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

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the quantum story

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the entangled particles had been created and were ‘on their way’ to their

respective detectors. Bohm and Aharonov had suggested this possibility in

1957, and Bell had restated the importance of such a test in his 1964 paper.

This, Aspect decided, would be the subject of his ‘thèse d’état’. He

persuaded Christian Imbert, a young professor at the Institute for Theoreti-

cal and Applied Optics in Paris, to act as his thesis advisor, and proceeded

to seek funding and assemble equipment in the basement of the Institute.

Imbert recommended that he talk to Bell, and in 1975 Aspect travelled

to CERN in Geneva to discuss his proposed experiments. He nervously

explained what he was intending to do, as Bell listened in silence.

‘Are you tenured?’ Bell ﬁ nally asked, concerned that experiments

designed to answer esoteric questions concerning the nature of reality at

the quantum level were hardly the stuff on which solid academic careers

could be built.

Aspect explained that he was still only a graduate student. He had yet

to secure his doctorate, although he held a permanent position at the

Institute.

‘You must be a very courageous graduate student . . . ,’ Bell replied.

Bell agreed that the experiments that Aspect was proposing would

represent a substantial improvement on previous studies, and offered his

encouragement.

Aspect published details of his proposed experiments in the journal

Physical Review in October 1976. He settled on excited calcium atoms as

the source of entangled photons. In the lowest energy ‘ground’ electronic

state of the calcium atom, the outermost atomic orbit is spherical and

ﬁ lled with two spin-paired electrons. If one of these electrons absorbs a

photon of the right wavelength, then the electron may be promoted to a

higher-energy, dumbbell-shaped orbit.

In this process, the photon that

is absorbed imparts a quantum of angular momentum to the electron in

the atom, and this appears as orbital angular momentum of the excited

electron.

The atomic orbitals in question are 4s and 4p, respectively.

This additional angular momentum cannot appear in the spin of the electron, since this is

ﬁ xed at s = ½.

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Polaroid polarized sunglasses reduce glare by ﬁ ltering scattered light with random polari-

zation to produce linearly polarized light.

Now suppose that it is possible to excite a second electron (the one ‘left

behind’ in the ground-state orbit) also into this same dumbbell-shaped

orbit, but in a way that maintains the alignment of the electron spins. In

other words, we create a doubly excited state in which the electron spins

remain paired. This doubly excited state undergoes a rapid cascade emis-

sion, producing two photons in quick succession as the electrons return

to the ground-state orbit. To conserve angular momentum in this proc-

ess, the two photons must be emitted in opposite states of circular polar-

ization. The photons are entangled, in precisely the way that Einstein,

Podolsky, and Rosen and, subsequently, Bohm and Bell had anticipated.

In fact, the two emitted photons have wavelengths in the visible region.

One photon is green, the second is blue.

Aspect and his colleagues would use two high-power lasers to pro-

duce the excited calcium atoms, which were formed in an atomic ‘beam’,

produced by passing gaseous calcium from a high-temperature oven

through a tiny hole into a vacuum chamber. Subsequent collimation of

the atoms entering the sample chamber would provide a well-deﬁ ned

beam of atoms. The low density of atoms at the point of intersection

with the laser beams would ensure that the calcium atoms did not collide

with each other or with the walls of the chamber before absorbing and

subsequently emitting photons.

The physicists would monitor the light emitted in opposite directions

from the atomic beam source, using coloured ﬁ lters to isolate the green

photons (which we will call photons A) on the left and the blue pho-

tons (photons B) on the right. The photons would then be passed into an

arrangement consisting of two polarization analysers, four photomulti-

pliers to amplify the signals from the detected photons, and electronic

devices designed to detect and record coincident signals from the pho-

tomultipliers.

The analysers transmitted light polarized parallel to the plane of inci-

dence (vertical polarization), and reﬂ ected light polarized perpendicular

to this plane (horizontal polarization).

