Actually, one can state a principle that describes the conditions under which a particle interferes with itself. Admittedly, to state a principle is not an entirely satisfactory solution, and definitely not a valid explanation, but at least it allows a synthetic presentation ofthe experiments, and thus constitutes the least 'committed' interpretation, the safest step. This principle, called the indistinguishability principle12, can be expressed like this:
Interference appears when a particle can take several paths in order to arrive at the same detector, and the paths are indistinguishable after detection.
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3.3.3 The experiment performed in Vienna in the experimental research into the transition between the dassical world and the quantum world, Zeiinger and Arndt have taken an important step. They have shown that some large molecules produce interference effects (Fig. 3.4). The molecules in question are collections of sixty carbon atoms and their symbol is C60. In these molecules, discovered in 1985, the atoms are arranged according to a particular symmetry, that of a football - indeed a traditional football, formed with hexagons and pentagons stitched together, having exactly sixty vertices, that is sixty points where three lines meet. Sixty carbon atoms arrange themselves according to the same structure in order to form C50 molecules.
Such beautiful molecules deserved a name other than that of their chemical composition. At the moment of baptism, the scientists were reminded of the work of Richard Buckminster Fuller, an American architect who had designed and built numerous glass domes whose supporting structure has the symmetry that we are talking about28. It is therefore in memory of Buckminster Fuller that the C60 molecules are not called footballenes, but fullerenes, and sometimes buckyballs.
As far as their size is concerned, fullerenes are dearly closer to atoms than cars or footballs and in this sense we are not surprised to see them display quantum behaviour. Nevertheless, the criterion for the observation of quantum behaviour is not the small size ofthe physical object, but the possibility of creating a situation ofindistinguishability. Viewed from this angle, we better understand that the interference of large molecules constitutes an important result In effect, the bigger the molecule, the more chance there is that some or other of its constituentparts will interact with the environment, and if on one ofthe possible paths a non-controlled interaction takes place, the interference is quicldy lost. Now, a molecule with sixty carbon atoms means a system of sixty nuclei - which for carbon means 360 protons and as many neutrons - and 360 electrons. In total, 1080 'elementary' quantum particles (I am disregarding the fact that protons and neutrons are in turn composed of three quarks each, because that final composition has some characteristics that merit a separate discussion).
The experimental observation of fullerene interference29 should not be considered as just a further verification of the quantum behaviour of matter, but rather as a real discoverj3° - we are far from demonstrating the interference of cars, but these are already large objects: it was not evident a priori that such a large collection of quantum particles would itself exhibit collective quantum behaviour3t. The way is open to investigating much bigger molecules, such as insulin and other 'biological' molecules. The rush for size has just begun.
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4.2.1 The interferometry of atoms The apparatus produced at Constance is a Mach-Zehnder interferometer, like that of Rauch. The particles used are atoms, rubidium atoms, to be precise. Atoms are quantum objects consisting of a nucleus, heavy and carrying a positive electric charge, and electrons, much lighter, negatively charged particles. We know this thanks to the well-known symbol in which the atom is represented like a small solar system with a few planet-electrons orbiting around a sun-nucleus. Again, as with the arrows we used to represent spin: the electrons and the nucleus themselves being quantum particles, this symbol is only a pale imitation ofwhat an atom really is; but it is a useflil picture to keep in mind.
From this structure of the atom some consequences ensue that are significant for the goal that interests us. On the one hand, the trajectory of the atom is essentially determined by the motion of the nucleus (if we can continue with the planetary analogy, we see clearly that the orbit of the enormous Jupiter around the Sun is only slightly affected by the presence of the satellites that gravitate around the planet). Consequently, in the experiment that we want to design, the beam splitters can be devised to act on the nucleus; and the electrons will follow the motion. On the other hand, it is relatively easy to modify the physical state of an electron, particularly that of 'external' eiwons (those that are furthest from the nucleus). Therein lies the solution: it is by modifying the state of an electron on the path, or to be precise, its energy, that we will be able to introduce distinguishability without influencing the motion of the nucleus.
