FOUNDATIONS OF QUANTUM MECHANICS

84 CHAPTER IV. THE COPENHAGEN INTERPRETATION
Bohr assumes that only the language and terms of classical physics are suitable for the description
of observational results. He writes (Bohr 1931, p. 692)
[. . . ] the unambiguous interpretation of any measurement must be essentially framed in
terms of the classical physical theories, and we may say that in this sense the language
of Newton and Maxwell will remain the language of physicists for all time.
This is a particularly radical point of view, and we will return to its motivation later.
The combination of both postulates now leads to the following reasoning. In all phenomena an
interaction exists between the system and the measuring apparatus which has a minimal order of magnitude
h > 0, after all, the most minute measurements always rely on a quantum phenomenon. But
in our description of the phenomenon we are forced to use classical concepts and this interaction, h,
cannot occur. The consequence is that in our description the interaction is not analyzable.
At the same time the classical character of the description makes it possible to speak again in
terms of properties of the object itself. Therefore, instead of the statement “the interaction between a
particle and a photographic plate resulted in a little black dot in a certain area of the plate”, we can
also say “the particle has been found at a position in that area”, where no longer is referred to the
measuring apparatus.
But the large difference with the classical situation is that we, by disregarding the interaction,
in a certain way make a mistake which remains without consequences within this phenomenon, but
prevents the description to be combinable with the information obtained under different experimental
conditions. If the object is coupled to another measuring apparatus there will be another interaction,
which will again not be analyzable. Descriptions of the object that have been obtained under different
measurement arrangements cannot be combined to one picture which covers it all. We will illustrate
this in a more concrete case.
IV. 2. 1
COMPLEMENTARY PHENOMENA
The most important examples of phenomena which give additional, but mutually excluding information
on an object are measurements of position and momentum. Bohr (1939, p. 22) writes
[. . . ] any phenomenon in which we are concerned with tracing a displacement of some
atomic object in space and time necessitates the establishment of several coincidences
between the object and the rigidly connected bodies and movable devices which, in serving
as scales and clocks respectively, define the space - time frame of reference to which
the phenomenon in question is referred.
In this case, therefore, the object has an interaction with an apparatus which is firmly bolted down
or anchored, so that its position remains secured. But the consequence is that a possible exchange
of momentum between object and apparatus cannot be analyzed. Such a transfer of momentum
will be absorbed by the fixed parts of the apparatus without leaving behind any trails. Within this
experimental setup we are therefore prohibited to say anything about the momentum of the object.