white water-- that's water without ink-- in a tank with a little separation and pull out the separation very delicately, then it's separate, blue on one side, white on the other side. Wait a while. Gradually, the blue mixes up with the white. And after a while, the water's luke-blue.
I mean, it's sort of 50-50, a color uniformly distributed throughout. Now, if we wait for a long time and watch this for a long time, it does not by itself separate. Or you could do something. You can get the blue separated again. You can evaporate the water and condense it somewhere else and collect the blue dye and dissolve it in half the water and put back this thing and so on. While you're doing all that, however, you yourself are causing irreversible phenomena somewhere else.
So by itself, it doesn't go the other way. And that gives us some clue. Let's look at the molecule. Suppose that we took a moving picture of the water, of the blue and the white water mixing. It would look funny if we ran it backwards because we'd start with uniform water, and gradually, the thing would separate and would be obviously nutty. Now we magnify the picture so that every physicist can watch, atom by atom, to find out what happened irreversibly, where the laws of balance, of forward and backward, broke down.
And so you start. And you look at the picture. And you have blue atoms. Let's ridiculous, but we'll call it that. We have atoms of one kind and atoms of another kind jiggling all the time in thermal motion, wiggling, bouncing. And if we were to start at the beginning, we would have mostly atoms of one kind on one side and atoms of the other kind on the other side.
Now, these atoms are jiggling around. That's too small a box. You need more to get this effect. Billions and billions of these atoms. Now, these atoms are jiggling around--
I just put one more, but I'm getting tired of making [INAUDIBLE]. Now, these atoms are jiggling around. And if we start all on one side and all on the other, we see, of course, that in their perpetual, irregular motions, they'll get mixed up. And that's why it gets to be more or less uniformly blue.
But let's watch any one collision. Here's a particular collision selected from that picture. Here's this molecule moving this way and this one moving this way. And they come together, say, in the moving picture. And they bounce off this way.
Now, you run that section of the film backwards, and you find a pair of molecules moving this way, bouncing off that way. And the physicist looks, with this keen eye, and measures everything, and says, that's all right. That's according to the laws of physics. If two molecules came this way, they would bounce that way. And if they came that way, they would bounce this way. It's reversible. The laws of molecular collision are reversible.
So if you watch too carefully, you can't understand it at all.
Because every one of the collisions is absolutely reversible. And yet, the whole morning picture shows something absurd, which is that the molecules start in the reverse picture. The molecules start in this condition-- blue, white, blue, white, blue, white, and so on, all mixed up. And as time goes on, through all the collisions, the blues separate from the whites. And they can't do that. That's not natural, that the accidents of life will be such that the blues will separate themselves from the whites.
Yet if you watch this reverse movie very carefully, every collision is OK. Well, you see that all there is to it is that the reversibility is caused by the general accidents of life, that if you start with a thing that's separated like this and just make irregular changes, it gets more uniform. But if you start with something that's uniform and make irregular changes, it doesn't get separated. It could get separated. It's not against the laws of physics that these things bounce around so that they separate. It's just unlikely. It just never happened in a million years. And that's the answer.
Things are irreversible only in the sense that going one way is likely to go, but going the other way, although it's possible and is according to the laws of physics, wouldn't happen in a million years. It's just ridiculous to expect that if you sit there long enough, the jiggling of the atoms will separate a uniform mixture of ink and water into ink on one side and water on the other.
Now, if I had put a box around here so that this was all the molecules that there were, as time went on, they would get mixed up. But if you're patient, I think you could believe that in a perpetual, irregular collisions of these molecules after some time-- not necessarily a million years, maybe only a year-- if you keep watching, accidentally they get back more or less like this-- in the sense, at least, they get back far enough to say that if I drew a line through all the whites on one side and all the blues on the other. It's not impossible.
However, the actual objects with which we work have not only four or five blues and whites. But they have four or five millions million million million atoms. And it's just not likely that four or five million million million million are all going to get separated like this. And so the apparent irreversibility of nature does not come from the irreversibility of the fundamental physical laws. It comes from the characteristic that if we start with an ordered system and have the irregularities of nature, the bouncing, then the thing goes one way.
