A proof that measured data and equations of quantum mechanics can be linked only by guesswork

Abstract

The design and operation of a quantum-mechanical device as a laboratory instrument puts models written in equations of quantum mechanics in contact with instruments. In designing a quantum-mechanical device of high precision, such as a quantum computer, a scientist faces choices of models and of instruments, and the scientist must choose which model to link to which ar- rangement of instruments. This contact is recordable in files of a Classical Digital Process-control Computer (CPC) used both to calculate with the equations and to manage the instruments. By noticing that equations and instruments make contact in a CPC, we rewrite equations of quantum mechanics to explicitly include functions of CPC-commands to the instruments. This sets up a proof that a scientist's choice in linking mathematical models to instruments is unresolvable without guesswork to narrow the set of models from which one is to be chosen. The proof presents the challenge of pursuing its implications. Scientists in any investigative endeavor inherit choices from the past and frame choices for the future, choices open to guesswork and visible in CPC files. To picture the framing of choices and relations among them, we adapt colored Petri nets. Constraining the events of the nets to produce output colors defined by definite functions of input colors excludes guesswork from the firing of net events, and by contrast highlights guesses entering a net fragment as colored tokens placed by a scientist or by instruments on input conditions. The availability of these net fragments makes choice and guesswork part and parcel of physics. Net fragments as a means of expressing guess-demanding choic- es are applied to portray guesswork needed in testing and calibrat- ing a quantum computer. The sample size required to test a quan- tum gate in a quantum computer is shown to grow as the inverse square of the error allowed in implementing the gate.