3.2 A NEW THEORY IS WROUGHT FROM THE CRISIS
Albert Einstein was the first to understand that Planck’s successful explanation of the energy spectrum of radiant heat fundamentally challenged classical theories because, he says:
the derivation presupposes implicitly that energy can be absorbed and emitted by the individual resonator only in quanta of magnitude in contradiction to the laws of mechanics and electrodynamics. The contradiction with dynamics was here fundamental whereas the contradiction with electrodynamics might be less fundamental as shown by the fact that the Stefan-Boltzmann law and Wien’s law are in agreement with experience. All this was clear to me shortly after the publication of Planck’s fundamental work; so that, without having a substitute for classical mechanics, I could nevertheless see to what kind of consequences this law of temperature radiation leads for the photoelectric effect as well as for the specific heat of solid bodies. All my attempts, however, to adapt the theoretical foundation of physics to this new type of knowledge failed completely.
Albert Einstein, Autobiographical Notes, (1949)
Bohr succeeded in advancing towards Einstein’s goal by guessing just how to combine classical dynamics and Planck’s work in order to explain the atomic spectra. While short of the new theoretical foundation sought by Einstein, Bohr’s model did inspire extensive work which was able to explain an ever-growing set of atomic experiments.
By 1924, however, it became clear that Einstein was right: Bohr-like improvisation was not enough and a new foundation had to be laid for explaining the quantum experience. As Wolfgang Pauli described it in his letter to Sommerfeld on December 6th of that year:
the conceptual models are in serious crisis now, you know, of a principal nature, which I believe will end in another radical sharpening of the contrast between classical and quantum theory. The concept of definite, clear electron orbits within the atom are probably hardly maintainable. One gets the impression from all models now that we are speaking an inadequate language for the simplicity and beauty of the quantum world.
Werner Heisenberg was the first to suggest an adequate language in his 1925 article Quantum-Theoretical Re-Interpretation of Kinematic and Mechanical Relations. A year later, alternative suggestions were published by Erwin Schrödinger and P.A.M. Dirac, each of which managed to bring together in a systematic manner all experimental results involving the inside of matter. Subsequently, these alternatives were shown to be fully equivalent to each other. Heisenberg suggested that the new theory should accept in it only measurable quantities such as the frequencies and amplitudes of spectral lines and proposed an algebra of non-commuting quantities to describe them. The dynamics of these quantities was modeled closely on the classical equations:
It seems sensible to discard all hope of observing hitherto unobservable quantities, such as position and period of the electron, and to concede that the partial agreement of the quantum rules with experience is more or less fortuitous. Instead, it seems more reasonable to try to establish a theoretical quantum mechanics, analogous to classical mechanics, but in which only relations between observable quantities occur.
W. Heisenberg, Quantum-Theoretical Re-Interpretation of Kinematic and Mechanical Relations (1925)
Schrödinger started from a completely different position altogether but ended up in the same place. In an attempt to eliminate the mysterious jumps between Bohr’s stationary states, the very idea of which was always distasteful to him, he observed that classical mechanics was to the yet uncreated quantum mechanics as geometric optics was to wave optics, an idea that had already been put forth by de Broglie in 1924. Therefore, the new mechanics must be a wave mechanics of some sort and the electron should be described by a wave function. The success of these theoretical developments prompted Heisenberg and Born to declare at the 1927 Solvay Conference that the revolution was over and nothing further was needed. We shall not reproduce here the birth and development of these different strands of quantum mechanics, nor dwell on their equivalency; excellent accounts are provided in the extensive historical and pedagogical literature. What is important to us, however, is the common position they all take, in one way or another, concerning the ontological question. Quantum mechanics has nothing to say about the way in which we should conceive of the quantum object whose behavior it describes. As Bohr’s complementarity principle makes clear, that question is sequestered behind the obvious necessity of developing a causal theory:
The very nature of the quantum theory thus forces us to regard the space-time co-ordination and the claim of causality, the union of which characterizes the classical theories, as complementary but exclusive features of the description.
Niels Bohr, The Quantum Postulate and the Recent Development of Atomic Physics, (1927)
That things should be so, is a consequence of the quantum postulate which according to Bohr:
implies that any observation of atomic phenomena will involve an interaction with the agency of observation not to be neglected.
Thus, to use his own argumentation:
On one hand, the definition of the state of a physical state claims the elimination of all external disturbances. But in that case, according to the quantum postulate, any observation will be impossible and, above all, the concepts of space and time lose their immediate sense. On the other hand, if in order to make observation possible we permit certain interactions with suitable agencies of measurement, an unambiguous definition of the state of the system is naturally no longer possible, and there can be no question of causality in the ordinary sense of the word.
Since in a rational theory causality must be preserved, no direct observation of a quantum object designed to inquire into what that object is can be permitted. As we shall indicate below, the time evolution of the wave function describing a quantum object is causal, but the outcome of measuring a property of that object is generally stochastic; in quantum physics, the act of observation destroys the causal behavior of the observed.
Needless to say, Einstein disagreed and continued to debate this point with Bohr on and off until 1935 when they finally agreed to disagree. According to Bohr:
The question at issue has been whether the renunciation of a causal mode of description of atomic processes involved in the endeavors to cope with the situation should be regarded as a temporary departure from ideals to be ultimately revived or whether we are faced with an irrevocable step toward obtaining the proper harmony between analysis and synthesis of physical phenomena.
Niels Bohr, Discussion with Einstein on Epistemological Problems in Atomic Physics, (1949)
This debate is central to our pursuit of the ontological question and we shall therefore return to the last installment of that debate in Section 4 of this Chapter when we shall be in a position, at long last, to raise our original question in a way in which we shall be able to do something with it. But before we can do that, we shall need to introduce some of the fundamental mathematical machinery of quantum mechanics.