Max Born was awarded the Nobel Prize in physics in 1954 for his statistical interpretation of solutions of Schrödinger's wave equation named wave functions. Schrödinger formulated his equation, which has come to serve as the basic mathematical model of the modern physics of quantum mechanics, in a moment of heavenly inspiration in the Alps in 1926 (together with one of his many girl friends), with the objective of interpreting the modulus squared $\vert\psi\vert^2$ of a wave function $\psi$ as charge distribution.
- I care little for the conception of $\vert\psi^2\vert$ as a probability...In the case of an H-atom there is for a given energy E, also a non-vanishing probability outside the sphere which electrons of energy E cannot leave.
- It is necessary to drop completely the physical pictures of Schrödinger which aim at a revitalization of the classical continuum theory, to retain only the formalism and to fill that with new physical content.
- The whole procedure was an act of despair because a theoretical interpretation (of black-body radiation) had to be found at any price, no matter how high that might be…I was ready to sacrifice any of my previous convictions about physics...For this reason, on the very first day when I formulated this law, I began to devote myself to the task of investing it with true physical meaning.
- Planck, himself, belonged to the sceptics until he died. Einstein, De Broglie, and Schrödinger have unceasingly stressed the unsatisfactory features of quantum mechanics and called for a return to the concepts of classical, Newtonian physics while proposing ways in which this could be done without contradicting experimental facts. Such weighty views cannot be ignored.
- Niels Bohr has gone to a great deal of trouble to refute the objections. I, too, have ruminated upon them and believe I can make some contribution to the clarification of the position. The matter concerns the borderland between physics and philosophy, and so my physics lecture will partake of both history and philosophy, for which I must crave your indulgence.
- The work, for which I have had the honour to be awarded the Nobel Prize for 1954, contains no discovery of a fresh natural phenomenon, but rather the basis for a new mode of thought in regard to natural phenomena.
- The first point is this: the work at the Göttingen school, which I directed at that time (1926-I927), contributed to the solution of an intellectual crisis into which our science had fallen as a result of Planck’s discovery of the quantum of action in 1900.
- At the beginning of the twenties, every physicist, I think, was convinced that Planck’s quantum hypothesis was correct. According to this theory energy appears in finite quanta of magnitude $h\nu$ in oscillatory processes having a specific frequency $\nu$ (e.g. in light waves). Countless experiments could be explained in this way and always gave the same value of Planck’s constant .
- Heisenberg, who at that time was my assistant, brought this period to a sudden end. He cut the Gordian knot by means of a philosophical principle and replaced guess-work by a mathematical rule. The principle states that concepts and representations that do not correspond to physically observable facts are not to be used in theoretical description.
- I was as excited by this result as a sailor would be who, after a long voyage, sees from afar, the longed-for land...I was convinced from the start that we had stumbled on the right path.
- The first non-trivial and physically important application of quantum mechanics was made shortly afterwards by W. Pauli who calculated the stationary energy values of the hydrogen atom by means of the matrix method and found complete agreement with Bohr’s formulae. From this moment onwards there could no longer be any doubt about the correctness of the theory .
- What this formalism really signified was, however, by no means clear. Mathematics, as often happens, was cleverer than interpretative thought.
- Wave mechanics enjoyed a very great deal more popularity than the Göttingen or Cambridge version of quantum mechanics. It operates with a wave function $\psi$, which in the case of one particle at least, can be pictured in space, and it uses the mathematical methods of partial differential equations which are in current use by physicists. Schrödinger thought that his wave theory made it possible to return to deterministic classical physics. He proposed (and he has recently emphasized his proposal anew’s), to dispense with the particle representation entirely, and instead of speaking of electrons as particles, to consider them as a continuous density distributions.
- I immediately took up Schrödinger's method and an idea of Einstein’s gave me the lead. He had tried to make the duality of particle-light quanta or photons and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons.
- This concept could at once be carried over to the $\psi$-function: it ought to represent the probability density for electrons (or other particles).
- It was easy to assert this, but how could it be proved?
- To us in Göttingen Schrödinger's interpretation seemed unacceptable in face of well established experimental facts. At that time it was already possible to count particles by means of scintillations or with a Geiger counter, and to photograph their tracks with the aid of a Wilson cloud chamber.
- However, a paper by Heisenberg containing his celebrated uncertainty relationship, contributed more than the above-mentioned successes to the swift acceptance of the statistical interpretation of the $\psi$-function.
- It showed that not only the determinism of classical physics must be abandonded, but also the naive concept of reality which looked upon the particles of atomic physics as if they were very small grains of sand.
- How does it come about then, that great scientists such as Einstein, Schrödinger, and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. Two closely knitted points of view are to be distinguished: the question of determinism and the question of reality.
- The determinism of classical physics turns out to be an illusion, created by overrating mathematico-logical concepts....and cannot, therefore, be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics.
- Are we still justified in applying to the electron the concept of particle and therefore the ideas associated with it?
- Somewhere in our doctrine is hidden a concept, unjustified by experience, which we must elim- inate to open up the road.
- To come now to the last point: can we call something with which the concepts of position and motion cannot be associated in the usual way, a thing, or a particle? And if not, what is the reality which our theory has been invented to describe?
- A perceived need to make the duality of particle-light quanta or photons and waves comprehensible.
- Because a Geiger counter gives a "click", what caused the "click" must be a "particle".
But the sad truth today is that nobody cares if the fundamentals of physics make sense or not: Quantum mechanics and relativity, although incompatible, is "settled modern physics" with all questions answered once and for all by now dead and gone physicists, who took the answers along into the grave.
Today, only a few hard core extremist like Lubos Motl claim that this is the final word to which nothing can be added. The historical dimension of this view is described by A. Pais in the opening of his Address to the Annual Meeting of the Optical Society in 1982 entitled Max Born and the Statistical Interpretation of Quantum Mechanics as follows:
- The introduction of probability in the sense of quantum mechanics, probability as an inherent feature of physical law, may well be the most drastic scientific change yet effected in the twentieth century.