Basic Considerations on the Interpretation of Quantum Mechanics A. Einstein (4)

We do not doubt that for such objects, there is a real spatial configuration (location) as well as a velocity (or impulse) for each quantity, i.e., a "real situation"—all with the approximation due to the quantum structure. We then ask: Does quantum mechanics (with the expected approximation) entail the real description of macrobodies provided by classical mechanics? Or, if this question cannot simply be answered with yes, when is this the case? Let us consider this using a concrete example. The specific example… The system consists of a ball of approximately 1 mm in diameter which travels back and forth (along the x axis of a coordinate system) between 2 parallel walls (approximately 1 m apart). The collisions are ideally elastic. In this idealized macrosystem, we think of the walls as being replaced by "sharp" potential energy expressions into which only the coordinates of the material points constituting the ball enter. Through cunning measures, it is arranged so that these reflection processes do not establish a pairing between the center-of-gravity coordinate x of the ball and its "inner" coordinates (including the angle coordinates). Thus, for the purpose we have been pursuing, the position of the ball (apart from its radius) can be described by X alone. In terms of quantum mechanics, this process involves sharp energy. The de Broglie wave (Ψ-function) is then harmonic in the time coordinate. Furthermore, it only differs between X= and 2= + of O.