Bell's great achievement was that during the 1960s he
was able to breathe new and exciting life into the foundations of
quantum theory, a topic seemingly exhausted by the outcome of the
Bohr - Einstein debate thirty years earlier, and ignored by
virtually all those who used quantum theory in the
intervening period. Bell was able to show that discussion of such
concepts as 'realism', 'determinism' and 'locality' could be
sharpened into a rigorous mathematical statement, 'Bell's
inequality', which is capable of experimental test. Such tests,
steadily increasing in power and precision, have been carried out
over the last thirty years.
Indeed, almost wholly due to Bell's pioneering
efforts, the subject of quantum foundations, experimental as well
as theoretical and conceptual, has became a focus of major
interest for scientists from many countries, and has taught us
much of fundamental importance, not just about quantum theory, but
about the nature of the physical universe.
In addition, and this could scarcely have been
predicted even as recently as the mid-1990s, several years after
Bell's death, many of the concepts studied by Bell and those who
developed his work have formed the basis of the new subject area
of quantum information theory, which includes such topics as
quantum computing and quantum cryptography. Attention to quantum
information theory has increased enormously over the last few
years, and the subject seems certain to be one of the most
important growth areas of science in the twenty-first century.
John Stewart Bell's parents had both lived in
the north of Ireland for several generations. His father was also
named John, so John Stewart has always been called Stewart within
the family. His mother, Annie, encouraged the children to
concentrate on their education, which, she felt, was the key to a
fulfilling and dignified life. However, of her four children -
John had an elder sister, Ruby, and two younger brothers, David
and Robert - only John was able to stay on at school much over
fourteen. Their family was not well-off, and at this time there
was no universal secondary education, and to move from a
background such as that of the Bells to university was
exceptionally unusual.
Bell himself was interested in books, and
particularly interested in science from an early age. He was
extremely successful in his first schools, Ulsterville Avenue and
Fane Street, and, at the age of eleven, passed with ease his
examination to move to secondary education. Unfortunately the cost
of attending one of Belfast's prestigious grammar schools was
prohibitive, but enough money was found for Bell to move to the
Belfast Technical High School, where a full academic curriculum
which qualified him for University entrance was coupled with
vocational studies.
Bell then spent a year as a technician in the
Physics Department at Queen's University Belfast, where the senior
members of staff in the Department, Professor Karl Emeleus and Dr
Robert Sloane, were exceptionally helpful, lending Bell books and
allowing him to attend the first year lectures. Bell was able to
enter the Department as a student in 1945. His progress was
extremely successful, and he graduated with First-Class Honours in
Experimental Physics in 1948. He was able to spend one more year
as a student, in that year achieving a second degree, again with
First-Class Honours, this time in Mathematical Physics. In
Mathematical Physics, his main teacher was Professor Peter Paul
Ewald, famous as one of the founders of X-ray crystallography;
Ewald was a refugee from Nazi Germany.
Bell was already thinking deeply about quantum
theory, not just how to use it, but its conceptual meaning. In an
interview with Jeremy Bernstein, given towards the end of his life
and quoted in Bernstein's book , Bell reported being perplexed by
the usual statement of the Heisenberg uncertainty or indeterminacy
principle ( x p , where x and p are
the uncertainties or indeterminacies, depending on one's
philosophical position, in position and momentum respectively, and
is the (reduced) Planck 's constant).
It looked as if you could take this size
and then the position is well defined, or that size and then the
momentum is well defined. It sounded as if you were just free to
make it what you wished. It was only slowly that I realized that
it's not a question of what you wish. It's really a question of
what apparatus has produced this situation. But for me it was a
bit of a fight to get through to that. It was not very clearly
set out in the books and courses that were available to me. I
remember arguing with one of my professors, a Doctor Sloane,
about that. I was getting very heated and accusing him, more or
less, of dishonesty. He was getting very heated too and said,
'You're going too far'.
At the conclusion of his undergraduate studies
Bell would have liked to work for a PhD. He would also have liked
to study the conceptual basis of quantum theory more thoroughly.
Economic considerations, though, meant that he had to forget about
quantum theory, at least for the moment, and get a job, and in
1949 he joined the UK Atomic Research Establishment at Harwell,
though he soon moved to the accelerator design group at Malvern.
It was here that he met his future wife, Mary
Ross, who came with degrees in mathematics and physics from
Scotland. They married in 1954 and had a long and successful
marriage. Mary was to stay in accelerator design through her
career; towards the end of John's life he returned to problems in
accelerator design and he and Mary wrote some papers jointly.
Through his career he gained much from discussions with Mary, and
when, in 1987, his papers on quantum theory were collected , he
included the following words:
I here renew very especially my warm
thanks to Mary Bell. When I look through these papers again I
see her everywhere.
Accelerator design was, of course, a relatively
new field, and Bell's work at Malvern consisted of tracing the
paths of charged particles through accelerators. In these days
before computers, this required a rigorous understanding of
electromagnetism, and the insight and judgment to make the
necessary mathematical simplifications required to make the
problem tractable on a mechanical calculator, while retaining the
essential features of the physics. Bell's work was masterly.
In 1951 Bell was offered a year's leave of
absence to work with Rudolf Peierls, Professor of Physics at
Birmingham University. During his time in Birmingham, Bell did
work of great importance, producing his version of the celebrated
CPT theorem of quantum field theory. This theorem showed that
under the combined action of three operators on a physical event:
P, the parity operator, which performed a reflection; C,
the charge conjugation operator, which replaced particles by
anti-particles; and T, which performed a time reversal, the
result would be another possible physical event.
