popper-logic-scientific-discovery

outside it. Schrödinger later showed that his wave-mechanics led to
results mathematically equivalent to those of Heisenberg’s particle
mechanics.
The paradox of the equivalence of two so fundamentally different
images as those of particle and wave was resolved by Born’s statistical
interpretation of the two theories. He showed that the wave theory too
can be taken as a particle theory; for Schrödinger’s wave equation can
be interpreted in such a way that it gives us the probability of finding the
particle within any given region of space. (The probability is determined
by the square of the amplitude of the wave; it is great within the wavepacket
where the waves reinforce each other, and vanishes outside it.)
That the quantum theory should be interpreted statistically was suggested
by various aspects of the problem situation. Its most important
task—the deduction of the atomic spectra—had to be regarded as a
statistical task ever since Einstein’s hypothesis of photons (or lightquanta).
For this hypothesis interpreted the observed light-effects as
mass-phenomena, as due to the incidence of many photons. ‘The
experimental methods of atomic physics have, . . . under the guidance
of experience, become concerned, exclusively, with statistical questions.
Quantum mechanics, which furnishes the systematic theory of
the observed regularities, corresponds in every way to the present state
of experimental physics; for it confines itself, from the outset, to
statistical questions and to statistical answers.’ 1
It is only in its application to problems of atomic physics that quantum
theory obtains results which differ from those of classical mechanics.
In its application to macroscopic processes its formulae yield with
close approximation those of classical mechanics. ‘According to quantum
theory, the laws of classical mechanics are valid if they are
regarded as statements about the relations between statistical averages’,
says March. 2 In other words, the classical formulae can be deduced as
macro-laws.
In some expositions the attempt is made to explain the statistical
interpretation of the quantum theory by the fact that the precision
attainable in measuring physical magnitudes is limited by Heisenberg’s
1 Born-Jordan, Elementare Quantenmechanik, 1930, pp. 322 f.
2 March, Die Grundlagen der Quantenmechanik, 1931, p. 170.
some observations on quantum theory 217