An Operational Analysis of the Double Slit Experiment

An attempt is made to reduce the discussion of the quantum mechanical interference patterns predicted to occur when a beam of particles of mass M and momentum p. is incident on two slits to macroscopic dimensional measurements of the sizes of slits, detectors, and collimators, and the macroscopic time measurements of whether or not detectors fire during macroscopic time intervals. By introducing detectors in the slits, the same apparatus yields statistical information about both single and double slit interference patterns, whose intensities add without interference, which can check the quantum mechanical prediction to arbitrarily high (statistical) precision. But discussion of the detectors themselves reveals that this scale invariant prediction (which depends only on ti and M) can be carried through only if the detecting systems in the detectors have masses m << M. The existence of a smallest mass (empirically, the electron mass) or the limiting velocity c and the mass-energy relation (via the Wick-Yukaw mechanism) break the scale invariance of the theory. We conclude, as did Bohr and Rosenfeld in their analysis of the measurability of the electromagnetic field, that the existence of a smallest mass prevents an operational definition of the meaning of space time intervals of order h/m,c or less. (To be published by the Philosophy of Science Association in a volume on quantum mechanics edited by P. Suppes.) * Work supported by the Department of Energy under contract number N-76-C-03-0515.