PRYCE: In this discussion I seem to stand for orthodoxy and you for unorthodoxy—that’s fair, isn’t it? For instance, you’d criticize the orthodox viewpoint on the ground that it doesn’t give enough prominence to actuality in physical theory. Is that right?
BOHM: That’s my point of view, yes. I think I could give an example which would help to clarify the reason why I’m opposed to the usual point of view. It is once more, basic-ally, the interference experiment with two slits. We begin with an electron gun, for example; accelerate electrons into a well-defined beam; pass them through a pair of slits fairly close together; and then detect them. One way of detecting electrons is with a photographic plate. Now, each electron leaves, as we all know, a track, a well defined track, on this plate. Let us suppose that we send in the electrons essentially one at a time. Let us say, for example, one per second. We know that each electron will leave one track as it arrives. A second later another electron comes and leaves another track. Eventually a large number of tracks accumulate on the plate and we get the well-known interference pattern which has been discussed earlier. As Professor Pippard said, there is no simple way to understand how the electron manages to produce a single track and yet show interference; that is, if two slits are open, the electron cannot arrive at certain places where it could arrive if only one slit were open. Let us now replace the single photographic plate by a moving-picture camera which takes a hundred pictures per second. Since there’s only one electron per second coming along, it’s clear that every frame will essentially receive either one electron or none.
PRYCE: These electrons are coming out at random from their source; it’s an averaged effect?
BOHM: An averaged effect, yes. Otherwise nothing is known about it. Now, after the films are developed, a scientist starts to look at them. He knows from the theory that it is possible that an electron may strike a particular plate before he has looked at it, and he may even compute the probability, even though this has no meaning for that one plate; the probability will have meaning only if he considers all the plates together and makes up the whole pattern which is the sum of the spots on all the plates. Nevertheless, everybody agrees there will be a single spot on a particular plate, an actual spot; that is, in the usual meaning of the word actuality.
PRYCE: Something that one sees when one looks down a microscope, you mean?
BOHM: That’s right. One sees it right there, actually produced by certain actions of the electron. The electron functioned in the plate to produce that spot, and once the spot is there it acts; it reflects light into our eyes and so on, it does everything that actual things are supposed to do.
PRYCE: SO that’s what you’re calling actuality here; the fact that there is an actual and visible effect. I think quite a lot of people looking at this experiment, which poses quite a difficult theoretical dilemma, would ask a question like this: Which hole did the electron actually go through? Here actually is used in the sense something that was part of the process before it got to the photographic plates. What would you say about actuality in that context?
BOHM: That is a very relevant question. In large scale physics for example, with billiard balls the answer would be quite clear. With the electron, we begin by not knowing what the electron is, and therefore we cannot answer the question, although I will try later to discuss projected or hypothetical answers.
PRYCE : But would you not allow the use of the world ‘actuality’ in the context of saying that whatever function took place was the kind of function that either went through one slit or through the other slit? ‘Actuality’ in this sense is still a kind of dirty word that one must avoid in physics.
BOHM: Well, it’s not that it’s a dirty word, but an inappropriate word. We must use careful logic here. If we see that something has functioned, it may resemble a particle in its functioning, or it may not. Do you remember Aesop’s fable about the seven blind men who encountered an elephant? One felt its trunk, and said: ‘This is obviously a rope,’ and another its leg, and said: ‘This is clearly a tree,’ and so on. Finally a man came along who could see, and he said it was one animal with all these various aspects. Now if the first blind man had tried to tie a knot in the elephant’s trunk, it would not behave as ropes usually do; if the other one had tried to make logs out of the ‘tree’, it would not have behaved as it should. They would have gotten into a great puzzle because they were supposing the elephant to be a rope or a tree, whereas actually it is something quite different. What I want to stress is that generally speaking most experimental results in physics are really the results of functioning. We make hypotheses which suggest what may be the actual process that produced the function, and then do another experiment to test the hypotheses.