Figure 4.2 illustrates the results of the experiment. The part on the left of the figure represents the initial apparatus, with the number of particles detected behind each output. We observe an interference fringe characterized by the fact that the peaks of intensity are complementary on either side, that is, a peak to the right corresponds to a trough to the left anuiffvice versa. The part on the right ofthe figure represents the modified apparatus - on one of the two paths, the energy of an external electron has been modified. Now, by measuring the energy of the electron we are able to learn which path it took. It is not necessary to add an instrument that effectively measures this energy to the apparatus - the important thing is that we have introduced distinguishability. The informalion encoded in the atom is sufficient for us to be able in principle to discern the two paths. As we see in the figure, the interference disappears. Thus, the mechanism proposed by Heisenberg does not explain the disappearance of interference completely. We must be content (for the moment at least) with the indistinguishability principle.
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The word complementarity was forged by Niels Bohr. The concept that it conveys is closely linked with the iridistinguishabiity principle that has been discussed in this book. In order to clarify the idea, let's go back to the apparatus of Fig. 1.3. Our description was this: if we do not know by which path the particles travel in the interferometer (two indistinguishable paths), all of the particles take a certain output (interference); if we detect the particles in the interferometer (distinguishability), the output will be random. Bohr would say instead that the path and the output are two pieces of complementary information - we cannot arrange it so that all of the particles4take the same path and the same output. At the risk of missing something very profound, we will remember that Bohr's complementarity principle says the same thing as the indistinguishability principle, from a different angle.
The future will tell us if one of these concepts will disappear to the benefit of the benefit of the other or they are destined to survive together, or if both will be erased by new, more precise notions.
The word uncertainty, as far as it goes, is unfortunate because in physics we already use it to describe the imprecision of measurements. If a length is measured with a ruler graduated in millimetres, the value that one reads is affected by an uncertainty of (give or take) a millimetre. In other words, with that ruler, one cannot discriminate two lengths that differ by less than a millimetre. The Heisenberg mechanism is an attempt to restore a principle of uncertainty in measurement to quantum physics, an attempt, in other words, to base the wealth of phenomena that we encounter in quantum physics on our technical limitations (essential or accidental). From experiments like that of Constance we learn that the principle of quantum physics is not a principle of uncertainty in that sense, rather a principle of indetermination - as precise as our measurements are, we will not be able to determine two pieces of information that are complementary in the Bohr sense. Quite the opposite, we have always worked under the assumption of perfect detectors - imperfect detectors could introduce so many counting errors that the quantum interference would be masked. In summary, the concept of uncertainty is ambiguous in physics; and, if we want to retain the traditional sense of 'limitation in the precision of measurement', then this concept is not adequate to describe quantum behaviour.
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6.3.3 Sending a message?
I have already subjected the students to a considerable tour de force we have reviewed the indistinguishability principle, introduced the notion of correlation and revealed interference in correlations.
Then, we saw that this prediction of quantum physics seems to throw back into question a well-known and well-established fact in physics, the fact that the speed of light is the limiting speed for communication. I cannot let it rest there, even if my audience is tired. I cannot depart leaving those who are listening to me with the impression that quantum physics could one day allow communication faster the light.
Whatever the explanation might be, the quantum particles introduced correlations at a distance. However, this phenomenon cannot be employed for communication, it cannot be used to send a message, whether faster or slower than light. The reason for this is: whether we are in a situation of perfect correlation, perfect anti-correlation, or whatever situation in between, concerning the correlation of two particles, nothing changes in the results that we obsen'e for each particle individually. Specifically, for the Franson interferometer that we have considered, we have said that for each side, half the particles are detected at one detector, the other half at the other. Alice, who observes only the particles that have gone to the left, sees random detections; on the right, Bob may modify his interferometer at will and nothing will change for Alice. It is only when Alice and Bob speak to each other (by telephone, for example) and they compare their results, that they notice the existence of correlations between the particles. An ordinary medium of communication (telephone, internet, meeting at a bistro) is therefore absolutely necessary in order to be aware of the quantum correlations - these correlations with only themselves do not allow communication.
