Quantum: A Guide For The Perplexed Read online

  Well, surprise, surprise, atoms just don’t behave like this. Instead, we see an interference pattern of light and dark fringes just as we did with light. The brightest part of the screen, believe it or not, is in the centre where we would not expect many atoms to be able to reach!

  We could have a stab at explaining how the pattern might be forming in the following way. Despite an atom being a tiny localized particle (after all, each atom hits the screen at a single point) it seems that the stream of atoms have somehow conspired to behave in a way similar to a wave. They wash up against the first screen, and those that manage to get through the slits ‘interfere’ with each other’s paths, via atomic forces, in a way that mimics exactly the pattern that is produced when the peaks and troughs of two waves come together. Maybe the atoms bump into each other in a particular coordinated way such as to guide each other onto the screen. Atoms, we would reason, are most certainly not like spread-out waves (such as light, or water waves, or sound waves); but then maybe we should not expect them to behave exactly like grains of sand either.

  So here is where this comforting prop is knocked away. To begin with, we see that the pattern of fringes on the back screen is connected somehow to the way two waves interfere. Just as with normal waves, its details depend on the width of the slits, the distance between them and how far away the back screen is.

  This in itself is not proof that the atoms are behaving in a wave-like fashion. However, not only has the double-slit experiment been performed with atoms, but it has also been done by firing individual atoms one at a time! That is, only when we see the flash of light on the back screen signalling the arrival of the atom do we fire the next one, and so on. There is only ever one atom travelling through our apparatus at any one time. Each atom that manages to get through the slits leaves a tiny localized spot of light somewhere on the screen. In practice, most of the atoms are stopped by the first screen rather than pass through its narrow slits, and so we are only interested in those that do get through.

  What we see is quite incredible. The spots gradually build up on the screen and light bands of an interference pattern slowly emerge where there is a high density of spots. In between these bands are dark regions where no or very few atoms land.

  It seems we can no longer argue that atoms emerging from one slit bump into atoms emerging from the other. The interference pattern cannot be the result of a collective behaviour. So what is going on? What makes this result particularly spectacular is that there are places on the back screen where atoms were arriving when only one of the slits was open. By opening the second slit we are providing another route for the atoms to go through, so you would expect to increase the chances of atoms reaching these places. Instead, with both slits open no atoms ever arrive at all. Somehow, if the atom really does only go through one slit then it must already know whether or not the other one is open, and act accordingly!

  To recap, each atom fired from the gun leaves it as a tiny ‘localized’ particle and arrives at the second screen also as a particle, as is evident from the tiny flash of light when it arrives. But in between, as it encounters the two slits, there is something mysterious going on, akin to the behaviour of a spread-out wave that gets split into two components, each emerging from a slit and interfering with the other on the other side. How else can we rationalize the way the atom has to be aware of both slits at the same time?

  When I used to perform conjuring tricks at my kids’ birthday parties – and they are now too old for such embarrassments – there were always a few smart alecs who would announce that they know how the tricks are performed. They would insist on looking up my sleeves and behind the screen and under the table to catch me out. Such normally annoying behaviour is positively encouraged in scientific experiments. So let us try to look up nature’s sleeve by lying in wait behind one of the two slits to see what the atoms actually do. This can be achieved by setting up an atom detector behind one of the slits so that it can catch any atom passing through that slit. We find that an atom is registered every now and then. We never catch part of an atom. At least that would prove that the ‘rest of the atom’ had gone through the other slit. Sometimes of course an atom will go through the other slit, as witnessed by a spot of light appearing on the screen. Naturally, the accumulation of many spots on the screen does not now have the feature of an interference pattern since atoms are only getting through one of the slits, just as they did in the first part of the experiment when only one slit was open. Now, instead of closing the second slit we have caught all the atoms that go through it in our detector.

  You should now be beginning to doubt the truth of what I am saying. It is one thing for atoms to magically transform themselves from tiny particles into spread-out waves whenever they encounter two possible routes through the first screen. Maybe there is an as yet unexplained physical process that takes place. But it is another matter entirely to suggest that the atom can somehow be aware of the detector hiding behind one of the slits ready to catch it in the act of its spread-out state. It is as though it knows beforehand that we are lying in wait ready to ambush it and cunningly maintains its particle persona!

  With both slits open, the atoms are fired through one at a time. Only after we see a spot appearing on the screen do we send the next one through. Each atom seems to land at a random spot on the screen and, to begin with, there is no obvious pattern. Gradually, as the number of spots builds up, an interference pattern of bands emerges. What is going on? How can the atoms conspire to form this pattern that is a result of wave-like behaviour? It seems that each atom is more likely to land in certain regions than in others. Clearly, some wave-like process is involved in the propagation of a single atom. But the interference pattern only arises when a wave goes through both slits. How does a tiny atom, which leaves the gun as a localized particle and hits the screen at a definite point, go through both slits at once?

