FOUNDATIONS OF QUANTUM MECHANICS

164 CHAPTER VIII. THE MEASUREMENT PROBLEM
between processes which serve as measurements and processes that do not. Every physical process
or every mutual influence of physical systems can, under suitable circumstances, be considered as
a measurement. Since it is the physical theory that indicates which physical processes in nature are
possible, the theory itself also provides the criterion for the kinds of measurements which are possible.
According to Von Neumann’s postulates, in quantum mechanics this is exactly the other way
around. First we must, according to the aforementioned postulates, have a criterion to know when a
process is a measurement, before we can indicate what the theory has to say concerning the process,
before we can apply the postulates. That the term measurement in this way gets a more fundamental
status than the physical theory, is also expressed by the words of Pauli as quoted in chapter I, p. 9,
that a measurement creating values is “outside the laws of nature”.
Intuition tells us that measurements are just an ‘ordinary kind’ of physical interactions, and this
intuition cannot easily be wept out, from which we will give an illustration. Consider a photon which
has gone through a slit and is on its way to a photographic plate. If we presume the interaction with
this photographic plate to be a measurement, the wave function of the photon must, according to the
projection postulate, collapse on arrival at the plate. But we also know that the photographic plate has
a microscopic structure. It contains silver atoms in an emulsion which can be excited by the photon
and start a chemical process in such a way that we can see something when the plate is developed.
Would it not be plausible that quantum mechanics could describe such a process using a Schrödinger
equation?
In every way this event looks like a physical interaction which falls completely within the well -
known laws of nature, instead of without. And if this is denied, how shall we decide at all when
a microscopic interaction between a photon and an atom can and when it cannot be labeled as a
measurement? Asking an experimental physicist how her measurement setup works, one will be
given an answer in which physical interactions, generally of electromagnetic nature, are of uppermost
importance. It seems absurd to deny that events take place in the laboratory that are “outside the laws
of nature”.
The clash between the conception that measurements do not differ from other physical interactions
on the one hand, and the fact that measurements in quantum mechanics acquired a special status
because they are not classified to be physical interactions on the other hand, is called the quantum
mechanical measurement problem in the broad sense.
VIII. 2
MEASUREMENT ACCORDING TO CLASSICAL PHYSICS
Although usually no special attention is given to measurements in classical physics, it is no problem
to give a general, schematic description of how a measurement is treated classically.
A measurement brings about a correlation between a quantity A of a physical system S which
is, within the context of a measurement, frequently called an object system, and a quantity R, where
the R comes from reading, which is characteristic for the measuring apparatus M, the apparatus
being a physical system also. In classical physics we assume that A has a certain value a ∈ R,
where a is an element from a set of possible values, for instance a 1 , . . . , a n ⊂ R, and that after the
measurement process R has a value r j = m(a j ), where m is a bijection of the possible values of A
before the measurement, to the possible values of R after the measurement.