PDF version of this
book

Next: Exploring
discretized wave equations Up: Relativity
plus quantum mechanics Previous: Bell's
theorem general proof   Contents

Experimental tests of Bell's inequality

At the time Bell's result first became known, the experimental record was
reviewed to see if any known results provided evidence against locality. None
did. Thus an effort began to develop tests of Bell's inequality. A series of
experiments conducted by Alain Aspect and his colleagues ended
with one reported in 1982 in which polarizer angles were changed at a rapid
enough rate to prevent light from either polarizer from reaching the more
distant detection in time to influence the result[2]. The
experimental design was like that shown in Figure 8.4.

The only reservation Aspect and his colleagues expressed for this experiment
concerned the lack of randomness in the polarizer settings.

A more ideal experiment with random and complete switching would
be necessary for a fully conclusive argument against the whole class of
supplementary-parameter theories obeying Einstein's causality[2].

This is a little surprising. In a previous paper Aspect pointed out
another problem.

Only two loopholes remain open for for advocates of realistic
theories without action at a distance. The
first one, exploiting the low efficiencies of detectors, could be ruled out by
a feasible experiment. The second one, exploiting the static character of all
previous experiments, could also be ruled out by a ``timing experiment'' with
variable analyzers now in progress[3].

The experiment ``now in progress'' was the one widely considered to
be conclusive at the time. This was true even though the detector efficiency
problem remained until an experiment in 2001[41]. That
experiment does not have adequate timing constraints and thus is still
inconclusive.

Aspect claimed conclusive results in an experiment prior to both of the above
reports.

Our results in excellent agreement with the quantum mechanical
predictions, strongly violate the generalized Bell's inequalities, and rule
out the whole class of realistic local theories[1]

Why all the confusion about what constitutes a conclusive experiment? There
are no doubt many reasons. Perhaps the biggest problem is the conviction among
most physicists that quantum mechanics is correct about this. When one is
certain about the expected results of an experiment, one's critical faculty is
handicapped. Its hard to fully consider all the possible ways that an
experimental claim may be overly broad.

Many physicists have an emotional investment in the outcome of these
experiments that compromises their objectivity. Einstein is universally regarded
as the greatest physicist of the twentieth century although he barely made it to
the middle of the century and all of his major work was done by the 1935 date of
the paper known as EPR which led to these experiments. There is
a strong conviction that physics has moved way beyond the naive realism of Einstein and these experiments are the objective proof of
that. If they ultimately turn out to vindicate Einstein this will be an enormous
blow to the ego of many physicists working in the foundations of quantum
mechanics,

Aspect's experiment was widely regarded at the time as conclusive especially
in the popular press. The reservation about randomly varying the polarizer
angles seemed like nitpicking. Were the photons suppose to figure out the
pattern and use it to time their detections?

In 1985 James D. Franson published a paper showing that the
timing constraints in this experiment were not adequate to confirm that locality
was violated[24]. The
difficulty is in establishing the time of detection. For that starts as a
microscopic event like the atom decay that determines the fate of Schrödinger's
cat. (See page .) While few believe the cat's fate remains undecided until one
opens the box the exact time at which that fate has become certain is unclear.
For timing in a test of Bell's inequality to be conclusive requires that we time
the occurrence of a macroscopic event. The trouble is there is no clear
definition of what a macroscopic event is. Franson observed the
following.

The time interval over which the probability amplitudes discussed
above may simultaneously exist and interact in the experiment by Aspect
Dalibard and Roger could conceivably be comparable to the 89-nsec lifetime of
the excited atomic state which produces the pair of photons. If the photon
emission time remains indeterminate for this length of time than it is
plausible that the final outcome of the event may remain indeterminate for a
comparable amount of time[24].

Franson introduced the phrase ``delayed determinism''. This
sounds very strange but, as he was at pains to point out in his paper, this is
an integral part of quantum mechanics and may well be part of a local realistic
theory. There is nothing in existing theory that says when an event is finally
determined. We know that microscopic systems can exist in a superposition of
states like the dead and live cat because we observe interference effects from
both states simultaneously. Any conclusive result must involve an unambiguously
macroscopic measurement of time. On that grounds Aspect's experiment failed.

In spite of Franson's objections and the additional problem of detector
efficiencies the belief remained widespread that Aspect's experiment was
decisive, ``Proposal for a Loophole-free Bell Inequality Experiment[36]'' was published
in 1993 detailing the problems in existing experiments and how they might be
overcome.

A major stride in addressing the timing was described in ``Violation of
Bell's inequality under strict Einstein locality''[50]. This
provided a much tighter (although not absolutely conclusive) constraint on
timing by separating the detections by 400 meters. Fiber optics made this
practical. It take light only 1.3
(1 is one millionth of a second) to travel 400
meters. The time between when the polarizer settings were changed and a
detection was registered was less than 100.
(1 is one billionth of a second.) The paper draws
the following conclusions.

While our results confirm the quantum theoretical predictions, we
admit that, however unlikely, local realistic or semi-classical
interpretations are still possible. Contrary to all other statistical
observations we would then have to assume that the sample of pairs registered
is not a faithful representative of the whole ensemble emitted. While we share
Bell's judgment about the likelihood of that explanation8.3, we agree that an ultimate experiment
should also have higher detection/collection efficiency, which was 5% in our
experiment.

