Abstract
Within the de Broglie-Bohm (dBB) theory, the measurement process and the determination of its outcome are usually discussed in terms of the effect of the Bohmian positions of the measured system S. %} This article shows that the Bohmian positions associated with the measurement apparatus M can actually play a crucial role in the determination of the result of measurement. Indeed, in many cases, the result is practically independent of the initial value of a Bohmian position associated with S, and determined only by those of M. The measurement then does not reveal the value of any pre-existing variable attached to S, but just the initial state of the measurement apparatus. Quantum contextuality then appears with particular clarity as a consequence of the dBB dynamics for entangled systems.
Highlights
In most cases, the number of Bohmian positions associated with M is much larger than that associated with S, and it seems natural that these positions should play a role
Many discussions of quantum measurements within de Broglie–Bohm (dBB) theory emphasize the role of the Bohmian position(s) associated with the microscopic system S, ignoring all those attached to the measurement apparatus M
We have learnt from the historical discussions between Einstein and Bohr [21], for instance the argument concerning an interference experiment with a moving pierced screen playing the role of a which way apparatus, that the quantum properties of the measurement apparatus cannot be ignored without running into contradictions
Summary
The number of Bohmian positions associated with M is much larger than that associated with S, and it seems natural that these positions should play a role. Informal discussions with colleagues physicists often reveal the belief that, within the dBB theory, the result of measurement is determined by the initial value of the Bohmian variable(s) attached to S. Various recoil effects affect the atoms inside the measurement apparatus: depending on the result of measurement, the atoms and molecules inside in the magnet recoil upwards or downwards, various localized phonon emission processes occur inside the glass plate, etc. Modelling these effects and the resulting changes of quantum states would be a complicated task. We will introduce an optical version of the experiment that seems to be more appropriate for a quantum treatment of single measurement events
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