PRYCE: I think I would agree with that, though I would perhaps not want to go into the philosophical description of what the theory does; Pm always much more interested in what the theory is predicting as the outcome of a particular situation. Though, again, prediction here is a bad word; it’s what the theory has to say about the systematization of the observations. Very often when we talk about prediction in physical theory we’re really talking about post-diction. We look at something and we say on the basis of our observations ‘This and that actually happened’ rather than ‘This and that will happen’. Don’t you agree that the emphasis on prediction, which is current in discussions of the philosophy of science, is a misplaced one? Prediction is by no means the most important function of a physical theory?
BOHM: I agree with you completely on that. Basically it’s one reason why I want to stress actuality; what we must do is to discuss, with the aid of theory, the actual relations that exist in the material under investigation. We don’t have to predict, but unless we have a good idea of what we’re talking about we cannot discuss the actual process with meaning. Now, in order to show better what I’m driving at, I will suggest a model, not a model that I necessarily believe in, but one that may help to get the idea across and that may be true. We have asked what the electron is actually doing. What might it be doing while it is passing from the source to the slit? That is the question. Well, I could propose, for example, that the electron is not a particle as we usually think of it, but a process. This process I am assuming to take place in a general medium—a ‘field’. In this field we suppose there is a pulse, a wave which moves inward and converges to a point producing a very strong pulse and then diverges and falls away. Imagine a series of such pulses one after another, all coming together to produce a series of intense pulsations on a certain line. These pulses will be so close together that the thing will look like a particle. It will act very much like a particle, too, in most cases, and yet it will act differently when it passes through a pair of small slits, because each one of the pulsations will form in a way which depends on how the whole incoming wave passes through the two slits. As a result, we have something which is neither particle nor wave. When you ask how the electron actually passed through the slit, and whether it actually went through one or the other, I would reply that the electron is, perhaps and in all probability, not the kind of thing that could pass through one slit or the other. In effect, it is actually something which is always form¬ing and dissolving, and this may be the way in which it actually happens.
PRYCE: Well, that’s fair enough, but of course it’s a rather vague sort of idea. It’s a vaguer interpretation of the process than one has in present physical theory. When you are being as vague as this, you have few points to which you can actually tie yourself to get further precision. And I think that precision of some kind is necessary in our descriptions. What would you say about the possibility of making a quantitative assessment of a situation, using a model or a language of that sort to describe the particular process?
BOHM: I would say first of all that it is premature to try to do this, quantitatively, with the very simple model that I proposed. This model is largely a guide to help to formulate our idea. The model can be developed further, and I have myself done so, in part, so as to put it into a more mathematical form. Let me give you an analogy: perhaps in ancient Greek times, certainly in the sixteenth century, atomic theory presented a rather vague picture of atoms moving around in a more or less complicated way, with the average results of this motion producing large-scale visible phenomena. Gradually the idea was made more precise—by applying it, for example, to the gas laws and to diffusion—until quite a bit later very precise ideas of atoms were available. Now, I think something similar has to be done here. We have to go slowly and to try to connect up to a precise experimental situation.
PRYCE: But you would agree that the present quantum theory does give a quantitative description of the outcomes of experimental situations such as you have described, quantitative in the sense that it predicts or specifies certain probabilities of things happening? So far as we know from having done experiments to verify the statements from the theory, the theory gives correct probabilities; but it does not give a complete description of the kind of intermediate actuality which I have asked you about. It does, of course, allow a certain amount of description of the actuality in the intermediate stages and of how the actuality enters into the theory. Isn’t that one of your main dissatisfactions with the present theory?
BOHM: Yes, I think I would call that the starting-point. Everybody agrees there is a certain kind of actuality at the large-scale level with which we do our ordinary experiments. For example, a spot actually forms on the plate and the mathematics cannot discuss that fact adequately, in my opinion. Now, I think that could be taken as a starting-point; but as soon as we start we discover that we cannot stop there. You see, if the spots which we find on the plate are actual, so for that matter is the whole plate, and so is the whole context, and so are the atoms on the plate. In other words, actuality is the kind of concept which is seen to be essentially one as soon as you try to analyse it in any logical way, and therefore it leads you on immediately to generalize the idea.
