Introduction
The ‘new’ quantum theory of Heisenberg and Schrödinger was immediately seen
to be extremely successful in practice. It could be used to predict energy levels for
a considerable number of systems, and Schrödinger’s approach in particular was
capable of describing many features of the atom, and predicting the results of a
great variety of experiments. Yet it was also clear that there were many surprising
and puzzling aspects to the theory, aspects that were certain to cause controversy.
In particular, the theory appeared to violate two Newtonian virtues, those of
determinism and realism. The first tells us that, if the state of a system is known at
time t, we should be able to predict its behaviour with certainty at all later times.
The aspect of the second that is stressed here is that a system should have definite
values of such observables as position and momentum at all times, even if these
are not measured. We may mention that the theory also appears to violate a third
Newtonian virtue, that of locality, which says that an event at one point in space
cannot have an immediate effect at a distant point. However, while the problems
with determinism and realism were immediately obvious and there was much
discussion of them in the early days of quantum theory, that with locality received
practically no attention until it was mentioned by Einstein and his collaborators
in the famous EPR paper of 1935.
Incidentally in this chapter we shall often remark along the lines that the theory
‘appeared to’ have certain difficulties. What is meant by this apparently rather
vague form of words is that the theory has these difficulties if the formalism
is interpreted in a fairly straightforward and natural way, without adding extra
elements beyond its explicit content. In particular no so-called hidden variables
are added, which might give extra information about an individual system, over and
above that contained in the wave-function.That there should be no hidden variables
was an essential part of the so-called orthodox interpretation (or interpretations)
of quantum theory, as will be discussed in Chapter 4. Einstein’s terminology, to
be discussed in Chapter 6 in particular, would be to say that the theory has these
difficulties if it is assumed that, without the addition of hidden variables, it is
complete, an assumption Einstein did not accept. Much of the rest of the book
3. Quantum Mechanics and its Fundamental Issues
will be concerned with attempts, particularly many using hidden variables, to go
beyond this basic approach, and hence to remove the difficulties, or, as Einstein
would say, to complete the theory.
The loss of realism was one aspect of the fact that, unlike clasical theory, quantum
theory provided no clear picture of the system. Even from the days of the old
quantum theory, wave-particle duality, as exemplified in Einstein’s light-particle
and de Broglie’s wave nature of the electron, had shown that simple classical
pictures had, at best, a restricted value. It could, of course, be argued that this
was not a genuine problem. One might suggest that, while the loss of a classical
picture, and even the loss of determinism and realism, might well be disturbing
for many and even anathema for some, it was not necessarily a conceptual failing
of quantum theory; some, in particular Heisenberg and Pauli, could claim it as a
liberating advance.
However there were aspects of this loss of realism that did present genuine
conceptual difficulties. Before measurement, a straightforward application of the
formalism suggests that the measured quantity will not usually have a specific
value, but when the measurement is performed a definite result is obtained; yet the
standard quantum evolution provides no mechanism whereby this may happen.
This difficulty may be termed the measurement problem of quantum theory; the
wave-function appears to change from a so-called pure state to a mixed state, but
quantum theory does not allow this to happen. Also, while quantum theory, as
has been said, suggests that microscopic systems do not demonstrate realism,
we usually take it for granted that objects of normal size, so-called macroscopic
objects, do behave in a realistic fashion. It must clearly be a challenge to explain
how classical realism occurs, or at least apppears to occur, at the macroscopic level
when it does not exist at the microscopic level.
Last edited by Samarda on 31 Oct 2011, 11:01 am, edited 2 times in total.
31 Oct 2011, 8:37 am
