An audio recording of an excerpt of a talk by Werner Heisenberg on the early days of quantum mechanics and the development of the Heisenberg uncertainty principle.
The recording can be found at https://youtu.be/JTEf5laJxRc
Full transcript:
The Uncertainty Principle as discussed by Werner K. Heisenberg
“When I finished my last year at school and entered university, one knew already about the Bohr model of the atom. And this model, as you know, was the following: the atom consists of an atomic nucleus and was surrounded by electrons in the same way as the planets surround the Sun. The electrons were supposed to move around the atomic nucleus in orbits, and the Bohr theory required the orbits to have a certain size, a certain shape, and so on, and in connection with the orbits were intended to explain the chemical behavior of the atom. So, this was the situation when I entered University and started my studies with Sommerfeld in Munich, and of course at that time, we tried to calculate atoms, and to prove, by calculation, the properties of the atoms which Bohr had more or less guessed. And then, in the first years, it turned out very soon that this was impossible. That is, first of all, the mathematical difficulties of a system with several electrons were enormous. Already, the so-called three-body problem could never be solved in classical astronomy. But then, also one had the impression that the whole system of orbits and quantum conditions, the Bohr-Sommerfeld quantum conditions, only worked in especially favorable cases. On the one hand, one knew about the Stark effect and the Zeeman effect, you know, the splitting of spectral lines in electric and magnetic fields, and the results of the Bohr theory were very great, and everybody was surprised to see such a good agreement between theory and experiment. On the other hand, at other points, there were very big difficulties, and it was difficult to reconcile these two facts.
“So, the atmosphere in the early years of my studies was this that this was a very funny kind of theory. First of all, the theory was only guessed by Bohr and never really achieved mathematically, and then, it gave excellent results in some cases and completely wrong results in other cases. So, we had innumerable discussions in our institute in Munich. We gradually talked ourselves away from the Bohr theory. My most important experience was a long walk when I met Bohr, Niels Bohr, for the first time in Göttingen. And he gave some courses in Göttingen in 1922, and discussed his theory. And then we went out for a walk on the Hineberg once, and then I made my objections, that I couldn’t believe the theory for such-and-such reasons, and he tried then to meet the objections. And during this discussion, I felt that we both talked ourselves away from the theory; that is, we both saw that the theory in that form which it had at that time couldn’t be correct and somehow the whole concept of orbits of the electron in an atom was wrong.
“But there was a difficulty that, for instance, in a cloud chamber you could see the electron moving, so to say that you say the water troubled, you saw the orbit of the electron if I may say it so. So, in a cloud chamber, there was an orbit of the electron, there was no doubt about that. On the other hand, we had very good reasons to believe that there was no orbit of the electron in an atom. And of course, this made difficulties we still have, but in this way, we gradually got the notion of some very different mathematical scheme which only resembled vaguely classical physics, so that we started talking about quantum mechanics which should replace classical mechanics. Of course, we didn’t know what quantum mechanics would be like, but still we felt it must be quite different from classical mechanics, that must come in some entirely new elements.
“And so, we ask ourselves, well, if quantum mechanics is so different from classical mechanics, what will persist in the new mechanics, and what will have to be dropped of the old mechanics? And those quantities which should persist somehow, because one can simply observe them in their experiments, where the frequencies which are emitted by the atom and the amplitudes belonging to these frequencies and so on. This word ‘quantum theoretical’, of course, was again a vague expression. We didn’t know exactly what it meant. But still, in this way, we got away from the classical notion of an orbit, but rather we thought of an assembly of frequencies and amplitudes and so on. And in this, we gradually, I got the notion that one should take this whole set of frequencies and amplitudes as representative of the orbit, so that only this representative would remain, but not the concept of an orbit would remain. And nowadays, we call such a thing a matrix.
