Understanding Quantum Physics: An Advanced Guide for the Perplexed

chapters,
with the help of protective measurement, the problem of interpreting the wave function
can be solved independent of how to solve the measurement problem. Since the
principle of protective measurement is based on the established parts of
quantum mechanics, namely the linear Schrödinger evolution of the wave function
(for microscopic systems) and the Born rule, its implications [45] , especially the suggested interpretation
of the wave function based on it, can be used to examine the existing solutions
to the measurement problem before experiments give the last verdict (cf.
Marshall et al 2003) [46] .
    In this chapter,
we will analyze the implications of protective measurement and the suggested
interpretation of the wave function based on it for the solution to the
measurement problem. It is first shown that the two main quantum theories
without wavefunction collapse, namely the de Broglie-Bohm theory and the
many-worlds interpretation, are inconsistent with protective measurement and
the picture of random discontinuous motion of particles. This result implies
that wavefunction collapse is a real physical process. Next, it is argued that
the random discontinuous motion of particles may provide an appropriate random
source to collapse the wave function. Moreover, the wavefunction collapse is a
discrete process due to the discontinuity of motion, and the collapse states
are energy eigenstates when the principle of conservation of energy is
satisfied. Based on these analyses, we further propose a discrete model of
energy-conserved wavefunction collapse. It is shown that the model is
consistent with existing experiments and our macroscopic experience. We also
provide a critical analysis of other dynamical collapse models, including
Penrose’s gravity-induced collapse model and the CSL (Continuous Spontaneous
Localization) model.
    4.1 The reality of wavefunction collapse
    At first sight,
the main solutions to the measurement problem, i.e., the de Broglie-Bohm
theory, the many-worlds interpretation and dynamical collapse theories, seem
apparently inconsistent with the suggested interpretation of the wave function.
They all attach reality to the wave function, e.g. taking the wave function as
a real physical entity on configuration space or assuming the wave function has
a field-like spatiotemporal manifestation in the real three-dimensional space
(see, e.g. Ghirardi 1997, 2008; Wallace and Timpson 2009). But according to our
suggested interpretation, the wave function is not a field-like physical entity
on configuration space [47] ; rather, it is a description of the random
discontinuous motion of particles in real space (and at a deeper level a
description of the dispositional property of the particles that determines
their random discontinuous motion). Anyway, in spite of the various views on
the wave function in these theories, they never interpret the wave function as
a description of the motion of particles in real space. However, on the one
hand, the interpretation of the wave function in these theories is still an
unsettled issue, and on the other hand, these theories may be not influenced by
the interpretation of the wave function in a significant way. Therefore, they
may be consistent with our suggested interpretation of the wave function after
certain revision.
    4.1.1
Against the de Broglie-Bohm theory
    Let's first
investigate the de Broglie-Bohm theory (de Broglie 1928; Bohm 1952). According
to the theory, a complete realistic 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 particles, called Bohmian particles, are guided by the
wave function via the guiding equation to undergo deterministic continuous
motion. The result of a measurement is indicated by the positions of the
Bohmian particles representing the pointer of the measuring device, and thus it
is always definite. Moreover, it can be shown that the de Broglie-Bohm theory
gives the same predictions of measurement results as standard quantum mechanics
by means of a quantum equilibrium hypothesis (so long as the latter gives
unambiguous predictions). Concretely speaking, the quantum equilibrium
hypothesis provides the initial conditions for the guidance equation which make
the de Broglie-Bohm theory obey Born's rule in terms of position distributions.
Moreover, since all