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- Herausgeber: Icon Books
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
'Gribbin has inspired generations with his popular science writing' Jim Al-Khalili A scintillating collection of short essays that really does cover 'life, the Universe, and everything'. From the mysteries of the subatomic world to the curious property of water that makes our planet inhabitable, master of popular science John Gribbin delves into the astonishing facts that underlie our existence. Some aspects of the quantum world really do seem impossible to 'common sense', but have been proved correct by experiments. Other features of the Universe appear obvious, such as the fact that atoms are mostly empty space. But this familiarity hides the truly amazing truths underpinning these observations. And some things merely seem improbable but are also hiding a Deep Truth, such as the fact that the Moon and Sun look the same size as viewed from Earth. This book will change forever the way you view the world.
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Praise for Six Impossible Things
‘[A]n accessible primer on all things quantum … rigorous and chatty.’
Sunday Times
‘Gribbin has inspired generations with his popular science writing, and this [is a] delightful summary of the main contenders for a true interpretation of quantum mechanics.… If you’ve never puzzled over what our most successful scientific theory means, or even if you have and want to know what the latest thinking is, this new book will bring you up to speed faster than a collapsing wave function.’
Jim Al-Khalili
‘Gribbin gives us a feast of precision and clarity, with a phenomenal amount of information … This could well be the best piece of writing this grand master of British popular science has ever produced.’
Brian Clegg, popularscience.co.uk
‘Elegant and accessible … Highly recommended for students of the sciences and fans of science fiction, as well as for anyone who is curious to understand the strange world of quantum physics.’
Forbes
Praise for Seven Pillars of Science
‘Light, to the point and hugely informative.… It packs in the science, tells an intriguing story and is beautifully packaged.’
Brian Clegg, popularscience.co.uk
‘[Gribbin] deftly joins the dots to reveal a bigger picture that is even more awe-inspiring than the sum of its parts.’
Physics World
Praise for Eight Improbable Possibilities
‘We loved this book … deeply thought provoking and a book that we want to share with as many people as possible.’
Irish Tech News
‘A fascinating journey into the world of scientific oddities and improbabilities.’
Lily Pagano, Reaction
‘Gribbin casts a wide net and displays his breadth of knowledge in packing a lot into each chapter … [it] may inspire readers to dig deeper.’
BBC Sky at Night Magazine
Impossible, Possible and Improbable
Science Stranger Than Fiction
John Gribbin
CONTENTS
ABOUT THE AUTHOR
John Gribbin’s numerous bestselling books include In Search of Schrödinger’s Cat, The Universe: A Biography, 13.8: The Quest to Find the True Age of the Universe and the Theory of Everything, and Out of the Shadow of a Giant: How Newton Stood on the Shoulders of Hooke and Halley. He is an Honorary Senior Research Fellow at the University of Sussex, and was described as ‘one of the finest and most prolific writers of popular science around’ by the Spectator.
ACKNOWLEDGEMENTS
I am grateful to the Alfred C. Munger Foundation for financial support while writing this book, and to the University of Sussex for providing a base and research facilities.
As with all my books, Mary Gribbin ensured that I did not stray too far into the thickets of incomprehensibility, and Improbability Eight owes a particular debt to her. The remaining infelicities are all mine.
PREFACE
Half the Answer
In The Hitchhiker’s Guide to the Galaxy, the answer to ‘Life, the Universe, and Everything’ is 42. The essays contained in the pages of this book do indeed cover life, the Universe and (more or less) everything, but as there are only 21 of them, the best I can claim is that they provide half the answer to those ultimate questions. Even this modest achievement, however, is more than I had in mind when, back in the days before COVID-19, I combined my fascination with quantum physics and my enjoyment of short-form writing to produce Six Impossible Things.
I am not alone in my fascination with quantum physics, so that choice of subject matter needs no explanation. But why try to confront the mystery of the quantum world in short essays rather than the big book that the topic seems to demand? Part of the answer is that I had already tried the ‘big book’ approach (more than once) and liked the idea of trying something completely different. But the main reason is that the short form offers a particular set of challenges that I enjoy, and a particular kind of satisfaction when it works. Explaining a scientific concept in 3,000 words is often much harder than explaining it in 30,000 words, but harder or not it is a different skill, just as the ability to paint tiny miniatures is a different skill from the ability to paint life-size portraits. I seem to have acquired this skill young – I was sometimes mildly reprimanded during English lessons at school for making my précis too short – and honed it during my time as a journalist, notably with New Scientist.