Detecting these linear polariza-

tion states is more straightforward than detecting circular polarization

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states and changing from one to the other does not affect the basis of

the correlation between photons A and B. The correlation is such that if

the optical axes of both analysers are aligned in the same direction, then

if photon A is detected in a state of vertical polarization, photon B must

also be detected in a state of vertical polarization.

Each polarization analyser was to be mounted on a platform which

allowed it to be rotated about its optical axis. Experiments could there-

fore be performed for different relative orientations of the two analysers,

which would be placed about 13 metres apart. The electronics would be

set to look for coincidences in the arrival and detection of the photons

A and B within a time window just 20 billionths of a second wide. Any

kind of ‘spooky’ signal passed between the photons, ‘informing’ photon

B of the fate of photon A, for example, would therefore need to travel the

13 metres between the detectors within this narrow time window. In fact,

it would take about twice this amount of time for a signal moving at the

speed of light to cover this distance.

The practical realization of these experiments took another ﬁ ve years.

Aspect, Grangier, and Roger published their ﬁ rst deﬁ nitive results in the

journal Physical Review Letters in August 1981.

The physicists performed four sets of measurements with four different

orientations of the two analysers. This allowed them to test a generalized

form of Bell’s inequality.

For the speciﬁ c combination of analyser orien-

tations chosen, the generalized form of the inequality demands a value

less than or equal to 2. Quantum theory predicts a value of 2.828.

The

This is a little different from the situation where we measured the spin orientations of

entangled atoms, which were correlated up–down. It results from the simple fact that left and

right circular polarization is deﬁ ned for photons moving towards their respective detectors. If

photon A moves to the left in a state of left circular polarization, then photon B must move

towards the right in a state of right circular polarization. But the right-hand detector sees right

circular (clockwise) rotation as left circular (counter-clockwise) rotation. This translates into

the expectation that the photons will ultimately be detected either as both vertically or both

horizontally polarized.

This was developed in 1969 by John Clauser, Michael Horne, Abner Shimony, and Richard

Holt. It involves extension to a fourth arrangement of the analysers but does not depend on the

assumption of ‘perfect’ correlation between the entangled particles. It is therefore valid for the

situation in which the experimental instruments are ‘imperfect’.

The quantum theory prediction is actually 2 multiplied by the square-root of 2.

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physicists obtained the result 2.697 ± 0.015, a violation of Bell’s inequality

by 83 per cent of the maximum possible predicted by quantum theory.

The quantum theory prediction of 2.828 assumes that the experimen-

tal apparatus performs ‘perfectly’. But real experimental apparatus is

imperfect. Not all the photons could be detected. The analysers would

occasionally ‘leak’, with a few vertically polarized photons being reﬂ ected

and horizontally polarized photons transmitted. All these instrumental

deﬁ ciencies serve to reduce the measured extent of the correlation below

the quantum theory predictions. If we think of entanglement as a kind of

quantum interference between distant particles, then the practical limi-

tations of experimental instruments in the real world tend to reduce the

extent of quantum interference that can be observed. Physicists refer to

this as a reduced ‘visibility’ of the full extent of quantum entanglement.

By taking the instrumental deﬁ ciencies into account, the physicists

obtained a modiﬁ ed quantum theory prediction of 2.70 ± 0.05, in excel-

lent agreement with experiment. And well in excess of the limit set by

Bell’s inequality.

The physicists concluded:

. . . our results, in excellent agreement with quantum mechanical predic-

tions, are to a high statistical accuracy a strong evidence against the whole

class of realistic local theories; furthermore, no effect of the distance

between measurements on the correlations was observed.

These results appeared to conﬁ rm that the photons remain mysteriously

bound to one another, sharing a single wavefunction, until the moment of

measurement. At that moment the wavefunction collapses and the photons

are ‘localized’ in polarization states that are correlated to an extent that sim-

ply cannot be accounted for in any local hidden variable theory. Measuring

the polarization of photon A does affect the result that will be obtained for

photon B, and vice versa, even though the photons are so far apart that any

communication between them would have to travel faster than the speed of

light. Nature, it seems, is inherently non-local, and ‘spooky’.

