FOUNDATIONS OF QUANTUM MECHANICS

86 CHAPTER IV. THE COPENHAGEN INTERPRETATION
The meaning Bohr attaches to the uncertainty relations can be summarized this way: the sharper
we can, in a phenomenon, define the position of the object, the fuzzier the momentum must be defined,
and vice versa. The quantities δq and δp in the relation δqδp ∼ h therefore represent the fuzziness in
the definition. Bohr emphasizes an epistemological role of these quantities stronger than an ontological
role.
IV. 2. 2
REMARKS AND PROBLEMS
Bohr’s supposition that classical language is a definite means of expression for physical observations
which cannot be improved upon, is radical and at first sight even fairly unacceptable. Language
develops and history teaches us that from time to time new concepts are necessary. Aristotle had,
for example, no momentum concept, Newton knew nothing of energy, Coulomb had no theory of
fields, etc. Doesn’t it speak for itself that quantum mechanics also asks for new concepts? Bohr,
however, (ibid., p. 16), says
[. . . ] it would be a misconception to believe that the difficulties of the atomic theory may
be evaded by eventually replacing the concepts of classical physics by new conceptual
forms.
Bohr emphasizes that with this point of view he does not reject the introduction of new entities,
e.g. quarks, superstrings or black holes. The aspects of classical language which are the reason
that it cannot be improved upon are, according to him, descriptions in terms of space and time and
descriptions in terms of cause and effect. These are the only categories with which we can describe
observational results.
Another problem with the idea that the classical concepts cannot be improved upon is Bohr’s
immediate conclusion that the quantum of action cannot occur in the description of a phenomenon,
because a statement such as ‘h = 6.6 · 10 −34 Js’ is also an unambiguous summary of experimental
evidence, although not of one phenomenon. The idea that h cannot appear in the language of observations
is a weak, and in fact untenable point in his argumentation. The prohibition of the use of h
in the language of observations also brought Bohr to the conclusion that the spin of an electron, 1 2 ,
would be fundamentally unobservable. This conclusion has been proven to be incorrect.
In some articles Bohr gives a more abstract explanation of the quantum postulate and emphasizes
the ‘symbolic’ role of h. It does not so much represent the inevitable interaction, or measurement
disturbance, between object and measuring apparatus, as the fundamental impossibility to make a
sharp distinction between object and observation apparatus. It is, in any case, clear that Bohr does not
regard the formalism of quantum mechanics, with its wave functions and operators, as an extension
or improvement of classical language. He emphasizes that this formalism is purely symbolic and
cannot be taken as a description, as the quantum state of a system is given without reference to the
experimental setup.
It should be noted that Bohr, at emphasizing the applicability of concepts, has more in mind than
the ‘logical’ question of ’definiteness’. For Bohr a term like ‘position of a particle’ is applicable if we
can in fact control and secure this position, using firmly bolted apparatuses. Bohr’s use of the term
‘determination’ refers both to a measurement as to a state preparation.