Experimental verification of the non-local predictions of quantum theory

As we discussed in 82.5, quantum theory has been successfully
applied to a truly enormous variety of problems, and its status as
a key part of modern theoretical physics, with applications ranging
from the behaviour of the early universe and the substructure of
quarks to practical matters regarding such things as chemical binding,
lasers and microchips, is unquestioned. New tests of such a
theory might therefore be seen as adding very little to our
knowledge. The reason why, in spite of this, the experiments which
we describe here have attracted so much attention is that they test
certain simple predictions of the theory which violate conditions (in
particular the Bell inequalities) that very general criteria of
localisability would lead us to expect.
Following the publication of the first of the Bell inequalities, in
1965, there have been a succession of attempts to test them against
real experiments. These experiments are, in fact, quite difficult to
do with sufficient accuracy and early attempts, although they
generally supported quantum theory, with one exception, were
rather inconclusive. We shall therefore confine our discussion to
the recent series of experiments which have been performed in
France by Aspect, Dalibard, Grangier and Roger.
In all these experiments a particle emits successively two photons
in such a way that their total spin is zero. We recall that photons
are the particles associated with electromagnetic radiation, e.g.
light. They are spin one particles, in contrast to the spin 1/2
particles which we have previously used in our discussion. It is
convenient to measure the ‘polarisation’ of the photons rather than
their spin projections. These are related in a way that need not concern us. The only difference we need to note is that in the
predicted expression for ( E ) the angle between the various directions
has to be doubled, i.e. we find
(E(a, b)) = -cos 2(a - b). (5.9)
In the first experiment the spin measurements were carried out in
such a way that a particle with spin + 1 in a chosen direction was
deflected into the detector and counted, whereas a particle with spin
- 1 in the same direction was deflected away from the detector and
not counted. The experiment then measured the number of coincident
counts, i.e. counts at both sides. Because of imperfections
in the detectors it could not be assumed that no count meant that
the particle had spin - 1, it could have had spin + 1 and just been
'missed'. To take this into account it was necessary to run the
experiment with one or both of the spin detectors removed, and
then to use a modified form of the Bell inequality. We refer to the
experimental papers, listed in the bibliography, for details.
The important quantity that is measured is a suitably normalised
coincidence counting rate, which is predicted by quantum theory to
be given by
(5.10)
The factor 0.984, rather than unity, arises from imperfections in
the detectors (some particles are missed). If this prediction holds
throughout the whole range of angles then the Bell inequality is
violated. In figure 26 we show the results. The agreement with
quantum theory is perfect.
To demonstrate how effectively these results violate the Bell
inequality, and hence forever rule out the possibility of a local
realistic description of the world, the authors measured explicitly
at the angles where the violation was maximum, namely with the
configuration shown in figure 27, i.e. with a - b = b - a' =
a' - b' = 22.5", and a - b' = 67.5". A particular quantity S which
according to the Bell inequality has to be negative, but which
according to quantum theory has to be 0.1 18 2 0.005, is measured
to be 0.126 2 0.014. It is very clear that quantum theory and not
locality wins.
In the next set of experiments both spin directions were explicitly
detected, so the set-up was closer to that envisaged in the proof of
the original Bell inequality. From the measurements, the value
of(F(a, a ’ , b, b’)), defined in the previous section, was calculated
as
Fexp=t 2.697 i 0.015 (5.11)
for the orientation given by figure 27. This exceeds the bound given
in the inequality by more than 40 times the uncertainty. On the
other hand it agrees perfectly with the prediction of quantum
theory which, again allowing for the finite size of the detectors, is
calculated to be
Fq‘ = 2.70 & 0.05 (5.12)
instead of 2,2, which is the result with perfect detectors.

The third experiment was designed to investigate the following
question. Quantum theory suggests that measurement at A, say,
causes an instantaneous change at B, and this seems to be confirmed
by experiment. It appears therefore that ‘messages’ are sent with
infinite velocity (see the next section for further discussion of this).
Such a requirement would, however, not be needed if it were
assumed that the spin detecting instruments somehow communi cate their orientations to each other prior to the emission of the
photons, rather than when a photon actually reaches a detector. In
order to eliminate this possibility it is necessary to arrange that the
orientations are ‘chosen’ after the photons have been emitted.
Clearly the time involved is too small to allow the rotation of
mechanical measuring devices, so the experiment had two spin
detectors at each side, with pre-set orientations, and used switching
devices to deflect the photons into one or the other detector. The
switches were independently controlled at random. Thus, when the
photons were emitted, the orientations that were to be used had not
been decided. We refer to the original paper for further details of
this experiment and here record only the result, which was again in
complete agreement with quantum theory, and in violation of the
Bell inequality. Of course, it could be that nothing is really random
and that the devices that controlled the switching themselves communicated
with each other prior to the start of the experiment.
Such bizarre possibilities are hard to rule out (though if we were
sufficiently clever we could arrange that the signals which switch the
detectors originate from distant, different, galaxies that, according
to present ideas of the evolution of the universe, can never
previously have been in any sort of communication).

In this series of experiments it was also possible to vary the
distance between the two detectors and so test whether the wavefunction
showed any sign of ‘reducing’ as a function of time, as it
would according to the type of theory discussed in 03.4. Even when the separation was such that the time of travel of the photons was
greater than the lifetime of the decaying states that produced them
(which might conceivably be expected to be the time scale involved
in such an effect), there was no evidence that this was happening.
Thus it appears that, once again, quantum theory has been
gloriously successful. Maybe most of the people who regularly use
it are not surprised by this; they have learned to live with its strange
non-locality. The experiments we have described confirm this
feature of the quantum world; no longer can we forget about it by
pretending that it is simply a defect of our theoretical framework.
We close this section by noting the interesting irony in the history
of the developments following the EPR paper. Einstein believed in
reality (as we do); quantum theory seemed to deny such a belief and
was therefore considered by Einstein to be incomplete. The EPR
thought experiment was put forward as an argument, in which the
idea of locality was implicitly used, to support this view. We now
realise, however, that the experiment actually demonstrates the
impossibility of there being a theory which is both complete and
local.