Therefore, the next question is, how did it get ordered in the first place? That is to say, why is it possible to start with the order? You see, the difficulty is that we start with an ordered thing. We don't end with an ordered thing. One of the rules of the world is that the conditions at the beginning-- I mean that the thing goes from an ordered condition to disorder.
Incidentally, this word order and disorder is another one of those terms of physics which aren't exactly the same as it is in ordinary life. The order need not be interesting to you, human beings. It's just a question that there's a definite situation. They're all on one side and all on the other or they're mixed up. And that's the order to disorder. Maybe you like it better mixed up. But that's more ordered, anyhow.
Now, the question is, then, how does the thing in the first place get ordered? And why, when we look at any ordinary situation which is only partly ordered, we can conclude that it probably came from more ordered? If I look at a tank of water in which it's very dark blue on the side and very clear, white water here and sort of bluish water in between, and I know that that thing has been left alone for 20, 30 minutes, then I will guess that it got this way because it was bluer before-- I mean that the separation was more complete in the past.
If I find, for example, two objects-- well, this is as good an example as any. If I wait longer, then the blue and white would get more intermixed. And if I know that this thing has been left alone for sufficiently long time, I can conclude something about the past condition. The fact that it's smooth in here could only arrive because it was much better in the past, much more satisfactorily separated. Because if it weren't more satisfactorily separated in the past, in the time since then, it would have gotten more mixed up than it is.
So it is therefore possible to tell from the present something about the past, although physicists have really not done this much. Physicists usually like to think that all you have to do is say, these are the conditions. Then what happens next? But all our sister sciences have a completely different problem. In fact, all the other things that are studied-- history, geology, and astronomical history all have a problem of this kind. I find they're able to make predictions of a completely different type than a physicist.
A physicist says, in this condition, I'll tell you what'll happen next. But a geologist will say something like this-- I have dug in the ground, and I've found certain kinds of bones. I predict that if you dig in the ground, you'll find a similar kind of bone. A historian, although he talks about the past, can do it by talking about the future. When he says Napoleon exists or that the French Revolution was in 1783, he means that if you look at another book about the French Revolution, you'll find the same date.
1789, maybe. That's pretty accurate for a physicist to have the third decimal--
Or three figures.
Now, the thing that he says is he makes a kind of prediction about something he has never looked at before. Documents that have still to be found. He predicts that the documents, if there's something written about Napoleon, will coincide with what is written in the other document. And the question is how that's possible.
And the only way that that's possible is to suggest that the past of the world was more organized, in this sense, than the present. Some people have proposed, at one time-- the physicists only have proposed this-- that the way it got ordered was this-- that the whole universe is just irregular motions like this. And then if you wait long enough with five atoms, of course it can get separated accidentally.
And all that has happened is that the world has been going on and going on and going on and going on and going on and it fluctuated. That's what this is called, when it gets a little bit out of ordinary. It fluctuated. And now we're watching the fluctuation undo itself again. How do we know that isn't the case? You say, oh, how long you would have to wait. I know. But if it didn't fluctuate far enough to be able to produce evolution, to be able to produce an intelligent person, we wouldn't have noticed it. So we had to keep waiting until we were alive to notice it. So we have to have at least that big a fluctuation.
But this is incorrect, I believe. I think that's a ridiculous theory for the following reason-- if the world much bigger, and there were atoms all over the place, and they started from a completely mixed up condition, all over, and I happened only to look at the atoms here and I find that the atoms here are separated, I have no way to conclude that the atoms anywhere else are separated. In fact, if the thing were a fluctuation, and I noticed something odd, the most likely way that it got there is that there's nothing odd anywhere else. That is, I have to borrow odds, so to speak, to get this thing lopsided. And there's no use borrowing too much.
It's much more likely, of all the possible ways in which these six atoms can be on one side and these seven on the other side, of all the possibilities, the most likely condition is the rest of the world is mixed up. And therefore, an astronomer looking at a start that he's never-- although when we look at the stars and we look at the world, we see it's ordered, there could be a fluctuation. The prediction would be that if we look at a place that we haven't looked at before, it will be disordered and a mess. The separation of the matter into stars, which are hot, and space, which is cold, which we've seen, although if you say it could be a fluctuation, then in places that we haven't looked, we would expect that the stars are not separated from the space.
