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Quantum Mechanics

Dr. David Bohm 

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from  https://www.youtube.com/watch?v=XO8hR2z8yW4

how the concept of QM came to be

Well, the quantum domain arises because, as we probed into the behavior of matter – round about the last century – we found that the atoms were behaving in a way which we could not understand in terms of classical physics, and that they [had] a very puzzling way of behavior.

And then it was Heisenberg who actually spotted how to change the description, from the classical description, into a quantum description which would then account for atom spectra, in particular. And the change in the mathematics was, in a way, quite dramatic. It changed from simply thinking about particles with positions and momentum and evolving in space and time to something which actually forbid us to talk about positions – to measure positions - and momentum simultaneously.

And if you make the argument that they must exist simultaneously then the classical domain is not open to you and then you have to have an entirely new way of describing the phenomena. And this occurs not at the macroscopic level but it becomes very evident as we get down to the atomic, the molecular, the sub-atomic levels.

We have to use instruments to “see” what is going on, and therefore we do not directly perceive what is going on. So we have to understand how our instruments are working in order to see, and what we find is that, if we assume that the instruments are doing what we think they are doing, [then] we get into this dilemma that it is not possible to find, to measure the position, and the momentum, of a particle at the same time, at one at the same time.

So, this now makes us say, ok, we’ve got a question now. Does it mean that atoms don’t have position and momentum at a given time, or [does] it simply mean that we can’t measure the position and momentum at a given time?

And this gives us the choice. The Copenhagen interpretation says, we don’t know whether they have a position and a momentum at the same time, but there’s nothing we can say about it even if they did have a position and a momentum at the same time.

And that left us with a very vague idea that we don’t know, we can never find out, what is going on underneath the measurements that we’re getting – and, therefore, there’s a concentration [of effort] on what we can measure and how the measurements are related to each other.

This is in contrast to people like Einstein and people in classical physics who believe that there is something underlying this and the question is, we can make speculations about this and actually try to develop a theory which shows us what is going on beneath this apparent uncertainty.

What is 'quantum potential'?

And it was this, the message, that David Bohm took up and showed that even within the Schrodinger equation, by technically splitting it into real and imaginary parts, splitting it into two coupled equations, that one suddenly saw that one equation looked very much like a classical equation, that is was a particle evolving along a trajectory, but it had a new feature to it, and it’s the feature that we have called the “quantum potential.” It seemed almost as if there was another force being generated from the sub-quantum medium. And the question has always been, what does it mean, is it there, and how do we get information about it?

Bohr had this idea that we could not say anything about the underlying reality, and people have taken that also to mean that there might not be an underlying reality. Einstein completely disagreed with this point of view. He thought there must be an underlying reality, and this underlying reality would produce the effects which we actually see in our instruments.

Now, the question then was, what is that underlying reality? At the time there was a feeling that because quantum mechanics was essentially statistical, we got all our results of measurements by repeating and getting a statistical value for these things, that maybe we can find something that can explain the statistics by introducing new variables, and these new variables were called “hidden variables.” And this set off a whole exercise in trying to develop hidden variable theories.

What Bohm did when he came along was to be influenced by Einstein, in a way, but he also felt that there was something underlying the statistical features. And what he did was to take the Schrodinger equation, split it into its real and imaginary parts, that is, split it into two equations which were coupled, one equation looked remarkably like a classical equation of motion – but it had a very big difference – and the difference was there was a new energy that seemed to be involved, and this new energy manifested itself in terms of a ”quantum potential” as they called it, and this gave rise to a new force which only worked in the quantum domain, and if you go to the classical domain this force becomes zero.

