The Implicate Order: A New Order for Physics<
by David Bohm
David Bohm is Professor of Physics at Birkbeck College, University of London. The following article appeared in Process Studies, pp. 73-102, Vol. 8, Number 2, Summer, 1978. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.
Transcribed and edited by Dean R. Fowler. Transcriberís note: The following essay is the transcribed version of an address given by David Bohm at a conference organized by the Center for Process Studies. As the transcriber, I have employed my editorial discretion in two primary ways. First, I have tried to make the written word flow at those points where the spoken word was somewhat awkward while maintaining the informal nature of Bohmís presentation. Second, numerous questions and points of clarification arose during the course of the address. I have been somewhat selective in regard to which topics should be preserved. Summaries of some of these comments are included as notes. Third, I have not included the presentation of the mathematics, which may be found in D. Bohm, Foundations of Physics 3, 139, 1973.
I am going to talk today about the implicate order, and perhaps I should first say why I became interested in the questions of order. Order obviously involves everything that is possible in the whole of life, so my interest in order extends to order in general. You cannot define order (I will take this for granted): order exists; order is perceived. But we can develop certain notions of order. One of the reasons behind my study of the notion of order is that the foundations of physics are not clear at present. There is something which I would call a "muddle" going on, and it has been going on since quantum mechanics has been developed. As we go along, I will try to bring out what the confusion is. What you have to try to do with confusion is to sort it out. It is no use arguing about confusion, because you will only get more confused. Now the first point is that relativity and quantum theory are not really compatible. I will go into this in some detail to show that the notions of implicate order grow naturally out of real physical and philosophical problems or questions in physics. They are not just imagined or dreamed up in some arbitrary way.
I. Relativity Theory
The first point I will discuss is relativity. If we go back to the nineteenth century, one of the major theories was the ether theory -- the notion that space is full of a pervasive medium consisting of material particles with strange properties. It was believed that this would explain, at the very least, electromagnetism and probably gravitation as a wave in the ether. People also wanted to explain matter itself as a structure in the ether. For example, there was the smoke ring vortex model of the electron. The theory was aimed ultimately as a total explanation of everything.
This is really what was behind Lorentzís approach to these questions. Lorentz considered the structure of matter as made of charged particles. Letís say that we have a crystal with some regular array of particles that are in equilibrium in a certain configuration and with a certain structure, so that the forces of attraction and repulsion due to positive and negative charges balance in this configuration. The Michelson-Morley experiment had shown that it was not possible to detect the velocity of the earth relative to the ether. Lorentzís explanation of this situation was along these lines: he showed, using Maxwellís equations (assuming that Maxwellís equations hold in the frame of the ether), that if the field of force is spherical in the rest frame of the ether then it contracts along the direction of motion: l = l0 .times the square root of 1 - v2/c2 Therefore the entire structure must collapse in that ratio, and, of course, if v = c it would collapse into a flat structure. If you tried to go faster, you would leave shock waves behind, and the entire system would fall apart. It is implied that matter cannot actually reach the speed of light or go faster than the speed of light in this notion, because matter is nothing but a structure in the ether and it cannot do anything which is not possible for such a structure.
In this way Lorentz explained the negative result of the Michelson-Morley experiment. In addition, because part of the inertia of a particle is due to the electromagnetic field around it, as you speed up such a particle the electric field produces a magnetic field, the changing magnetic field produces a back EMF, and this whole reaction of the field produces a resistance to acceleration. Therefore, there was a contribution to the mass coming from the electromagnetic field, and this contribution depended on the structure of the electron. You could have said that the effective mass was equal to the mechanical mass plus some sort of electromagnetic mass, which had the property of increasing with the velocity in the ratio of 1 divided by the square root of 1 - v2/c2, because as the field gets stronger the whole system contracts.
If you assume that the mass was all electromagnetic or that it all behaved in the same way as electromagnetic (which was perhaps suggested by cathode ray experiments which showed that the ratio of e by m actually went as 1 divided by the square root of 1 - v2/c2, then it follows that particles get heavier in this ratio. Furthermore, if you went into the way in which the force fields changed, you would deduce a change in the behavior of clocks, both because their components got heavier and because the force fields which hold the clocks together alter. Therefore, you were able to show that if t0 is the period of the clock at rest in the ether, the clock slows down in the ratio of t=t0 divided by the square root of 1 - v2/c2.
The third point, namely the change of simultaneity, was the most fundamental one. Two clocks together (call them A and B) would both slow down if running together. But if one was slowly separated from the other and then brought back to the same velocity, you would see that the two clocks were out of phase from one another. While separating, the second clock B is going more slowly than the first clock A. Thus, A and B get out of phase. They no longer register the same time. If you brought them back together, they would, however, get back in phase.
As a result we obtain a shift among the clocks as to what is meant by "at the same time." This was the most fundamental new concept of the relativity of Lorentz. Changes of clocks and rulers were already well known in physics due to temperature and pressure and so on. However, now they might also be due to the velocity relative to the ether.
But the change in what was meant by "at the same time" produced more serious problems. Philosophically, it had previously been thought that there is a unique moment of time over the whole universe and that there is a series of such moments. It became hard to define what that view of time meant experimentally because separated clocks ceased to read the same time.
If you use the three concepts -- change of length, change of time, and rate of change of simultaneity -- you can deduce the Lorentz transformation, (It can also be deduced in other ways.) If you apply the Lorentz transformation you will get the result
c2t2 - x2 - y2 - z2 = c2tí2 - xí2 - yí2 - zí2
where x, y, z, t is one system of coordinates and xí, yí, zí, tí is another. From this, it follows that there is no way to tell what your speed is relative to the ether. This was really the problem which arose.
A great deal of confusion came about through this situation. It gave a tremendous impetus to the positivist philosophy. People said that if the frame of the ether is unobservable we should drop it. In a way that was right, but in a way it was not. The ether, I think, was dropped for the wrong reason. That is, people made the right step for the wrong reason. That brings about confusion, because the situation is neither right nor wrong anymore. If you accept it, it is wrong, and if you reject it, it is wrong. Confusion is much more difficult to deal with than just plain error. If you have an error, you may simply say: "That is wrong. Letís give it up." But if you give up what is confused, you are just in the same state as if you keep it. What you have to do with confusion is to be very patient and sort it out.
The confusion was this: People had said that we should really be able to observe the ether, and if we can never observe it, something is wrong. Of course, that does not prove that there is no ether. But if we can never get a hold of the thing experimentally at all, it is not clear what we mean by it, at least as a concept. To infer from this that we should go back to the phenomena again was correct. This ether was merely an idea. Nobody had ever actually seen it or proved its existence. You have plenty of evidence of the existence of air, although it is invisible. You can burn it, you can compress it, you can weigh it. But there was no such evidence of this ether.
In one sense, what Einstein did was just to go back to the phenomena in order to look at things afresh. But the problem is that what Einstein and others did, they did for reasons of a positivist philosophy. The positivists said that entities which are unobservable should never be considered in physics. From this it followed that we should drop the ether. This was a correct step, but the principle behind it was wrong. Let me explain. Thousands of years ago Democritus proposed the notion of atoms. Nobody was able to observe them for 1500 years or more, but gradually people found out how to observe atoms. Now if you were to say that you would not even think about atoms until you were able to see them and you could not see them with your naked eye or with simple instruments, then you would never find them at all. I must consider the idea of something unobservable if I am ever going to find it. First I must think about it. I must think how I am going to find it if it is there. Then I look and see if I can find it. If I say that it is of no significance until it comes before my eyes, I am stuck.
The positivist philosophy became commonly accepted -- at least various versions of it: empiricism, operationalism, etc. Some of the positivists argued not that you have to look at something for it to exist, but that it must be a part of some operation in the laboratory or some other empirical structure. I am going to call all of these ideas together by the name "positivism." Although the various versions of positivism are all somewhat different, they have one point in common. They all say that the essential point is the phenomena and that physics or any law of science consists of nothing but a correlation of these phenomena. If you have no phenomena, you have nothing to talk about. This is the basic point of view which became very popular.
Einstein, however, did not hold to positivism. He went back to the phenomena, but later said that we must go forward to the essence. So he did not stick to the phenomena.l When he was 16 years old, he thought of the question: what would happen if I moved with a light ray and, for example, tried to look into a mirror? You would never see anything. This is a perception through the mind. Light is in some way different from sound. You can catch up with and overtake sound, but not light. Also, Einstein felt that light was inherently dynamic; yet at the speed of light you would see a static wave. Something was wrong. This perception was the germ or key of relativity. Perceptions of this nature are generally the origin of new discoveries -- not the experiments, but the perception of the nature of our thought.2
II. Appearance and Essence
I now want to say a few things about the relation of appearance and essence. This is necessary because positivism, in the broad sense of the term, has permeated science since the late nineteenth century. Positivism has gained prestige partly through the misunderstanding of the question of the ether and partly through its accidental attachment to relativity. People thus inferred that if positivism is supported by science, it must be right.
We begin with appearances whenever we look. Things appear to us in various ways. Appearances are limited; they are particular; they are contingent; and they are always changing. Appearances are not significant in themselves. The Greeks emphasized this point. They said that the main point was reason. For example, if you walk around the table, its appearance will change all the time, but you know that the table has a constant form. Piaget has made experiments, I think, asking small children to draw a table. They always draw it straight up, showing the way they think it is, and not the way it appears. It is a very subtle thing to draw with perspective. It is necessary to rediscover how something looks, as distinct from how it is.
