Heisenberg told this story:
In the spring of 1926, I was invited to address this distinguished body [University of Berlin] on the new quantum mechanics, ...Einstein is credited with abolishing the aether, absolute space, absolute time, etc., but maybe that is not how he thought about it at all. He went on to try to develop unified field theories that were completely detached from observation.[Einstein said] "What you have told us sounds extremely strange. You assume the existence of electrons inside the atom, and you are probably quite right to do so. But you refuse to consider their orbits, even though we can observe electron tracks in a cloud chamber. I should very much like to hear more about your reasons for making such strange assumptions."
“We cannot observe electron orbits inside the atom," I must have replied, "but the radiation which an atom emits during discharges enables us to deduce the frequencies and corresponding amplitudes of its electrons. After all, even in the older physics wave numbers and amplitudes could be considered substitutes for electron orbits. Now, since a good theory must be based on directly observable magnitudes, I thought it more fitting to restrict myself to these, treating them, as it were, as representatives of the electron orbits."
"But you don't seriously believe," Einstein protested, "that none but observable magnitudes must go into a physical theory?"
[Heisenberg] "Isn't that precisely what you have done with relativity?" I asked in some surprise. "After all, you did stress the fact that it is impermissible to speak of absolute time, simply because absolute time cannot be observed; that only clock readings, be it in the moving reference system or the system at rest, are relevant to the determination of time."
"Possibly I did use this kind of reasoning," Einstein admitted, "but it is nonsense all the same. Perhaps I could put it more diplomatically by saying that it may be heuristically useful to keep in mind what one has actually observed. But on principle, it is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which decides what we can observe.
I've always found Einstein's position (a position not unique to him) a little strange: he seems to want to discuss what cannot be in any way inferred from the data obtained by any experiment or by any number of experiments.
ReplyDeleteNo ideal observable in quantum theory corresponds directly to actually recorded data. For momentum, for example, we would require a perfect, infinitely extended diffraction grating, say, but we must be content to infer a result for such an ideal measurement from the results obtained by using a number of different well-characterized but imperfect diffraction gratings.
Any algorithm we can think of and that takes actually recorded data as input is an observable. Is there something other than all that in an empirical science that I'm not noticing? I can see that something that we put into a physical theory that makes no contact whatsoever with any data and any conceivable algorithm might offer a reliable intuitive benefit, but I suppose we can only trust such intuitions insofar as we can also verify them with explicit computations?