So he developed his ideas of particles following trajectories, but to do that he did not have to introduce hidden variables. All he used was the variables that would be used in quantum mechanics anyway, but he was using them more like classical variables, the abstract operators as the conventional approach uses.

non-commutative math

So what we’ve got here is we can describe quantum phenomena in terms of the variables of classical physics – but how can this be? – because Heisenberg has already shown us that we can’t use the classical variables without changing the mathematical structure into what is known as “non-commutivity”, that is, the way x and p behave, if you talk about x first and then p, it’s different from talking about p first and then x, so the whole idea of the evolution of a quantum process is non-classical, something new would have to be involved in this.

And it was actually Durac who said, well, we can’t talk about a trajectory going through in the classical sense, but what we can do is to look at the process of slowly unfolding into one process and then enfolding into another process, so it’s a whole process of unfolding and enfolding actually occurring, and there is a transition between these states. And it’s this transition that we’ve been focusing on recently.

Remember we’re talking about wholeness. We have to have wholeness in here, and here we agree with Bohr [who] pointed out that it was very important, the new features of quantum mechanics, is a kind of wholeness, which means we cannot analyze things by cutting them up into little bits as we do in classical physics. But what we can do, if we want to cut it up, [is to acknowledge] that the way one bit goes into the next bit actually involves unfolding into the whole and then enfolding back again into a particular region. And so you get this idea of unfolding, enfolding, unfolding, enfolding – so what looks like a continuous trajectory is actually a series of [un]foldings and enfoldings.

And Dirac essentially had this idea but gave it up. What Bohm has done is to say, don’t give it up. Dirac’s thought that the uncertainty principle would be violated if you went down this road, and in fact Dirac actually got the equations which were almost the Bohm equations, but he dismissed them. He got them to first order “h bar”, the Planck’s constant, but he dismissed them because he thought the Heisenberg uncertainty would be violated.

What David Bohm did was to show that it would not be violated, that you would still retain the uncertainty principle, but then the question of what these trajectories mean becomes important. And this is where he then said, well, let me be bold and say there is this, there is this unfolding and enfolding actually going on – nothing to do with measurement – it is the actual process itself unfolding.

And we can make speculations about this unfolding, and this is in fact what people were doing in field theory, but they abandoned it because measurement seemed to be the primary aim of physicists. If we’re talking about measurements we know what we’re talking about, seems to be the way the [reasoning] goes, rather than saying, what we should be talking about, as Einstein suggested, was speculations about the underlying movement, which then produced observable effects, and we then go to the laboratory and see, do these effects, are they actually there?

What David Bohm was suggesting was, we agree with the assumptions that you make, namely, that there is a guidance condition, in the mathematics, and that the equation, the “real” part of the Schroedinger equation, is telling us something about the energy distribution in a given system. And what you see is an energy conservation equation, provided you introduce this new quality of energy call the “quantum potential” energy. And this quantum potential energy only functions when quantum phenomena appear; that is, in the particle approaching two slits it is the quantum potential that organizes the way that the individual trajectory work. So there is a dynamic whole process going on in which the quantum potential appears.

Now, do you want to take that as “real” or not? Well, the new thing coming on the scene is, that we can actually perhaps measure effects which will reveal this quantum potential. And then if the experiments tell us that the way it reveals itself is correct, then we can say that the quantum potential is actually there.

But there is a big debate about what it is actually going to be because, remember, this is coming from the non-commutative underlying process. And nowadays we are beginning to think that underlying process is actually to do with the structure of space and time. That itself may not be continuous as we imagine. We don’t have continuous geometries but we have a non-commutative geometry, and the big question is, what is the form of that non-commutative geometry, what sort of insights do we get about it, how are we going to think about it, how are we going to reformulate our ideas to find out what non-commutative geometry means in everyday terms?

The question of existence is very interesting here. Because what we see is, in the non-commutative structure, there doesn’t appear to be any quantum potential. But when we projected into a face-space (?), a space-time manifold, a classical … - the quantum potential appears. So now does that mean the quantum potential is real, or not? Can I take an analogy with that?

Let’s go back to gravity. Remember that gravitational force is not a force [but it] arises because space-time has a curvature in it, but space-time is not Euclidean, it’s Riemannian.