PRYCE: I think you would always like to be able to ask questions such as the following: When did the spot actually occur, or when did actualization of the possibilities take place? Whereas I think that there are certain questions of this kind which are grammatically acceptable questions, but meaningless in the physical context, and I suspect that this is one of them. I would prefer always to do my physics by avoiding this kind of question on the grounds that it is not a question of physics but a question of philosophy, and I would rather avoid that kind of philosophical question. I know it’s a matter of taste, and you, I think, would take the opposite attitude in this.
BOHM: Yes, at one level we could say our disagreement is a matter of taste, and then the person who wants to decide between us would have to decide on the basis of his taste. At another level we can each try to present such arguments as we have to back our particular choice. For I think that philosophy does enter into everything we do. Even if a physicist or any other scientist regards himself as guided purely by empirical considerations, he is none die less a philosopher, following an empiricist philosophy, whether he admits it or not. If you insist on looking merely at the facts, you cannot know whether it is better to be guided only by the facts, or whether it is better to be guided only by general opinions or ideas, or to combine these in some way or other.
PRYCE: Well, of course, I find my philosophy a little difficult, because my philosophy is to avoid philosophy. I know that even to make that statement is in itself a philosophical statement, so I’m rather in a trap here.
BOHM: Yes, that is why I said that no matter what happens you are bound to have some philosophy. It seems to me that the best thing to do is to recognize this as inevitable, to try to understand your own philosophy, to develop it and to criticize it, to allow other people to criticize it, and to see if you can’t become free of those arbitrary features which are in it.
PRYCE: I think your objection to present physical theory is that it’s inadequate from a philosophical point of view. You don’t like some of the philosophical connotations that it has, whereas I would take completely the opposite viewpoint: that I’m quite happy with the theory because it gives what I would call precise answers to precise questions. But the degree of precision here is something which is limited by the nature, I would believe, of the physical world. There are certain questions to which I can’t get an answer because, in the context of what the physical world is, they have no real meaning. And some of the questions concerning actuality are, for me, questions of that type. Now you, on the other hand, would like to say you are dissatisfied with the present theory, not because it gives false predictions in any physical situation, but because it’s philosophically unsatisfying. You’d therefore like to amplify it; but, in so doing, you want to put in quite a lot of new things which at the moment one doesn’t know how to verify experimentally because they seem to have no experimental or verifiable consequences. This I find unsatisfying from my point of view.
BOHM: Well, I’m not as completely satisfied with the present theory as all that. It does do a large number of things correctly, it gives statistical predictions quite well, but it does not discuss the individual process, the individual process which actually takes place, and it claims that it is not necessary to do this. But this claim is based only on the fact that it doesn’t do it and that if you attempt such discussion within the present framework you cannot succeed. However, other frameworks exist in which you can make the attempt, and the question is: Why not try them? Thus, the notion that atoms might be important was first considered for philosophical reasons long ago. Even some physicists of the sixteenth and seventeenth centuries were guided to some extent by such ideas as that there might be an atomic constitution to matter, though many others objected that this was only speculation, philosophical speculation; that one shouldn’t take it seriously and had better stick to questions of fact.
PRYCE: But, of course, it has been verified experimentally since then.
BOHM: Yes, but there always had to be a time when it wasn’t verified, and somebody had to entertain the idea before it was verified.
PRYCE: Fair enough.
BOHM: And now if we have a situation where people are dis-couraged for philosophical reasons from entertaining new ideas because they may be philosophical, this may impede the progress of physics.
PRYCE: Oh, I think so too. I think everybody should be left absolutely free to criticize everything that is taught as orthodoxy. It’s only a question of whether you’re really going to make progress by speculating on certain lines or speculating on other lines. And this is rather a matter of taste and human ability. Some people are adepts at speculating along lines which nobody else would have explored, and a certain fraction of the major discoveries of physics have come in this way; somebody exploring something which seems to be absolutely crazy has hit upon what is the right explanation. The physical world does work in a crazy way, sometimes. On the other hand, to make that a prescription for how everybody should think about the physical world would be going too far, because then there would be chaos in the way that we look at physics.