Looking back at some of my early books, it is obvious that they were really a series of New Scientist-level essays labelled as ‘chapters’ and put between covers. Developing from this into ‘proper’ books with a narrative thread running from the beginning through the middle to the end was a notable achievement, I felt, but I was increasingly attracted to the idea of combining this achievement with writing something shorter to convey the maximum information as briefly (and intelligibly) as possible. The biggest challenge of this kind would be quantum physics – so the idea for Six Impossible Things was born. It seemed to work, and as there was a demand for more, the obvious subject to tackle next (as being almost as difficult to understand as quantum physics) was life. As one reviewer commented, the next book should probably have been called Seven Pillars of Life, but my journalistic training led me (probably mistakenly, I now realise) to the mild alliteration of Seven Pillars of Science. I hope nobody found that too confusing.
The possibility of expanding the series seemed at that point highly improbable, but while re-reading the complete Sherlock Holmes stories during lockdown (actually, listening to the superb narration by Stephen Fry), I was reminded of one of my favourite quotations – ‘When you have excluded the impossible, whatever remains, however improbable, must be the truth’ – which must also have been a favourite of Conan Doyle, since it appears in slightly different versions in several of the stories. ‘What’, I mused, ‘were the most improbable things we have discovered about the Universe?’ To complete the trilogy along the lines I had begun, I had to select Eight Improbable Possibilities, taking me halfway to the answer proposed by Douglas Adams. Which seems like a good place to stop and take stock of the story so far.
John Gribbin February 2022
SIX IMPOSSIBLE THINGS
The ‘Quanta of Solace’ and the Mysteries of the Subatomic World
CONTENTS
LIST OF ILLUSTRATIONS
Richard Feynman
The double-slit experiment
Electron diffraction
John Bell
Niels Bohr
Erwin Schrödinger
Werner Heisenberg
Louis de Broglie
David Bohm
David Deutsch
Anthony Leggett
Lee Smolin
‘Alice laughed: “There’s no use trying,” she said; “one can’t believe impossible things.”
“I daresay you haven’t had much practice,” said the Queen. “When I was younger, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.”’
Alice’s Adventures in Wonderland
SOLACEn. (pl. -es) comfort or consolation in a time of great distress.
PREFACE
What’s it all About, Alfie? The Need for Quantum Solace
Quantum physics is strange. At least, it is strange to us, because the rules of the quantum world, which govern the way the world works at the level of atoms and subatomic particles (the behaviour of light and matter, as Richard Feynman put it), are not the rules that we are familiar with – the rules of what we call ‘common sense’.
The quantum rules seem to be telling us that a cat can be both alive and dead at the same time, while a particle can be in two places at once. Indeed, that particle is also a wave, and everything in the quantum world can be described entirely in terms of waves, or entirely in terms of particles, whichever you prefer. Erwin Schrödinger found the equations describing the quantum world of waves, Werner Heisenberg found the equations describing the quantum world of particles, and Paul Dirac proved that the two versions of reality are exactly equivalent to one another as descriptions of that quantum world. All of this was clear by the end of the 1920s. But to the great distress of many physicists, let alone ordinary mortals, nobody (then or since) has been able to come up with a common sense explanation of what is going on.
One response to this has been to ignore the problem, in the hope that it will go away. The equations (whichever version you prefer) work if you want to do things like design a laser, explain the structure of DNA, or build a quantum computer. Generations of students have been told, in effect, to ‘shut up and calculate’ – don’t ask what the equations mean, just crunch the numbers. This is the equivalent of sticking your fingers in your ears while going ‘la-la-la, I can’t hear you’. More thoughtful physicists have sought solace in other ways. They have come up with a variety of more or less desperate remedies to ‘explain’ what is going on in the quantum world.