Editor’s note: “Riemannian geometry, also called elliptic geometry, one of the non-Euclidean geometries that completely rejects the validity of Euclid’s fifth postulate and modifies his second postulate. Simply stated, Euclid’s fifth postulate is: through a point, not on a given line, there is only one line parallel to the given line. In Riemannian geometry, there are no lines parallel to the given line. Euclid’s second postulate is: a straight line of finite length can be extended continuously without bounds. In Riemannian geometry, a straight line of finite length can be extended continuously without bounds, but all straight lines are of the same length. The tenets of Riemannian geometry, however, admit the other three Euclidean postulates. Although some of the theorems of Riemannian geometry are identical to those of Euclidean, most differ. In Euclidean geometry, for example, two parallel lines are taken to be everywhere equidistant. In elliptic geometry, parallel lines do not exist. In Euclidean, the sum of the angles in a triangle is two right angles; in elliptic, the sum is greater than two right angles. In Euclidean, polygons of differing areas can be similar; in elliptic, similar polygons of differing areas do not exist.”

Therefore what is revealed as a force is actually a feature of the underlying geometry. And what I feel is that the quantum potential is a feature of the underlying non-commutative geometry. Now in that sense is it real or is it artificial? The point is, it’s pointing to the fact that we need a new geometry, and we’re trying to find out features of that non-commutative geometry, and that’s a very active field at the moment with many speculations about how this would arise.

The quantum potential is a way of talking about this thing, to take some of the mystery out of the quantum phenomena. With the quantum potential you don’t have schizophrenic cats that are alive and dead at the same time. With the quantum potential the cat is either alive or dead. With the quantum potential you explain the qualities that give you the interference, without the need for introducing a wave function.

And the wave function has been getting in the way, in my view, because we have this wretched measurement problem in which the wave function is behaving in an evolutionary manner through Schrodinger’s equation, and then, when we look at it, it collapses. And we have this collapse problem which has been going now for 50, 60 – 100 years, and it still has no solution. And maybe it has no solution because it is not relevant. We’ve got the thing wrong.

When I first joined David Bohm, we didn’t talk about his 1952 hidden-variable paper. What we were talking about was, how could we get quantum mechanics and gravity, general relativity, into one theory. How could we quantize the gravitational field?

Fortunately, we had Roger Penrose with us at the time at Birkbeck (University of London). [The three of us] and some mathematicians used to meet and talk about this problem. So we were talking about ideas like “pre-space,” how can we put quantum mechanics into this pre-space idea, so that we would have quantum space-time emerging from this. So what is a quantum space-time? This is what the discussion was about.

Roger Penrose was talking about his spin-networks, which has now become quite a big industry in some areas. He was developing his “twisters.” And [this] led me into a Clifford algebra approach, which is a non-commutative algebra, which is why I’m always talking about non-commutative algebras.

At that time David Bohm was creating a new idea which was called “structure process” – that, basically, we want to start with process, not particles moving in space-time, but a process from which both particles and space-time could emerge. Very radical ideas.

During those discussions, what we were thinking about was – how are we going to describe this process? And then I think I was reading some [mathematics] work by [Marcel] Grossman and Clifford, way back in the 1850s to the 1900s, and they were talking about process essentially but they weren’t calling it process, they were talking about activity, and order.

And they were saying, Grossman in particular, that, really, mathematics was not about material processes, it was about thought. If we are thinking about the underlying processes in terms of some sort of new radical idea, we need to develop the mathematics to actually encompass that. And what was coming to the fore all the time was that we needed an algebra. And an algebra is essentially something that has both addition and multiplication. And the multiplication became the order of succession, so that if you had a process unfolding, multiplication was the way it unfolded. Addition was the way it co-existed.

So this was pinching an idea from Leibniz, who had this idea of what time was. Time was the order of succession, but then there was also an order of co-existence. Now can we actually develop an algebra which will encompass that philosophical idea, and that’s what we were developing, and that’s what I think Penrose was developing with his “twister” theory… but that shows you that was in the background.