BOHM: I don’t really see that there would be chaos if everybody considered his philosophical ideas. Perhaps it’s the other way round, that chaos will occur if everybody has philosophical ideas without noticing that they are philosophical. I would put it this way: that nobody should be compelled to adopt a certain philosophical idea; that would be ridiculous, and would impede the progress of science. Besides, it could have no justification whatsoever. But we must come back to this fact, that everybody does have philosophical ideas. If somebody has an idea without knowing it, and he is simply following it mechanically, then he may be limited, so that he doesn’t consider new phenomena. For example, we’ve had this situation with parity conservation recently, where it seemed quite natural to suppose that the world is symmetrical and that parity should be conserved under reflection. But when eventually it was conceded that it might not be conserved, this disclosed a whole range of new phenomena. An important part of progress in physics is, therefore, to free ourselves from preconceptions which we are following mechanically because we don’t notice where our thoughts come from.
PRYCE: Yes, it’s difficult to free one's self from preconceptions. One doesn’t know one’s got them; one doesn’t realize that they are preconceptions. This is, of course, where one has to cultivate the art of criticizing the basis of everything that one is doing. It’s easy enough to do negative criticism, but it’s very much more difficult to put the right new concept in the place of the old. This is where the flash of intuition is required.
BOHM: Perhaps we ought to ask ourselves what we mean by intuition, because it is commonly accepted that every now and then a brilliant intuitive flash will occur. But there are certain conditions required for intuition to operate, and one of them is to work on the problem from a number of angles so as to disclose your preconceptions and free your mind. In other words, when intuition doesn’t operate it is mainly because something is preventing it from operating, namely, the previous conceptions, the general framework, if I may put it that way.
PRYCE: We would both agree, I think, that one of the difficulties at the moment is that a great deal of our physical theory is couched in terms of space and time, in terms of certain things happening at certain places and certain times. In the theory, these places and times are regarded as being well specified or well specifiable; but everybody would agree that this can’t be satisfactory, because when we ask how we would specify a place in space, and a particular time associated with it, we can think of no physical means by which we could give it a sharp enough meaning to act as a background for the theory that we want. Yet we’re so conditioned to thinking in terms of space and time that we find it extremely difficult to formulate any alternative conceptual framework.
BOHM: I’m very glad you brought this up, because it is really the key question that physics faces today. The mere application of quantum mechanics, as you say, has raised doubts whether we have a correct conception of space and time. Now, what can we do about this? That is the question that I ask myself. Here, I think, philosophy can guide us, not only in helping us to criticize our previous ideas, to know where they came from and to follow their evolution and development, but also in another way. In common experience we find reflected all kinds of possible ideas; but we tend to stress certain ones, for example the Cartesian idea of space and time in which it is assumed that every point can be measured and specified in terms of a set of continuous co-ordinates. Physics has relied on this idea for the past three centuries, but it is not actually a natural idea, nor is it the one which people had before. I want to propose another idea of space and time, the topological idea. By this I mean the study of the non-quantitative aspects of relationships in space (and, of course, in time also). For example, ‘inside’, ‘outside’, ‘before’, ‘after’, ‘between’, ‘connected’ and so on. I might mention one typical idea: How do we actually locate something in space? If we wanted to locate a glass on a table, do we give its latitude and longitude, for example, which is what the Cartesian notion would be? Obviously not. What we do is to say it is on the table, which is in the room which is in the building on the street in this city, and so on. This is a series of topological relations of being within or upon. Now, we get a whole series of such relations and that is how in common experience we locate something.
PRYCE: I agree, but the difficulty with the topological idea, at least for people who are trained with the mathematical techniques current in this part of the twentieth century, is that the mathematics is rather unfamiliar. One doesn’t know so well how to put physical laws into quantitative form using topological concepts as with the more familiar algebraic and Cartesian concepts.
