Understanding Quantum Physics: An Advanced Guide for the Perplexed

discontinuous
motion of particles. They are the definite position, momentum and energy of the
particles at each instant. Though these variables are not continuous and
deterministic, their random motion might just lead to the stochastic collapse
of the wave function and further account for the emergence of random
measurement results. We will discuss this possibility in detail later on.
    Lastly, we analyze
the hypothetical interaction between the Bohmian particles and the wave
function in the de Broglie-Bohm theory. It can be seen that the guiding
responsibility of the wave function assumed by the theory is inconsistent with
the meaning of the wave function. As noted above, the wave function represents
the property of particles that determines their random discontinuous motion.
Accordingly, the wave function indeed guides the motion of particles in some
sense. However, the wave function guides the motion of the particles not in a
deterministic and continuous way as assumed by the de Broglie-Bohm theory, but
in a probabilistic and discontinuous way; the modulus square of the wave
function determines the probability density of the particles appearing in
certain positions in space. Moreover, the motion of these particles is ergodic.
By contrast, the motion of the Bohmian particles is not ergodic, and the time
averages of the Bohmian particles’ positions typically differ remarkably from
the ensemble averages (Aharonov, Erez and Scully 2004).
    Although one may
assume that a quantum system contains additional Bohmian particles besides its
non-Bohmian particles that undergo random discontinuous motion, the motion of
the Bohmian particles cannot be guided by the wave function of the system. For
the wave function of the system represents the property of the non-Bohmian particles
of the system, and its efficiency is to guide the motion of these particles in a probabilistic way. In particular, the wave function is neither a
field-like entity distributing throughout space nor a property of the Bohmian
particles that may guide their motion, and at every instant there are only
non-Bohmian particles being in positions that are usually far from the
positions of the hypothetical Bohmian particles. Note also that the non-Bohmian
particles cannot have known interactions such as gravitational and
electromagnetic interactions with the Bohmian particles either; otherwise the
theory will contradict quantum mechanics and experiments. Without being guided
by the wave function in a proper way, the motion of the Bohmian particles will
be unable to generate the right measurement results in conventional impulse
measurements.
    In conclusion, we
have argued that the de Broglie-Bohm theory is inconsistent with the results of
protective measurement and the meaning of the wave function implied by them when
considering its physical contents.
    4.1.2
Against the many-worlds interpretation
    Now let's turn to
the second approach to avoid wavefunction collapse, the many-worlds
interpretation. Although this theory is widely acknowledged as one of the main
alternatives to quantum mechanics, its many fundamental issues, e.g. the
preferred basis problem and the interpretation of probability, have not been
completely solved yet (see Barrett 1999, 2011; Saunders et al 2010 and
references therein). In this subsection, we will mainly analyze whether the
existence of many worlds is consistent with the results of protective
measurement and the picture of random discontinuous motion of particles.
    According to the
many-worlds interpretation, each component of the wave function of a measuring
device that represents a definite measurement result corresponds to each world
among the many worlds (Barrett 2011). This means that in one world there is
only one component of the superposed wave function and the other components do
not exist, and thus these components that correspond to the other worlds cannot
be observed in this world. As a result, in every world the whole superposed
wave function of the measuring device cannot be measured. If all components of
the superposed wave function of the device can be observed in one world, then
they will all exist in this world, which obviously contradicts the many-worlds
interpretation.
    It is unsurprising
that the existence of such many worlds may be consistent with the results of
conventional impulse measurements, as the many-worlds interpretation is just
invented to explain the emergence of these results, e.g. the