Understanding Quantum Physics: An Advanced Guide for the Perplexed

accumulate only when time is
discrete. As a result, wavefunction collapse will be a discrete process, and
the collapse states will be the energy eigenstates of the total Hamiltonian of
a given system in general. Thirdly, we propose a discrete model of
energy-conserved wavefunction collapse based on the above analysis. It is shown
that the model is consistent with existing experiments and our macroscopic
experience. Lastly, we also give some critical comments on other dynamical
collapse models, including Penrose’s gravity-induced collapse model and the CSL
(Continuous Spontaneous Localization) model.
    In the last
chapter, we give some primary considerations on the unification of quantum
mechanics and special relativity in terms of random discontinuous motion of
particles. It is argued that a consistent description of random discontinuous
motion of particles requires absolute simultaneity, and this leads to the
existence of a preferred Lorentz frame when combined with the requirement of
the constancy of speed of light. Moreover, it is shown that the collapse
dynamics may provide a method to detect the frame according to our
energy-conserved collapse model.

 
    Chapter 2
    Meaning of the Wave Function
    What does the ψ-function mean now, that
is, what does the system described by it really look like in three dimensions?
    —Erwin
Schrödinger
    The physical
meaning of the wave function is an important interpretative problem of quantum
mechanics. Notwithstanding more than eighty years’ developments of the theory,
however, it is still a debated issue. Besides the standard probability
interpretation in textbooks, there are various conflicting views on the wave
function in the alternatives to quantum mechanics. In this chapter, we will try
to solve this fundamental interpretive problem through a new analysis of
protective measurement and the mass and charge density of a single quantum
system.
    The meaning of the
wave function is often analyzed in the context of conventional impulse
measurements, for which the coupling interaction between the measured system
and measuring device is of short duration and strong. As a result, even though
the wave function of a quantum system is in general extended over space, an
impulse position measurement will inevitably collapse the wave function and can
only detect the system in a random position in space. Then it is unsurprising
that the wave function is assumed to be only related to the probability of
these random measurement results by the standard probability interpretation.
However, it has been known that there also exist other kinds of measurements in
quantum mechanics, one of which is the protective measurement. Protective
measurement also uses a standard measuring procedure, but with a weak and long
duration coupling interaction. Besides, it adds an appropriate procedure to
protect the measured wave function from collapsing (in some situations the
protection is provided by the measured system itself). These differences permit
protective measurement to be able to gain more information about the measured
quantum system and its wave function. In particular, it can measure the mass
and charge distributions of a quantum system, and it turns out that the mass
and charge density in each position is proportional to the modulus square of
the wave function of the system there.
    The key to unveil
the meaning of the wave function is to find the origin of the mass and charge
density. Historically, the charge density interpretation for electrons was
originally suggested by Schrödinger when he introduced the wave function and
founded wave mechanics. Although the existence of the charge density of an
electron can provide a classical explanation for some phenomena of radiation,
its explanatory power is very limited. In fact, Schrödinger clearly realized
that the charge density cannot be classical because his equation does not
include the usual classical interaction between the densities. Presumably since
people thought that the charge density could not be measured and also lacked a
consistent physical picture, this initial interpretation of the wave function
was soon rejected and replaced by Born’s probability interpretation. Now
protective measurement re-endows the charge density of an electron with reality
by a more convincing argument. The question is then how to find a consistent
physical explanation for it [1] .
Our following analysis can be regarded as a further development