Instead of ending the matter decisively, the Aspect experiments

were sufﬁ ciently perturbing and provocative to encourage even more

speculation and debate. Diehard proponents of local hidden variable

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theories could point to the fact that the polarization analysers in these

ﬁ rst Aspect experiments were set in position before the correlated pho-

tons were emitted by the calcium atoms. Could it be that the photons

were somehow inﬂ uenced in advance by the way the apparatus was set

up? Though seemingly improbable, this is not impossible. This is referred

to as the ‘locality loophole’.

But Aspect had intended to meet this challenge from the very begin-

ning, and with his colleagues Jean Dalibard and Gérard Roger he sought

to close this loophole just a year later. The physicists modiﬁ ed their origi-

nal experimental arrangement to include devices which could switch the

paths of the photons, directing each of them towards two differently ori-

entated analysers. This prevented the photons from ‘knowing’ in advance

along which path they would be travelling, and hence through which ana-

lyser they would eventually pass. The results were equivalent to changing

the relative orientations of the two analysers while the photons were in ﬂ ight.

The physicists obtained the result 2.404 ± 0.080, once again in clear

violation of the generalized form of Bell’s inequality. Taking account of

instrument deﬁ ciencies allowed them to obtain a modiﬁ ed quantum the-

ory prediction of 2.448, once again in excellent agreement with experi-

ment.

They submitted a paper on their results to Physical Review Letters in

September 1982. It was published in December.

Ever more sophisticated experiments performed since have not altered the

basic conclusions of the Aspect experiments. Much more efﬁ cient sources

of entangled photons were subsequently obtained from something called

type-I and type-II parametric down-conversion. This involves the con-

version of photons from an intense source, such as a laser, into pairs of

photons of longer wavelength by passing them through certain types of

crystalline materials. The polarization states of such photons are entan-

gled and, because they are generated in ﬁ xed spatial directions, no photon

pairs are ‘lost’ as a result of being emitted in the ‘wrong’ directions.

Using the calcium atom source, Aspect and his colleagues were able

to measure up to about 40 detection coincidences per second, each

It could still be argued that the switching between the photon paths was not completely

random. The locality loophole was closed decisively in experiments reported in December 1998

by Anton Zeilinger and his colleagues at the University of Innsbruck.

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corresponding to detection of a correlated photon pair. Using type-II

parametric down-conversion, coincidence rates as high as 360,800 per

second have been recorded. In experiments using this method reported

in 1998, a result for the generalized form of Bell’s inequality of 2.6979

± 0.0034 was obtained.

In August 1998 a research group from the University of Geneva

reported the results of experiments demonstrating a clear violation of the

generalized form of Bell’s inequality using entangled photons detected at

observer stations located in Bellevue and Bernex, two small Swiss villages

outside Geneva almost 11 kilometres apart.

From these experiments it is

possible to estimate that any ‘spooky’ action at a distance would need

to propagate from one detector to another with a speed at least 20,000

times that of light. In more recent experiments, entangled photons have

been measured at La Palma and Tenerife in the Canary Islands, at separa-

tion distances of 144 kilometres.

A further loophole, called the ‘efﬁ ciency loophole’, was closed in 2001.

In all the experiments described above the numbers of photon pairs

detected were considerably smaller than the numbers of pairs generated.

Why does this represent a loophole? Because if only a very small pro-

portion of the pairs that are generated are ultimately detected, then we

are required to assume that the detected pairs represent a true statistical

sample (called a ‘fair’ sample) of the properties and behaviour of the total

number of pairs of particles.

With more than a little ingenuity, it is possible to devise a local hidden

variable theory which, because of data rejection, predicts the same meas-

urement outcomes as quantum theory. Although such theories demand

what seems like some kind of grand conspiracy on the part of nature,

physicists were determined to close the efﬁ ciency loophole as well.