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Entanglement will free itself from the maze of interpretations to get closer to the laboratory mostly thanks to the work of john Bell. But before talking about Bell, this brief history of the EPR argument brings us to our first meeting with David Bohm. Bobm's name is known by most physicists through an ingenious one-particle interference phenomenon that he predicted with his student Yakir Aharonov, and that naturally bears the name Aharonov-Bohm. Most physicists, on the other hand, have not heard of the interpretation of quantum mechanics proposed by Bohm, because it
Brief history of quantum correlations
does not conform to the orthodox doctrine, and does not therefore have the right to be mentioned in institutional courses. We will talk about it in Chapter 9, because Bohm's 'mechanics of pilot waves' is the most elaborate alternative interpretation, and it is highly instructive for clearing up its problematic aspects. Here, we are concerned with Bohm's contribution to the EPR argument. This contribution is rather technical in nature - Bohm rewrote the EPR argument in terms of two particle spins, whereas Einstein, Podoiski and Rosen had used dynamic variables of position and momentum. It is an important step, because in the mathematical formalism of quantum physics the spin is the easiest system to deal with. This simplification opens the way for the work of Bell.
7.2.4 john Bell, the person
Serious and rather reserved, john Bell worked actively in a mainstream research domain (he was a particle physics theorist at CERN in Geneva), but he obtained his principal result by working on the 'philosophical' subject of quantum correlations. As we said above, the first step that he took consisted of removing the restraint of von Neumann's theorem, then by constructing an explicit localvariable model for single quantum particles. As a next step, he set out to find the local-variable model for two particles... and he came up with his own impossibility theorem. Is this theorem bound to fail as von Neumann's? This is highly improbable (in my view, utterly impossible): in his time, von Neumann's theorem was accepted almost without criticism; while Bell's theorem has already undergone forty years of intensive studies and has resisted any attack - moreover, as we saw in this very text, the formulation of the theorem is not difficult.
As for philosophical preferences, John Bell would have liked to find a local-variable model reproducing the whole of quantum physics: a priori, he favoured 'local realism'. But he honestly accepted the conclusion of his theorem and of the experiments. His premature death achieved his ascension to the status of cult phys
apparent in the recollections of those who met him. We know now that for two particles the indistinguishability principle, that is, quantum theory, predicts correlations whose characteristics are the following:
1. quantum correlations do not disappear by increasing the distance between the particles, and therefore their origin cannot be the reception of a common signal;
2. quantum correlations violate Bell's inequality, and therefore nor can their origin be a common decision taken at the source.
In other words, if quantum theory is correct, neither of the two usual mechanisms that explain correlations can be invoked! But is quantum theory correct? Will correlations be maintained over a great distance? Are they really going to violate Bell's inequality?
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8.2.1 The Aspect experiment carried to perfection
So we have jumped sixteen years and about a thousand kilometres to find ourselves in Innsbruck in 1998. In the city of the Golden Roof, we meet up again with the group of Anton Zeilinger, the whole of which is about to move to Vienna - where, the reader will recall, they will notably demonstrate interference for the large C60 molecules.
The experiment65 performed by Zeilinger and his collaborators Gregor Weihs, Thomas Jennewein, Christoph Simon and Harold Weinfurter is the definitive version of the Aspect experiment of 1982. The photons emitted by the source - a source, moreover, of a different type and more efficient than that used in Orsay - travel along optical fibres installed in the campus ofthe University of Innsbruck, to the analysers, which are found at a distance of 400 metres apart (in Aspect's experiment, the whole apparatus was confined to a laboratory, therefore the distance between the analysers was a few metres). At such distances and with judicious electronics, it is possible to implement rapid and random changes that assure that each particle cannot be informed about the configuration that its companion will encounter. The correlations persist in violating Bell's inequality - the locality loophole is permanently closed!