These remedies, the quanta of solace, are called ‘interpretations’. At the level of the equations, none of these interpretations is better than any other, although the interpreters and their followers will each tell you that their own favoured interpretation is the one true faith, and all those who follow other faiths are heretics. On the other hand, none of the interpretations is worse than any of the others, mathematically speaking. Most probably, this means that we are missing something. One day, a glorious new description of the world may be discovered that makes all the same predictions as present-day quantum theory, but also makes sense. Well, at least we can hope.
Meanwhile, I thought it might be worth offering an agnostic overview of some of the main interpretations of quantum physics. All of them are crazy, compared with common sense, and some are more crazy than others, but in this world crazy does not necessarily mean wrong, and being more crazy does not necessarily mean more wrong. I have chosen six examples, the traditional half-dozen, largely in order to justify using the quotation from Alice. I have my own views on their relative merits, which I hope I shall not reveal, leaving you to make your own choice – or, indeed, to stick your fingers in your ears while going ‘la-la-la, I can’t hear you’.
Before offering those interpretations, though, I ought to make it clear just what it is we are trying to interpret. Science often proceeds in fits and starts. In this case, though, it seems appropriate to begin, with another nod to Charles Lutwidge Dodgson, with two fits.
FIT THE FIRST
The Central Mystery
The weirdness of the quantum world is encapsulated in what is formally known as the ‘double-slit experiment’. Richard Feynman, who was awarded the Nobel Prize for his contributions to quantum physics, preferred to call it ‘the experiment with two holes’, and said that it is ‘a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery … the basic peculiarities of all quantum mechanics.’* This may come as a surprise to anyone who only remembers the experiment from school physics, where it is used to ‘prove’ that light is a form of wave.
The school version of the experiment involves a darkened room in which light is shone on to a simple screen – a sheet of card or paper – in which there are two pinholes, or in some versions two narrow parallel slits. Beyond this screen there is a second screen, without any holes. Light from the two holes in the first screen travels across to the second screen, where it makes a pattern of light and shade. The way light spreads out from the two holes is called diffraction, and the pattern is called an interference pattern, because it is the result of two beams of light, one from each of the two holes, spreading out and interfering with each other. And it exactly matches the pattern you would expect if light is travelling as a form of wave. In some places, the waves add together and make a bright patch on the second screen; in other places the peak of one wave coincides with the trough of the other wave, so they cancel each other out to leave a dark patch. You can see exactly the same kind of interference pattern in the ripples produced on a still pond if you drop two pebbles into it at the same time. One of the distinctive features of this kind of interference is that the brightest patch of light on the second screen is not directly behind either of the two holes, but exactly halfway between those points, just where, if light was actually a stream of particles, you would expect the second screen to be completely dark. If light was made of a stream of particles, you would expect to see a bright patch behind each hole, and darkness in between those patches of light.
Richard FeynmanGetty Images
So far, so good. This proves that light travels as a wave, as Thomas Young realised at the beginning of the nineteenth century. Unfortunately, at the beginning of the twentieth century another kind of experiment showed light behaving as a stream of particles. These experiments involved electrons being knocked out of a metal surface by a beam of light – the photoelectric effect. When the energy of the ejected electrons was measured, it turned out that for any given colour of light the energy of each electron was always the same. For a bright light there are more electrons ejected, but they still all have the same energy as each other, and this is the same as the energy of each of the smaller number of electrons ejected when the light is dimmed. It was Albert Einstein who explained this in terms of particles of light, what we now call photons – or in his language, quanta of light. The amount of energy carried by a photon depends on the colour of the light, but for any colour all photons have the same energy. As Einstein put it, ‘the simplest conception is that a light quantum transfers its entire energy to a single electron’. Turning up the light just provides more photons (light quanta), each with the same energy to give to the electrons. It was for this work, not his theories of relativity, that Einstein was awarded the Nobel Prize. After a hundred years of thinking of light as a wave, physicists had to start thinking of it as a particle – but how could that explain the experiment with two holes?
When light passes through two slits in a screen, waves spread out from each slit to make an interference pattern, like ripples on a pond.