BOHM: I admit that, but it cannot be regarded as a criticism. In the sixteenth century people didn’t know differential equations, and this was one of the main difficulties in the way of the development of classical physics. In fact, it was a gigantic achievement for Galileo to be able to describe accelerations algebraically. Until he did this, he was just as lost as everybody else in the problem of acceleration. So mathematics is one of the keys. But I do not believe topology is as difficult as people generally think it to be. What is more, I see very strong analogies between the way in which topological relations would be expressed and the way in which the laws of quantum mechanics are now expressed in terms of operators and matrices. The fact is that you can set up topological co-ordinates which are discrete; you could select o and i, for instance —‘zero’ if it’s ‘outside’, ‘one’ if it’s ‘inside’. Series of similar discrete numbers have been arising in quantum mechanics all the time, so there is already a certain a revolution in thinking which will make quantum mechanics look like a minor change. If you will only look into the way we actually use our (I cannot get away from the word) actuality space and time, you must admit that this notion is very, very general; it appears in every part of mathematics and physics so far. Some day in the future we may not use actuality—nobody knows what the future will bring, of course. But we have not yet exhausted what can be learned by thinking about the meaning of the word ‘actuality’.
PRYCE: Nor have we exhausted what we can do with the quantum mechanics of fields in their present context.
BOHM: Except that we have discovered contradictions and inadequacies so that nobody knows quite how to proceed. I am suggesting that there should be something that cuts off the infinities due to the fact that we have points— precisely-defined mathematical points. Let’s go back to the question: ‘Are there any such things as precisely- defined mathematical points? Are they not pure abstractions? Well, the answer is that obviously they’re pure abstractions and they have served their purpose; we have reached their limit. If we go back to topology, from which these abstractions came, then perhaps we can make some progress. The topology must not only be the topology of space but the topology of time, because space and time are shown by relativity theory to be deeply related. If that is the case, we have no other alternative but to talk of actuality; to discuss action as the fundamental conception; to say that one thing changes and becomes another, and that this defines the process of space and time.
PRYCE: Wouldn’t you say that it’s not really space and time that you want to talk about now? These topological relationships are in ordinary life the relationships between objects; the space and time are, so to speak, a medium of thought that you put there to embed them in.
BOHM: I agree with you completely on that. The whole direction of my thinking is to recognize this and to free myself from this medium of thought. I say that the actual process which takes place is fundamental, and space and time are the means of describing the order in this process. Instead of beginning with space and time, as if they were fully in existence, and then placing various objects in it, we first begin with the whole process as it is and then try to discuss the order of things in space. But I also want to add, of course, time, since I am discussing the topology of process.
PRYCE: Well, I come back to my difficulty about this. If you are going to develop a topological theory of this kind you’re putting into what you’re going to discuss a lot of things which are not in the present theory. Not only several more things, but infinitely many more things, are playing a part in your kind of formulation of the physical world, and these are things which somehow don’t seem to come into the apprehension of what one does in the laboratory. There’s so much arbitrariness in what you’re doing. This I dislike.
BOHM: But there is also very much arbitrariness in what has already been put in. For example, the whole idea of co-ordinates is, to some extent, an arbitrary injection largely based on mathematical convenience. It worked, up to a point, and now we all admit that it doesn’t work.
PRYCE: ‘Arbitrary’ is the wrong word there. It’s an abstraction that has been abstracted too abstractly, isn’t that it? But it’s not arbitrary so much as going too far in the direction of abstraction.
BOHM: And going too far in an arbitrary manner. You see, anything which goes beyond correctness is arbitrary. In so far as it is not correct, what we have added is arbitrary. So I think we must say that the very use of co-ordinates is, to some extent, arbitrary. This is the key focal point where the trouble arises at every step of mathematical calculation.
PRYCE: Well, it’s not arbitrary, because this is something which we find in mathematical textbooks. We know how to use it and we don’t know what else we would put in its place. In that sense it’s not arbitrary.
BOHM: But that conclusion is based only on our present deficiencies. Suppose, for example, that somebody had not been trained in differential equations, and therefore did not know how to solve a problem in classical physics. This would be an arbitrary restriction from one point of view; because of the inadequacies of his background, he could not solve the problem. From another point of view, of course, we could explain why he cannot solve it. But there would still be arbitrariness if he insisted that whatever he had learned before must be the correct method of solving, and that he found it too difficult to learn other forms of mathematics. If the man acted in that way, you could say there was a certain arbitrariness in his procedure.
