FOUNDATIONS OF QUANTUM MECHANICS

IV. 2. BOHR AND COMPLEMENTARITY 87
Speaking of ‘partially defined positions and momenta’, Bohr considers the uncertainty relation
between position and momentum as the possibility to come to a compromise with the complementarity
between position and momentum. Here we can think of a context of measurement in which the
object interacts with a part of the apparatus which is linked with the rest of the apparatus by means
of a spring with a finite spring constant, an intermediate form between ‘freely movable’ and ‘firmly
bolted’. He has, however, not developed this compromise. This point of view does in fact not fit the
usual mathematical derivation of the uncertainty relations for position and momentum. They make,
for two given (sharp) quantities p and q, a statement about spreading in quantum states, not about the
well-definedness of the quantities. It has been attempted to prove this compromise mathematically,
by the introduction of ‘blurred quantities’, e.g. Busch, Grabowski and Lahti (1995).
Of fundamental importance in Bohr’s point of view is that in a phenomenon an object and experimental
setup are involved. The setup determines which frame of concepts applies to the object. In
many cases the contrast between object and measuring apparatus coincides with that of the microscopic
and macroscopic system, respectively. But that is not necessarily so. A macroscopic system
can also be considered as an object while a microscopic system can serve as a measuring apparatus.
We can consider, for example, a macroscopic measuring apparatus to be the object of another measurement.
As soon as we do this the macroscopic system can, according to Bohr, no longer execute
its role as a measuring device. It becomes an object itself, to which the quantum formalism must be
applied. This functional contrast between object and measuring apparatus is therefore more essential
than that between microscopic and macroscopic systems.
For a good understanding of Bohr’s position, and Heisenberg’s for that matter, it is important to
notice that measurements do not require the presence of consciousness. Decisive for applicability of
classical concepts is the presence of a measurement context. Therefore, subjectivity does not play
a role in any form, for applicability of a concept as ‘momentum’ it does not matter if a conscious
observer, a computer or another measuring apparatus carries out the momentum measurement.
Also, from Bohr’s refusal to assign a realistic meaning to the quantum mechanical description, the
conclusion cannot be drawn that he supports an anti - realistic or ‘instrumentalist’ view on physics,
where instrumentalism is roughly the thesis that a scientific theory is only an instrument to carry out
calculations of which we compare the outcomes with the indications of measuring apparatuses, in
particular, that a theory is no ‘knowledge of the world’, that it does not provide a faithful picture of
what reality is. An object such as an electron has, besides its quantum mechanical state, more than
enough permanent properties, such as the super - selected quantities mass and charge which are not
subject to complementarity, to conceive it as a real, existing object.
IV. 2. 3
AGREEMENT AND DIFFERENCE BETWEEN HEISENBERG AND BOHR
Both Heisenberg and Bohr emphasize that quantum mechanics is a complete theory which cannot
be extended into a more detailed description with hidden variables. Bohr says (Schilpp 1949, p. 235)
[. . . ] in quantum mechanics, we are not dealing with an arbitrary renunciation of a more
detailed analysis of atomic phenomena, but with a recognition that such an analysis is in
principle excluded.