The positivists began to talk as though pointer readings and measurements and various things like that were the essence of physics. But pointer readings are not very significant unless they are reading something. Thus, an ammeter is supposed to read electric current. Physicists would be rather bored with the game of just trying, for example, by direct manipulation of the needles, to make their meters read certain numbers. Evidently it would not be very interesting to arrange beforehand in this way to have all the numbers agree with predictions. The main point is that the readings are supposed to be reading something of essential significance, which is beyond the readings.
As mentioned above, young children are similarly looking for the essence behind the appearance -- the relatively constant, universal thing, rather than just the immediate appearance. Science is merely going on with this approach, and going deeper. The ether theory and the atomic theory were two of the early theories which attempted to give some view of the essence.
According to atomic theory everything is made of atoms, which are permanent. They move through space. Their changing arrangements give the explanation of all the changes in the appearance of matter, not only the changes as you look at it, but all the changes which occur, such as burning, decay, generation. These are nothing but a rearrangement of atoms. It was not treated just as an appearance. This point is very important, and it is what positivism neglects.
Letís suppose that we are studying some actual fact A. We have all sorts of immediate particulars, 1, 2, 3, . . . n, which I shall call P1. These might be pointer readings or appearances of animals or plants or descriptions of various kinds. These particulars are very superficial and are merely the result of the fact that some very tiny aspect of reality has been abstracted and we say that that is what we have seen. When we come to some universal explanation, the immediate particulars are translated into what we will call the "essential particulars," Pe. For example, in the atomic theory the essential particulars are the structures and arrangements of atoms. We are no longer talking about the way that something looks, but about the way that we think it is. (And not necessarily the way that it is; that is a more subtle question)3 The key point is that the universal theory does not merely correlate the phenomena, but it explains the very existence of the phenomena and also correlates them if it is a good theory.
The positivist approach (or empiricist, or phenomenalist) emphasizes that the phenomena are given and are correlated by the formulae. While positivism may free you from certain assumptions, it involves problems. Thus, people take a certain view of the essence, which becomes too rigid. For example, classical physics or the atomic theory came at a certain stage to be regarded as the absolute truth -- the essence. The positivist was able, by means of his philosophy, to free himself from classical physics by saying that such notions were just metaphysics, so that he could consider other ideas. But in freeing himself in the first step, he became entrapped in the next step, because the phenomena inevitably depend on previous ideas to be expressed in thought. You must use some ideas to describe the phenomena, some way of thinking, and that way of thinking is generally the old way of thinking. The old way of thinking is whatever is at hand. You donít even notice that you are using the old ideas when you describe the phenomena; for example, you put them into time and space or say that objects are solid. When you describe them, you use thought, and that thought is the old thought. Therefore, the phenomenalist point of view at first appears to free you from fixed thought, but in the very next step, it makes you very subtly a prisoner of that thought. It tends to prevent new ideas, rather than to help to fathom new ideas. Therefore, although positivism made it possible to make a step in the beginning, it has had a generally negative effect. It could also have been called "negativism," I suppose.
I will return to Einstein to give further clarification to this point. Einstein went back to the phenomena, and he developed the theory of relativity, which in the beginning was a theory of the phenomena. That is, there were certain observations to be taken in time and space that were connected by the Lorentz transformation. When the theory of relativity came in, the old view of the essence was gone, and there was at that moment no new view of the essence. Therefore, it was a theory of phenomena in the first instance, and we should consider it to be that.
The old idea in science was that there was a permanent, final essence which we are looking for, although perhaps we have not got it yet. Positivism freed us from that idea to some extent. But as I have pointed out, positivism held us in a new form of rigidity. We have to be free from both forms of rigidity: the rigidity of the idea of a permanent essence and the rigidity of positivism.
Our inquiry at this moment is not into nature itself, but into our way of thinking about nature. This is what is at stake. We must give quite a bit of our attention to our thinking, which itself is a part of reality. As a part of reality our thinking requires attention, just as any part of reality does. The distinction between appearance and essence is always present in our thinking. It is part of the order of thought. There is a distinction made at any moment between the content of appearance and of essence. For example, even in immediate experience, you have the table which is there and the table as you see it. But essence is not permanent either. Essence is perceived through the mind. Probably that is the case with appearance too. To say "I have a flash of understanding, and I see" is a form of perception -- a perception of relationship, of necessity, and so on. I call this "insight." Theory is basically a form of insight. There is no meaning to the idea, I propose, that a particular insight is an ultimate or absolute truth. There is always room for a new insight, which shows the limits of a previous insight. Each thing appears to the senses, and its essence shows to the mind; that is, they are both kinds of appearances.4
Einstein probably implicitly understood this sort of thing because he gave up positivism after he had obtained a new law of the phenomena in relativity. The right approach is sometimes to go back to the phenomena. But we donít stay there forever.
Relativity has led to a very serious problem, because in relativity there is no way to make the connection between Pi and Pe. This is one of the key problems behind relativity, and it will be the same problem that underlies quantum mechanics. I am going to suggest that both relativity and quantum mechanics have not yet gone beyond the phenomena. They are correlations of phenomena, and people have gotten so used to correlating phenomena that they implicitly assume that that is all that they can ever do.
It was proposed in the ether theory that reality was made of ultimate material particles constituting the ether. But as I have suggested, the ether theory was given up for the wrong reasons. As long as you had the ether theory, you had a view of the essence, namely, the ether. Matter, then, was taken as an appearance, inside the ether -- for example, as a vortex or a smoke ring. But any attempt to make a theory of particles relativistically leads to impossible problems. One view is that a particle is some extended structure. Now if I make a space-time diagram of a particle at rest whose boundaries are given by two lines and then suddenly accelerate it to another velocity, I see that if I push on one side of the object it immediately responds on the other side. However, in Einsteinís views of relativity, this is not permitted. An impulse or a signal cannot be carried faster than the speed of light. Consequently, you cannot have a rigid or extended body in relativity.
The original atomic theory had rigid bodies of some sort, but rigid bodies are not possible after Einstein. Letís say that a particle is made of smaller bodies -- of subparticles. Each of the subparticles, if it is extended, will meet the same problem as a rigid body. Therefore, a particle cannot be made of extended subparticles. Now then, what if it is made of particles with no extension at all, such as points whose tracks in space-time can be represented by lines? You will find that the fields around these point particles are infinite, leading to inconsistencies such as infinite mass and infinite charge and so on (especially in quantum mechanics). These inconsistencies can be removed to some extent by renormalization. But it is not logical just to remove infinity by calling it zero. You may get certain right answers by irrational procedures. For example, if x/y = z, then if I write x = 2x and y = 2y, I will get the same answer for z even if x and y are not zero. I can thus have a complete contradiction and get the right answer. Having the right answer is no proof that you are logical. However, when you try to work out something else, the contradiction is going to muddle things up. Similarly, people get right answers out of renormalization calculations by using irrational or illogical procedures. They may be right to do this, because it could be a clue to something, but they are not really understanding what is happening.5
Therefore, neither the point particle nor the extended particle can be used to make a theory which would enable us to understand what is happening. Relativity indeed implies that we have to have a world tube in which something is going on -- a process, a structure. Also, it implies that there is a field extending beyond that world tube, gradually falling off, and that there is another world tube which gradually emerges from the field of that world tube. So there is one inseparable universe. However, in some abstraction (that is, in the appearance) there is a separation of these particles, because the field in between is weak and may be neglected. Nevertheless, in essence, there is no separation in this view.
A serious problem exists, because nobody has in fact succeeded in making this kind of a theory. That is, the theory of relativity does not have a theory of matter.
To bring this out, I first point out that Einstein said that the basic concept is a point event. The thing that gives the point event content is a field (x,t). There can be no extended structure for the reasons given above, so that we cannot discuss the permanent identity of a particle as continuing in time. So there is nothing left but to say that the basic concept is the point event -- something with no extension in space or time. Everything is built out of that.6
The point event, as considered by how it would appear to some observer, would look like something which no sooner came into existence than it went out of existence. It would have no idea whatsoever. It would flash in and out of existence in the very same step. That is, it is the field at that point. You might think of the field over a period of time as an entity of some sort having an identity, but this will not work, because you could have taken equally as well another Lorentz frame in which the identity was the field along another space-time track. In other words, it is highly arbitrary to associate field points along a certain line and say they belong to some mathematical entity. In fact nothing but this point event is a basic concept. Anything you build is a structure of point events -- an interrelated or correlated structure. But any such structure is a process. Any order of point events can only be understood in this flowing movement -- as process. The essence is process.7
The serious problem in relativity is that it implies that we are committed to make an explanation of matter as a structure of events, of field events. We must look for differential equations to determine the laws of the field (as Einstein said) because only differential equations describe the infinitesimal, contiguous connections of events. This is a linear model with no long-range connections. But if the equations are only linear, any structure will diffuse away and, therefore, must have some nonlinear terms. One would hope that the stability of matter would be explained as a solution to such nonlinear equations, meaning that matter is a structure of these primitive, undefined space-time events. Einstein and others have sought to explain matter in this way. The immediate appearance of matter would be translated into this essence, that is, a certain structure of events. Matter as it appears to us immediately is some "thing" which is in itself stable. But according to the theory I am describing, matter is no longer a "thing"; it is translated into the essential particulars as a structure of primitive events.8 You can see how Einsteinís thinking was going. He fully appreciated the importance of not sticking to the appearances.