  But even here we have not really added anything new to the original set-up. Presumably the detector somehow has the ability to convert a spread-out ‘wave’ atom back to a localized particle just as the back screen does whenever an atom reaches it.

  The detector can be set up in a less intrusive way so as to be able to simply register a ‘signal’ as an atom passes through that slit on its way to the screen. If an atom is not detected but a hit is recorded on the back screen then it must have gone through the other slit.2 Of course, I am over-simplifying here; we will see later that the detector cannot register a signal without being very intrusive.

  So, you might think that we have proof at last that the atoms do indeed go through either one slit or the other, as we have every right to expect, and not simultaneously through both like a spread-out wave. But before you get too smug take a look at the screen. Once enough atoms have registered a signal in the detector as they pass through the slit that is under surveillance and you are thus convinced that half went through one slit and half through the other, you will find that the interference pattern has disappeared! In its place are just two bright patches due to the collection of a pile of atoms behind each slit. The atoms are now behaving like particles, just like the grains of sand. It is as though each atom behaves like a wave when it is confronted by the slits, unless we are spying on it in which case it innocently remains as a tiny particle. Crazy, isn’t it?

  With a detector in place that records which slit each atom passes through, the interference pattern disappears. It is as though the atoms do not wish to be caught in the act of going both ways at once, and only travel through one slit or the other. Two bands form on the screen adjacent to the slits as a result of particle-like behaviour, similar to what happens with the sand.

  With the detector turned off we now have no knowledge of the route taken by each atom. Now that their secret is safe, the atoms revert to their mysterious wave-like behaviour and the interference pattern comes back!

  Of course you might be the kind of person who is very hard to please and even now think this not too surprising. Maybe the mere presence of a large detector in the path of the atoms might somehow upset its strange and delicate behaviour. But it seems this is not the problem, for switching the detector off – and therefore having no knowledge of which slit the atom has passed through – allows the interference pattern to build up again. It is only when the atom is being watched that it remains as a particle throughout. Clearly the act of observing the atom is crucial.

  As if all this is not enough, there is one final twist to the trick. Even if we admit that atoms are crafty little things, maybe they are not crafty enough! How about if we let the atoms get through the slits, one at a time of course, and allowing them to do whatever it is that atoms do in order to give the interference pattern on the back screen. But this time we make sure we catch them in the act. In what are known as ‘delayed choice’ experiments it is possible to have a detector in place and only switch it on after the atom has gone through the slits. We can be sure of this by controlling the energy of the fired atoms and thus knowing how long it would take for any atom to reach the first screen.

  This sort of experiment has indeed been carried out using photons rather than atoms, but the argument remains the same. With modern high-speed electronics the detector can be close enough to one of the slits to be able to tell whether the atom had come through it, and yet it need only be switched on after the atom, behaving like a spread-out wave, has emerged from both the slits, but before it reaches the detector. Surely now it is too late for the atom to suddenly decide to behave like a localized particle that has only passed through one of the slits. Apparently not. In such experiments, the interference pattern is nevertheless found to disappear.

  What is going on? This seems like magic, and I suspect you probably do not believe me. Well, physicists have spent many years trying to come up with a logical explanation for what is seen. Here is where I must be careful to qualify what I mean by a ‘logical explanation’. I am using it in the loose, everyday sense, meaning an explanation that sits comfortably within the bounds of what we might regard as rational, reasonable and sensible, and not in contradiction or conflict with the behaviour of the other phenomena of which we have more direct experience.

  In fact, quantum mechanics does provide us with a perfectly logical explanation of the two-slit trick. But it is an explanation only of what we observe and not of what is going on when we are not looking. But since all we have to go on is what we can see and measure, maybe it makes no sense to ask for more. How can we assess the legitimacy or truth of an account of a phenomenon that we can never, even in principle, check? As soon as we try, we alter the outcome.

  Maybe I am asking too much of the word ‘logical’. After all, there are many instances in everyday life where we might regard the behaviour of something as illogical or irrational. All this means is that this behaviour was unexpected in some sense. Eventually, we should in principle be able to analyse the behaviour based on the notion of cause and effect; that this happens and therefore that happens as a consequence and so on. It does not matter how complex the chain of events are that lead to a certain behaviour, or even that we can fully understand each step. What matters is that, somehow, what is observed can be explained. There may be new processes at work, new forces or properties of nature that have not yet been understood or even discovered. All that matters is that we can use logic, however convoluted, to explain what might possibly be going on.

  Physicists have been forced to admit that, in the case of the double-slit trick, there is no rational way out. We can explain what we see but not why. However strange you may find the predictions of quantum mechanics, it must be emphasized that it is not the theory – mankind’s invention – that is strange, but rather Nature herself that insists on such a strange kind of reality on the microscopic scale.

