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.

This article introduces the method of protective measurement and discusses its deep implications for the foundations of quantum mechanics.

This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but (...) discontinuous and random. This result suggests a new interpretation of the wave function, according to which the wave function is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wave function disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the random discontinuous motion of particles may provide an appropriate random source to collapse the wave function. (shrink)

It is a fundamental and widely accepted assumption that a measurement result exists universally, and in particular, it exists for every observer, independently of whether the observer makes the measurement or knows the result. In this paper, we will argue that, based on an analysis of protective measurements, this assumption is rejected by the many-worlds interpretation of quantum mechanics, and worlds, if they indeed exist according to the interpretation, can only exist relative to systems which are decoherent with respect to (...) the measurement result. (shrink)

It is argued that the components of the superposed wave function of a measuring device, each of which represents a definite measurement result, do not correspond to many worlds, one of which is our world, because all components of the wave function can be measured in our world by a serious of protective measurements, and they all exist in this world.

Recently Lewis et al. [Phys. Rev. Lett. 109, 150404 ] demonstrated that additional assumptions such as preparation independence are always necessary to rule out a psi-epistemic model, in which the quantum state is not uniquely determined by the underlying physical state. Their conclusion is based on an analysis of conventional projective measurements. Here we demonstrate that protective measurements, which are distinct from projective measurements, already shows that distinct quantum states cannot be compatible with a single state of reality. This improves (...) the interesting result obtained by Pusey, Barrett and Rudolph [Nature Phys. 8, 475 ]. (shrink)