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8.2.2 Correlations at 10 km
The Austrians' article appears in the December 7th 1998 edition of the journal Physics! Review Letters. A month and a half prior, on October 26th, another quantum-correlation experiment had appeared in the same journal66 It was by Wolfgang Tittel, Jflrgen Brendel, Hugo Zbinden and Nicolas Gisin. The Geneva group is doing it again: those who in 1996 had demonstrated the feasibility of quantum cryptography over long distances (20 km) demonstrate two years later that quantum correlations are equally stable and violate Bell's inequality over distances of kilometres. While Zeiinger's group ran their own optical fibres through the university campus at Innsbruck, the Geneva group adopted another strategy - asking the Swiss telecommunications operator to be allowed to use, for several hours, the fibres already installed between the telecom stations. On the appointed day, the physicists distribute themselves between the stations at Cornavin (in the heart of Geneva), Bernex and Bellevue (two outer suburban areas). At Cornavin they put the source of the pairs of photons, and at Bemex and Bellevue the two analysers - it is a Franson interferometer. For the non-locality, what is important is the distance between the two analysis stations, Bellevue and Bernex - 10.9 km as the crow flies. The correlations violate Bell's inequality just as in the Innsbruck experiment, without any possible ambiguity.
The Geneva physicists have not added rapid switching to their experiment. Unlike that of Innsbruck, their experiment is not designed to dose the locality loophole, but to demonstrate the violation of Bell's inequality over large distances. This experiment is probably the one that has caused the most excitement. When, in the year 2000, the American Physical Society wanted to record, in ten posters, the stages marking twentieth century physics, quantum correlations gained a place in these posters thanks to the Geneva experiment.
8.3 A curious argument
We have before us some experiments, reproduced by several independent research groups, which confirm the theoretical prediction: all of the criteria appear to be assembled so that we are able to conclude that quantum interference of distant particles is confirmed experimentally. It is in fact the conclusion drawn by the majority of physicists.. . and what objection could we still raise?
One objection has nevertheless been put forward, based on the imperfection of the detectors. Current photon counters have a fairly limited efficiency - they detect at best (let's be optimistic to simplify things) half of the photons. In order to understand the argument, which we call the detection loophole, I will begin with an example inspired by everyday life.
Let's suppose that police radars only measure the speed of half the cars. This could be due simply to the slowness of the electronics within the radar, which, after having measured the speed of one car, has a certain amount of dead time before being able to measure another. In this case, the statistics for offences are significant, all the same. But there could be another reason for the fact that the radar does not see half the vehicles - the police could have badly installed their radar, such that only vehicles that are tall enough send back a signal, so sports cars, always lower than average, are not seen. In this case, all of the sports cars can exceed the speed limit without being seen - the statistics for offences will be distorted, because we only measure the speed of the slower vehicles.
The detection loophole is based on the same idea. Current detectors detect less than half the photons that are sent This is a fact, but as in the example of the cars, it is legitimate to ask ourselves whether or not the photons detected constitute a representative sample of all of the photons. It could be that it is not the case, that only certain photons, suitably 'programmed', activate our detectors. These photons, the detection loophole argument continues, could be, furthermore, programmed to violate Bell's inequality, but if we detected all of the photons, we might see that Bell's inequality is not violated.
In order to grasp the weirdness of this loophole, it is necessary to remember the sessions in the school laboratory or even at university. Atone time or another, every one ofus obtains an experimental result that disagrees with the theoretical prediction. We have looked for the error, and if we failecito find it, we have written in our report a loose statement like, 'the instruments are too imprecise'. We have cited the uncertainty of the measurements to explain the disagreement between the experiment and theoretical calculation. The detection loophole is perhaps the first example in the history of physics where the imprecision of the measurements is cited to explain the perfect agreement between theory and experiment!