And since every time we make a prediction that in a place that we haven't looked we'll see the same statement about Napoleon or we'll see stars in a similar condition or that we'll see bones like the bones that we've seen before, the success of all those sciences indicate that the world did not come from a fluctuation but came from a condition which was more separated, more organized in the past than the present time.
And therefore, I think it's necessary to add to the physical laws the hypothesis that in the past, the universe was more ordered, in a technical sense, less mixed up than it is today and that this statement is the added statement that's needed to make sense and to make an understanding of the irreversibility. That statement, of course, is itself lopsided in time. It says something about the past is different than the future. But it comes outside of the province of what we ordinarily call physical laws because we try today to distinguish-- maybe someday we won't do that. But we do today distinguish between the laws which tell how something moves if you start it in a certain way and those statements about how the universe got the way it gets or has been, what it was in the past and what it's going to get to be.
No, excuse me. The statement of the physical laws which govern the rules by which the universe developed and the law which states the condition that the world was in the past. That's considered to be astronomical history. Perhaps someday that will also be a part of physical law.
Now, there are a number of interesting features of irreversibility that I think I would like to illustrate. One of them is to see how exactly an irreversible machine really works. Suppose that we build something that we know ought to work only one way. And what I'm going to build is a wheel with a ratchet on it. A ratchet means just this, that we a notched wheel with steps. So I've drawn the wrong way from when I'm used to thinking about it. No, I had it right.
It would be this way. Then there's another notch and a saw-toothed wheel like this with sharp up-notches and relatively slow down-notches all the way around. And then this is a wheel on a shaft. And then on this thing, there's a little piece of pawl-- a thing called a pawl-- which is on a pivot here and which is held down by a spring. It gets in the way of the wheel, but that's a small technical difficulty.
This is two-dimensional. And actually, it's set a little bit below. Now, this wheel can only turn one way. If you try to turn it this way, than these straight-edged part of the teeth get jammed against the pawl, and it doesn't go. Whereas if you turned it the other way, it would just go right over the thing. It goes, snap, snap, pop, pop, pop, pop. They still use them in clocks. So when you wind watches, they have this kind of a thing inside so that you only can wind it one way. And after you've wound it, it holds a spring. And now we want to discuss-- you see, it's completely irreversible in the sense that the wheel can only turn one way.
Now, this irreversible machine, this wheel that can only turn one way, has been imagined that you could use it for a very useful thing, a very interesting thing. Because of molecular irregularities, because of molecular motion, there's a perpetual motion of molecules. And if you build a very delicate instrument, it'll always jiggle because it's being bombarded irregularly by the air molecules in the neighborhood.
So what's very clever, we'll connect this with a shaft, which is hard to illustrate in three dimensions. It goes way out here. You connect this to it with a shaft with vane-- a wheel that has four vanes. Actually, my angles and things have gotten a little bit mixed up. Look down on the shaft. This thing's got four vanes like this.
And those are bombarded. They're in a box of gas here. And they're bombarded all the time by the molecules, irregularly. So the thing is pushed sometimes one way, sometimes the other way. But when it's pushed one way, this thing gets jammed. But when it's pushed the other way, it goes around. So we find the wheel perpetually going around. And we have a kind of perpetual motion. That's because this wheel is irreversible.
But actually, we have to look into the details. The way this works is that when the wheel goes one way, it lifts the pawl up. And then the pawl snaps down against the next tooth. And it will bounce. If it's perfectly elastic, it'll go bounce, bounce, bounce, bounce all the time, and the wheel can just go down around the other way when the pawl accidentally bounces up. So this will not work unless it's true that when the pawl comes down it sticks or stops or bounces and cuts out.
If it bounces and cuts out, there must be what we call damping, or friction, again. And in the falling down and bouncing and stopping, which is the only way this will work one way, heat is generated by the friction. So this part of the wheel over here will get hotter and hotter. However, when it begins to get quite warm, something else happens. Just as there's Brownian motion, or irregular motions, in the gas here, so whatever this is made out, the parts that this is made out of are getting hotter and are becoming more irregular.
So a time comes when this is hot enough that the pawl is simply jiggling because of the molecular motions of the things on the inside. And so it bounces up and down on here because of molecular motion, the same thing that was making this vane turn around. And in bouncing up and down on here, it is up as much as it is down. And when it is up as much as it is down, a tooth can go either way.
