The Einstein-Podolsky-Rosen thought experiment

In 1935, Einstein, Podolsky and Rosen published a paper entitled
‘Can Quantum-Mechanical Description of Physical Reality Be
Considered Complete?’ (Physical Review 47 777), which has had,
and continues to have, an enormous influence on the interpretation
problem of quantum theory. In this paper, they proposed a simple
thought experiment and analysed the implications of the quantum
theory predictions for the outcome of the experiment. These made
explicit the essentially non-local nature of quantum theory and,
according to the authors, proved that the theory must be
incomplete, i.e. that a more complete (hidden-variable) theory
exists and might one day be discovered. Much later, as we discuss
in the next section, John Bell carried the analysis considerably
further and showed that no local hidden-variable theory could
reproduce all the predictions of quantum theory. Naturally this
work prompted experimentalists to turn the thought experiments
into real experiments, and so check whether these predictions are
correct, or whether the actual results deviated from them in such
a way as to permit the existence of a satisfactory local theory. These
experiments, which we discuss in 05.5, beautifully confirm
quantum theory.
We shall refer to the general class of experiments with the same
essential features as that proposed by Einstein, Podolsky and
Rosen as EPR experiments. The orginal work is sometimes called
the EPR paradox, or the EPR theorem.
The particular EPR experiment that we shall describe is
somewhat different from the original, but is more suited to our
later discussion. We consider the situation shown in figure 20, in
which a particle with zero spin at rest in the laboratory decays spontaneously
into two, identical, particles, each with spin 112. These
particles, which we call A and B respectively, will move apart with
velocities that are equal in magnitude and opposite in direction.
(This ensures that their momenta add to zero so that the total
momentum, which was initially zero, is conserved.)
The experiment now consists of measuring the spin components
of the two particles in any particular directions-in fact, for
simplicity, we consider only directions perpendicular to the direction
of motion. Thus we have an apparatus that will measure the
spin component of particle A in a direction we can specify by the
angle a. Similarly we have an apparatus to measure the spin component
of B in a direction specified by some angle b. The full
experiment is illustrated in figure 21. The form of the apparatus
used to measure the spin is irrelevant for our purpose, but in order
to demonstrate that the measurement is possible we could consider
the case in which the spin 1/2 particles are charged, e.g. electrons.
In that case the particles would have a magnetic moment which
would be in the same direction as the spin. Then to measure the spin along a specific direction we could have a varying magnetic
field in that direction which would deflect the electron, up or down
according to the value of the spin component In order to discuss the form of the results we must digress a little
to think about spin. We first recall, from the earlier discussion of
spin in 53.7 (also Appendix 8), that a measurement of a spin component
of a spin 1/2 particle in any given direction will always give
a value either + 1/2 or - 1/2, i.e. the spin is always either exactly
along the chosen direction or exactly contrary to it. Suppose, for
example, that we know the particle has a spin component + 1/2 in
a particular direction (see figure 22). Whereas according to classical
mechanics we would obtain some value in between + 1/2 and - 1/2
for this second measurement, in fact, according to quantum
theory, we will obtain either of the two extremes, each with a
calculable probability. This probability will depend on the angle
between the two directions, and will be such that the average value
agrees with that given by classical mechanics. Within quantum
theory it will not be possible to predict which value we will obtain
in a given measurement; the situation in fact will be very analogous
to the choice of reflection or transmission in the barrier experiment
of 51.3. Further details of all this are given in Appendix 8. For the following
discussion the important fact we shall need to remember is that,
in quantum theory, the spin of a particle can have a definite value
in only one direction. We are free to choose this direction, but once
we have chosen it and determined a value for the spin in that direction,
the spin in any other direction will be uncertain. The fact that
when we measure the spin in this new direction we automatically
obtain a precise value implies that the measurement does something
to the particle, i.e. it forces it into one or the other spin values along
the new line. This of course is an example of wavefunction reduction
about which we have already written much.
The next thing that we need to learn is that the total spin, in any
given direction, for an isolated system, remains constant, Readers who know about such things will recognise this as being related to
the law of conservation of angular momentum. It is true in quantum
mechanics, as well as in classical mechanics; in particular, it
is true for individual events and not just for averages, a fact which
has been experimentally confirmed.