Jun

9

There was one other pearl of information of a technical sort that I got from Oppenheimer, although it took me about ten or fifteen years to really appreciate it, but it shows how his mind worked. I asked him about two partial differential equations - one the Laplace equation and the other the Wave equation (d'Alembert's equation). The two were almost alike except that one has a plus sign and the other has a minus sign; and the conventional interpretation of the Wave equation is of two waves moving to the right and the left, and this is something you can read in any textbook. And I asked him why one could not have the same kind of an interpretation of the Laplace equation because you could get from the one to the other by changing one of the coordinates from real to imaginary units.

Oppenheimer said without any hesitation that the solution of two waves going in opposite directions didn't tell you a damn thing about the answer, contrary to whatever you read in the textbook. That tells you nothing beyond the continuity of the answer and, in fact, the real interest in those problems is not where the solution exists, but at the boundaries or the initial conditions where the continuity and solution breaks down; and that really controls what the answer is all about. In other words it is not where the equation is satisfied. It is where the equation is not satisfied that really describes a specific problem. The same happens to be true for Laplace's equation; it's the poles and the singularities where the analytic properties break down that really controls what the solution of Laplace's equation is like.

Well, the idea that you understand the theory and how a theory is determined is not the way it works but the way it does not work is a very useful idea. As I said it took me ten or fifteen years to suddenly realize, or gradually realize, that this was a very profound and important piece of mathematical and physical philosophy. You can in a sense relate it to Popper's ideas (that is Karl Popper), that a theory is not a theory unless you can show where it breaks down and then you begin to understand it. It is not where it works but where it does not work that really gives you enlightenment as to what it is all about and, of course, this statement of Oppenheimer's is an example of this. That it is the boundaries and the initial conditions where the equation breaks down that really control what is going on in any particular problem.

From his daughter, Melita Osborne's biographical document available here [MS word .docx file, approx 300 Kb].


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