As a matter of fact, the thing will be driven backwards. If this one was hot and this one was cold, the wheel that you thought would go only one way would go the other way because in the terrible bouncing up and down of this wheel, every time it comes down, it comes down on an inclined plane. And so it pushes the wheel this way. Then it bounces up again, comes down on another inclined plane, and so on.
And so if this side is hotter than this side, it'll go around this way. What's it got to do with the temperature of this side? Suppose they didn't have that at all. Oh. Then if it's pushed forward by falling on an inclined plane, the next thing that'll happen is it'll bounce against that tooth and the wheel will bounce back. But in order to prevent the wheel from bouncing back, we put a damper on it and put vanes in the air so [INAUDIBLE].
And then it will go one way, but the wrong way. And so it turns out that no matter how you design it, a wheel like this will go the one way if this side is hotter and go the other way if this side is hotter.
But after there's a heat exchange between the two, when everything has calmed down, it will neither go one way or the other. And so that's the technical way in which the phenomena of nature will go one way as long as they are out of equilibrium, as long as one side is quieter than the other or one side is bluer than the other.
The conservation of energy would let us think that we have as much energy as we want. Nature never loses or gains energy. Yet the energy of the sea, for example, the thermal motion of all the atoms in the sea is practically unavailable to us. In order to get that energy organize, herded, used, make it useful, make it available for use, we have to have some place that's at a different temperature. We have to use a difference in temperature or else we'll find that although the energy is there, we cannot make use of it.
There's a great difference between energy and availability of energy. The energy of the sea, for example, is a large amount. But it's not available to us. I think I can give an analogy to give some idea of what the difficulty is this way-- the conservation of energy means that the total energy in the world is kept the same. But in the irregular jiggling, that energy can be spread about so uniformly in certain circumstances that there's no way to make more go one way than the other. There's no way to control it anymore.
I don't know if you've ever had this experience, but I have-- going to the beach with many towels and so on and sitting happily on a beach and having a tremendous downpour suddenly come, picking up the towels as quickly as you can and running into the bath house. Then you start to dry yourself, and you find that this towel's a little wet, but its drier than you are. And you keep drying this one. Then you find that one's too wet. It's wetting you as much as it's drying you. And you try another one.
And pretty soon, you discover a horrible thing-- all the towels are damp, and so are you.
And you keep picking them up and putting them down and rearranging them. And there's no way to get any drier, even though you have many towels. Because there's no difference, in some sense, between the wetness of the towel and the wetness of yourself. I could invent a kind of a quantity, which I could call ease of removing water or-- yeah, let's call it ease of removing water. The towel has the same ease of removing water from it as you have. And so when you touch the towel to you, as much water comes from the towel to you as it goes from you to the towel.
It doesn't mean there's the same amount of water in the towel as there is on you. A big towel will have more water in it than a little towel. But they have the same dampness. So when things get to the same dampness, then there's nothing you can do any longer.
Now, the water is like the energy because the total amount of water isn't changing. But if we had a world which was limited-- you see, if the bath house door is open, and you can run into sun and get dried out or find another towel, OK. That's different. Then you got saved. But if you have everything closed, and you can't get away from these towels, you can't get any new towels-- so if you imagine a part of the world that was closed. Wait long enough, and then the accidents of the world, the energy, like the water, will be distributed all over all the parts evenly. And there's nothing left of of one-way-ness. There's nothing left of the real interest of the world as we experience it.
Thus in this situation here, which is a limited one, in which nothing else is supposed to be involved, the temperatures gradually become equal on both sides and the wheel doesn't go around either one way or the other. And in the same way, this situation is that if you leave a system long enough, it gets the energy thoroughly mixed up in it. And no more energy is really available to do anything.
Incidentally, the thing that corresponds to the dampness is called the temperature. And although when I say two things at the same temperature, when things get balanced, it doesn't mean they have the same energy in them. It just means it's just as easy to pick energy off of one as to pick it off the other. So as you put them next to each other, nothing apparently happens. They pass energy back and forth equally. The net result is nothing.