  A few years ago I read that Robert Frost’s poem The Road Not Taken had been voted by Americans as their most popular poem of all time. Frost, long regarded as America’s best-loved 20th-century poet, spent most of his life in New England where he wrote mainly about the rural life in the surrounding countryside of New Hampshire. The somewhat melancholic The Road Not Taken is a beautiful example of this. It also happens to touch – quite unintentionally on the part of Frost – on the very essence of what the quantum world must be like:

  Two roads diverged in a yellow wood,

  And sorry I could not travel both

  And be one traveller, long I stood

  And looked down one as long as I could

  To where it bent in the undergrowth;

  Then took the other as just as fair,

  And having perhaps the better claim,

  Because it was grassy and wanted wear;

  Though as for that the passing there

  Had worn them really about the same,

  And both that morning equally lay

  In leaves no step had trodden black.

  Oh, I kept the first for another day!

  Yet knowing how way leads to way,

  I doubted if I should ever come back.

  I shall be telling this with a sigh

  Somewhere ages and ages hence:

  Two roads diverged in a wood, and I –

  I took the one less travelled by,

  And that has made all the difference.

  While we are often burdened with regrets about the choices we make in life, quantum mechanics tells of a very different reality at the subatomic level. Meeting it for the first time, the quantum world may seem unbelievable to us when judged according to the prejudiced views of our everyday experiences – what we call common sense. But the alien way that quantum objects behave is beyond any doubt. A single atom can travel down both roads in Frost’s yellow wood… no regrets for atoms; they can sample all possible experiences simultaneously. Indeed, they follow the advice of the great American baseball player, Yogi Berra, who said, ‘If you come to a fork in the road, take it.’

  The quantum skier. To highlight just how strange the behaviour of quantum particles really is, it would be as though a skier, faced with having to go round a tree blocking his path, decided instead to go both ways at once. Clearly, this would be regarded, in our everyday world of trees and skiers, as some kind of hoax. But it really does happen in the quantum world.

  What we have seen in this chapter is just one example of the way in which the quantum phenomenon known as ‘superposition’ manifests itself. I could have described any one of a number of equally baffling ‘tricks’ that rely on quantum superposition, along with several other fascinating features unique to the quantum domain. I hope this chapter has not put you off continuing on the exciting journey ahead.

  Buckyballs and the Dual-Slit Experiment

  Professor Markus Arndt & Professor Anton Zeilinger

  Department of Physics, University of Vienna

  We usually think of a physical body as a localized object while the notion of a wave is intimately linked to something extended and delocalized. Contrary to this common belief quantum physics claims that both, seemingly contradictory, notions can apply to one and the same object in one and the same experiment.

  We have recently implemented such an experiment with large carbon molecules called buckyballs. These molecules, known as C60 and C70, contain sixty or seventy carbon atoms each, arranged to form the smallest known replica of a soccer ball, with a diameter no bigger than one millionth of a millimetre. In spite of their small size these molecules are the most massive objects ever used to demonstrate the wave-like nature of matter to date.

  The experiment is set up as follows. The molecule source is a simple oven, filled with the carbon powder. The molecules can escape from a hole, like water vapour escaping from a hot kettle. They then fly through two collimating slits towards a laser detector with high resolution that can be shifted to record the spatial distribution of the molecular beam.

  On the way towards the detector the molecules may encounter three different possibilities – either no obstacle at all, or a very narrow slit or a very fine grating, which is a membrane with several slits.

  The molecular beam profile for the first, ‘empty’, case is a single narrow peak and is in complete agreement with our naïve expectation, assuming that each molecule can be regarded as a free-flying classical ball.

  However, the first weirdness occurs in the second case: If we place a single, very narrow slit – 70 nanometres (millionths of a millimetre) wide – in between the source and the detector we find a profile on the screen that differs from the empty case. We notice a strong broadening – instead of the narrowing, which we would have expected if the molecules were just little soccer balls. This is a consequence of diffraction, a property of waves.

  The situation becomes even stranger when we replace the narrow slit by a grating. This structure is now composed of several openings, slightly narrower (nominally 50 nanometres) than the first slit. The slits are regularly spaced (about 50 nanometres apart). If molecules were simple particles we would expect an increased signal everywhere on the screen. But – to the surprise of our common sense – we now find that there are positions where we hardly detect any molecules at all.

  Opening two or more pathways in the wall, instead of only one, reduces the number of detected molecules at certain places. This is very counterintuitive and can no longer be explained with the model of classical balls flying along well defined paths, but it is in perfect agreement with a model based on the wave-nature of single molecules. Here we give up on the concept of a ‘trajectory’ and allow the molecules to simultaneously explore an extended space, which is orders of magnitude larger than the molecule itself, resulting in quantum interference.