We had understood the mathematical scheme, and we also had 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 electron in a cloud chamber comes about, because they would see the orbit, but still we had 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 [before] - 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, Mach's philosophy, but whether I really believed in it, he couldn't see. Well, I told him that I had understood that he has produced his theory of relativity just on this philosophical basis, as everybody knew. Well, he said, that may be so, but still it's nonsense. And that of course was quite surprising to me.
Then he explained that what can be observed is really determined by the theory. He said, you cannot first know what can be observed, but you must first know a theory, or produce a theory, and then you can define what can be observed....
And could it not be the other way around? Namely, could it not be true that nature only allows for such situations which can be described with 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 it be described with a 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 by turning it around, one could at once see that now it's possible, if I say nature only allows such situations as can be described with 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.
From "The Development of the Uncertainty Principle", an audiotape produced by Spring Green Multimedia in the UniConcept Scientist Tapes series, © 1974.