So when things have become all at the same temperature, then there's no more energy available to do anything. And the principle of irreversibility is that if things are at a different temperature and are left to themselves, as time goes on they become more and more at the same temperature and the availability of energy is perpetually decreasing. This is another name for what's called the entropy law, which says entropy is always increasing. But never mind the words. To state it the other way, the availability of energy is always decreasing.
And that's a characteristic of the world in the sense that it's due to the chaos of molecular, irregular motions. Things of different temperature, left to themselves, tend to become of the same temperature. But if you have two things at the same temperature, like water on an ordinary stove without a fire, the water isn't going to freeze and the stove get hot. But if you have a hot stove with ice, it goes the other way. So the one-way-ness is always the loss of the availability of energy.
Well, that's all I want to say on the subject. But I want to make a few remarks about some characteristics. Here, we have an example in which an obvious effect-- the irreversibility-- is not an obvious consequence of the law. But the effect is rather far from the basic law. It takes a lot of analysis to understand why this effect and that the effect is of first importance in the economy of the world, in the real behavior of the world, in all obvious things-- my memory, my characteristics, the difference between past and future are completely involved in this. And yet the understanding of it is not prima facie available by knowing about the laws. It takes a lot of analysis.
It is often this way, that the laws of physics are different, or the laws of physics do not have a direct obvious relevance to the experience, but that the laws are abstract from the experience to varying degrees. In this particular case, the fact that the laws are reversible although the phenomena are not is an example.
There are often great distances between the details, the detail laws, and the main aspects of really phenomenon. For example, it's something of this kind that if you watch a glacier from a distance and you see the big rocks falling into the sea and the way the ice moves and so forth and so on, it isn't really essential to remember that it's made out of little hexagonal ice crystals, that the ice crystals are hexagonal.
And yet, the character of the little hexagonal ice crystals, if understood well enough, is in fact the-- the consequence of this is, in fact, the motion of the glacier. But it takes quite a while to understand-- in fact, nobody knows enough about ice, now how much they study the crystal, yet-- to really understand all the behavior of the glacier. But the hope is that if we do understand the ice crystal, we'll ultimately understand the glacier.
But there's a large-- in fact, although we've been talking in these lectures about the fundaments of the physical laws, I must say immediately that one does not, by knowing all the fundamental laws as we know them today, immediately obtain an understanding of anything much. It takes a while, and even then it's only partial.
Nature, as a matter of fact, seems to be so designed that the most important things in real world seem to be a kind of complicated, accidental result of a lot of laws. To give an example, nuclei-- which involve several nuclear particles, protons, and neutrons-- are very complicated. They have what we call energy levels. They can sit in states or conditions of different energy values. And various nuclei have various energy levels. And it's a complicated mathematical problem, which we only can partly solve, to find a position of the energy level.
Now, you can understand that it's complicated, and therefore it is no particular mystery about the fact that nitrogen, with 15 particles inside, happens to have a level at 2.4 million volts and that at another level it's 7.1, and so on. And the exact position of the levels is obviously a consequence of an enormous complexity.
But the remarkable thing about nature is that the whole universe, in its character, depends upon precisely the position of one particular level in one particular nucleus. In the carbon-12 nucleus, there's a level at 7.82 million volts. [? It's so hot. ?] And that makes all the difference in the world. The situation is the following-- that if we start with hydrogen, and it appears that in the beginning or in the earliest times, the world was practically all hydrogen, then as the hydrogen condensed, comes together under the gravity and gets hotter, nuclear reactions can take place, and it can form helium. And then the helium can combine only partially with the hydrogen and produce a few more elements-- a little heavier, but they distinction right away back into helium.
So it was for a while a great mystery about where all the other elements in the world came from because starting with hydrogen, the cooking processes inside the stars would not make much more than helium and a few others, half a dozen other-- less, as a matter of fact-- other elements. Faced with this problem, Professor Hoyle said that there is one way out. I think Salpeter also. He's here, so I have to be very careful.
If three helium atoms could come together to form carbon, we can easily calculate how often that should happen in a star. And it turned out it should never happen much, except for one possible accident. If there happened to be an energy level at 7.82 million volts in carbon, then the three helium atoms would come together, would stay a little longer than they ought to on the average if there were no level there before they come apart. And staying there a little longer is enough time for something else to happen and to make other elements.