It got worse. After seeing the wave nature of light cast into doubt by the photoelectric effect experiments, in the 1920s physicists were discomfited by evidence that electrons, the archetypal particles of the subatomic world, could behave as waves. The experiments involved beams of electrons being fired through thin sheets of gold foil, between one ten-thousandth and one hundred-thousandth of a millimetre thick, and studied on the other side. The studies showed that the electron beams had been diffracted as they passed through the gaps between the array of atoms in the metal, just like light being diffracted as it passed through the experiment with two holes. George Thomson, who carried out those experiments, received a Nobel Prize for proving that electrons are waves. His father, J.J. Thomson, had received a Nobel Prize for proving that electrons are particles (and was still around to see George get his prize). Both awards were justified. Nothing demonstrates more clearly the weirdness of the quantum world. But this still isn’t the whole story.
The puzzle of wave-particle duality, as it became known, lay at the heart of theorising about the meaning of quantum mechanics from the 1920s onward. Much of this theorising about the foundations of quantum mechanics provided the solace for physicists that I discuss later. But the puzzle was brought forth in all its glory in a series of beautiful experiments beginning in the 1970s, so for now I shall skip half a century of solace-seeking to give you the up-to-date facts about the central mystery. If you find what follows hard to accept, remember that as Mark Twain put it, ‘truth is stranger than fiction, but it is because Fiction is obliged to stick to possibilities; Truth isn’t.’
In 1974, three Italian physicists, Pier Giorgio Merli, Gian Franco Missiroli, and Giulio Pozzi, developed a technique to monitor the equivalent of the experiment with two holes for electrons. Instead of a beam of light, they used a beam of electrons, boiled off from a hot wire, which travelled through a device called an electron biprism. The electrons go into the biprism through a single entrance, but encounter an electric field which splits the beam in two, with half the electrons emerging from one exit, and half emerging from another exit. Then they arrive at a detector screen, like a computer screen, where each electron makes a white spot as it arrives. The spots persist, so as more and more electrons pass through the experiment a pattern builds up on the screen. When a single electron is fired through the biprism, there is a 50:50 chance of it going one way or the other, and it makes a single spot on the screen. When a beam of many electrons is fired through the experiment, they make many overlapping spots on the screen, and these spots combine to make a pattern – the interference pattern expected for waves.
In itself, this is not too alarming. Even if the electrons are particles, there are a lot of them in the beam, and they could be interacting with each other on their way through the experiment to make the interference pattern. After all, water waves make interference patterns, and water is made up of molecules, which can be regarded as particles. But there is more.
The Italian experiment was so precise that individual electrons could be fired through it one at a time, and sent on their way like airliners departing from a busy airport. Like those aircraft, the electrons were widely spaced. The distance from the electron source (actually a bit more sophisticated than a hot wire) to the detector screen was 10 metres, and each electron in the stream did not leave the source until its predecessor had already arrived at its destination. You can (I hope) guess what happened when thousands of electrons were fired one after the other through the experiment to build up a pattern on the detector screen. They made an interference pattern. If the individual particles were acting together to make a pattern in the same sort of way that water molecules interact to make a pattern, then the interaction was taking place across both time and space. This kind of experiment became known as ‘single-electron double-slit diffraction’.
When electrons are fired one at a time through the equivalent of the double-slit experiment for light, each electron makes a blob of light on the detector screen. But the blobs build up over time to make an interference pattern, as if they were waves (see image below).
Adapted from A. Tonomura et al., Am. J. Phys. (1989)
Although the Italian team published these startling results in 1976, they failed to make waves of their own in the world of physics. At that time, few physicists worried about how quantum mechanics worked, as long as it did work, in the sense that they could use equations to make calculations and to predict correctly the outcome of experiments. Just how an electron, or a beam of electrons, gets from A to B does not matter to an engineer designing, say, a TV set. You might make an analogy with that vanishing breed of racing drivers who didn’t care what went on under the bonnet of their car, but could fling it around the circuit at high speed. The only slightly tongue-in-cheek advice given to students who wanted to know why the equations worked was, as I have mentioned, ‘shut up and calculate’ – that is, use the equations but don’t worry about what it all means.
