FOUNDATIONS OF QUANTUM MECHANICS

VIII. 2. MEASUREMENT ACCORDING TO CLASSICAL PHYSICS 165
Take, for example, S to be yourself and M to be a balance, A is your weight and R is the reading
of the pointer of the balance. Now you have an unknown weight value, a, which is revealed by
the balance indicating r = m(a) = 63 kg. The role of a measurement is pragmatic; the value of
a physical quantity of the object system which is not directly or not easily observable, for example
mass, is correlated to a quantity that is directly observable, in this case the position of an pointer. For a
correlation to occur between A and R there must be an interaction between S and M. This interaction
can, potentially, influence the value of A in such a way that the value before the measurement can
change to another value after measurement. Measurement is a process looking towards the past and
its aim is to reveal the value of A before the interaction with M.
If it is possible to predict, from the value a and the interaction between S and M, the value a ′
which A has after measurement, then the measurement also looks at the future and acts like an apparatus
which prepares a state of S in which A has the value a ′ . Think, for example, of an ammeter
in an electric circuit with an energy source of V volt; if the current through a resistor R is I = V R
without the ammeter, then, after the ammeter has been connected in series with the resistor, the current
I ′ V
equals
R+R s
, where R s is the internal resistance of the ammeter. In case a ′ equals a, the
measurement is called non - disturbing or ideal. The measurement process thus has two aspects; what
happens to the measuring apparatus M, and what happens to the physical system S, i.e. measurement
and state preparation.
In classical physics the measurement interaction can be taken to be arbitrarily small, in which
case the value of A is not disturbed. Therefore, the transition in such an ideal measurement process
is
(a j , r 0 ) (a j , r j ) = ( a j , m(a j ) ) . (VIII. 1)
Notice that the characteristics of the measurement are left out of the consideration. The method
of measuring does not have anything to do with the phenomenon one wants to get information about.
The motion of the planets in the gravitational field of the sun is studied by looking at them, i.e., by
using the fact that the planets reflect sunlight. The optical instruments that are used have nothing to
do with the gravitational motion under examination.
Also notice that in this consideration the question how to measure A is only transformed into the
question how to find the value of R. If we also would have to measure the value of R, this could
lead to an infinite chain of measuring apparatuses. This is avoided by assuming that the quantity R is
directly observable, hence the term pointer reading for R, where we have to take the term ‘pointer’
very generally, for instance, screens showing results of measurements or results printed on paper are
included in the term.
We appeal in our description to a distinction between two different types of quantities; the directly
observable quantities, that is, observable to the naked eye, versus the not directly observable or unobservable
quantities. But this is not a distinction which corresponds to a fundamental distinction of
these quantities, in classical physics all quantities are treated as properties of objects. The fact that we
stop at a directly observable quantity R is a decision based on purely contingent factors, particularly
human physiology and the physics of the human senses.