“And so, well, in 25 [1925], then I felt I must seriously try simply to drop the idea of electronic orbit altogether, and to replace it by some mathematical notion of a matrix, and to set up what later on was later on called matrix mechanics. I first tried it with the hydrogen atom, and I failed completely because it was too complicated. And then I tried the simplest possible model of course, an anharmonic oscillator. Harmonic oscillator would have been too trivial, but an anharmonic oscillator was just that degree of complication which could one, one could possibly master. And then, it turned out that for such a system, one actually could get a consistent scheme of equations which gave good results and in which the orbit was replaced by this set of frequencies and amplitudes. So, this was then the beginning of the mathematical scheme of quantum mechanics which shortly afterwards was then developed independently by Born and Jordan in Göttingen on the other hand, and Dirac in Cambridge on the other hand. And all these different mathematical schemes seemed to be without any inner contradictions and difficulties, or then one had at least a good basis.
“You know, in 1924, I think already, de Broglie had published a paper that even an electron might be something like a wave, not only a particle, but something like a wave. Now, to begin with, it looked quite absurd, well, but since we were already accustomed to many absurdities at that time, so we didn’t feel too surprised. Then Schrodinger in 1926, it was about half a year after we had published this paper on quantum mechanics, he produced his idea of wave mechanics, which was a further development of the ideas of de Broglie.
“And, of course, we exchanged letters, and we were quite worried because now we had two entirely different schemes to tackle problems of atomic structure. And only one of the two schemes, so we felt, could be correct, the other one could not. But then, Schrodinger very soon wrote to us that he had now proved that the two mathematical schemes are equivalent, that means that his wave mechanics equations can be translated into matrix equations and vice-versa. So then, of course, everybody seemed to be quite happy because at least we have now a unique mathematical scheme.
“Just to describe the difficulties, I might mention that Schrodinger then, to begin with, hoped that he could interpret his wave mechanical scheme quite differently from our interpretation of matrix mechanics. Namely, he wanted his waves to be three-dimensional classical waves like Maxwell waves, sound waves, or so, so that–and then, all then all the quantum terms would disappear. And you would not talk about energies, but only talk about frequencies, and there would be no discontinuous element, no jumping from one state to another state, and so on.
“And this was, then, very generally believed by very many physicists, especially by experimental physicists, because they dislike intensely this rather funny idea of quantum jumps, you know, which is very irrational. I mean, how does an electron jump? I mean, well, you know you can not really picture that. In a quantum jump, the electron first moves in an orbit, then all of a sudden thinks, “Now I have to change my mind and then I go down to another orbit”. This ought, of course, is a very absurd notion.
“And so then, a rather strong controversy occurred between Schrodinger and our group. Our group means Niels Bohr and Pauli and myself. And I remember here in Munich in, I think July 1926. Schrodinger was invited to give a paper, to give a talk at some of our seminar. And of course all the experimental physicists, Wein and so on, they appear. And well, in the discussion, of course, I tried to explain to Schrodinger that if he really took his interpretation serious, he would have no chance to explain even the Planck formula because the Planck formula really rests on the idea of discrete energies and could not be derived by the idea of frequencies. Really Wein, who was an old gentleman, really the head of the department at that time, he was so upset about my remark that he said, “Well, now, young man, you know that I understand that you are a bit sorry that all this old story of quantum jumps and so on has to be forgotten now, but we can’t help it, and you will see that Schrodinger will solve all these questions, so you better sit down.” Well, that of course, finished my discussion so far, but Schrodinger was more worried than Wein was, that I could see.
“And then we invited Born and we invited Schrodinger to Copenhagen in September 1926. And, then it came to really serious discussions, which were, of course, mostly done by Niels Bohr, who knew more about the whole history of the thing. And it was a rather strange situation because Bohr, who was else a very nice gentleman and very polite and so on, he could be a complete fanatic in this discussion, so he would always stand at the side of Schrodinger and tell him, “Well, Schrodinger, you must understand, you must understand.” After 3 days, he became simply sick. He went to bed, and Mrs. Bohr would bring tea and cake, and again Bohr would sit at his bedside and say, “But Schrodinger, can’t you understand that?” and so on. And it was a very hard discussion. At the end, I remember Schrodinger saying, “Well, if it really shall remain that all these quantum jumps, then I regret that I have ever taken part in this atomic physics business,” Then, Bohr replied, of course, “But we, all of us, we are so grateful to you that you have done so.” I mean because after all, wave mechanics was, of course, an enormous progress.