That attitude became increasingly questioned in the 1980s, not least because of the developments which I describe in Fit the Second. So when a Japanese team, headed by Akira Tonomura, carried out similar experiments to those of the Italian pioneers, but using the improved technology of the late 1980s, their results, published in 1989, made a bigger splash. So much so that in 2002, a poll of readers of the journal Physics World voted single-electron double-slit diffraction to be ‘the most beautiful experiment in physics’. But there was one detail of these experiments that niggled. In the electron biprism experiments there is no physical barrier, like the first screen in the classic double-slit experiment with light, and both routes through the apparatus, both ‘channels’, are always open. In 2008, Pozzi and another group of colleagues took a step further. They developed an experiment in which electrons could be fired one at a time through two genuine, nano-sized physical slits in a thin screen, to be detected on the other side in the usual way. As expected, the electrons arriving at the detector screen built up an interference pattern. But when the Italian team blocked off one of the slits and carried out another run of the experiment, there was no interference. The pattern on the detector screen was a simple blob directly behind the slit, just as you would expect to be produced by a stream of particles. How does an individual electron travelling alone through the experiment through a hole in a wall ‘know’ whether there is another hole nearby that it might have gone through, and whether that hole is open or closed, and adjust its subsequent flight path accordingly?
The next step was obvious, in theory, but incredibly difficult in practice. Build an experiment with two holes, on the nano scale, in which the holes could be opened or closed while the electrons were still in flight. Could they be fooled by changing the experimental setup after they had started on their journey? The challenge was taken up by a team based in the USA but headed by Dutch-born Herman Batelaan, who announced their results in 2013. I described their experiment in my Kindle essay ‘The Quantum Mystery’, and since it involves accurate numbers I cannot improve that description, so here it is again.
The experimenters made two slits in a silicon membrane coated with gold. The membrane was just 100 nanometres ‘thick’ (‘thin’ would be a better word), coated with 2 nanometres of gold. Each slit was 62 nanometres wide and 4 micrometres long (a nanometre is a billionth of a metre; a micrometre is a millionth of a metre). The parallel slits were 272 nanometres apart (measuring from the centre of one slit to the centre of the other slit), and, in the crucial new development, a tiny shutter could be slid across the membrane by an automatic mechanism (a piezoelectric actuator) to block one slit or the other.
In the experiment, the electrons passed through the apparatus at a rate of one per second, taking two hours for the pattern to build up on the screen. The whole process was recorded on video. In a related series of runs, the team observed what happened when both slits were open, when one slit was closed, and when the shutter was moved across to block the other slit. As expected, the pattern that built up showed interference when both slits were open, but none for either of the two single-slit options. Once again the electrons ‘knew’ how many slits were open, on top of all the mysteries revealed (or perhaps I should say confirmed) by the Italian and Japanese experiments. Each electron seemed to ‘know’ not only what the exact experimental setup was at the time it made its flight through the apparatus, but also what had happened to the electrons that went before it and the ones that would come after it.
Richard Feynman had predicted this would happen, half a century earlier. Drawing on what people knew by then about the behaviour of light, and the discovery of electron waves, he imagined doing the double-slit experiment with electrons. He said in his Lectures on Physics that he would describe a thought experiment ‘that you should not try to set up’ because ‘the apparatus would have to be made on an impossibly small scale to show the effects we are interested in’. What was impossible in 1965 proved possible in 2013. It would have delighted Feynman, who among other things was fascinated by nanotechnology. As Batelaan and his colleagues put it, they achieved ‘the full realization of Feynman’s thought experiment’. It did, indeed, reveal the central mystery of the quantum world laid bare; ‘the heart of quantum physics … the only mystery’. And nobody knows how the world can be like that.
*Lectures on Physics, Volume III. In this context, the terms ‘quantum physics’ and ‘quantum mechanics’ are interchangeable. ‘Classical’ physics means everything before relativity and quantum theory.
FIT THE SECOND
The Tangled Web
Before moving on, it’s important to take away one more lesson from the experiment with two holes. It isn’t that things like electrons are seen behaving as both wave and particle at the same time. They seem to travel through the experiment like waves, but they seem to arrive at the detector screen like particles. Sometimes they behave as if they were waves, sometimes they behave as if they were particles. The as if is important. We have no way of knowing what quantum entities ‘really are’, because we are not quantum entities. We can only make analogies with things we have direct experience of, such as waves and particles. The physicist Arthur Eddington pointed this out in memorable fashion back in 1929. In his book The Nature of the Physical World, he said:
No familiar conceptions can be woven around the electron … something unknown is doing we don’t know what. [This] does not sound a particularly illuminating theory. I have read something like it elsewhere —
The slithy toves
Did gyre and gimble in the wabe.
