Stern-Gerlach Experiment and Bohm Limit

Stern-Gerlach experiment is a paradigm of measurement theory in quantum mechanics. Notwithstanding several analysis given in literature, no clear understanding of the apparent collapse has been given so far. Indeed, one can imagine a Stern-Gerlach device where all environmental effects are removed and ask the question on how the measurement goes on. In this letter we will prove that a the Stern-Gerlach device behaves as a true measurement apparatus, as expected by the Copenaghen interpretation, by the Ehrenfest theorem. In this way we recover, by other means, a limit on the Stern-Gerlach device, given by Bohm, based on scrambling of phases due to a large oscillation frequency. A Stern-Gerlach experiment represents a classical paradigm of quantum measurement. As it can be seen by the classical description due to D. Bohm [1], we can see the appearance of all the peculiarities of the measurement process. Indeed, an entangled state between the apparatus and the quantum system appears and it is very difficult to understand what could make the “collapse” happens. Recently, a proposal for the experimental verification of the reality of “collapse” has been given in [2]. Such an experiment is aimed to prove the physical reality of the “collapse” that some authors ascribe to some stochastic effects, maybe due to quantum gravity [3, 4, 5, 6]. Besides, a theory has been proposed where time is treated as a stochastic variable [7] and could also explain the appearance of the final result of the SternGerlach experiment. Decoherence studies have been carried out [8, 9] and ∗ e-mail:[email protected]