Implications of protective measurement on de Broglie–Bohm trajectories

Moncy V. John, Kiran Mathew

Robert H. Parmenter, R.W. Valentine

Gillie Naaman-Marom, Noam Erez A, Lev Vaidman A

Yakir Aharonov, Berthold‐Georg Englert, Marlan O. Scully

Aurélien Drezet

Protective measurements which were defined by Aharonov and Vaidman in 1993 played an important role in the discussion about the interpretation of quantum mechanics. In 1999, following an early work by Englert et al., Aharonov et al. wrote an article in which they showed that protective measurements can be used to demonstrate the `surrealism' of Bohmian mechanics. Bohmian mechanics also known as pilot-wave interpretation is certainly the best-known hidden variable interpretation of quantum mechanics. It played a fundamental role in the discovery by Bell of his famous non locality theorem. Therefore, any attacks against pilot-wave interpretation is particularly interesting and instructive to learn something new about the mysterious quantum universe. It is the aim of this chapter to review the debate surrounding protective measurement and pilot-wave and to show if it is possible to reconciliate the different interpretations of the results given in the work by Aharonov et al.

Shan Gao

There are three possible interpretations of the wave function in the de Broglie-Bohm theory: taking the wave function as corresponding to a physical entity or a property of the Bohmian particles or a law. In this paper, we argue that the first interpretation is favored by an analysis of protective measurements. The de Broglie-Bohm theory is an alternative to standard quantum mechan-ics initially proposed by de Broglie (1928) and later developed by Bohm (1952). According to the theory, a complete description of a quantum system is provided by the configuration defined by the positions of its particles together with its wave function. The wave function follows the linear Schrödinger equation and never collapses. The motion of the particles, which are usually called Bohmian particles, follows the so-called guiding equation. Although the de Broglie-Bohm theory is mathematically equivalent to quantum mechanics, there is no clear consensus with regard to its physical interpretation. In particular, the interpre-