However, it was not possible to do this in any satisfactory way. As a result, relativity has no theory of matter in it at all. There are no measuring instruments; no matter; no people. There is nothing in this theory. There is nothing but appearances. It is not a theory of the essence. Einstein fully hoped that it would become a theory of the essence, and he saw that it was necessary to make it one.9
III. Quantum Mechanics
Quantum mechanics is in the same situation as relativity, and perhaps even a worse one. As you know, Planck brought up the idea of discrete quanta of radiation, and Einstein, the photoelectric effect. Originally, people thought atoms were jelly-like things. Therefore, it was quite easy to see why atoms would exclude each other and form stable matter. But with the planetary atom of Rutherford there was no longer any stability in matter. The atom had a nucleus with electrons orbiting around it. Because of radiation, the electron would quickly spiral into the nucleus, and the atom would not exist at all. Therefore, matter would not exist. So you have the same problem in quantum mechanics as in relativity. Behind the problem was the fundamental question of the existence of matter.
Bohr, by a certain insight, was led to suppose that there is a lowest orbit, for reasons that are entirely outside of our understanding at present. The electron will never fall below that orbit, and this would explain the stability of matter. This was a most radical step. It followed that there might be other orbits which are also discrete, which would explain the discrete spectra, and so on. But everyone realized that this was an ad hoc theory, somewhat arbitrary. It had no explanation of the movement of matter at all.
Later on came the matrix mechanics of Heisenberg, the wave theory of Schroedinger, the Born probability interpretation, the transformation theory of Dirac, and others. These developments led to a systematic structure which made possible tremendous success in the computation of all sorts of results. It accounted for the stability of atoms, molecules, large bodies of macrodimension. And it showed that actual calculations were possible in a wide range of fields with impressive numerical agreement with observed facts.
Most physicists thought that at last a new essence had been arrived at. They were so impressed with the success of quantum mechanics, that they felt that this must be the essence. However, I would suggest that it is not, because quantum mechanics, while very successful, is just correlating phenomena. There are serious problems as to what quantum mechanics means, and I will summarize them briefly.
We have the wave function which Schroedinger brought in as a function of x and t. (Notice that he still used the old ideas of time and space coordinates.) Typical probabilities determined by the wave function were (x,t)2 , the probability of density of particles in space. If you "Fourier analyze" the wave function, you get a probability of momentum, and so on. The wave function was at the heart of a system of computing probabilities.
The most interesting new point was that the many-body wave-function is a function of all the coordinates of all the particles. This is called the configuration space. You could no longer picture the wave as being in space at all. It was totally abstract. The idea of calling it a wave was really wrong. This point is crucial because this multidimensional wave was necessary for all the essential results of quantum mechanics. Without it, quantum mechanics would collapse; it would give results of trivial significance. Therefore, there was no picture at all of what sort of essence the wave function might be referring to. It was just a characteristic function from which you could compute all sorts of probabilities.
The Heisenberg Uncertainty Principle was an important part of the interpretation. Let us think of an electron microscope giving the situation of a target T with an atom A in the target with an electron coming in and being scattered by the atom. An electron lens then focuses the electron onto a plate, leaving a spot P. In classical physics from the spot P we infer the position of atom A. From the spot P, the track PP1, and from knowledge of how the lens works, we could also know the momentum of the particle. Thus, you could compute from this where the atom is which scattered the electron and how much momentum was transferred to the atom A. Although atom A would be disturbed, you could make the disturbance negligible, either by using light particles or by making corrections for the disturbance. Therefore, in classical physics the reference of A to P could be dropped. The whole experimental arrangement, while necessary to obtain knowledge about atom A, is quite independent of the essence of the atom in itself. The atom exists in itself in a certain state of position and momentum. Once you know about the atom, you can forget about the apparatus.
On the other hand, Heisenberg, because of the quantum nature of light or matter, said there is a minimum disturbance of _p of atom A. Heisenberg considered it to be unknowable, unpredictable, and uncontrollable, and hence uncertain. Letís say there is an electron of momentum p which gets scattered through some angle so that the momentum is p sin . You cannot know the angle from the spot P, because the electron may have come in through the aperture of the lens anywhere. Therefore, there is to a certain extent an unknown transference of momentum to this electron. Also, if this electron which links A and P had wave-like properties, you would not know exactly where it came from. It would come from an unknown region of size _x = sin . (Notice that you are using two pictures of the atom at the same time. You are saying that the link electron is both a wave and a particle. This is illogical. You are describing it simultaneously using two sets of properties which it couldnít really have together.) Thus because of the wave nature of light or matter, there is a minimum disturbance or uncertainty _x . From this, it follows quite directly that _x _p _ h. This was Heisenbergís uncertainty relationship.
With this relationship you could no longer infer what the properties of an object are from the observed spot P, and from a knowledge of how the apparatus was arranged, and so on. This point is crucial because whether you used light or matter as the link, you could show that there was always an uncertainty. There was no way out of this because the laws of quantum mechanics were used in the link process. Using this argument, physicists criticized the classical determinism, namely that given all the positions and velocities of all the particles in the universe, everything would follow. No longer was it possible to know them, because knowing them now consisted of interacting with them by using particles which obeyed the very laws into which you were inquiring. And these laws had a minimum disturbance which could not be reduced because of the quantum nature of matter.
Heisenberg raised the uncertainty relationships to a principle by saying not merely can they be deduced from the laws of quantum mechanics, but by making the assumption that there is no way out of this situation no matter how far you went. That is, he turned from a deduced relationship to a principle, but there is no reason why this should necessarily follow. People accepted this principle, in spite of the fact that there were no reasons why it should be accepted or rejected. It was just an idea. And this is how I would criticize the generally accepted procedure.
A second point to add, which is not usually made clear, is that particular experimental conditions determine the shape of a cell in phase space, representing the uncertainty in the classical properties of the electron. The area is h, but the shape is variable. The properties of the electron thus, become ambiguous within some sort of roughly defined cloud of area h, but the shape of this cloud may vary considerably. Thus, x may be relatively well defined but not p or vice-versa, depending on the particular experimental arrangements, such as the microscope and the particles that are used. Mathematically, the range of uncertainty of properties is determined roughly by the region in which the wave function of the particle is appreciable; i.e., the region of position space and momentum space. Instead of using classical concepts of precisely defined x and p we will now say that the wave function describes the state of the particle as accurately as possible. According to the experimental arrangement you get a corresponding wave function, and the appropriate probability distribution in x and p.
Now returning to the experimental arrangement, we see that the results are irreducibly dependent upon the interaction with the observer. We can compare this to two views of nature. One view is that nature is totally independent of us, and we just find out what it is. The other is that nature is an artifact made by us, which afterwards may exist independently until we do something to it again. From Heisenbergís point of view you could say that the electron state is to some extent an artifact. We help to make it.
Heisenberg was not a completely consistent positivist. He said that the electron has in some sense a position, which is disturbed. Thus he used a highly nonpositivist argument to justify a positivist conclusion, which is perfect confusion, you see. It is nonpositivist to say that the electron is disturbed in an unknown way, but he concluded from this that there is an ultimate limitation on our knowledge of precisely where the electron is, which is very positivistic. From the unknowable, Heisenberg thus concluded something about the limits of the knowable.10
Heisenbergís view is not actually consistent with quantum mechanics. A more coherent form of the view I have been describing would probably be closer to that of Von Neumann. Von Neumann says that as a result of this interaction with the electron, the atom is left in a certain state. It continues in that state, moving in its natural way until something interacts with it again. The result of this interaction depends statistically upon the wave function. That is, you can compute the probability that in the next experiment you will get a certain result, if you know the result of the previous experiment.
Bohr has produced yet another view, which is probably the most consistent one. It is quite different from Heisenbergís, although Heisenberg has subscribed to Bohrís view, thus adding to the confusion. Bohr said that the experimental arrangement has to be described classically. It was essential to Bohrís point of view, and probably to most of the others, that quantum mechanics introduced no change of concept at all. The concepts of position and momentum were the same ones in classical physics as in quantum physics. In classical physics they were unambiguous in principle. In quantum physics they were ambiguous to the extent of the Uncertainty Principle. But Bohr went further by saying that this ambiguity was fundamentally related to the experimental conditions. He said that the form of the experimental conditions and content or the meaning of the experimental results were a single whole which could not be further analyzed. A way to picture Bohrís view is to think of the pattern in a carpet. There may be birds or people or trees in the pattern, but the carpet is not constituted of birds and people and trees. Rather, they were merely abstractions from the whole, which have no meaning in themselves. Bohr said indeed that there is no microobject. So actually nothing is observed. There is nothing but the phenomena, and in this sense he was parallel to Kant. The phenomena constitute the whole. We may use words like "particle" and so on, but they are just picturesque language. We would probably be better off without such language.
The algorithm of quantum mechanics then applies statistically to these phenomena. The phenomena are described through classical language, but instead of using classical calculus to predict from one phenomenon to the next, we replace the classical calculus with the quantum algorithm -- wave functions, matrices, and so on. The essential point that Bohr demonstrated is that it is consistent to do this. I believe that his demonstration is right. And he is, as far as I am concerned, the only one who has presented a consistent view of the whole thing.
