Understanding Quantum Physics: An Advanced Guide for the Perplexed

that an electron
indeed has the charge of an electron (and the mass of an electron). A possible
way to avoid the inconsistency is to assume that an electron has twice the
charge of an electron: one for its wave function and the other for its Bohmian
particle. In this case, since what protective measurement measures is the mass
and charge distributions relating to the wave function, not the masses and
charges of the Bohmian particles, the above inconsistency can be avoided.
However, this theory seems too clumsy and unnatural to be true. Moreover, it
will introduce more problems. For one, there is a dilemma concerning the
electromagnetic interaction between the wave function and the Bohmian particle
of an electron. If they do have usual electromagnetic interaction, then the
theory will be inconsistent with quantum mechanics and experiments. If they
have no electromagnetic interaction, then this will add more problems. For
instance, the manifestation of the charge of a Bohmian particle will be much
stranger; it is not only passive but also selective. One needs to explain why
the charged Bohmian particle of an electron responds not to the magnetic vector
potential generated by the wave function of this electron, but to the magnetic
vector potential generated by the wave function of another electron. As we will
see later, a more serious objection concerns the guiding responsibility of the
wave function.
    [53] This is also admitted by most interpretations of the de Broglie-Bohm
theory.
    [54] This conclusion may not hold true if the guiding equation is not exactly
the same as the above, e.g. the guiding equation contains an additional
stochastic damping term (Valentini and Westman 2005). Although such revised
theories make predictions different from quantum mechanics, they may be
consistent with existing experiments.
    [55] The reality of the trajectories of the Bohmian particles has been
questioned based on analysis of weak measurement and protective measurement
(Englert, Scully, Sussmann and Walther 1992; Aharonov and Vaidman 1996;
Aharonov, Englert and Scully 1999; Aharonov, Erez and Scully 2004). However,
these objections may be answered by noticing what protective measurement
measures is the wave function, not the Bohmian particles (see also Drezet
2006). For a comprehensive answer to these objections see Hiley, Callaghan and
Maroney (2000).
    [56] Note that protective measurement in general requires that the measured
wave function is known beforehand so that an appropriate protective interaction
can be added. But this requirement does not influence our argument, as the
superposed wave function of a measuring device can be prepared in a known form
before the protective measurement.
    [57] This objection does not apply to the de Broglie-Bohm theory, according
to which the wave function of a measuring device does not collapse either, but
it exists only in one world.
    [58] Note that this objection is more serious than the problem of approximate
decoherence for the many-worlds interpretation. The interference between the
nonorthogonal components of a quantum state can not be detected for individual
states, but only be detected for an ensemble of identical states. Moreover, the
presence of tiny interference terms in a (local) quantum state does not imply
that all components of the state wholly exist in one world.
    [59] According to these theories, the physical state always evolves in a
deterministic way and may be superposed and indefinite, while the mental state
is always definite but evolves randomly. In some sense, these theories can be
regarded as hidden-variable theories like the de Broglie-Bohm theory. The
latter assumes the definite positions of Bohmian particles provide observers
with definite measurement records, while the former assumes the definite mental
states of the observers, though which are non-physical parameters, directly provide
observers with definite measurement records.
    [60] As in the many-worlds case, the random discontinuous motion does not
result in the emergence of many minds either. Since the brain state of a
quantum observer is definite and only assumes one brain state in the
superposition at a given instant, even if there are many minds with different
conscious perceptions at the instant, these perceptions are irrelevant to those
corresponding to the brain states in the superposition except the present brain
state. Thus such a theory of many minds cannot be consistent with the above
experience.