In February 2001, physicists from the National Institute of Standards

and Technology in Boulder, Colorado, and the Department of Physics at

the University of Michigan published the results of experiments they had

In fact, these photons were entangled in energy and time, mirroring the position–momen-

tum entanglement originally envisaged by Einstein, Podolsky, and Rosen.

In May 2009, reports appeared conﬁ rming that entangled photons had been bounced off

an orbiting satellite back to a receiver station on earth.

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conducted on entangled states created from positively charged beryllium

ions. When they tested the generalized form of Bell’s inequality, they

obtained the result 2.25 ± 0.03.

In these experiments it was not necessary to assume the fair sampling

hypothesis: all the entangled ion pairs created were detected and contrib-

uted to the measured results. To salvage local hidden variable theories

from this experimental evidence we would need to invoke a very grand

conspiracy indeed, one that somehow exploits both locality and efﬁ -

ciency loopholes at the same time, but not independently.

This brings to mind another of Einstein’s famous quotations: ‘The Lord

is subtle, but he is not malicious.’

In case there should be any remaining doubts about the validity of

Bell’s theorem and Bell’s inequality, in 2000 Anton Zeilinger and his

team at the University of Innsbruck created entangled triplets of photons.

These three-photon entangled states are known as Greenberger–Horne–

Zeilinger (GHZ) states, after physicists Daniel Greenberger, Michael

Horne, and Zeilinger.

The Innsbruck physicists made measurements of various combinations

of linear and circular polarization states of the photons. The GHZ states have

properties such that the polarization combinations predicted by local hid-

den variable theories are the exact opposite of the combinations predicted

by quantum theory. The experimental results conﬁ rmed the predictions of

quantum theory, once again ruling out all classes of locally real theories.

It seems therefore that we can establish the ‘reality’ of the state of one

quantum particle by choosing what kind of measurement to perform

on another, no matter how far apart these particles are at the time of

measurement. In 1935, Einstein, Podolsky, and Rosen were convinced

that invoking such ‘spooky’ action at a distance is unnecessary and that

quantum theory is incomplete, though they were not explicit about the

way in which the theory might be ‘completed’.

These experimental tests demonstrate that the very basis of the Ein-

stein, Podolsky, Rosen argument is unfounded. Although the precise

The phrase ‘Rafﬁ niert ist der Herr Gott. Aber Boshaft ist Er Nicht’ is carved in stone above

the ﬁ replace in a room in Fine Hall, Princeton University, in memory of Einstein.

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nature of the ‘spookiness’ remains a subject for debate, the simple fact

is that any theory which attempts to describe physical reality as local is

doomed to fail.

Reality at the quantum level is determinedly non-local.

The reality advocated by the proponents of hidden variable theories

does not have to be a local reality, as was demonstrated by Bohm in 1952.

It is nevertheless clear that these experiments leave the realist with a lot

of explaining to do. It seems we have no alternative but to change radi-

cally the way we think about reality and abandon our natural, but naïve,

presumptions. Aspect agreed:

But of course we already know that, since we knew quantum mechanics

looks like a good theory, and that quantum mechanics is not compatible

with the naïve image of reality. But here we have shown that in this kind

of very unusual situation quantum mechanics works very well, and so this

must convince us that truly we must change the old picture of the world.

But these experiments did not spell the end of the story. Commenting on

the Aspect experiments in 1985, Bell observed:

It is a very important experiment, and perhaps it marks the point where

one should stop and think for a time, but I certainly hope it is not the end. I

think that the probing of what quantum mechanics means must continue,

and in fact it will continue, whether we agree or not that it is worth while,

because many people are sufﬁ ciently fascinated and perturbed by this that

it will go on.