“But I just tell this story to say that it was really very hard fighting and it was really very difficult to get down to the bottom of problems. And even after Schrodinger left, Bohr and I were not at all happy about the situation because we still felt, well, we have understood the mathematical scheme and we also have understood that certainly we need the discrete energy levels and the quantum jumps and so on, but we could not even explain how such a thing as an orbit of an atom in a cloud chamber comes about because there we see the orbit and still we have no notion of the orbit in our mathematical scheme.
“And at that time, I remembered a long discussion which I had with Einstein about a year ago. It was my first meeting with Einstein. I had given a talk on quantum mechanics in the Berlin colloquium. And Einstein had taken me to his room, and he first asked me about this idea, which I had said in my lecture, that one should only use observable quantities in the mathematical scheme. And he said, he understood the ideas of Mach math philosophy, but whether I really believed in it, he couldn’t see. Well, I told him that I had understood that he had produced his theory of relativity just on this philosophical basis, as everybody knew. And he said, “Well, that may be so, but still it’s nonsense.” And that, of course, was quite surprising for me. And then he explained that what can be observed is really determined by the theory. He said, “You can not first know what can be observed, but you must first do a theory or produce a theory, then you can define what can be observed.”
“And finally, I remembered this discussion with Einstein. And then Bohr was away for a skiing trip, and I decided, could it not be said the other way around? Namely, could it not be true that Nature only allows for such situations which can be described as a mathematical scheme? Up to that moment, we had asked the opposite question. We had asked, “Given the situations in Nature, like the orbit in a cloud chamber, how can we describe the mathematical scheme?” But that wouldn’t work, because by using such a word like ‘orbit’, we, of course, assumed already that the electron had a position and had a velocity.
“But turning it round, one could at once see that now it’s possible. If I say, Nature only allows such situations as can be described as a mathematical scheme, then you can say well, this orbit is really not a complete orbit. Actually, at every moment, the electron has only an inaccurate position and an inaccurate velocity. And between these two inaccuracies, there is this uncertainty relation. And only by this idea, it was possible to say what such an orbit was.
“So, this was, for me, a complete liberation, because I first felt, “Well, now I can really get down to the bottom.” I can see that I can even describe such an orbit because I need not assume that the electron at every moment has a position and a velocity. It is sufficient that it has both only with that limited accuracy.
“Well, then, after two weeks or so, Bohr came back from his skiing trip, and of course, we both saw that this was the right interpretation. Bohr had developed his idea of complementarity in the meanwhile, and these things had to be fitted with my uncertainty relation. But then after one or two months, we had agreed that this was the right interpretation.
“And so, the final story was then that at the Solvay meeting in 1927, Einstein and Bohr would fight it out. That this, well, of course Pauli and I were there also there for assisting, but mostly these two people fought it out, and usually happened like this: at breakfast, we stayed at the same hotel–Einstein would come in and would say, “Now I have an experiment where I can really disprove the uncertainty relation,” and so he would explain this experiment. Then Bohr would be terribly worried, and we would go to the conference hall, and we would all three try now to say what was wrong with Einstein’s idea. And usually, at dinner time, we had found the flaw in the thing, and we explained it to Einstein. Then Einstein was very sorry and very sad and said, “Well yes, you are right this time in this part. Well, I will see.” And the next morning, he would come with a new experiment, the next evening again it would be disproved, and this game was played the whole week. And at the end of the week, we felt we were through. He was not convinced but he could not say anything against it anymore.”
END