Baggott J. The Quantum Story: A History in 40 Moments

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the quantum story

350

by philosophers down the centuries. These philosophers have continued to ask imperti-

nent, brain-teasing questions such as: If a tree falls in a forest with nobody around to hear,

does it make a sound?

Bell had not trusted the Copenhagen interpretation of quantum theory and, like

Einstein, felt that the theory was incomplete. Leggett, too, was distrustful. In 1976 he

had left his post at the University of Sussex in England to take up a temporary teaching

exchange at the University of Science and Technology in Kumasi, Ghana. Lacking access

to the most up-to-date research papers at the University’s library, he had applied him-

self instead to a problem that had attracted his attention some years earlier. Taking his

cue from Bohm, Leggett examined the predictions of a general class of non-local hidden

variable theories.

On his return to England, he drafted a paper presenting his ideas but did not get

around to submitting it for publication. He put the manuscript in a drawer and forgot all

about it. It was only with the advent nearly thirty years later of reliable sources of entan-

gled photons of the kind that had been used to test Bell’s inequality that he decided to take

the manuscript out of the drawer and dust it off.

He had in the meantime moved to a professorship at the University of Illinois at Urba-

na-Champaign, and was awarded a share (with Alexei Abrikosov and Vitaly Ginzburg)

in the 2003 Nobel Prize for physics for his work on superconductors and superﬂ uidity.

His paper on non-local hidden variable theories was published in the journal Founda-

tions of Physics in October 2003.

At a scientiﬁ c conference in Minnesota the following May, Leggett shared his results

with German physicist Markus Aspelmeyer, who worked alongside Anton Zeilinger’s

group at the University of Vienna and the Institute for Quantum Optics and Quantum

Information. In his paper Leggett had derived a new set of inequalities that could be used

to test not just locality, but realism too. The inequalities relate to a broad general class of

non-local hidden variable theories. Here, once again, was another straightforward test. If

quantum theory failed, this would be direct evidence that it was not complete. If it passed,

then our preciously held assumptions about the nature of reality at the quantum level

could no longer be revised, they would have to be abandoned.

The experiments didn’t seem too difﬁ cult.

Leggett had looked at it this way. In a cascade emission process of the

kind that had been used in the Aspect experiments, we assume that the

properties of the photons are governed by some, possibly very complex,

set of hidden variables. These hidden variables possess unique values

the persistent illusion

351

that determine the states of the photons and their subsequent interac-

tions with their respective measuring devices. We further assume that

the photons are emitted with a statistical distribution of variables and

that the form of this distribution is determined only by the physics of the

emission process and not by the way the measuring apparatus is set up.

The outcomes of the measurements to be made on the correlated

photons are determined by the settings of the polarization analysers and

the values of the hidden variables. So far, so familiar.

Local hidden variable theories are characterized by two further assump-

tions. In the ﬁ rst, we assume (as did Einstein, Podolsky, and Rosen) that

the outcome of the measurement on photon A can in no way be affected

by the outcome of the measurement on the distant photon, B, and vice versa.

In the second, we assume that the outcome of the measurement on pho-

ton A can in no way be affected by the setting of the polarization analyser

used to perform the measurement on B, and vice versa.

One or other of these assumptions is invalidated by the experimental

demonstration of the violation of Bell’s inequality. In particular, experi-

ments designed to close the ‘locality loophole’ show that despite ran-

domly changing the settings of the analysers whilst the photons are in

ﬂ ight towards them, the correlations predicted by quantum theory are

nevertheless maintained. This kind of result does not allow us to conclude

which assumption is invalidated, since changing the analyser setting will

obviously also change the outcome of the subsequent measurement.

Leggett chose to relax the setting restriction. In other words, he chose

to allow the behaviour of the photons and the outcomes of subsequent

measurements to be inﬂ uenced by the way the measursing devices are

set up. He understood well enough that allowing the outcome of a meas-

urement to be affected by the setting of a distant analyser was, to many

physicists, highly counter-intuitive:

But in physics we are normally accustomed to require some positive reason

before we accept a particular part of the environment as relevant to the out-

come of an experiment. Now the [distant] polarizer . . . is nothing more than

(e.g.) a calcite crystal, and nothing in our experience of physics indicates

that the orientation of distant calcite crystals is either more or less likely to

affect the outcome of an experiment than, say, the position of the keys in the

experimenter’s pocket or the time shown by the clock on the wall.

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352

But in the face of the experimental evidence, something had to give. In

choosing to relax the setting restriction, Leggett was allowing for some

unspeciﬁ ed non-local inﬂ uence of the analyser settings to affect the out-

comes of measurements on distant particles. In this sense he was being

consistent with Bohr’s response to Einstein, Podolsky, and Rosen’s origi-

nal challenge:

. . . there is in a case like that just considered no question of a mechanical

disturbance of the system under investigation during the last critical stage

of the measuring procedure. But even at this stage there is essentially the

question of an inﬂ uence on the very conditions which deﬁ ne the possible types of

predictions regarding the future behaviour of the system.