Just as for john Bell, it is difficult for me to believe that quantum theory gives precise predictions only because of the poor efficiency of the detectors, and that it is destined for a miserable failure the day our detectors are perfect69. It is equally necessary to know that techniques exist (ion traps) in which the detectors are practically perfect, and the quantum correlations do not disappear. These experiments dose the detection loophole, but unfortunately the particles (ions, that is, atoms that have lost or gained one or more electrons) are very close to each other, and therefore the locality loophole stays open70. At the time of writing this book, what is lacking in order to convince the last sceptics is an experiment in which both loopholes are closed. A few proposals exist, and it is possible that, by the time the reader reads these lines, this experiment will have been performed. The two loopholes of locality and detection will have disappeared from the scene then, last witnesses to the great discussions about two-particle correlations begun by the sceptic Albert Einstein and the orthodox Niels Bohr in 1935.
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9.3 Other foundations
Second on my list was the approach of those who attempt to derive the indistinguishability criterion from other principles that are judged more fundamental, but that are not of a physical nature. One example of this approach comes from the school called 'quantum logic'. The reader glimpsed the subject of quantum logic in Chapter 2, when we saw that the properties of a quantum system, unlike the properties of the sets of cars, are not connected to each other according to the rules of set theory. Let's take for example the work of the school in Geneva, a quantum logic approach initiated by Josef Jauch and continued by Constantin Piron.
Piron showed that one can derive the indistinguishability criterion from five axioms. The first three axioms are a formalization of the two following postulates. (I) If a physical system acquires a new property, it inevitably loses another that it possessed beforehand. An ordinary example: if i acquire the property 'being seated', I lose the property 'being standing' that I possessed beforehand. For a quantum example, we have already seen that the property 'exhibiting interference' can be lost to acquire the property 'being in a given path'. (II & III) Every property is the opposite of another. This simply means that if 'being seated' is a property, 'not being seated' is also a property. Each of us accepts such postulates much more easily than the indistinguishability criterion - it would be nice if we could derive the criterion only from postulates as intuitive as these. Unfortunately, things take a turn for the worse with axioms IV and V, which are strictly mathematical requirements81 for which, despite significant efforts, neither Piron nor any member of his school knew how to find a simple interpretation. At this stage, then, we are faced with a choice: either we accept all five of Piron's axioms, in which case the indistinguishability principle is no longer a first
The mechanistic interpretation of pilot waves
principle but a consequence; or we admire the truly remarkable effort of the Geneva school, but we retain the indistinguishability criterion as a first principle - as I did in this book.
The school of quantum logic is only one example of a much broader class of interpretations that rapidly sink into deep epistemological discourse. All ofthese interpretations are not incompatible with the orthodox approach, and concede that if we restrict ourselves to the framework of physics we cannot say much. The program of looking resolutely outside physics to solve the conundrum of quantum phenomena is, in principle, very sound, but in my opinion has never bçen carried through satisfactorily - the surprising or 'incomprehensible' side of the indistinguishability principle does not disappear, is it simply pushed a degree further away, whether in the epistemological hypotheses or in the axioms.
9.4 The mechanistic interpretation of pilot waves
Among the unorthodox interpretations, I will focus on the most complete and successful: the interpretation of the 'pilot wave' initiated by Louis De Broghe and re-elaborated by David Bohm.
We saw in the first chapters of this book that quantum particles sometimes behave like corpuscles (each particle only stimulating one detector), sometimes like waves (interference). De Broglie's ingenious idea consists of exploring the possibility that the corpuscle and the wave are both a physical reality. More precisely, quantum particles could be corpuscles, very localized, which move around guided by a wave. It is the wave that explores all the possible paths, and it is the modification of the properties of the wave that influences the 'choice' made by the corpuscle at each beam splitter. It is just like a cork floating in a river, downstream of an island: certainly, the cork passed on only one side of the island; nevertheless, its trajectory after the island is also influenced by the water that has taken the other path. This example illustrates the explanation of Young's double-slit experiment by a pilot wave.
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