More quantum mystery

Quantum theory has been the basis of almost all the theoretical
physics of this century. It has progressed steadily, indeed gloriously.
The early years established the idea of quanta, particularly
for light, then came the applications to electrons which led to all
the developments in atomic physics and to the solution of
chemistry, so that already in 1929 Dirac could write that ‘The
underlying physical laws necessary for the mathematical theory of
a large part of physics and the whole of chemistry are thus com pletely known.. .’ (Proceedings of the Royal Society A123 714).
The struggle to combine quantum theory with special relativity,
discussed in the preceding section, occupied the period from the
1930s to the present, and its successes have ranged from quantum
electrodynamics to QCD, the theory of strong interactions. We are
now at the stage where much is understood and there is confidence
to tackle the remaining problems, like that of producing a quantum
theory of gravity.
The interpretation problem has been known since the earliest
days of the subject (recall Einstein’s remark mentioned in 0 1. l),
but here progress has been less rapid. The ‘Copenhagen’ interpretation,
discussed in the next section, convinced many people that the
problems were either solved or else were insoluble. The first really
new development came in 1935 with the EPR paper, which, as we
have seen, purported to show that quantum theory was incomplete.
We must then wait until the 1950s for Bell’s demolition of the von
Neumann argument regarding the impossibility of hidden-variable
theories, and, later, for his theorem about possible results of local
theories in the EPR experiment. Throughout the whole period there
were also steady developments leading to satisfactory hiddenvariable
theories. At present, attempts are being made to see if
these are, or if they can be made, compatible with the requirements
of special relativity.
What progress can we expect in the future? In the very nature of
the case, new insights and exciting developments are unlikely to be
predictable. We can, however, suggest a few areas where they
might occur.
Let us consider, first, possible experiments. There is much interest
at present in checking the accuracy of simple predictions of
quantum theory, in order, for example, to see whether there is any
indication of non-linear effects. No such indications have been seen
at the present time, but continuing checks, to better accuracy and
in different circumstances, will continue to be made.
Another area where there is active work being done is in the
possibility of measuring interference effects with macroscopic
objects, or at least with objects that have many more degrees of
freedom than electrons or photons. The best hope for progress here
lies in the use of SQUIDS (superconducting quantum interference
devices). These are superconducting rings, with radii of several
centimetres, in which it is hoped that interference phenomena, as predicted by quantum theory, between currents in the rings can be
observed. Such observations will verify (or otherwise) the predictions
of quantum theory for genuinely macroscopic objects. In
particular, it should be possible to see interference between states
that are macroscopically different, and thereby verify that a system
can be in a quantum mechanical superposition of two such states
(cf the discussion of Schrodinger’s cat, etc, in 44.3).
The success of quantum theory, combined with its interpretation
problems, should always provide an incentive to experimentalists to
find some result which it cannot predict. Many people would
probably say that they are unlikely to find such a result, but the
rewards for so doing would be great. If something could be shown
to be wrong with the experimental predictions of orthodox quantum
theory then we would, at last, perhaps have a real clue to
understanding it.
It must be admitted that the likelihood of there being any practical
applications arising from possible discoveries in this area is
extremely low. There are many precedents, however, that should
prevent us from totally excluding them. We have already noted in
$5.6 that genuine observation of wavefunctions, were it ever to be
possible, might lead to the possibility of instantaneous transmission
of signals. To allow ourselves an even more bizarre (some would
say ridiculous) speculation, we recall that, as long as the wavefunction
is not reduced, then all parts of it evolve with time according
to the Schrodinger equation. Thus, for example, the quantum
world contains the complete story of what happens at all subsequent
times to both the transmitted and reflected parts of the wavefunction
in a barrier experiment. Suppose then that a computer is
programmed by a non-reduced wavefunction which contains many
different programs. In principle this is possible; different input keys
could be pressed according to the results (‘unobserved’, of course)
of a selection of barrier type experiments, or, more easily, according
to the spin projections of particles along some axis. As long as
the wavefunction is not reduced, the computer performs all the
programs simultaneously. This is the ultimate in parallel processing!
If we observe the output answer by normal means we select one
set of results of the experiments, and hence one program giving a
single answer. The unreduced output wavefunction, however, contains
the answers to all the programs. It is unlikely that we will
ever be able to read this information, but . . . On the theoretical side, we have already mentioned the passibility
that the difficulties with making a quantum theory of gravity
just might be related to the defects of quantum theory. Maybe
some of our difficulties with non-locality suggest that our notions
of time and space are incomplete. If, for example, our three dimensions
of space are really embedded in a space of more dimensions
then we might imagine that points of space which seem to us to be
far separated are in reality close together (just as the points on a
ball of string are all close, except to an observer who, for some
reason, can only travel along the string).
Bearing in mind the issue of causality, we might ask why we
expect this to exist in the first place, in particular, why we believe
that the past causes the present. Indeed we could wonder why there
is such a difference between the past, which we remember, and the
future, which we don’t! In case we are tempted to think these things
are just obvious, we should note that the fundamental laws of
physics are completely neutral with regard to the direction of time,
i.e. they are unchanged if we change the sign of the time variable.
In this respect time is just like a space variable, for which it is clear
that one direction is not in any fundamental respect different from
any other. Concepts like ‘past’ and ‘present’, separated by a ‘now’,
do not have a natural place in the laws of physics. Presumably this
is why Einstein was able to write to a friend that the distinction
between past and present was only a ‘stubbornly persistent
illusion’.
It may well be that, in order to understand quantum theory, we
need totally new ways of thinking, ways that somehow go beyond
these illusions. Whether we will find them, or whether we are so
conditioned that they are for ever outside our scope is not at
present decidable.