We might, indeed, be better off thinking of slithy toves gyring and gimbling in the experiment with two holes, rather than of electrons behaving as waves and particles. To avoid overkill, I won’t be including the ‘as if’ every time I refer to an event or an entity in the quantum world. But take it as read.
Indeed, ‘gyre’ might be a better term than the one usually used to denote a fundamental quantum property of electrons, and other ‘particles’, usually referred to as ‘spin’. Spin is a cosy, familiar term, like wave or particle – and just as misleading as either of them. For one thing, the equations tell us that a quantum entity has to rotate twice to get back to where it started, whatever that means in physical terms (and I certainly can’t picture it). But spin is a useful property in discussing many quantum phenomena, because it comes in two kinds, which can be thought of as ‘up’ and ‘down’. This simplifies discussions which might otherwise be horrendously complicated.
For example, probability. It was the German physicist Max Born who put the concept of probability, in the context of quantum mechanics, on a secure mathematical footing. But without going into all the mathematics, we can get a feel for its importance using the example of electron spin (or tove gyre, as Eddington might have preferred). It is possible to describe, using the equations of quantum mechanics, an experiment in which an atom emits an electron which travels off through space (this is a real process, called beta decay). In an idealised version of the experiment, the electron has a definite spin. It is either up or down. But there is no way to say in advance what it will be. There is a 50:50 chance of either possibility. If you do the experiment a thousand times, or simultaneously with a thousand atoms, you will find 500 electrons (plus or minus a few, maybe) with spin up, and 500 electrons with spin down. But if you catch a single electron and measure its spin you cannot tell which it will have until you look.
Nothing surprising yet. But Einstein realised that something very surprising is predicted by the equations of the quantum theory for two electrons flying off in opposite directions.* In certain circumstances, a conservation law applies, which says that the electrons must have opposite spin, one up and one down, so that in effect they cancel out. But the equations say that at the time the electrons are emitted from their source, they do not have a definite spin. Each of them exists in what is called a superposition, a mixture of up and down states, and the electron only ‘decides’ what spin to settle into, in accordance with the rules of probability, when it interacts with something else. The point Einstein seized upon is that if the electrons must have opposite spin, at the moment electron A ‘decides’ to be spin up, electron B must become spin down, no matter how far apart the two electrons are. He called this ‘spooky action at a distance’, because at first sight it seems as if the electrons are communicating faster than light, which is forbidden according to the special theory of relativity.
Einstein’s idea was developed into a scientific paper, published in 1933, with the help of two colleagues, Boris Podolsky and Nathan Rosen (some might say hindrance, rather than help, since the paper is badly worded and does not bring out the argument clearly). From their initials, this is known as the EPR paper, and the point Einstein wanted to make is known as the EPR Paradox, although it isn’t really a paradox at all, just a puzzle. In 1935, in a scientific paper which introduced another famous ‘paradox’, Schrödinger gave the name ‘entanglement’ to the way two quantum systems seem to be connected by spooky action at a distance. The EPR paper said that quantum theory ‘makes the reality of [the properties of the second system] depend on the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this.’ Their resolution of the puzzle was that ‘we are thus forced to the conclusion that the quantum-mechanical description of physical reality … is not complete’. Einstein thought that there must be some kind of underlying mechanism, known as hidden variables, which would ensure, in this example, that the electrons did not really have a choice about whether to be spin up or spin down while they were flying away from their source, but that everything was predetermined.
Although the publication of the EPR paper provoked fierce debate among the experts, real progress towards an insight into the implications of entanglement was delayed for three decades, largely because one of the most eminent mathematicians of his day, John von Neumann, made a mistake in an influential book on quantum mechanics that he published in 1932, before the EPR paper appeared. In that book, von Neumann gave a ‘proof’ that hidden variables theories could not explain the behaviour of the quantum world – that they were impossible. He was so eminent that everyone believed him, without checking his equations. Well, almost everyone. A young researcher in Germany, Grete Hermann, spotted the flaw in his reasoning and published a paper drawing attention to it in 1935, but only in a philosophy journal not read by physicists and only discovered by them much later. Although, as I shall describe in the second Solace, von Neumann’s mistake did not entirely stop people working on ‘impossible’ hidden variables theories, it wasn’t until the mid-1960s that a physicist took von Neumann’s argument apart, showed what was wrong with it, and reinvigorated the hidden variables idea. But his revival of hidden variables might not have pleased Einstein, since it also proved that all such theories must include the spooky action at a distance that he abhorred, what is more formally known as non-locality.