And if there was a level of 7.82 million volts in carbon, then we could understand where all the other elements in the periodic table come from. And so, by a backhanded, upside-down argument was predicted that there is in carbon a level of 7.82 million volts. And then experiments in the laboratory with carbon show, indeed, that there is.
And therefore, the existence in the world of all these other elements is very closely related to the fact that there is this particular level in carbon. But the position of this particular level in carbon seems to us, after knowing the physical laws, be a very complicated accident of 12 complicated particles interacting.
So I wish to illustrate, by this example, that an understanding of the physical laws doesn't give an understanding in a sense of understanding significance of the world in any way. The details of real experience are very far, often, from the fundamental laws.
There are, in a way of speaking, in the world-- we have a way of discussing the world which you could call-- we discuss it at various hierarchies or levels. Now, I don't mean to be very precise-- there's a level of another level of another level. But I will indicate by describing a set of ideas to you, just one after the other, what I mean by hierarchies of ideas.
For example, at one end we have the fundamental laws of physics. Then we invent other terms for concepts which are approximate who have, we believe, the ultimate explanation in terms of the fundamental laws. For instance, heat. Heat is supposed to be the jiggling. And it's just a word. A hot thing is just a word for a mass of atoms which are jiggling. So that fundamentally, we should think of the atoms jiggling. But for a while, if we're talking about heat, we sometimes forget about the atoms jiggling just like when we talk about the glacier, we don't always think of the hexagonal snowflakes which originally fell.
Another example of the same thing is a salt crystal-- looked at fundamentally, a lot of protons, neutrons, and electrons. But we have this concept of salt crystals, which carries a whole pattern already of fundamental interactions. Or an idea like pressure.
Now, we go higher up from this, in another level, we have properties of substances like refractive index, how light is bent when it goes through something; or surface tension-- the fact that the water tends to pull itself together-- is described by a number. I remind you that we have to go through several laws down to find out that it's the pull of the atoms and so on. But we still say surface tension and don't worry when we're discussing surface tension of the inner workings always. Sometimes we do, sometimes we don't.
Go on up in the hierarchy. With the water, we have the waves. And we have something like a storm. We have a word for storm, which represents an enormous mass of phenomena. Or sunspot or star, which is an accumulation of things. And it's not worthwhile, always, to think of it way back. In fact, we can't because the higher up we go, we have too many steps in between, each one of which is a little weak when you haven't thought them all through yet.
And we go up in this hierarchy of complexity. We get to things like [? fog ?] or nerve impulse, which, you see, is an enormously complicated thing in the physical world involving an organization of matter in a very elaborate complexity. And then we go on. We come to things, words, and concepts like man and history or political expediency and so forth.
Which is a series of concepts that we use to understand things at an ever higher level. And going on, we come to things like evil and beauty and hope. Now, which end is nearer to the ultimate creator or the ultimate or, if I make a religious metaphor, which end is nearer to God? Beauty and hope, or the fundamental laws?
I think that the right way, of course, is to say that the whole structural interconnections of the thing is the thing that we have to look at. And that all the sciences and all the effortf-- not just the sciences but all the efforts of intellectual kind-- are to see the connections of the hierarchies is to connect beauty to history, to connect history to man's psychology, the man's psychology to the working of the brain, the brain to the neural impulse, the neural impulse to the chemistry, and so forth, up and down, both ways.
And today, we cannot-- and there's no use making believe we can-- draw carefully a line all the way from one end of this thing to the other. In fact, we've just begun to see that there is this relative hierarchy.
And so I don't think either end is nearest to God. And to stand at either end and to look out off the end of the pier only, hoping out in that direction is the complete understanding, is a mistake. And to stand with evil and beauty and hope, or the stand with the fundamental laws, hoping that way to get a deep understanding of the whole world with that aspect alone is a mistake. And it is not sensible, either, for the ones who specialize at one end and the ones who specialize at the other end to have such disregard for each other. They don't, actually. But the people say they do. Sorry.
But actually, the great mass of workers in between, connecting one step to another, are improving all the time our understanding of the world, both from working at the ends and working in the middle. And in that way, we are gradually understanding this connection, this tremendous world of interconnecting hierarchies. Thank you.
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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.