Farewell to Reality (9 page)

Going back to our coin analogy, a hidden variables extension would have the properties of the two coins fixed at the moment they split apart and separate. The coins are assumed to be locally real.

This seems perfectly reasonable, but quantum theory, in contrast, demands that the two photons or the two coins are non-local and entangled; they are described by a single wavefunction. They continue to be non-local and entangled until one, the other or both are detected, at which point the wavefunction collapses and the two photons or the two coins become localized, replete with the properties we measure.

This is Bell's theorem: ‘If the [hidden variable] extension is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local. This is what the theorem says.'
¹⁶

Bell was able to devise a relatively simple direct test. Hidden variable theories that establish some form of local reality predict experimental results that conform to something called Bell's inequality. Quantum theory does not.

Bell published his ideas in 1966. The timing was fortuitous. Sophisticated laser technology, optical instruments and sensitive detection devices were just becoming available. Within a few years the first practical experiments designed to test Bell's inequality were being carried out.

The most widely known of these experiments were performed by French physicist Alain Aspect and his colleagues in the early 1980s. These made use of two high-powered lasers to produce excited calcium atoms, formed in an atomic ‘beam' by passing gaseous calcium from a high temperature oven through a tiny hole into a vacuum chamber. Calcium atoms excited in this way undergo a ‘cascade' emission, producing two photons in quick succession. The physics of the atom demands that angular momentum is conserved in this process, and the two photons are emitted in opposite states of circular polarization. This means that when they are passed through linear polarization filters, both photons will have the same linear polarization state, either both vertical or both horizontal.
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The photons are entangled.

The two photons have different energies, and hence different frequencies (and different colours). The physicists monitored green photons (which we will call photons A) on the left and blue photons (photons B) on the right. Each polarizing filter was mounted on a platform which allowed it to be rotated about its optical axis. Experiments could therefore be performed for different relative orientations of the two filters, which were placed about 13 metres apart.

Imposing this separation distance meant that any kind of ‘spooky' signal passing between the photons at the moment the wavefunction collapsed, ‘informing' photon B of the fate of photon A, for example, would need to travel at about twice the speed of light.

The results came down firmly in favour of quantum theory. The physicists performed four sets of measurements with four different orientations of the two polarizing filters. This allowed them to test a generalized form of Bell's inequality. For the specific combination of orientations of the polarizing filters chosen, the generalized form of the inequality demands a value that cannot be greater than 2. Quantum theory predicts a value of 2.828.
^**
The physicists obtained the result 2.697±0.015.
¹⁷
In other words, the experimental result exceeded the
limit predicted by Bell's inequality by almost fifty times the experimental error, a powerful, statistically significant violation.

In subsequent experiments the physicists modified their arrangement to include devices which could switch the paths of the photons, directing each of them towards two differently orientated polarizing filters. This prevented the photons from ‘knowing' in advance along which path they would be travelling, and hence through which filter they would eventually pass. This was equivalent to changing the relative orientations of the two polarizing filters while the photons were in flight.

The physicists obtained the result 2.404±0.080, once again in clear violation of the generalized form of Bell's inequality.

Similar experiments were carried out in August 1998 by a research group from the University of Geneva. They measured pairs of entangled photons using detectors positioned in Bellevue and Bernex, two small Swiss villages outside Geneva almost 11 kilometres apart. The results showed a clear violation of Bell's inequality. This suggests that any spooky action-at-a-distance would need to propagate from one detector to another with a speed at least twenty thousand times that of light.

Quantum entanglement has opened up intriguing possibilities in quantum information processing, cryptography and teleportation (‘Beam me up, Scotty' for photons). Such possibilities are based inherently on the kind of non-local spookiness required to breach Bell's inequality and which Einstein had hoped to avoid. In May 2012, a team of physicists from various institutes in Austria, Canada, Germany and Norway, led by Austrian Anton Zeilinger, reported successful teleportation of photons from La Palma in the Canary Islands to Tenerife, 143 kilometres distant.
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There is no escaping the conclusion. Reality at the quantum level is decidedly non-local.

Testing non-local hidden variable theories

But the reality advocated by the proponents of hidden variable theories does not have to be a local reality. The influences of the hidden variables could be non-local. This would still leave us with an action-at-a-distance that is somewhat spooky, but at least it would get rid of
the collapse of the wavefunction and the inherent quantum ‘chanciness' that this implies.

Like Bell, Anthony Leggett was also rather distrustful of the Copenhagen interpretation of quantum theory. He understood that local hidden variable theories (of the kind that Bell had considered) are constrained by two important assumptions. In the first, we assume that whatever
result
we get for photon A, this can in no way affect the result of any simultaneous or subsequent measurement on the distant photon B, and vice versa.

The second assumption is rather subtle. We assume that however we
set up
the apparatus to make the measurement on photon A, this can in no way affect the result we get for photon B, and vice versa. Remember, in response to the challenge posed by Einstein, Podolsky and Rosen, Bohr argued that the properties and behaviour of photon B are
defined
by the way we set up the measurement on photon A.

We know from the experimental tests of Bell's inequality that one or other or both of these assumptions must be wrong and that something has to give. But the experiments do not tell which of them is invalid. Leggett wondered what would happen if, instead of abandoning both assumptions, we keep the ‘result' assumption but relax the ‘set-up' assumption.

In essence, relaxing the set-up assumption means that the behaviour of the photons and the results of measurements
can
be influenced by the way we set up our measuring devices, just as Bohr had argued. This is still pretty weird. It requires some kind of curious, unspecified non local influence to be exerted by the choices we make in a possibly very distant laboratory.