That physicist was John Bell, who was taking a break from his work at CERN, the European particle physics laboratory, to work in the USA for a few months on whatever took his fancy. The two papers that emerged from this break from the day job changed what ‘everybody knew’ about the quantum world as dramatically as anything since the discovery of wave-particle duality. First, Bell explained what was wrong with von Neumann’s argument. Then, he showed how it would be possible in principle to design an experiment which would test for the effects of non-locality. More precisely, the experiment would test the assumption of ‘local reality’. ‘Local’ here means that there is no spooky action at a distance – things only influence other things in their locality, defined in terms of how far light can travel in a certain time. ‘Reality’ is the idea that there is a real world that exists whether or not anyone is looking at it, or measuring it. Because of the probabilistic nature of the quantum world, Bell’s proposed experiment would need to involve measurements of large numbers of pairs of particles (such as electrons or photons) passing through the apparatus. The hypothetical experiment was designed in such a way that after a large number of runs, two sets of measurements would be produced. If one set of numbers was greater than the other, it would prove that the assumption of local reality is valid. This ratio became known as Bell’s Inequality, and the package of ideas as Bell’s Theorem. But if the other set of numbers was greater, Bell’s Inequality would be violated, which would mean that the assumption of local reality was incorrect. If quantum mechanics is correct, Bell’s Inequality must be violated. You can have a real world, with spooky action at a distance. Or you can have locality, at the cost of saying that nothing is real unless it is observed.
John BellScience Photo Library
Physicists have been down a similar path before, although many physicists themselves do not appreciate it. When, in the seventeenth century, Robert Hooke and Isaac Newton developed their ideas about gravity they realised that the Moon is held in orbit around the Earth by a force that attracts them to each other, and that the planets are held in orbit around the Sun by the same kind of force. They recognised that this was action at a distance. Although neither of them described it as ‘spooky’, the fact that they did not know how it worked was why Newton famously commented Hypotheses non fingo (Latin for ‘I make no hypotheses’, meaning ‘your guess about how gravity works is as good as mine’). He was as baffled by gravitational action at a distance as we are by quantum action at a distance. In the twentieth century, Einstein, with his general theory of relativity, replaced the idea of spooky gravitational action at a distance with the idea of distortions in the fabric of space caused by the presence of matter (although it has to be admitted that some people also find this idea spooky). Perhaps spooky quantum action at a distance will someday be replaced by a less spooky idea by some future Einstein. For experiments have now proved that the phenomenon is real.
Actually carrying out a Bell-type experiment involves technology beyond what was available in the mid-1960s, and Bell did not expect to see the experiment done. But by the early 1980s experiments had been carried out (using photons, rather than electrons) which proved that Bell’s Inequality is violated. Many more such experiments, with increasing technical sophistication, have confirmed this since. Local reality is not a valid description of the world; in John Bell’s own words, spoken at a meeting in Geneva in 1990, ‘I don’t know of any conception of locality which works with quantum mechanics. So I think we’re stuck with non-locality.’ Einstein may have felt that ‘no reasonable definition of reality’ could allow this, but the conclusion must be that reality is, in his terms, unreasonable. But the most impressive feature of all this is often overlooked. Although the jumping-off point for Bell’s Theorem was an attempt to understand quantum physics, and those words were spoken at a quantum physics meeting, these results do not apply only to quantum physics. They apply to the world – the Universe. Whether or not you think that quantum physics might one day be replaced as a description of how the world works, this will not change things. The experiments show that local reality does not apply to the Universe. Whether you choose to find solace in keeping reality and accepting non-locality, or in keeping locality and rejecting reality, is a matter of personal preference, as we shall see. But you can’t have both (although you could have neither, if you really want to make your brain hurt). Before we seek solace for our aching brains, though, it its worth bringing the story of entanglement up to date, since it has significant practical applications.