But you must accept this view that the phenomena are irreducible if you are to go along with Bohr. This is what Bohr called "individual." For example, if you look at somebody, you can say that is what he is. There is no use to analyze the person any further. The second point is that one might ask why the thing has to be described in classical language. Bohrís answer is that no other unambiguous description is possible. Bohr felt that the description must be unambiguous. (At least the ideal is that.) And also he felt that you really couldnít change the terms of common sense language, refined where necessary to classical concepts of position and momentum. He felt that the common sense notion was built into the human condition. For example, one might say, "Suppose that you try some other concepts." Bohr would answer that with language you donít know which way is up and which is down. Bohr felt that there was something inherent in the human condition or situation which required his approach.11 And I would not accept Bohr at this point.
Von Neumann did not accept Bohrís view at all, and Heisenberg was straddling between Bohr and Von Neumann. Von Neumann said that the quantum state is an objective fact -- it is a microobject. The microstate is merely a state that happens to be to some extent an artifact made in the laboratory, but it is still there. According to Von Neumann there is a cut between the quantum system and the classical world. I will call the quantum state Q. Now the location of this cut can be put fairly arbitrarily. Somehow the quantum state interacts with the classical world, leaving an observable result from which you can know the quantum state. The problem is that the cut, being arbitrary, could be put at various points. Von Neumann mentioned that eventually this leads to an infinite regress, because there is always a further classical world. Anything could be called quantum mechanical and could be observed by a further system that is classical, and so on. This infinite regress would not be satisfactory.
Wigner has suggested that this regress may end in the consciousness of the observer (making his theory a phenomenalist theory, probably). But Wigner goes further than this by saying that the consciousness of the observer plays an essential role in making the quantum state definite. Therefore, Wigner says that the consciousness of the observer is inherently involved in the world. You may hold this view, but it may be criticized in a number of ways.12
One way is to say that if you introduce the consciousness of the observer as one of the variables of the world you are still in a regress since it implies that there is an awareness of the consciousness by a further observer who sees his state of consciousness, and so on. I think that this is no really clear point of view along these lines. You cannot introduce the observer into the account explicitly. Whatever is in the account is by the very form of the situation that which is observed. If the state of consciousness is part of the account, then consciousness is what is being observed. It is always implied that there is an observer who is implicit -- that is, not mentioned in the account.
I think this illustrates that the interpretation of quantum mechanics has by no means been settled. A great many people have developed different variations. For example, Von Neumannís view was not satisfactory to those who followed him; indeed, Von Neumannís solution is not clear and cannot be made clear. Bohrís solution is relatively clear, but I would consider it to be based on an arbitrary assumption about our human situation. Heisenberg is not clear because he says he follows Bohr, when in fact he does not. Bohr never follows Heisenberg.13 Thus, you have the same situation in quantum mechanics as in positivism -- people take the right step for the wrong reasons. The right steps lead to successful results, but because the reasons are wrong, this brings about a muddle further down the line. A deeper reason for the confusion is that most of the physicists were not sufficiently interested in the interpretation at all. Because the quantum theory was so successful, they mainly wanted to get on with working out the results. They thought that it was fine for anyone who wanted to try to work out an interpretation. In fact in Einsteinís biography it is pointed out that that is also how Einstein looked at the situation described here. That is, very few people understood what Bohr had to say, not even Heisenberg and certainly not Von Neumann, but most people still accepted Bohrís interpretation. Yet everyone seemed to think that everyone was saying the same thing. While people felt that it was in principle necessary to clear up the issue of interpretation, they felt that it was really a side issue. The important thing was to calculate results.
I would say that we have no quantum essence, because we have not yet given a consistent description of matter. Bohrís view takes the classical description of matter, but no one believes that the classical description is the explanation. Bohr avoids this criticism by saying that we can go no further, because that is the human condition. Heisenberg implied an essence by saying there was a particle which was disturbed in an unknown way, but it was never clear how one could discuss this. Von Neumann implied an essence, but again, unclearly. Thus, in essence, matter has not been explained in quantum mechanics. To be consistent we should say that quantum mechanics is a theory of the phenomena. It is consistent in that it predicts and correlates the phenomena, but it does not translate the appearances into an essence in a consistent way. Although people do translate the phenomena to some extent through pictures, these pictures are not consistent. They help the intuition, but to say that a thing is both a particle and a wave is not a consistent picture. It is merely an aid to thinking. It would be closer to the fact to say that quantum mechanics is a theory of the phenomena which is very successful up to a point, but not very successful when it comes to trying to connect it with relativity, and not successful at all in questions of interpretation.
I am going to take the point of view that we have no relativistic essence and no quantum essence. Both are laws of the phenomena. They may be clues to some new essence which is not relativistic and not quantum. Perhaps relativity and quantum theory will be special or limiting cases or appearances of some deeper, more fundamental essence. But I will not take that deeper essence as the final essence either. This is part of the process or movement by which we are continually learning about the world or nature.
For reasons which I developed above, relativity indicates that the essence should be of the nature of movement or process or flux. "Process" is based on the word "proceed" -- to move forward. You might think of process as a structure of movement rather than as a structure of objects. The word "structure" in the dictionary means having to do with construction -- how you make things. But structure is the order, arrangement, connection, and organization and form not necessarily of things but also of movements. For example, we may discuss the structure of a language or the structure of a thought, as well as the structure of a house or of a crystal. In physics, the question of the kind of connection is probably one of the basic features of the structure. Physics has generally looked for immediate contiguous connection of events. So if things are far apart but connected, we assume that there is a series of intermediate connections which are local and contiguous. That has been the pattern that people have wanted to use.14
Newton introduced action at a distance (although he hoped to get rid of it), which allows for an immediate connection of distant events at the same time. That is not inconsistent with classical mechanics although people prefer not to have it. The quantum laws allow for discrete jumps and connections of things not connected by a series of stages of contact. Thus, in discussing the issue of structure, we are discussing how things are connected, contacted, and related, and so on.
I think it is necessary to go into the Einstein Podolski Rosen story (EPR) because that is the basic new feature of quantum mechanics, in my view. All the other developments, while somewhat new, are not all that different from previous ideas.
The EPR story deals with the fact that the wave function which describes the quantum state is not a function of space and time, but is a function of as many variables as there are particles (and possibly as many moments of time as there are particles, if you tried to do it relativistically). Einstein considered the EPR experiment to be a criticism of quantum mechanics, showing not that it is wrong, but that it is incomplete conceptually. Something fundamental is missing from the concepts, although the thing may be right experimentally, up to the present anyway.
The original experiment is a bit harder to interpret than another one. Think of two particles forming a molecule, with the total spin equaling zero. (In classical terms you might think of one particle spinning one direction and the other spinning in exactly the opposite direction). Now suppose that this molecule is disintegrated by electric forces which do not affect the spin at all and that these atoms start coming apart. (Letís say they come apart very slowly.) For the sake of argument you take them a long way apart -- miles or millions of miles -- and all the time the total spin would remain constant. Each one would be opposite to the other. They would be correlated. In a classical situation, if you measured the spin on one particle after a week of separating, you would immediately know that the other particle had the opposite spin. There is nothing mysterious about this at all -- it is just correlation. That is obvious, at least in classical mechanics.
Now, quantum mechanics has an entirely different structure. We let a represent a particle with spin up, b with spin down. The wave function for the combined systems is = a (1)b (2) -- a (2)b (l). This combination of wave functions with the minus sign is necessary to have a state of spin zero (or if there is a plus sign, a spin of + 1). That is to say, the way these wave functions are combined is essential to properties of the whole system. Let us think of any individual particle. We say that its spin cannot be exactly defined in all directions. It can be defined in any direction you please -- letís say z. Then, according to quantum mechanics, the other two components of the spin are fluctuating at random so that the spin vector is located somewhere on a cone whose z direction is always the same. It is not known exactly where it is in that cone. But if we say that the particle is spinning in some other direction, then the cone points in the corresponding direction. So there is a cone of uncertainty whose axis is in that other direction. The quantum state of the particle thus determines the directions in which the spin is uncertain. That is, the quantum state implies that some things are uncertain and some are certain. The wave function determines both. The uncertainty is just as much a part of the quantum state as the certainty.
This really shook Bohr, and for one night he couldnít sleep. However, Bohr came up with a very nice answer. He said, "Well, Einstein, that is exactly what Iíve been saying." The trouble was that Bohr had previously been half accepting Heisenbergís view of disturbance. Suddenly he saw that he should just give Heisenberg up altogether. Disturbance is never the question at all in the uncertainty principle. Nothing is involved but a phenomenon. The fact that this takes place over some time merely obscures the issue, but the phenomenon in question is the whole of the phenomenon. This has nothing to do with time and space. The phenomenon as a whole, however long it takes, is still just one whole phenomenon in this pattern. There is nothing to explain, because this phenomenon is an indivisible whole. There is no inconsitency in asserting the phenomenon in this way. The inconsistency is in trying to explain the phenomenon by our usual way of thinking in physics.
So Bohr gave a very nice answer. As a result, Einstein really knocked the last nail into the structure when he hoped to knock it down. For afterwards everyone said, "Well, if even Einstein cannot get away with trying to criticize quantum theory, who am I to try?"15
Now this really is the most crucial feature of quantum mechanics, which I call non-locality of distant connections. Suppose you made a theory, for example, hidden variables, in which it was possible to explain this in another way by saying there was a hidden force which connected these things. It would have implied that this force was transmitted instantaneously. That would lead you into the problem of relativity. You might have to criticize relativity in some way.
The other way is to have an entirely different view which is closer to the implicate order, which would question the whole idea of being interconnected in a certain way, namely, the ordinary idea of causal connection in past and future and that things are locally connected so that one thing affects another nearby.