In the context of our coin analogy, keeping the result assumption means that the result we get for coin B
cannot
depend on the result we get for coin A. We're still assuming that the faces of both coins are fixed at the moment they split apart. However, relaxing the set-up assumption means that the result we get for coin B can be influenced by
how we look
at coin A to see what result we got.

We can be reasonably confident that Einstein wouldn't have liked it.

By keeping the result assumption, Leggett defined a class of what he called ‘crypto' non-local hidden variable theories. The most important thing to note about this class of theories is that the individual quantum particles are assumed to possess defined properties before we measure
them. What we actually measure will, of course, depend on the way we set up our measuring devices, and changing these will affect the properties and behaviour of distant particles.

Here's the bottom line. This comes down to the rather simple question of whether or not quantum particles have the properties we assign to them
before the act of measurement.

Leggett found that keeping the result assumption but relaxing the set-up assumption is still insufficient to reproduce all the predictions of quantum theory. Just as Bell had done in 1966, Leggett now derived a relatively simple inequality that could provide a direct test.

Experiments designed to test Leggett's inequality were performed in 2006 by physicists at the University of Vienna and the Institute for Quantum Optics and Quantum Information. The greatest difference between the predictions of quantum theory and the prediction of this whole class of crypto non-local theories arises for a specific arrangement of the polarizing filters.
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For this arrangement, the class of non-local hidden variable theories predict a value for the Leggett inequality of 3.779. Quantum theory predicts 3.879, a difference of less than 3 per cent.

Nevertheless, the results were once again unequivocal. For the arrangement mentioned above, the experimental value was found to be 3.852±0.023, a violation of the Leggett inequality by more than three times the experimental error.
¹⁹

Things-as-they-are-measured

In his response to the challenge from Einstein, Podolsky and Rosen, Bohr appeared to accept that there could be no ‘mechanical disturbance', no ‘ripple' effect arising from the outcome of the measurement on photon A. It's not clear from his writings if he believed that, despite the absence of a mechanical disturbance, both the result and set-up assumptions inherent in the presumption of local reality should be abandoned: ‘… even at this stage there is essentially the question of
an influence on the very conditions which define the possible types of predictions regarding the future behaviour of the system'
.
²⁰

However, the experimental tests of Leggett's inequality demonstrate that we must indeed abandon both the result
and
the set-up assumptions. The properties and behaviour of the distant photon B
are
affected by both the setting we use to measure photon A and the result of that measurement. It seems that no matter how hard we try, we cannot avoid the collapse of the wavefunction.

What does this mean?

It means that in experimental quantum mechanics we have run right up against what was previously perceived to be a purely philosophical barrier. The experiments are telling us that we can know nothing of reality-in-itself.

We have to accept that the properties we ascribe to quantum particles like photons, such as energy, frequency, spin, polarization, position (‘here' or ‘there'), are properties that have no meaning except in relation to a measuring device that allows them to be projected into our empirical reality of experience. We can no longer assume that the properties we measure necessarily reflect or represent the properties of the particles as they really are.

Perhaps even more disturbing is the conclusion that when we try to push further and ascribe to reality-in-itself properties that might help us to reconcile and understand our observations, we get it demonstrably wrong.

This is all strangely reminiscent of a famous philosophical conundrum. If a tree falls in the forest and there's nobody around to hear, does it make a sound?

Philosophers have been teasing our intellects with such questions for centuries. Of course, the answer depends on how we choose to interpret the use of the word ‘sound'. If by sound we mean compressions and rarefactions in the air which result from the physical disturbances caused by the falling tree and which propagate through the air with audio frequencies, then we might not hesitate to answer in the affirmative.

Here the word ‘sound' is used to describe a physical phenomenon — the wave disturbance carried by the air. But sound is also a human experience, the result of physical signals delivered by human sense organs which are synthesized in the mind as a form of perception.

As we have seen, sense perceptions can be described using chemical and physical principles, up until the point at which the perception
becomes a mental experience. And the precise details of this process remain, at present, unfathomable.

The experiences of sound, colour, taste, smell and touch are all secondary qualities which exist only in our minds. We have no basis for our common-sense assumption that these secondary qualities reflect or represent reality as it really is. So, if we interpret the word ‘sound' to mean a human experience rather than a physical phenomenon, then when there is nobody around, there is a sense in which the falling tree makes no sound at all.

What the experimental tests of Bell's and Leggett's inequalities tell us is much the same. We have no basis for our common-sense assumption that the properties of quantum particles such as photons reflect or represent reality as it really is.

Who would have thought that the theory of light would lead to such philosophy? It should now be apparent why the Reality Principle given in Chapter 1 is so structured.

But look back through this chapter. The conclusions of quantum theory may be utterly bizarre, but this is a theory founded on solid observational and experimental fact. It has been tested over and over again. Whether we like it or not, it is here to stay. It is ‘true'. It describes the properties and behaviour of light better than any theory that has gone before, and is an essential component of the authorized version of empirical reality.

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Or track 6 if you're not familiar with the structure of a long-playing record.

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Think about the destructive forces unleashed when the energy contained in a tsunami strikes land.

^*
See
http://pdg.lbl.gov.
Click ‘Summary Tables' and select the top entry ‘Gauge and Higgs Bosons (gamma, g, W, Z, …)'. The photon is here referred to as ‘gamma'. The rest mass is the mass that a photon would have if it could be (hypothetically) slowed down and stopped.