By preserving the outcome restriction, Leggett was deﬁ ning a class of

non-local hidden variable theories in which the individual particles pos-

sess deﬁ ned properties before the act of measurement. What is actually

measured will of course depend on the measurement settings that the

particles encounter, and changing these settings does affect the behav-

iour of distant particles. But maintaining this restriction meant that

there was no way that a measurement made on photon A could affect

the outcome of a simultaneous or subsequent measurement on photon

B, and vice versa. Leggett referred to this broad class of theories as ‘crypto’

non-local hidden variable theories.

Leggett went on to show that relaxing the setting restriction is in itself

insufﬁ cient to reproduce all the results of quantum theory. Just as Bell

had done in 1964, Leggett now derived inequalities that were obeyed by

such hidden variable theories but which for certain combinations of

measurement settings were predicted by quantum theory to be violated.

At stake then, was the rather simple question of whether or not quantum

See Chapter 16, p. 146–147.

Leggett not only sought to preserve the outcome restriction, but also to ensure that

sub-ensembles of polarized photons would obey Malus’ law, i.e. they would interact with polari-

zation analysers in a manner consistent with quantum theory predictions (Tony Leggett, personal

communication to the author, 4 August 2009). Note that Bohm’s non-local hidden variable theory

does not belong in this class. The effects not only of changing analyser settings but also of meas-

urement outcomes affect the shape of the quantum potential and consequently inﬂ uence instanta-

neously the behaviour of distant particles. The outcome restriction is not relaxed in this case.

the persistent illusion

353

particles have the properties we assign to them before the act of measure-

ment. Put another way, here was an opportunity to test whether quantum

particles have ‘real’ properties before they are measured.

The experiments implied by Leggett’s work were not so very different

from the experiments that had been performed to test Bell’s inequal-

ity. There were some subtleties and some challenges, however. All the

experiments conducted to this time had measured the polarization states

of photons in a single basis (such as vertical/horizontal) using analyser

orientations varied within a single plane. Testing the Leggett inequalities

would require measurements in two bases (linear and elliptical polariza-

tion) and in two planes, such as the xz- and yz-planes. This was why the

results of the earlier tests of Bell’s inequality could not be used to deter-

mine the validity or otherwise of the Leggett inequalities.

By allowing non-local inﬂ uences due to the settings of the measure-

ment devices, the predictions of the general class of non-local hidden

variable theories considered by Leggett were, not surprisingly, so much

closer to the predictions of quantum theory. It was possible to discern

a pattern. Imposing both the outcome and setting restrictions (local

reality) results in a relatively large difference between the predictions of

quantum theory and local hidden variables. Lifting the setting restric-

tion (non-local reality) closes this gap but does not eliminate it. Relax-

ing the outcome restriction closes the gap completely: it is impossible to

differentiate between quantum theory and this class of non-local hidden

variable interpretations of quantum theory using experiment.

To discriminate between quantum theory and the crypto non-local

hidden variable theories studied by Leggett would require the highest

quality entangled photons and the highest ‘visibility’. These tests would

make the earlier experiments look like a walk in the park.

Aspelmeyer returned to Vienna and, with Leggett’s help, worked together

with a local theorist to re-derive Leggett’s inequality for a speciﬁ c experi-

mental arrangement that could be realized in the laboratory. Aspelmeyer’s

student Simon Gröblacher carried out these experiments over one weekend.

The physicists took the results to Zeilinger, who agreed to repeat them.

The two groups submitted their joint results for publication in the Brit-

ish journal Nature in December 2006. They were published in April 2007.

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354

For the kind of arrangement used in these experiments, the Leggett

inequality demands that the value of the experimental correlation is

restricted to be less than or equal to the value given by 4 − (4/p)|sin(j/2)|,

where j is the angle difference between two analyser orientations in both

the xz- and yz-planes. Quantum theory predicts the value |2(cosj + 1)|.

The maximum divergence between these two sets of predictions occurs

for j = 18.8°. At this angle, the general class of crypto non-local hidden

variable theories studied by Leggett predicts the value 3.792. Quantum

theory predicts 3.893, a difference of less than 3 per cent.

Nevertheless, the results were once again unequivocal. Violations of

the Leggett inequality were observed for j between 4° and 36°, with a

maximum violation around 20°. For this angle the experimental value

for the correlation was found to be 3.8521 ± 0.0227, compared with the

Leggett inequality prediction of 3.779 and the quantum theory prediction

of 3.879. This is a violation of the Leggett inequality by more than three

standard deviations.

The Vienna physicists ensured that the same arrangement yielded

results that could be used in a simultaneous test of the generalized form

of Bell’s inequality. For the same difference angle j, they obtained a cor-

relation 2.178 ± 0.0199 compared to the Bell limit of 2, a violation of Bell’s

inequality by nine standard deviations.