Further improvements, e.g. having a human observers choose the
analyzer directions would again necessitate major improvements of technology
as was the case in order to finally, after more than 15 years, go
significantly beyond the beautiful 1982 experiment of Aspect et al[2]. Expecting
that any improved experiment will also agree with quantum theory, a shift of
our classical philosophical positions seems necessary. Among the possible
implications are nonlocality or complete determinism or the abandonment of
contrafactual conclusions. Whether or not this will finally answer the eternal
question: ``Is the moon there, when nobody looks?''[38], is certainly
up to the reader's personal judgment[50].

The authors admit that the detector efficiencies make the experiment less
than conclusive yet they are completely confident that no future experiment in
this area will contradict quantum mechanics. The problem with this attitude is
illustrated by their speculation on what this means. They can ask ``Is the moon
there when nobody looks?'' because quantum mechanics says nothing about physical
state between observations. The only thing that evolves between observations is
a wave function of probability densities in configuration space. I suspect
something physical does happen between observations and that alone makes quantum
mechanics incomplete. Given the complete ignorance about what is happening
between the creation of the photon pairs and their detection it would seem that
a higher degree of skepticism about a truly conclusive experiment is called for.

There was a similar experiment about the same time that achieved even greater
separation of detectors[45].

We now come to the most recent experiment that finally addresses the detector
efficiency problem. The following portion of the abstract describes what was
accomplished in this experiment.

Here we have measured correlations in the classical properties of
massive entangled particles (Be
ions): these correlations violate a form of Bell's inequality. Our measured
value of the appropriate Bell's `signal' is 2.25
.03, whereas a value of 2 is the maximum allowed by local realistic theories
of nature. In contrast to previous measurements with massive particles, this
violation of Bell's inequality was obtained by use of a complete set of
measurements. Moreover, the high detection efficiency of our apparatus
eliminates the so-called `detection' loophole[41].

At the end of the article the authors say they were not able to overcome the
timing or ``light cone loophole'' in this experiment. Thus we have experiments
that individually address these two loopholes but no single conclusive
experiment. In addition the timing loophole is somewhat ill defined because of
the lack of a a clear distinction between microscopic and macroscopic.

It is not difficult to see why most physicists are confident in their
expectations for these experiments. Quantum mechanics is a spectacularly
successful theory producing extraordinary predictions many of which have
astounding accuracy far surpassing anything possible with classical physics. One
can easily understand Bell's skepticism about the detection efficiency loophole.

...it is hard for me to believe that quantum mechanics works so
nicely for inefficient practical set-ups and is yet going to fail badly when
sufficient refinements are made[7].

How can a theory that has been so spectacularly reliable and
successful suddenly falter because of improved detector efficiency? That is one
way to look at things and the way most physicists do.

An alternative view focuses on how extraordinary these predictions are and on
how convoluted and improbable a theory quantum mechanics is. Locality is the
most powerful simplifying assumption in physics. Without it any event in the
universe can influence any other and physical theories become problematic if not
impossible. How is it that the universe violates locality but only does so in
obscure and difficult experiments that we have yet to achieve? One would expect
that a universe containing the complexity required for nonlocality would be
spectacularly nonlocal. One would hardly expect a theory like relativity that is
local at its core to be one of the two dominant theories in such a universe. Of
course the universe does not have to live up to our expectations but simplicity
and elegance have often been a guide to deeper and richer physical theory and
these predictions of quantum mechanics are about as far from simplicity and
elegance as one can get.

Bell proved that the configuration space model of quantum theory cannot be
mapped into physical space except with an explicitly nonlocal model such as
Bohm's[9]. So we
are faced with action at a distance (that is not relativistic) or a model like
configuration space that is not relativistic in its structure but can be to a
limited degree in its predictions. In addition quantum mechanics says nothing
about what happens in physical space between observations. If it is meaningful
to talk about an objective physical state that changes continuously than quantum
mechanics which lacks such a description is incomplete.

Quantum mechanics fails to define measurement. Does it take a human conscious
observation? Is a macroscopic event enough? If so how big is macroscopic? Is a
gage than can be read by a human enough? How about the change in state of a
single bit in a computers memory? If there is an objective definition of
measurement than quantum mechanics is an incomplete theory.

One can argue that the philosophy of contemporary physics is to define as
meaningless what one does not understand. It is one thing to avoid such problems
because one has no idea how to deal with them and quite another to say that we
need to modify our philosophical principles. These predictions deserve a high
level of skepticism no matter how many inconclusive experiments agree with
quantum mechanics.

The conviction that quantum mechanics will not be falsified by these
experiments stems in part from the difficulty of imagining how an alternative
local theory could account for the existing experimental record. In the next
section we speculate about the properties of discrete models based on the wave
equation. Such a model might account for the existing experimental results. This
speculations is far from being a new theory. That is how one must start if the
models can only be developed in conjunction with experiments as seems likely.

PDF version of this
book

Next: Exploring
discretized wave equations Up: Relativity
plus quantum mechanics Previous: Bell's
theorem general proof   Contents

Mountain Math Software
| home
| about | software | physics | measurement FAQ | more complete
theory | infinite | book |

Comments to: mailto:[email-masked]