You can question the ordinary idea of connection by suggesting instead that there is an inner design in the whole structure. (In some ways this is close to what Bohr is saying, but also different because this inner design can be studied.) The idea that all things happen independently when they are distant is thus what I am calling into question. Experiments have been done which in essence verify the view I am proposing up to several meters of separation of the apparatus. One was recently done at Birkbeck College, University of London, at 21/2 meters. There is no place where the quantum theory has been disproved up to this separation. So it is not merely a theoretical prediction. Thus it seems that we should take this issue of non-locality seriously.16
I think there is some new principle here which is non-local connection. Perhaps the speed of light in this new domain is an irrelevant limitation. But Einstein may be right that the possibility of sending a signal depends on the speed of light but not connection in general. Sending a signal requires maintaining the order of the connection in a complex process, because a signal depends on a whole series of steps having meaning. It might not be possible to use non-local connection to send a signal, but still it might be a genuine connection. We might criticize Einsteinís view of signal as a basic concept for physics. To say that physics is defined by the possibility of a signal may not be as relevant as Einstein wanted to suggest. Rather, there are connections which are more fundamental. If there is no signal you will not get into inconsistency with speeds faster than that of light. Therefore, the situation in physics is pointing to some new essence.
IV. The Implicate Order
Every period of science seems to have its particular notion of order. There was the Greek order of perfection going out to its circles of heavens. And this was given up in the Newtonian order, which was mechanical movement. The Newtonian order was expressed through Cartesian coordinates. The very word "coordinate" contains the word "order." The Cartesian order is highly suited to the idea of contiguous connection in classical physics. Cartesian order has been maintained even in relativity, in its mathematics. While relativity uses curvilinear coordinates instead of rectangular coordinates, they are still minor extensions of the Cartesian order. We could say that even in quantum mechanics people still use the Cartesian order to specify the wave function, even though it is describing things that do not fit into the Cartesian order. The content is no longer Cartesian, because things jump from one orbit to another without passing in between. Therefore, the Cartesian form has been maintained even though the content is no longer Cartesian.
Thus, there is a contradiction arising. Indeed, if we look at quantum mechanics and relativity together, we see that they are very different in one sense, for relativity ultimately implies complete, perfect describability in all the details of the universe, while quantum mechanics implies through the uncertainty principle that complete, perfect describability cannot be achieved. So the attempt to define the structure of the world tube precisely in relativity would violate quantum mechanics. That is the basic reason why quantum mechanics and relativity do not fit together. On the other hand, they have in common this notion of unbroken wholeness. That is, if relativity were able to explain matter, it would say that it would be all one form -- a field -- all merging into one whole. Quantum mechanics would say the same thing for a different reason, because the indivisible quantum links of everything with everything imply that nothing can be separated. Therefore, this notion of unbroken wholeness seems to be the one common feature which might unite relativity and quantum mechanics, whereas they fall apart on the attempt to describe in detail how things happen. Of course, people have generally concentrated upon the attempt to describe things in detail, but that is just the point at which it doesnít work very well -- when you try to understand the quantum mechanics and relativity together.
The implicate order is the proposal of another order which will be suitable for this unbroken wholeness, not the Cartesian order. In other words, when we have the implicate order, we will not use the Cartesian order for the description of phenomena, except in some superficial way. We will say that the immediate particulars are going to be the Cartesian order, but the essential particulars will now be the new universal, or the implicate order.
The lens has been the basic instrument to give content to the Cartesian order, and the point is the basic entity. If you have a lens, it forms very nearly an image so that to each object point there is an image point. Since what corresponds are the points, our attention is brought to the notion of point as the major notion. By means of the lens, we are able to see things through point correspondences which are too small or too big or too fast to be seen by the eye. The idea arose that eventually we would be able to see everything this way. And the universe could be understood and observed as a structure of points.
The hologram, invented some time ago by Gabor, approached this very differently. It was made possible by the laser, which produced highly coherent light. A half-silvered mirror reflects some of the light to an object, and some of the light goes on. The two beams interfere in a complicated pattern which is rather minute in its detail and doesnít look like anything at all. You can make a photograph of this pattern and then send a similar laser light through it. This will produce similar diffraction patterns, and you will see the whole object in three dimensions. People have emphasized the three dimensionality of the object, but that is not what I will emphasize here. The main point is that from each part of the interference pattern, or hologram, you will still see the content of the whole object, but with less detail or less points of view. That is to say, in each part of the hologram information concerning the whole object has been registered. (You can see this from the way in which the light waves from the whole object come into each part of the hologram.) This is the key notion indicating another order.
I should point out that the photograph is really a secondary issue, in that it helps to render the thing visible in this way. The major point is not the photographic plate, but that there is a movement taking place all the time. I call this the "holomovement." ("Holo" is the Greek word meaning "whole." "Hologram" merely means to write the whole.) In this case, the hologram takes on the form of light waves. But holograms can be made with sound waves or with deBroglie waves, in principle, or with electron waves. And according to the theory of quantum mechanics, all matter is wave-like, so the hologram could be of all forms of matter know-n and unknown.
This general category I will call "holomovement." The holomovement has the property that each part of it contains the whole in some sense. The whole is folded into each part, and that is why I use the word "implicate" for this order. The Latin word implicare means to be folded inward. To explicate is to fold outward. To multiplicate is to multifold, and so on.
In this order, the points are not the fundamental notion anymore. Rather, what is fundamental is some region which contains, in some sense, the order of the whole. In ordinary physics, this situation is described by saying that the Cartesian order is the essential order and all this (movement, change) is merely a secondary or inessential appearance going on inside the Cartesian order. That is the usual way of looking at it. But I am turning it around and saying that this (the implicate order) is the essential order and Cartesian order is the inessential order -- an appearance going on in the holomovement.
In this view, the Cartesian order is a particular case of the universal holomovement, of the implicate order. We will develop this as we go along. One can illustrate this implicate order in another way which is not quite as accurate, but is easier to picture.
There is a device which has been made at the Royal Institution in London, consisting of two cylinders of glass -- one of them static and the other one turning around, with a viscous fluid, such as glycerin, in between. You turn it very slowly so that no diffusion takes place. Therefore, the effect is reversible when the cylinder is turned back. You put a drop of soluble ink in the fluid, and as you turn the cylinder, the ink gets spread out in a band, and finally it becomes invisible. It is spread all over the place. It gets drawn out. Then if you turn it backward, it tends to draw the ink back together, and suddenly the droplet emerges more or less as before. (It is not exactly perfect since some of the ink is diffused, but it shows the point.)
We can say that the droplet of ink is folded up in the glycerin, like an egg folded up into a cake. You cannot unfold the egg out of the cake because of diffusion, but you can unfold the ink back into a droplet. You can say that there is an order here which does not show. It would have been called "randomness" in the ordinary way of looking at it. But it is not randomness; it is an order. If you took another droplet and enfolded it, it would look the same, but it is different. That difference is a difference of order. Now what you could do, for example, is to enfold a whole grid of droplets and have it look like a muddle inside. But actually there is an implicit Cartesian order in the fluid -- an implicate Cartesian order which has been folded up into this system. It merely shows that there is an order there which is not visible, in the sense that the parts are enfolded into this whole. It is very similar to what happened to the light in the hologram, where all the parts are enfolded into each part.
This is an expression of the new order, which I call the implicate order. A similar order is involved in quantum mechanics because the waves, the deBroglie waves from each particle, are enfolded the same way as light is.
There is a parameter here which I will call the "implication parameter." For the sake of description, suppose you turn the cylinder n times. You must distinguish between a drop which has been turned n times and one that is turned 2n times, and so on. They are different. They may look the same, but they are different, because one of them can be enfolded in ii turns and the other in 2n turns. So we are making a distinction according to the implication parameter. This distinction is not very important in the Cartesian order. In fact, you would generally not consider it all. Suppose now that I take a droplet and I enfold it n times, and then I take a different droplet and at a slightly different position enfold it n times, carrying the first droplet two enfoldments. And I take a third droplet, which I enfold n times, which carries the second droplet 2n times and the first droplet 3n times. So I have enfolded a structure of droplets.
Now if I start unfolding, one droplet after another will emerge, each in a slightly different position. If I do it rapidly, it will appear as if a droplet is crossing this fluid. That is a metaphor of what I mean by a particle in the enfolded order. In other words, it involves the whole, exactly as Bohr says. In that sense we agree, but we disagree in how we describe the whole. Every particle is actually a manifestation of this whole. Therefore, we no longer reduce the world to particles, but we regard it as a state of the whole. We turn the classical physics upside down.
We are saying that nothing can be understood except within the context of the whole. We may now ask this question: "If everything is to be understood only within the context of the whole, how are we to comprehend what happens in physics where people have so nicely and successfully analyzed the world into parts?" We cannot ignore that experience. What we will have to do is to assimilate and comprehend our experience in a new way. We are going to say the old view is all appearance -- a certain appearance within this new essence.
The holomovement, which we cannot define, is going to be considered to be the new essence. That is my primitive concept. Its meaning will unfold as we go along. The word "holomovement" is merely a metaphor to point our mind in a certain direction. It is not to be taken as defined in any literal sense to begin with. The laws of holomovement will be the laws of the whole, which we can call "holonomy." Any law of the whole is a regular order within the holomovement. If we say that the regular order is such to produce particles, that will be a particular law of the whole. So the existence of particles is now described through an order in the holomovement. It does not exist in itself at all. Particles are an appearance. In fact, it is not this little thing that you see, because you are only able to see ink droplets when they are of a certain density. We donít see the whole thing.