And only much later – I think it was after 10 years of working with David – [the two “Chris” grad students] came up to me and said, why don’t you talk about the 1952 paper? And that’s when I said, because I think it’s wrong. And then [one asked], Basil, had you read the paper? And I had to [admit[ that I hadn’t. And [later when I read it] I said, how on earth can he get trajectories out of this non-commutative structure? What do these trajectories look like? What does this quantum potential look like? We can calculate it from known solutions of Schrodinger’s equation, and that’s what Chris was an absolute master at, was actually developing computer programs, simulating this, and let’s have a look at what’s going on here.

But, unfortunately, people thought – and I speak for myself now – that we believed this. No, I was puzzled and always have been puzzled. Even when I wrote the book “Undivided Universe” with David Bohm I was still puzzled. How is it that you can have trajectories in this deeper process? We told a story, which I think was a very good story, but it wasn’t the final story. We left the final chapter open where we said that we needed more radical ideas. [But David’s time came too soon, 1992.] Since then I have been trying to develop a continuation of these original process-based ideas developing a theory of structure-process.

In quantum mechanics there’s no such thing as a vacuum – empty of everything. Bear in mind that even Maxwell did not think of the vacuum as being empty. He defined the vacuum as being everything that we can take out of it, that we know how to take out of it. So that leaves the unknown unknown possibilities. And now in quantum field theory we have inequivalent vacuum states. So these are states in which there is still activity present. So we never get to the stillness of nothingness. All is in flux.

It’s not a plenum of particles buzzing backwards and forwards. It’s this idea of the energy. Energy is a very interesting concept. We always think that energy goes with particles. We fire a particle with kinetic energy and it goes bang and causes trouble when it hits something. It releases its energy. But does energy have to be concentrated on particles? Quantum field theory tells us no. There is a field, this field carries energy in a non-local way.

The problem is for us, we’re trying to describe the universe by getting outside it, and then saying, look, there’s the valleys, there’s the fields, and so on, it’s the God-like view of reality. Unfortunately, we’re right in[side] it. I’m saying there’s no hill we can climb up. That’s the illusion. When we do that we fragment everything. We are in it right at the beginning; irreducibly in it, we can’t separate ourselves, and we depend upon it – light coming in, our sounds, all our perceptions are coming it, and then we have the arrogance to say, oh, I’m important, I’m on top of the hill, you’re not. And so we get into this conflict, which is going to go on and on. Unfortunately, we’re all in it together.

One thing I want to emphasize as I’ve been talking here, I have not got a theory which is complete and ready to solve all the problems of the universe. I’m on a journey, the journey is a process. What David and I have done is to open up the discussion, which I find when I’m talking to young people, that they’re very interested in trying to proceed further with these ideas. In other words, some of them have actually got it, as I put it, they know that in their basic feelings that this is an interesting way to go.

One of the problems that I see happening is that when they talk to their colleagues, shall I go in this direction?, they’ll be told, no, it’s not safe. But perhaps I should recount a personal story. I remember when I started out and was working with David Bohm, I was told that if I worked with David Bohm my career would not develop. Fortunately, I’m so pig-headed, I did not take any notice of them, and if this is a failed career I’m quite happy with it. What we’ve got to do is to encourage radical thoughts. The problem always is that amongst those radical thoughts there is always a lot of stuff which is just crazy. And so there’s always a difficulty in this area, what should we encourage people to follow, and what we should discourage. And I can see no other way, if someone is interested in the ideas I’m developing, if they understand where they’re coming from, is to encourage them to take it further… I don’t think being “safe” is going to solve problems in this area of wholeness…

What I feel is that the universe is organic. It’s not the parts that determine the whole, but the whole, the wholeness, determines the parts. And the way we talk about is through process, and not through particle interaction.