Bell was to be proved right. Now fully awake to the evidence threaten-

ing to undermine completely our attempts to understand reality at the

quantum level, more and more physicists turned to questions concern-

ing fundamental quantum theory. The theory would be tested in ways

that could not have been dreamt of during the great debate between

Bohr and Einstein, the debate which had established the supremacy of

the Copenhagen orthodoxy over all other rivals.

CERN physicists reported the discovery of the W and Z bosons in 1983 and pushed hard to

ﬁ nd the top quark. However, there did not appear to be much doubt that the few remain-

ing matter particles required to complete the three generations of the Standard Model and

the particles carrying forces between them would be found. It was only a matter of time.

But the noise from the community of physicists concerned with the foundations of

quantum theory was growing. This was noise about the very meaning of the theory on

which the Standard Model was constructed. Aspect and his colleagues had shown that

quantum reality is non-local, but what did this mean? Was it possible to probe more

deeply into the essence of quantum theory’s interpretation, perhaps to penetrate to the

very meaning of complementarity itself ?

In his classic Lectures on Physics, ﬁ rst published in 1965, Richard Feynman had

introduced a hypothetical variant of the famous two-slit interference experiment, in this

case using electrons instead of light. By introducing a light source behind the two slits

he proposed to observe through which slit a particular electron had passed on its way to

a detector. This is directly analogous to one of the early gedankenexperiments that

Einstein had used in his great debate with Bohr.

In Feynman’s version, a ﬂ ash of light scattered by the electron as it emerges from one

or other of the two slits reveals through which slit it has passed. Feynman goes on to

conclude that the very act of trying to gain this kind of ‘which-way’ information must

The Quantum Eraser

Baltimore, January 1999

See Chapter 13.

328

the quantum eraser

329

prevent us from observing interference effects. And, as in Bohr’s initial defence of quan-

tum theory in the face of Einstein’s early challenges, he cites the ‘clumsiness’ of the meas-

uring instrument combined with the uncertainty principle as the mechanism by which

we are prevented from observing simultaneous particle-like (which-way) and wave-like

(interference) behaviour. Feynman wrote:

If an apparatus is capable of determining which [slit] the electron goes through, it can-

not be so delicate that it does not disturb the [interference] pattern in an essential way.

No one has ever found (or even thought of ) a way around the uncertainty principle. So

we must assume that it describes a basic characteristic of nature . . . if a way to ‘beat’ the

uncertainty principle were ever discovered, quantum mechanics would give inconsist-

ent results and would have to be discarded as a valid theory of nature.

But, although Bohr had initially resorted to a defence based on the clumsiness of the

measurement, he was eventually forced to abandon this approach in the face of EPR’s

‘bolt from the blue’. He had to do this for the simple reason that such a defence requires

an almost classical realist conception of the initial measurement interaction, a conception

entirely consistent with EPR’s ‘reasonable’ deﬁ nition.

Bohr had no option but to deny the validity of this deﬁ nition and he therefore shifted

his defence to a much more subtle (and rather vague) argument to the effect that the com-

plementary wave–particle nature of quantum particles essentially precludes simultaneous

observation of wave-like and particle-like behaviour. This incompatibility, he claimed,

derives from the limits placed on our ability to acquire deeper knowledge of the quantum

world using classical-scale measuring instruments.

From Bohr’s shifting position we can infer that complementarity prevents us from

watching the electrons in the way that Feynman proposed, not clumsiness of the kind that

he associated with the uncertainty principle. It suggests that if we could ever ﬁ nd a way

of ‘beating’ the uncertainty principle as Feynman had speculated, then the results of any

such experiments would still remain consistent with quantum theory’s predictions.

The essential duality of wave and particle behaviour—complementarity—would

ensure this. This duality is what Feynman described as the central mystery at the heart of

quantum theory.

The prospect of ‘beating’ the uncertainty principle (strictly speaking, ‘beat-

ing’ the clumsiness constraint) in the way Feynman described seems very

slight, if not negligible. At the level of individual quantum interactions it

would appear that we will always be defeated by the essential parity in