Now what we have is called "relative autonomy": autonomy means self-rule, and relative autonomy is the order in which the whole unfolds. There are various orders which can be abstracted from the whole, and these orders have relative autonomy. If you carry it far enough, you will find that these orders are not totally autonomous. They all depend on each other. The EPR experiment is a case in point. For each particle of physics, say an electron, you would expect a relatively autonomous order. Each particle would move along in its own order, somewhat modified by the order of another particle which comes near it, because the two orders penetrate together. But you would ordinarily expect that distant things should be generally relatively autonomous. In our new view, however, things that are called distant merely appear to be distant, and they are really only relatively autonomous. They all involve the whole. Distance is thus actually an appearance by which we can describe relative autonomy. There is no distance in this essence. Distance is not a fundamental quality of the implicate order.
Relative autonomy is limited, as we have seen in the EPR experiment. Two things that we thought to be quite autonomous are not. They may be miles apart, yet are not autonomous. Now in the holomovement, there is no reason why things miles apart should always be autonomous. Everything comes from the whole. It may come from here; it may come from there; but there is no reason why the order in which they come should be totally independent. They may or they may not be independent. We would have to find out the actual fact in each situation. Relative autonomy is always limited. It is not the essential category. The essential category is wholeness -- unbroken wholeness.17
I can also explain the subsistence of matter in a similar way, by saying that the holomovement provides for the subsistence of matter. Matter continues to exist up to a point, but it may not be perfectly subsistent. We know that matter need not be entirely self-subsistent. Thus, there is the annihilation of particles as well as the creation. So subsistence is not absolute.
A particle is not a substance. A substance would be self-generated and self-maintained. But subsistence merely means that it depends on something else to be maintained. Democritusís original idea was that the atoms were substances -- self-maintaining and eternal. But now we are saying that particles are subsistants and not substances. This fits the facts of modern physics, because as I have just said, all particles can be created and destroyed and transformed, and so on. Therefore, there is no sign that they are independent substances. We will say that particles are orders in the holomovement, which have the character of subsistence, a certain repetitiveness, stability, and so on. And that ties up with the autonomy, for the order in which they are subsistants is also only relatively autonomous. This allows for an explanation of the appearance of various things in the world which can be analyzed and treated in themselves up to a point.
In this view, the holomovement is the essence. The order of the holomovement and not merely the movement is the essence. Without the order, the laws of physics would be merely empty forms, because there would be no content to physics at all.
We now have to say that the laws of physics are applying to a different order. We have to develop this order of the holomovement. We have very little to say about it to begin with, but we should expect that it would explain the previous orders as abstractions of various kinds, as suggested above. It will be necessary, of course, also to develop a mathematical description of the order along with a physical description of theí order. I would just anticipate by saying that algebra seems to provide a good mathematical description of the implicate order and that quantum mechanics is basically an algebra. Therefore, the implicate order will fit very nicely into the sort of thing that is happening in physics. As the calculus was the description of the Cartesian order, the algebra is the description of the implicate order. So the algebra must replace the calculus. Thus there are no differential equations. We donít start with the differential equations. We do not start with the continuous space, but instead we will say that space has no absolute order that can be described. Every order is as good as every other order. This is a sort of extension of the principle of relativity. Einstein showed that the order of one observerís frame is as good as the order of the others. The laws of physics take the same form in every order. But it has to be a continuous order, he said. Now what we will suggest is that it neednít be a continuous order. For example, suppose I say that the electron is described in terms of our own perceptual order, which is taken as explicate. The electron has then to be regarded as enfolded in the way that I have suggested. But there might be a principle of relativity which says that the electron order could be taken as given or explicate and we are enfolded in the order of the electron in the same way that the electron is enfolded in our own order. The content of the laws of physics must come out the same whichever order we call "explicate" and whichever order we call "implicate." There is no absoluteness to being folded or unfolded. It is the relationship of folding and unfolding that counts. We will not say that one order is the unfolded order and the other the folded one; rather, one is folded in relation to the other.18
A. Time. If an object is thought of as being at a certain point, you have lost your mental grasp of its movement. If you think of it in movement, it is not clear where it is. In movement, it must be essentially considered over some range of time. Another way of looking at that is to consider the usual representation of time by means of a line with past, present, and future. You may consider this point to be moving, but that, of course, brings in time at another level. But if we just take the present moment p, the past is gone. It is never present. The future is not yet; it is also never present. So. if p divides past from future, it divides what does not exist from what does not exist. Therefore, it could hardly be said that the present exists either. In other words, there is a complete paradox if we attempt to look at the ordinary physicistís view of time as anything more than an abstraction. It is useful for calculation, but is not an actual description of the state of affairs.
How are we to look at time? I would put it this way. There is no future. There is nothing but the present and the past at any moment, because that is all that can be described. But the past is present, in the form of memory. The past is recorded: what has been photographed and written, the traces in the rock. It is all present. It may be unfolded in your mind as an image that appears to be actually happening, but it is not actually happening. The past is gone. Whatever is present of the past is an abstraction. It is not the past as it actually was. So we will say that the past is a part of the present. Now we have an intrinsic order here, because we can say that there is a series of moments; the later present and the present present. The later present contains the present of this moment as a part of its past enfolded. I say that this moment is not only present as a trace, but it is generally enfolded in the implicate order. So the past is present, generally speaking, in an enfolded way.
This might be relevant to brain structure and memory. We may say that memory is some enfoldment of the past in the brain. That could be a reasonable approach, in my view. That would be a holographic enfoldment of some sort. But there is a hierarchy of order here, because each moment has its past enfolded in it, which in turn has its past enfolded in it, etc. Each one contains in itself what came before, which is, in turn, reenfolded. So we could look at time as enfoldment. And we are saying that the next moment will contain all of this in a similar way.
I would say that we donít make predictions, because in this view the present does not determine the future, fundamentally. The future is entirely open, if I may use that word. Or to make it more striking I could say that there is no future. It doesnít actually exist ever. So there is an intrinsic order of enfoldment. If you try to make a prediction, you are never sure that something new may not come in. There is always a contingency. Therefore, literally speaking, perfect predictions are not actually possible. Although very reliable predictions are sometimes possible, there might still be a contingency. So I would rather say that we anticipate the future. "Anticipate" is a good word because it comes from the same root word as "perception." Perception means to grasp it thoroughly; anticipation means to grasp it beforehand.
Actually, we donít anticipate the future as such. Rather, we anticipate the past of the future. All we know of the present is actually the past. Anything known is gone already. What is actually happening cannot have yet entered knowledge. It is being perceived. It has not yet entered the recording, the registering process. Therefore, anything that we really know is already gone. In the future, something will have happened, and we may predict what will have happened. So we anticipate what will have happened. That is, when tomorrow comes, certain things will have happened, either a second ago or a minute ago, and so on. And we will anticipate that state of affairs. Therefore, our theory (the implicate order) will consist of relationships which, informally speaking, are always in the past of some moment which is called the present. All language, all knowledge, I should say, must basically refer to that.
We will be discussing the unknown presently. (We really shouldnít even be discussing it.) Given the present, the next step is completely open in principle. There may be some situations where there is tendency for one current situation to be followed by another. In this way we can regard the form of matter and of thought as very similar (or of feeling, as Whitehead might have put it).
Letís look at thought. The next thought is not determined by the previous thought in any usual causal sense. But within a thought, there will be some tendency for one thought to be followed by another again and again. Given that a certain structure has been registered, it has in it a tendency to react to a situation to produce a certain further structure of a similar form. But it is not absolutely determined. Any number of contingencies come in to change it: information, influences, and so on.
So perhaps we could say that matter has a kind of memory of what supposed to be in the implicate order. And therefore, matter has a tendency to go on with a certain general form, although it could change at any moment. In other words, there is always room for a creative step outside the whole structure that we are talking about. Of course, by the time we get to the domain of classical physics there is such an overwhelming structure of memory that it is very well determined, but even then perhaps not absolutely. That is the way I would like to look at the indeterminism that people have brought into the quantum mechanics.
We are going to have to abstract the order of time from the implicate order. This will come out through the mathematics. In other words, time is not given as something there beforehand. That is, we should not say things happen in time. Rather, there are many kinds of time. This is the spirit of relativity. A system moving at one speed has one kind of time; one moving at another has another kind of time. There may be an implicate time which involves many moments of what we call ordinary time. In fact, I should say that is the kind of experience we have of an implicate time in memory. In one moment of what we call time, there is a vast sweep of implicate time. Usually, we take our ordinary time as the basic reality or the essence, but it might be in the fundamental view that the various kinds of time are all put on the same footing of interrelationship.
The point is that in the implicate order we are merely forming an order of development for the description of process. Process is some regular proceeding order. I could here usefully introduce the notion of a moment. The word "moment" is based on the word "movement." It could be thought of in a very broad sense like a moment in history, a century, a second. There is no particular amount of time involved in the concept of moment. I think you could use the idea of "actual occasion" as not being merely a split second. It could be very variable. Thus, if you think of a symphony, it has a movement which becomes another movement and another movement. I would say that a moment is characterized by a movement -- a certain form of movement. When we put our attention on a particular movement, we call that a moment. You see, a moment is a feature of our attention. And in the description of process we have moments of variable size and shape and duration. These moments come about in a series of order, which I call the implicate order -- the unfolding from one moment to the next. That is the sort of picture I am trying to paint.
