FOUNDATIONS OF QUANTUM MECHANICS

10 CHAPTER I. CONCEPTUAL PROBLEMS
to an essential indeterminacy of that position. Pauli states that the question whether the ‘position’
of a body would also exist without observation is fundamentally unanswerable and for this reason
meaningless.
In this example the problem of the transition between the microscopic and the macroscopic levels
arises. Our intuition tells us that somewhere along the way the quantum mechanical probability
description must turn into a classical description of an ensemble, an ensemble of objects that have
properties. But if we accept at the same time that quantum mechanics applies as well to macroscopic
bodies as to microscopic ones, our expectation is refuted. This transition of the one type of ensemble
to the other is a problem which invariably emerges in considerations concerning the ‘measurement
problem’. We will come back to this in chapter VIII.
The previous discussion follows rather closely the formulations of Einstein and Pauli in the
years 1948-1954, as can be found in the correspondence between Born and Einstein (Born 1971).
An interesting aspect is that the discussion actually takes place over Born’s head. Born saw Einstein
as the one who had, in his theory of relativity, abolished the idea of absolute simultaneity by means of
the argument that it is meaningless to want to speak about something you cannot measure in principle.
Einstein reacts (ibid., p. 188)
There is nothing analogous in relativity to what I call incompleteness of description in
the quantum theory. Briefly it is because the ψ - function is incapable of describing certain
qualities of an individual system, whose ‘reality’ we none of us doubt (such as a
macroscopic parameter).
Moreover, Born continues to believe, despite everything Einstein writes, that Einstein objects
to the indeterministic character of quantum mechanics, i.e., the fact that it only provides probability
statements, instead of objecting to the alleged completeness of quantum mechanics, until Pauli
intervenes in the discussion and explains Einstein’s position to Born (ibid., pp. 217-219).
(iv) The last example is Schrödinger’s notorious cat paradox (Schrödinger 1935b).
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along
with the following diabolical device (which must be secured against direct interference
by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small
that perhaps in the course of one hour one of the atoms decays, but also, with equal
probability, perhaps none; if it happens, the counter tube discharges and through a relay
releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this
entire system to itself for an hour, one would say that the cat still lives if meanwhile no
atom has decayed. The first atomic decay would have poisoned it. The Ψ - function for
the entire system would express this by having in it the living and the dead cat (pardon
the expression) mixed or smeared out in equal parts.
In this example a number of problems is combined. In the first place there is again the difference
between a classical state and a quantum state. If the standard interpretation is extended consistently,
the cat cannot be considered dead or alive as long as the chamber is not opened and the cat is not
observed. (One may wonder what the cat itself thinks of this.)
The question whether it is permitted to extend the standard interpretation in this way coincides
with the question if and to what extent the quantum mechanical description can be transferred from