Unfortunately Gerhard Lüders and Wolfgang Pauli proved the same
theorem a little ahead of Bell, and they received all the credit.
However, Bell added another piece of work and
gained a PhD in 1956. He also gained the highly valuable support
of Peierls, and when he returned from Birmingham he went to
Harwell to join a new group set up to work on theoretical
elementary particle physics. He remained at Harwell till 1960, but
he and Mary gradually became concerned that Harwell was moving
away from fundamental work to more applied areas of physics, and
they both moved to CERN, the Centre for European Nuclear Research
in Geneva. Here they spent the remainder of their careers.
Bell published around 80 papers in the area of
high-energy physics and quantum field theory. Some were fairly
closely related to experimental physics programmes at CERN, but
most were in general theoretical areas.
The most important work was that of 1969
leading to the Adler-Bell-Jackiw (ABJ) anomaly in quantum field
theory. This resulted from joint work of Bell and Ronan Jackiw,
which was then clarified by Stephen Adler. They showed that the
standard current algebra model contained an ambiguity.
Quantisation led to a symmetry breaking of the model. This work
solved an outstanding problem in particle physics; theory appeared
to predict that the neutral pion could not decay into two photons,
but experimentally the decay took place, as explained by ABJ. Over
the subsequent thirty years, the study of such anomalies became
important in many areas of particle physics. Reinhold Bertlmann,
who himself did important work with Bell, has written a book
titled Anomalies in Quantum Field Theory , and the two
surviving members of ABJ, Adler and Jackiw shared the 1988 Dirac
Medal of the International Centre for Theoretical Physics in
Trieste for their work.
While particle physics and quantum field theory
was the work Bell was paid to do, and he made excellent
contributions, his great love was for quantum theory, and it is
for his work here that he will be remembered. As we have seen, he
was concerned about the fundamental meaning of the theory from the
time he as an undergraduate, and many of his important arguments
had their basis at that time.
The conceptual problems may be outlined using
the spin-1/2 system. We may say that when
the state-vector is + or - respectively,
sz is equal to /2 and - /2
respectively, but, if one restricts oneself to the Schrödinger
equation, sx and sy
just do not have values. All one can say is that if a measurement
of sx, for example, is performed, the
probabilities of the result obtained being either /2 or
- /2 are both 1/2.
If, on the other hand, the initial state-vector
has the general form of c+ ++ c-
-, then all we can say is that in a measurement of sz,
the probability of obtaining the value of /2is |c"
2|, and that of obtaining the value of - /2is
|c-2|. Before any measurement, sz
just does not have a value.
These statements contradict two of our basic
notions. We are rejecting realism, which tells us that a
quantity has a value, to put things more grandly -- the physical
world has an existence, independent of the actions of any
observer. Einstein was particularly disturbed by this abandonment
of realism -- he insisted in the existence of an observer-free
realm. We are also rejecting determinism, the belief
that, if we have a complete knowledge of the state of the system,
we can predict exactly how it will behave. In this case, we know
the state-vector of the system, but cannot predict the result of
measuring sz.
It is clear that we could try to recover
realism and determinism if we allowed the view that the
Schrödinger equation, and the wave-function or state-vector, might
not contain all the information that is available about the
system. There might be other quantities giving extra information
-- hidden variables. As a simple example, the state-vector
above might apply to an ensemble of many systems, but in addition
a hidden variable for each system might say what the actual value
of sz might be. Realism and determinism
would both be restored; sz would have a
value at all times, and, with full knowledge of the state of the
system, including the value of the hidden variable, we can predict
the result of the measurement of sz .
A complete theory of hidden variables must
actually be more complicated than this -- we must remember that we
wish to predict the results of measuring not just sz,
but also sx and sy,
and any other component of s. Nevertheless it would appear
natural that the possibility of supplementing the Schrödinger
equation with hidden variables would have been taken seriously. In
fact, though, Niels Bohr and Werner Heisenberg were convinced that
one should not aim at realism. They were therefore pleased when
John von Neumann proved a theorem claiming to show rigorously that
it is impossible to add hidden variables to the structure of
quantum theory. This was to be very generally accepted for over
thirty years.
Bohr put forward his (perhaps rather obscure)
framework of complementarity, which attempted to explain
why one should not expect to measure sx
and sy (or x and p)
simultaneously. This was his Copenhagen interpretation of
quantum theory. Einstein however rejected this, and aimed to
restore realism. Physicists almost unanimously favoured Bohr .
Einstein 's strongest argument, though this did
not become very generally apparent for several decades lay in the
famous Einstein -Podolsky-Rosen (EPR) argument of 1935,
constructed by Einstein with the assistance of his two younger
co-workers, Boris Podolsky and Nathan Rosen. Here, as is usually
done, we discuss a simpler version of the argument, thought up
somewhat later by David Bohm.
Two spin-1/2particles are
considered; they are formed from the decay of a spin-1/2particle,
and they move outwards from this decay in opposite directions. The
combined state-vector may be written as (1/√2)(
1- 2+ - 1- 2+), where
the 1s and 2s for particles 1
and 2 are related to the s above. This state-vector has a
strange form. The two particles do not appear in it independently;
rather either state of particle 1 is correlated with a particular
state of particle 2. The state-vector is said to be entangled.
Now imagine measuring s1z.
If we get + /2, we know that an immediate measurement
of s2z is bound to yield - /2,
and vice-versa, although, at least according to Copenhagen, before
any measurement, no component of either spin has a particular
value.
The result of this argument is that at least
one of three statements must be true:
(1) The particles must be exchanging
information instantaneously i.e. faster than
