FOUNDATIONS OF QUANTUM MECHANICS

I
CONCEPTUAL PROBLEMS
Anyone who is not shocked by quantum theory has not understood it.
— Niels Bohr
I think it is safe to say that no one understands quantum mechanics.
— Richard Feynman
I. 1 INTRODUCTION
Quantum mechanics emerged at the beginning of the 20 th century from an attempt to understand
the interaction between atoms and radiation. The presence of discrete lines in the emission
and absorption spectra of chemical elements indicates that this interaction takes the form of discrete
quanta. When, in the years 1925 and 1926, a coherent theory was developed by the unified efforts of
Werner Heisenberg, Paul Dirac, Max Born, Pascual Jordan, Wolfgang Pauli and Erwin Schrödinger,
and this theory was axiomatized seven years later by John von Neumann, the question about the
physical interpretation of the mathematical symbols of the theory arose.
The central mathematical concept in quantum mechanics is ψ, in the form of a wave function ψ(q)
in Schrödinger’s wave mechanics, or of a vector |ψ⟩ in Hilbert space, à la Von Neumann. According
to Born, its physical meaning is that ψ determines probabilities for results of measurements, and a
key question is then how such probabilities must be interpreted. By means of four examples we will
give an idea of the conceptual problems raised by quantum mechanics.
(i) Consider as a first example the decay of radioactive nuclei of a certain kind, as discussed by
Einstein (P.A. Schilpp (1949, p.667, ff). We see the unstable nuclei decay at various times, one almost
immediately, another only after a long time; the α - particles are radiated in ever different directions.
Quantum mechanics describes these nuclei by a non-stationary wave function, and using this function
one can calculate the expected lifetime of the nuclei.
A natural reaction is to assume that the nuclei differ from each other, and that this difference is
the cause of the mutually different individual life spans and the different directions the α - particles
are radiated in. In this view, the quantum mechanical expectation value would be comparable to
the average life span in a population. However, this does not fit in a natural way in the quantum
mechanical description. Quantum mechanics describes all nuclei by the same wave function. If this
description is complete, the fact that quantum mechanics gives only expected life spans is not due to
a lack of knowledge. Rather, there simply is nothing more to know concerning the nuclei than their
wave function and the probabilities that follow from it.
On the other hand, we see before our eyes that the nuclei do not behave the same way, they decay
at different times and send the α - particles in ever different directions. This suggests that more can