Erwin Schrödinger
(1887-1961)
Erwin Schrödinger is perhaps the most complex figure in twentieth-century discussions of quantum mechanical uncertainty.
In his early career, Schrödinger was a great exponent of fundamental
chance in the universe. He followed his teacher Franz S. Exner, who was himself a student of the great
Ludwig Boltzmann. Boltzmann used randomness in molecular collisions to derive the increasing entropy of the Second Law of Thermodynamics.
Most physicists, mathematicians, and philosophers believed that the
chance described by the calculus of probabilities was actually completely determined. The "bell curve" or "normal distribution" of random outcomes was itself so consistent that they argued for deterministic laws governing individual events. We simply lack the knowledge necessary to make exact predictions for these individual events.
Pierre-Simon Laplace was first to see in his "calculus of probabilities" a universal law that determined the motions of everything from the largest astronomical objects to the smallest particles.
On the other hand, in his inaugural lecture at Zurich in 1922, Schrödinger argued that the evidence did not justify our assumptions that physical laws were deterministic and strictly causal. His inaugural lecture was modeled on that of
Franz Serafin Exner in Vienna in 1908.
"Exner's assertion amounts to this: It is quite possible that Nature's laws are of thoroughly statistical character. The demand for an absolute law in the background of the statistical law — a demand which at the present day almost everybody considers imperative — goes beyond the reach of experience. Such a dual foundation for the orderly course of events in Nature is in itself improbable. The burden of proof falls on those who champion absolute causality, and not on those who question it. For a doubtful attitude in this respect is to-day by far the more natural."
Several years later Schrödinger wrote
"Fifty years ago it was simply a matter of taste or philosophic prejudice whether the preference was given to determinism or indeterminism. The former was favored by ancient custom, or possibly by an a priori belief. In favor of the latter it could be urged that this ancient habit demonstrably rested on the actual laws which we observe functioning in our surroundings. As soon, however, as the great majority or possibly all of these laws are seen to be of a statistical nature, they cease to provide a rational argument for the retention of determinism.
"If nature is more complicated than a game of chess, a belief to which one tends to incline, then a physical system cannot be determined by a finite number of observations. But in practice a finite number of observations is all that we can make. All that is left to determinism is to believe that an infinite accumulation of observations would in principle enable it completely to determine the system. Such was the standpoint and view of classical physics, which latter certainly had a right to see what it could make of it. But the opposite standpoint has an equal justification: we are not compelled to assume that an infinite number of observations, which cannot in any case be carried out in practice, would suffice to give us a complete determination.
Despite these strong arguments against determinism, just after he completed the wave mechanical formulation of quantum mechanics in June 1926 (the year Exner died), Schrödinger began to side with the determinists, including especially
Max Planck and
Albert Einstein.
Schrödinger's wave equation is a continuous function that evolves smoothly in time, in sharp contrast to the discrete, discontinuous quantum jumps of the Bohr-Heisenberg matrix mechanics. His equation seemed to Schrödinger to restore the continuous nature of classical mechanics and dynamics. It could be visualized as wave packets moving in space time. Bohr and Heisenberg insisted that visualization of quantum events was not possible.
Max Born, Werner Heisenberg's mentor and the senior partner in the team that created matrix mechanics, shocked Schrödinger with the interpretation of the wave function as a "probability amplitude." It was true, said Born, that the wave function evolves deterministically, but its significance is that it predicts only the probability of finding an atomic particle somewhere. When and where particles would appear - to an observer or observing system like a photographic plate - was completely and irreducibly random, said Born. Schrödinger could not restore continuous deterministic behavior and return physics to strict causality. Schrödinger did not like this idea and never accepted it despite the great success of quantum mechanics, which uses Schrödinger's wave functions to calculate Heisenberg's matrix elements for atomic transition probabilities.
Discouraged, Schrödinger wrote to his friend Willie Wien in August 1926
"[That discontinuous quantum jumps]...offer the greatest conceptual difficulty for the achievement of a classical theory is gradually becoming even more evident to me."...[yet] today I no longer like to assume with Born that an individual process of this kind is "absolutely random." i.e., completely undetermined. I no longer believe today that this conception (which I championed so enthusiastically four years ago) accomplishes much. From an offprint of Born's work in the Zeitsch f. Physik I know more or less how he thinks of things: the waves must be strictly causally determined through field laws, the wavefunctions on the other hand have only the meaning of probabilities for the actual motions of light- or material-particles."
Why did Schrödinger not welcome Born's absolute chance? It was strong evidence that Boltzmann's assumption of chance in atomic collisions was completely justified. Exner thought chance was absolute, but did not live to see how fundamental it was to physics. And the early Epicurean idea that atoms sometimes "swerve" could be replaced by the insight that atoms are always swerving - when near other atoms.
Could it be that senior scientists like Max Planck and Albert Einstein were so delighted with Schrödinger's work that it turned his head? Planck, universally revered as the elder statesman of physics, invited Schrödinger to Berlin to take Planck's chair as the most important lecturer in physics at a German university. And Schrödinger worked closely with Einstein in their failed attempts to develop a unified (and deterministic) field theory. He won the Nobel prize in 1933. But how different our thinking about absolute chance would be if the greatest theoretician of quantum mechanics had accepted it in 1926.
In his vigorous debates with
Neils Bohr and
Werner Heisenberg, Schrödinger attacked the probabilistic Copenhagen interpretation of his wave function with a famous thought experiment called
Schrödinger's Cat.
Important papers by Schrödinger:
What Is A Law Of Nature? (1922 Inaugural Lecture at University of Zurich)
Indeterminism In Physics (1931 Lecture to Society for Philosophical Instruction, Berlin)
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