It is a matter of art to find the right kind of moment for correctly revealing the unfolding of a certain order. If it were in music, you would have to consider using the right structure and time to unfold a theme. If you used too short a moment, it wouldnít work; if you used too long a moment, it wouldnít work. You cannot provide an absolute description of how to go about it. The right use of the time becomes a sort of art. I think in music you see that most vividly exemplified. In music, the meaning of the thing is intimately involved in the order of unfolding.
B. Vacuum. Next, I want to discuss the question of the vacuum. This is crucial, I think, to the whole context within which we are operating. We have called attention to the intrinsically unknown, namely, the future. In physics, we also have what is called the vacuum state. In quantum mechanics, any vibration does not go down to zero energy, but in its lowest state there is its certain zero point energy. This has been verified in material oscillators of all kinds. Also, this theory has been applied to the oscillator of empty space: oscillators of electromagnetic field radiation.
It is basic to quantum electrodynamics to assume that each of these oscillators has a zero point energy. Although you cannot prove this directly, you can confirm it indirectly. The renormalization calculation equations of charge do in fact confirm that all the effects that zero point energy ought to have are there, very precisely and quantitatively.
Now suppose that we say that this zero point energy of space is a reasonable concept. Then one question to ask is "how much energy is there in space?" Of course, there is an infinite amount of energy in space, because, according to present calculations, there is an infinity of these vibrations. Eventually, that is where we run into trouble trying to get a logical or consistent theory of the electron. Suppose we say instead that somehow the energy is finite. We have to find some reason to cut off the theory at some new maximum frequency or shortest wave length. There is no reasonable cutoff until we come to gravitational theory. According to Einstein, the gravitational tensor gv, determines a length as gvdxdxv. Einsteinís field equations allow you to calculate this length in classical physics. In quantum physics, however, gv, becomes uncertain, so that such lengths will fluctuate and become indefinable. You cannot know exactly what is meant by length or time. Therefore, all the concepts of geometry must break down at a certain state where the frequency is so high the fluctuations of gv are of the same order as gv itself. At this point the length is totally uncertain. Thus the meaning of space and time become totally undefined. This can be calculated to be a length of about 10-33 centimeters, which corresponds to a frequency of about 1043 cycles per second. Thus 10-43 seconds tends to be the shortest time that has meaning in the ordinary geometry (which is really very short compared to anything we ever work with in physics thus far).
Suppose we take this as the first reasonable place where the theory might break down. If we do that, we can compute the amount of energy in a cubic centimeter of space, which comes out about 1040 times the energy which would result from the disintegration of all the matter in the known universe. In other words, the energy in empty space is immensely greater than the energy of matter as we know it. Therefore, matter in itself is a kind of ripple in empty space.
Matter is a relatively stable and autonomous ripple in the emptiness. Those of you who have studied the theory of solid states may not find this notion of emptiness entirely unfamiliar. For example, in a crystal of very dense material at absolute zero, if the crystal is of perfect order, electrons go right through it as if nothing were there.
The suggestion is then that emptiness is really the essence. It contains implicitly all the forms of matter The implicate order really refers to something immensely beyond matter as we know it -- beyond space and time. However, somehow the order of time and space are built in this vacuum. That is what is suggested.
There is at present no law that determines the vacuum state. Depending on what you assume the vacuum state to be, you will get various physical properties. And that would be very crucial to determining what the implicate order is. In other words, I am proposing that what is now called the vacuum state must ultimately contain the actual order of space, time, and matter enfolded in it.20
The following are comments made during the course of Bohmís presentation.
1Francis J. Zucker (Max-Plank-Institute) mentioned that Heisenberg once confronted Einstein by saying that Einstein had given Heisenberg positivist arguments. Einstein replied that Heisenberg was a fool to believe all that nonsense.
2Zucker: This point may be sharpened. Einstein says that he never knew of the Michelson-Morley experiment.
3Fred A. Wolf (San Diego State University): Are the immediate particulars readings on meter dials and the essential particulars what we think those readings mean? Bohm: That is right in terms of an universal explanation. However, I would not just use the word "think." We can think anything. We can dream up anything. The essential particulars are considered as an explanation which is universal and necessary. John Blackmore (Harvey Mudd College): Is the universal essence primarily designed to understand the particulars P1, P2, etc., or is it designed to understand the external world apart from the appearances? Bohm: No, it is designed to explain what is actually there. The meter only helps indicate what is actually there. The meter only helps indicate what is actually there. Blackmore: Then it is only secondary that the universal essence helps us describe the relationships between appearances, hut primary in that it helps us to understand the real world? Bohm: Primarily it explains the essence, but the appearances are necessary to get a hold on the essence. Roger Sperry (California institute of Technology): Is the universal explanation something we are all trying for? Is it considered to be the goal? Bohm: Iíll come to that, but it will take some time to explain, It is not quite so simple. Sperry: I would question that the universal explanation is the goal (of science) that we are all looking for. It is hard company to keep. Bohm: I am not going to accept that idea exactly as it is. We will come to that a little further on. C. A. Muses (Santa Barbara, California): But the pointer readings are also a part of reality. Bohm: Obviously, but a very superficial part. They donít have an independent being. They are dependent on something else, which we call the essence.
4Blackmore: Clarification: are you saying that both the essence and the understanding of the essence change, or just one or the other? Bohm: Obviously, our penetration into reality increases, but reality may be inexhaustible, so we may not get to the end. Also, because of what we do, things change, essentially. For example, man changes nature through technology. Blackmore; Is essence independent or contingent on our understanding? Bohm: It is both in some way. What I am saying is that essence and appearance are both modes of thought. The question is whether our perception is correct up to a point. Any view of the essence has only a limited applicability. Karl Pribram (Stanford University): Can we be Kantian here? Bohm: No. Kant has too great a separation between appearance and essence. There are different types of thought which come very fast, immediately, and unconsciously, as well as a more reflective type of thought that comes more slowly, and then there is the flash of perception which comes when you see something new. Essence and appearance are both categories of thought. We are discussing them now. They are both relative and limited. But one covers things more permanently and more broadly than the other. At any moment we have that distinction in thought between essence and appearance. But the content of what is called "essence" may change as our experience changes. What I am saying is that essence and appearance are both modes of thought and that the correlation of essence and appearance is the test of the correctness of our thought. Pribram: I think we are confused about the usage of words. In psychology "perception" has a special, defined meaning.
[Editorís note: At this point in the discussion there was a long debate over the meaning of words, especially the meaning of "perception." At the conclusion Bohm summarized his position as follows (not a direct quotation): The problem is that many people think of essence as something which is unchanging. Bohmís point is that we are part of reality. Thought is a part of reality. So as we change, we are contributing to what reality is. Therefore, even if only for this reason, reality is changing, and so the essence is changing. As Bohm put it: "We are actually contributing to the world, and if the world is infinite in its depth, then the essence is not knowable. Any essence that we know must be of this relative nature. That is what I am going to mean by the word Ďessence.í I will later propose that the essence is the implicate order. What I am saying is that we are constantly dividing reality up into essence and appearance which are really one. The proper viewí of essence is that essence and appearance are correlated."] Sperry: What is the relation of this notion to the notion of whole and part? Bohm: They are somewhat similar. Zucker: What do you mean by "correlate"? Bohm: There is an important clarification to make, regarding the levels at which we are operating. For example, at one stage atoms are regarded as the essence, but at another stage atoms may be an appearance as explained by elementary particles. At each stage there is a clear difference between essence and appearance, but it is not permanent. It changes. Its content changes. But all these changing forms are correlated in their content, rather than independent.
5Pribram: Donít these problems always arise when we deal with mathematical infinities? Bohm: They arise because we have assumed that the particle is a point. I am saying that we are not able to have a rational view of this if we assume that the particle is a point.
6[Editorís note: In his hand-written notes, Bohm mentioned at this place that the point event is the limit of Whiteheadís actual occasion.]
7Pribram: What do you mean by "process"? Bohm: Process means that movement is fundamental. What is, is nothing but movement itself, as Heraclitus pointed out. Zucker: There appears evidence (and you, Dr. Pribram, are an expert in this field) that there is perception of movement before that of space and time. It is thinkable that space and time are a later evolutionary development. Fritjof Capra (University of California -- Berkeley): The term "movement" is a bad choice since it has so many connotations in classical physics. Why not use the word "change"? Bohm: Change, movement process -- use whatever you like. Process really means to proceed, to step forward. Wolf: One way out of the question is to put your head at the speed of light where there is no space and time, but there is movement. Bohm: I will deal with that later in the implicate order. We will discuss movement which is prior to space and time. Space and time are an order which is abstracted from what we call "movement." We have a problem. Our linguistic convention says that if there is a change, there is something which undergoes change. I suggest that we alter that convention. Change is first, and what changes is abstracted from the change. I am proposing that change is basically an undefined concept. We will gradually unfold the meaning of it.
8[Editorís note: In his hand-written notes Bohm has written: This demands a total revolution. Essence is not permanent material substance but a process in a field (x,t). There is no identity whatsoever in field elements. Matter is to be explained as a relatively stable order, arrangement, connection, or organization of relationships in field variables. In other words, P1, is "matter," Pe is field relationships. Matter is no longer the essence, but a particular form in a universal process. Energy (work from within) is more fundamental than matter. . . .]
