Observationally Complete Theories: Some Observations on Quantum Theory (1958)

(1) Classical physics allows for the existence of physical situations which cannot be discovered by any observation whatsoever. As an example1 consider the case of two banknotes, both printed with the help of the same printing press, the one under legal circumstances, the other by a band of burglars, using the very same press at night, and illegally. If we assume that the two banknotes have been printed on the same day, and that they even exhibit the same numbers, and if we further assume that somehow they have been mixed up, then we shall have to say that by virtue of their different histories they possess certain properties, different for both, which we shall yet never be able to discover.∗ Another example which is frequently being referred to is the intensity of the electromagnetic field at a given point.2 Any method of measuring this field uses bodies of finite extension and of finite charge which therefore react only to a certain average value of the field, but do not allow for the exact determination of the field at a welldefined 〈sic〉 point. As there exists a law of nature (we refer now to classical physics only) according to which the size of every testbody possesses a lower limit, it is even physically impossible to perform a measurement which would lead to such a determination. Again we are presented with a physical situation which exists, and yet cannot be discovered by any observational means.