The physicists concluded their paper as follows:

We believe that our results lend strong support to the view that any future

extension of quantum theory that is in agreement with experiments must

abandon certain features of realistic descriptions.

Further reports followed hard on the heels of this paper. The Vienna

group and a group from the Universities of Geneva and the National

University of Singapore conﬁ rmed the violation of Leggett’s inequality

under less restrictive conditions, expanding the class of non-local hidden

variable theories that could now be ruled out.

Zeilinger had not studied quantum theory as a student in Vienna in

the 1960s and so came late to its paradoxes and conundrums. ‘Quantum

mechanics is very fundamental,’ he explained, ‘Probably even more funda-

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355

mental than we appreciate. But to give up on realism altogether is certainly

wrong. Going back to Einstein, to give up realism about the moon, that’s

ridiculous. But on the quantum level we do have to give up realism.’

What does it mean?

If a tree falls in the forest when there’s nobody around to hear, we might

hypothesize that it produces certain wave disturbances—compressions and

rarefactions in the air around it. We might hypothesize that some of these

disturbances will have characteristic audio frequencies. We might predict

that if a measuring device (a human being or an audio tape recorder) was

to be placed near the location of the tree then the result will be the hearing

or recording of an audio signal. We might even call this signal a sound.

But we commonly use the word ‘sound’ in two senses. We sometimes

refer to wave disturbances with frequencies in the audio range as sound

waves, even though we might not actually hear them. In this sense, the

word ‘sound’ is used to describe a physical phenomenon—the wave dis-

turbance, with characteristic amplitude and frequency. Sound is also a

human experience, the result of physical signals delivered by human sense

organs (speciﬁ cally the tympanic membrane) which are synthesized in

the human mind as a form of perception.

Now, to a large extent, we can interpret the action of human sense

organs in much the same way we interpret the actions of mechanical

measuring devices. The human auditory apparatus simply translates one

set of physical phenomena into another, leading eventually to stimulation

of those parts of the brain cortex responsible for the perception of sound.

It is here that the distinction comes. Everything to this point is explicable

in terms of physics, but the process by which we turn electrical signals in

the brain into human perception and experience in the mind remains, at

present, unfathomable.

Philosophers have long argued that sound, colour, taste, smell, and

touch are all secondary qualities which exist only in our minds. We have no

basis for our commonsense assumption that these secondary qualities

reﬂ ect or represent reality as it really is. Like the prisoners in Plato’s cave,

we may well live in a world of crude appearances of objects, which we

mistake for the objects themselves.

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356

If we interpret sound in terms of human experience rather than just

physical phenomena, then when there is nobody around there is a sense

in which the falling tree makes no sound at all.

And this is what the tests of Leggett’s inequality suggest. We must

now accept that the properties we ascribe to quantum particles, such as

spin-up, vertically polarized, ‘here’ and ‘there’ are properties that have

no meaning except in relation to a measuring device. We can no longer

assume that the properties we measure necessarily reﬂ ect or represent

the properties of the particles as they really are. As Heisenberg had ear-

lier argued:

. . . we have to remember that what we observe is not nature in itself but

nature exposed to our method of questioning.

This does not mean that quantum particles are not real. What it does

mean is that we can ascribe to them only an empirical reality. This is a

reality that depends on our method of questioning, a reality that can be

affected by the outcomes of measurements on distant particles.

Although we may speak of electron spin, position, orbital angular

momentum, and so on, these are empirical properties we have assigned

to an electron based on our experiences of them. Each property becomes

‘real’ only when the electron interacts with an instrument speciﬁ cally

designed to reveal that property. These concepts help us to correlate and

describe our observations, but they have no meaning beyond their use as

a means of connecting the object of our study with the measuring device

we use to study it.

Before measurement, the properties of quantum particles such as

electrons and photons are clearly constrained by the physics that pro-

duced them, but they are in a sense ‘undetermined’. Their properties are

‘vanilla’: incipiently spin-up or spin-down, vertical or horizontal, but

undetermined until the act of measurement. The nature of the interac-

tion with a measuring device somehow ‘determines’ these properties, in

a way that we may never hope to fathom.

See Chapter 12, p. 109.

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357

‘Reality is merely an illusion,’ Einstein once admitted, ‘albeit a very

persistent one.’

Like Bell before him, Leggett had been encouraged by a general scepti-

cism of the Copenhagen interpretation to develop a theorem which led

ultimately to a decisive experimental test. Whilst he accepts that the

experimental results mean that realism is no longer tenable, he still does

not accept that quantum theory is complete.

‘I’m in a small minority with that point of view,’ he demurred, ‘And I

wouldn’t stake my life on it.’

Or, if you prefer: ‘Reality is that which, when you stop believing in it, doesn’t go away.’

Philip K. Dick.

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PART VII

Quantum

Cosmology