PRYCE: Yes, though I think one is still in a difficulty. Nature is behaving in certain ways that we can understand. It’s also behaving in certain ways that we can’t completely understand. It doesn’t give us any clear-cut sign that our concepts are absolutely wrong; they’re just slightly in-adequate. And we’re in the unfortunate situation that if we adopt your point of view of trying—so to speak—to undermine the whole conceptual framework of present- day physics, we don’t know what to put in its place. We can’t make any alternative prediction about what kind of phenomena to look for in which your new ideas would have verification. We would like to be in the position where Nature forces us to think in certain ways. But in the present situation Nature is not playing the game. We know that our theory is fairly inadequate, but we are not being given the vital clue. We can’t tell what sharp break in our habits of thought we must make.
BOHM: Couldn’t we perhaps say that Nature is not playing the game because we’re not playing it either? If you have a game, you cannot expect it to be played by one side only. In other words, we have to take some active steps to look at it in another way. I don’t think the situation is so difficult; there is something inadequate, but with certain modifications of theory we could at once enter a whole new domain of questions which can be investigated as soon as we know how to frame them.
PRYCE: Well, how do you think we ought to handle this when we’re talking with students in universities? Should we say to them: ‘Look, all the theory that we have is really quite inadequate, and you shouldn’t pay too much attention to it? Or should one be fairly dogmatic about what the theory has achieved, and leave it to the pundits and the experts to criticize the theory?
BOHM: That is a question that I’ve considered a great deal, and I think there is a way out which is not so extreme. In fact, I’ve just encountered the problem recently in giving some courses in quantum mechanics and atomic physics to elementary students. It seems to me you could get out of the difficulty, essentially, by saying that all of our theories are in some way false, but there is a great deal of true relationships in the false theory. For example, in the sixteenth century people may have treated matter as continuous and not atomic, but a great many true relations of pressure and temperature were obtained thereby. When we discover the atomic constitution of matter, we change the idea that matter is continuous, but we do not change the relationships, at least within a certain approximation. As science develops it is continually trying to find what is the real truth in what we are saying, and where it is false. On that basis we can go forward. In any case, it is essential for us to recognize that a great deal of what we say is probably wrong, although we don’t realize it.
PRYCE: That’s rather negative. Very often we’re in the position that we realize that there’s something lacking in the theory, but we don’t know what it is that’s lacking. Don’t you think that that is a negative approach?
PRYCE: Confusing, rather than constructive, in discussing with people who have less experience of what it’s all about.
BOHM: It needn’t be. You see, it could be negative, but it needn’t be. We tend too much to talk only about the solutions to our problems, and not about the problems themselves. People seem to become discouraged when they see a problem. That’s their first reaction. Therefore we don’t mention problems; it’s more or less keeping a stiff upper lip. And then other people play on this: they would like to talk always about solutions, to show how much they know, perhaps. I think that we can admit that we have certain problems and talk about them and recognize they’re there, without necessarily becoming completely discouraged by them. This is really something which ought to be changed in the teaching of physics.
PRYCE: Well, yes, I think that’s right. It’s much easier to give finished and completed results, finished pieces of work, rather than to come along and say: ‘Look, I’ve been thinking about so-and-so. I think the theory is in a very unsatisfactory state, but I don’t know very much what to do about it. This is the difficulty.
BOHM: Part of the proper training of a scientist is to get used to this situation. This is inevitably what they will be meeting, at least when they graduate and start to do research. It is no use pretending to ourselves that the theory is all perfectly correct, because as soon as they begin to do research they will discover that it is not. Why delay the shock until then?
PRYCE: I think you’ve probably got the right idea. After all, if you’ve got a good man you can’t keep him down, so you may as well let him know the worst at once. Then he’ll be in a better position to do what we can’t do.
BOHM: Yes, and maybe even the people who don’t seem to have that much ability will be more ready to take the facts than one thinks. You see, there is a desire for everybody to feel that everything is all right—that’s comforting. But if we simply state that we have made certain achievements and we also have certain problems I think that most people will finally accept that that’s the situation as it is.
Transcribers note: First transcription on September 5, 2015. Version 1.0