9[Editorís note: At the conclusion of the section on relativity theory a lengthy discussion ensued. Capra pointed out that in physics relativity provides the framework phenomena which the physicist studies. Bohm agreed and mentioned that his point is that there is no consistent theory of the particles in relativity theory. There is no way of getting beyond the phenomena. Everyone uses the relativity framework, but somehow that framework is inadequate because it has no theory of the essence. At the conclusion of the discussion Bohm summarized his position] Bohm: There are two points being made. One is the point of the description of the phenomena. The original point in relativity theory is that there are two different descriptions of the phenomena, which will have the same content with different form. The second point (which has not been achieved in relativity) is to get beyond the phenomena and to understand the essence. If the second point were achieved, we should see that process is primary and space and time are abstracted from it. But it is necessary in relativity to explain the essence of matter, and this has never been done. This situation has led to confusion, because people sometimes act as if matter has been explained and sometimes as if it hasnít, and nobody knows exactly what the situation is. Finally, the main point I am making is that ordinarily people think of the essence as something permanent and unchanging, fixed or reified. We are saying that movement or flux or flow is fundamental.
10[Editors note; Bohmís notes clarify this point as he writes: He accounted for the uncertainty of classical properties of the atom by means of a disturbance In general Heisenberg was influenced by positivism. . . . But here there is a strange mixture. He assumed that the precise value of x at p existed, but was unobservable, and also there was an unobservable disturbance. By such an extremely anti-positivist procedure at this point he justified his positivist approach to the detail of particle orbits.]
11[Editors note: In Bohmís notes he has written: Bohr made "a kind of metaphysical assumption about language and concepts which means (as always with positivist, operationalist, or phenomenalist approaches) that we fix our concepts to those that have been developed before."]
12[Editorís note: In his notes Bohm clarifies his criticism: If we had two kinds of matter, Q and C, this would be coherent. But we say all C is actually Q, and this leads us into Cí Cíí, . . . an infinite regress.]
13Capra; Explain how Heisenberg does not follow Bohr. Bohm: Heisenberg says that there is a microobject which is disturbed, but Bohr never used this idea because it would be inconsistent with his point of view.
14Capra: I feel that I will have to interrupt. I do not feel that you do justice to Heisenberg in his later years. Bohm: I forgot. I should have said that Heisenberg has given up his positivistic position in his later years. Unfortunately, people generally take Heisenberg in his earlier years. Heisenberg in his later years would be close to my viewpoint, at least in its general view, if not in the details.
15Capra: Would you please elaborate on Bohrís answer to Einstein. Bohm: The answer would get rather complicated. In short, Bohrís answer was that time is irrelevant. The actual fact as it happens implies no paradox at all. It is merely the attempt to explain it which makes the paradox.
16Zucker: This point is already upheld before quantum mechanics in the classical Feynman radiation experiments concerning the speed of light Bohm: Experiments indicate that the speed of light is irrelevant. There is no evidence that the speed of light is involved in this correlation. For example, in the Birkbeck experiment, the results do not depend on the separation.
17[Editorís note: In his notes Bohm writes: The holomovement is what sustains all. The order of all is implicit in holomovement. The implicit order is the essence of all.]
18Muses: There could be no evolution in this view, could there? Bohm: Evolution would have to be explained as an unfolding.
19Muses: Explain your view of indeterminism again. Bohm: I believe in indeterminism because the future does not exist. The present view of determinism holds that the future already exists. It is determined by the past. When you think of determinism, you must first think of a back stretch of time which is infinite. First there is time, then there are differential equations. But I am saying that we should not be in with time at all. We are beginning with the implicate order. We cannot predict the future, because there is no future. The future is being generated from the implicate order, not from the past, but from the unknown. What is implicit from the implicate order is not the past, but the unknown. What is implicit behind the implicate order is the unknown, which cannot be specified. Zucker: How can you say "the implicate order structures." To me the word order means structure. Bohm: The implicate order is the order of the past and any order which can be described is restricted to the past. William Scott (University of Nevada -- Reno): But the creative act is not included in the implicate order. Bohm: It is implicit in the implicate order. Scott: But what the creative act could be is not determined by the implicate order? Zucker It is a little confusing to use the word "order" for the matrix out of which comes creativity Bohm: No, it is not the matrix. The order is the mode of description of what emerges from creativity. Zucker: We should be aware that in talking this way we are working at the limits of logic. The time which is now is the time of logic. We must be aware that in the new order, we must offer a whole new logic for the next order which is beyond the Boolean logic. Quantum logic is a first step in that direction. You donít have the logic to embed it in. Bohm: It is said that Aristotle said that the law of the excluded middle does not apply to the unknown future. I am aware that we are going to have to change our notions of logic and identity, but we have to do it in some sort of order.
20[Editorís note: At the conclusion of Bohmís presentation there was a lengthy discussion, which follows.] Blackmore; Are you defining a vacuum as the absence of matter, rather than as the absence of everything? Bohm: Yes. The vacuum is where everything moves freely. It is the absence of every thing, you see, because "things" are made of matter. But beyond this vacuum there must be something even more. We are abstracting from an immense unknown of energy beyond our imagination. Some people talk about the creation of the universe as a big bang, while it is really a little ripple. To us it appears as a big bang, because we are a part of it. The disturbance involved in creating the universe out of the vacuum would be much less than the disturbance in this room from my talking. The laws that relate matter to the vacuum might be of an entirely different character than the common laws of matter itself, relating one part of matter to another. Matter is somehow enfolded in the vacuum. This is what I am suggesting. We could make a comparison to consciousness in the brain. The brain has a tremendous function beyond thought, such as attention, awareness, and so on. Thought itself is merely a function of memory acting to produce some imitation of something that was perceived. You could say that thought introduces a certain kind of order of time into the brain. Thought is to the whole function of the brain as matter is to the vacuum. In fact, thought might have some relative autonomy, but ultimately not so. Similarly, matter might have some relative autonomy, but ultimately not so. Therefore, something unknown enters. Part of it is knowable, but ultimately it will go off beyond anything we can know.
Scott: Can you think of connectivity in the vacuum? Bohm: There is connection in the implicate order, because the vacuum is the whole, because all connection is through the implicate order. Space and time are implicit in the vacuum. Scott: Are you saying that in the EPR experiment, for example, there is connectivity in the vacuum? Bohm: Yes. Blackmore: You use the term "vacuum." But donít you imply absence when you want to imply plenitude? Bohm: Both. I would like to coin a word that has vacuum on one side and plenitude on the other. The way we experience it is as vacuum, but the way we think of it is as plenitude. Zucker: Perhaps "vacutude." Dean Fowler (Marquette University): Perhaps it is a vacuum epistemologically but a plenitude ontologically. That is, we don recognize "things," but it is a fullness ontologically. Bohm; Yes, but I donít think we should make this sharp distinction between knowledge and being. Knowledge is. Knowledge is a certain movement in thought, and the being we are talking about is some other movement.
Zucker: The wave function which seems so mysterious represents the amplitude of information (potential information), but when we look, the wave function collapses because we have the information. It is no longer potential or probable. This is the meaning of the collapse of the wave function. If we accept this demystification of the wave function, it suggests that the EPR experiment is really talking about a whole. Is this a possible interpretation? Bohm; Do you mean the change from potentiality to actuality? Wolf That way of speaking is confusing. The point of the EPR paradox is that the two events are space-like separated. There is no first observer, who knows the collapse of the wave function. That is the causality game. Bohm: We have to deal with the question of "self reference" in order to understand the issue of the wave function. The present theory involves the idea of reference to something else, such as a piece of apparatus, and that to something else, etc., and finally to the consciousness of some observer. This makes it a phenomenalist theory. My view would develop the idea of a thing existing in self reference. Then the observer no longer lays a fundamental part. I will propose that the density matrix, rather than the wave function, is more fundamental. Some algebraic property is more fundamental and allows for self reference, because then the observer is a part of the whole thing. His thought is a part of the whole structure. This leads to the problem of an infinite regress. There is a further observer of the observerís thought, etc. There is no collapse of the wave function. Recall my view of time. Each moment enfolds its past. The new wave function is more than the past. It includes the actuality of the new present. The old past becomes irrelevant. The wave function does not collapse. Rather it enriches, and this may be connected to entropy. The enrichment of the wave function will describe the change of entropy. There is an inherent relation between time and entropy. Instead of saying first there is time and then we discover that entropy should increase with time, we will say that entropy is inherent in time, that we would not have time without entropy, because there would be nothing irreversible. This irreversibility is the appearance, it is an abstraction, It is irreversible because whatever symbol you use to represent the p resent time, it needs the earlier time as a part of it. It is, and it contains more than merely those symbols. However, there may be a statistical tendency, so that a certain structure will imply a certain structure later. We must find some way of defining our symbol so that it will take the implicate of time into account. What we call time must involve some sort of averaging.
Fowler: Is it better perhaps to think of time as antientropic? With time we are measuring the increase of order or at least the change of order. Zucker; That is a common mistake. The entropy increase does not mean an increase in disorder. What it means is that no further changes tend to take place. It is a misinterpretation to think of disorganization as the end. The increase in entropy is the condition for the possibility of the creation of forms in the universe. You cannot have the formation of crystals, you cannot have the formation of living organisms, unless you are in a universe in which the entropy is increasing. Bohm: But the point is that energy is limitless. So even if the increase of entropy means that the energy becomes inaccessible, there is still the possibility of new forms. Only if you believe that there is a limited amount of energy and a limited amount of freedom will you face these problems. But each new moment is a new degree of freedom.