Understanding Quantum Physics: An Advanced Guide for the Perplexed

electrons. In
the experiment, the single electron is emitted from a source one after the
other, and then passes through two slits to arrive at the detecting screen.
Each electron is detected only as a random spot on the screen. But when a large
number of electrons with the same energy arrive at the screen, these spots
collectively form an undulant double-slit pattern. The ridges in the pattern
are formed in the positions where more electrons reach, and the valleys in the
pattern are formed in the positions where nearly no electrons reach. In
particular, the double-slit interference pattern is significantly different
from the direct mixture of two one-slit patterns, each of which is formed by
opening each of the two slits independently. It is well known that classical
mechanics cannot provide a satisfactory explanation of the double-slit
experiment. Unfortunately, quantum mechanics cannot either.
    The quantum
mechanical "explanation" of the double-slit experiment with electrons
can be formulated as follows. A wave function is prepared and emitted from the
source of electrons. This mathematical wave function then passes through two
physical slits, and its evolution follows the linear Schrödinger equation. At
last, the superposed wave function reaches the detecting screen and is measured
there. By the collapse postulate, it instantaneously and randomly collapses to
a local wave function, which corresponds to a determinate, random measurement
result, a spot on the screen. Moreover, according to the Born rule, the
probability density of the appearance of the spot is given by the modulus
square of the wave function (immediately before the measurement) there.
Although the predictions of quantum mechanics for the probability distribution
of measurement results agree with the double-slit interference pattern to
astonishing precision, it keeps silent as to what physical process happens from
the preparation to the measurement of a single electron; there is only a mathematical
wave function that spreads, superposes and collapses during the whole process.
    As Feynman once
claimed, the double-slit experiment contains the only mystery of quantum
mechanics. In fact, there are two mysteries, corresponding to the above two fundamental
problems of quantum mechanics. First of all, it is unknown what physical state
the mathematical wave function describes. Exactly what is an electron? Is it a
localized particle or a spreading wave or both or neither? How does it pass
through the two slits? Note that the wave function lives not in the real
three-dimensional space but in the multi-dimensional configuration space for a
many-body system. Then what does the system described by it really look like in
real space? Next, it remains unclear how come the Schrödinger equation and the
Born rule. This is the key to account for the double-slit interference pattern
and all other quantum phenomena. Why does the wave function of a single
electron obey the linear Schrödinger equation when not being measured? Why does
it undergo collapse when being measured? Is the collapse of the wave function a
real physical process? If the answer is negative, then how to explain the
emergence of definite measurement results? If the answer is positive, then why
and how does the wave function collapse?
    In this book, we
will try to solve these problems from a new angle. The key is to realize that
the problem of interpreting the wave function may be solved independent of how
to solve the measurement problem, and the solution to the first problem can
then have important implications for the solution to the second one. Although
the meaning of the wave function should be ranked as the first interpretative
problem of quantum mechanics, it has been treated as a marginal problem,
especially compared with the measurement problem. As noted above, there are
already several alternatives to quantum mechanics which give respective solutions
to the measurement problem. However, these theories in their present stages are
unsatisfactory at least in one aspect; they have not succeeded in making sense
of the wave function. Different from them, our strategy is to first find what
physical state the wave function describes and then investigate the
implications of the answer for the solutions to other fundamental problems of
quantum mechanics.
    It seems quite
reasonable that we had better know what the wave function is before we want to
figure out how it evolves, e.g. whether it collapses or