Those applications involve a phenomenon known as quantum teleportation. It rests on the now experimentally proven fact that if two quantum entities, such as two photons, are entangled then no matter how far apart they are, what happens to one of them affects the other. In effect, they are separate parts of a single quantum entity. This cannot be used to convey information faster than the speed of light, because what happens to each particle involves probability and randomness. If one photon is tweaked into a random quantum state, the other one is simultaneously tweaked into another quantum state. But anyone watching the second photon only sees a random change obeying the rules of probability. In order for this change to convey information, whoever tweaked the first photon has to send a message by conventional means (slower than light) to tell the second experimenter what is going on. But by tweaking one photon in a certain way, it is possible to change the second photon into an exact copy (sometimes called a clone) of the first photon, while the state of the first photon is scrambled up. In effect, the first photon has been teleported to the location of the second photon. But since the state of the first photon is scrambled, this is not duplication. Once again, the process has to be completed by sending information by a sub-lightspeed process. The teleportation conveys information, but it requires both a ‘quantum channel’ and a ‘classical channel’.
A huge research effort has gone into developing such systems, primarily because the technique offers the prospect of producing uncrackable codes, which would be immensely valuable both to industry and to governments. The essential point is that if any eavesdropper tried to listen in on the quantum channel this would scramble the data, making it useless and revealing the interference. It doesn’t matter if the eavesdropper reads the classical channel – as quantum cryptographers point out, it could be printed in the newspapers or published on social media for all the good it would do the eavesdroppers. You need both channels to unlock the coded information. And entanglement is also involved in the development of quantum computers, a topic that is often in the headlines these days. The vision of the researchers is of a totally secure quantum internet, using quantum computation, entanglement, and teleportation to share information utterly securely.
Experiments of this kind have now moved out of the laboratory and into the world at large – and beyond. In 2012, a Chinese team teleported quantum information in this way across the Qinghai Lake, a distance of 97 km. The same year, a European team teleported photons across 143 km, between the islands of La Palma and Tenerife in the Canaries. Both experiments, as an aside, confirmed the violation of Bell’s Inequality, something now taken as much for granted by physicists as the fact that apples fall downward from trees.
The Canary Islands experiment involved ground stations on mountains about 2,400 metres above sea level, where the thin air reduces atmospheric interference. But the air is even thinner higher up, and less than 143 km straight up from La Palma takes us to the edge of space. In 2016, China launched the Micius satellite (named after a Chinese philosopher of ancient times), from which beams of entangled pairs of photons were sent to separate receiving stations high in the mountains of Tibet and 1,200 km apart. The satellite was moving at nearly 8 km per second during the experiment, but kept the photon beams on target. To nobody’s surprise, but in a triumph of technology, the behaviour of the photons confirmed predictions in line with Bell’s Theorem. Although the experiment only operates at night, because sunlight dazzles the detectors, and the success rate of ‘recovering’ the photons at the ground was only about one in every six million sent from the satellite (fortunately, photons are cheap), there are already plans for a family of satellites with stronger beams that could be detected even in daytime, providing the basis for a quantum communication network, and to teleport photons up to the satellite from the ground. There will probably be more progress, and more headlines, by the time you read this. But while the technologists may continue to ‘shut up and calculate’, still the physicists cannot agree on what it all means – why the world is the way it is.
It’s time to look in more detail at some of the ways in which they seek solace. But to bring us back down to Earth, think again about the experiment with two holes. In the experiment, each electron seems to ‘know’ how many holes are open, and where it is going. Does entanglement – spooky action at a distance – come into the story here as well? If a pair of photons flying in opposite directions are in effect part of a single quantum system, might we regard the whole double-slit experiment and the electron – all of the electrons? – as part of a single quantum system? Maybe the electron knows which holes are open because the state of the holes is also part of the state of the electron. But even the notion of entanglement still lay in the future when physicists first sought solace in an interpretation of quantum mechanics which became the standard view for decades.
* Einstein actually discussed this surprise in slightly different terms, but the spin version is easier to get a handle on.
SOLACE1
The Not So Wonderful Copenhagen Interpretation
The interpretation of quantum physics that became the standard way of looking at things for decades is based on the idea of waves – and on largely forgetting the caveat ‘as if’. In the 1920s, physicists already knew that the quantum world could be described in either of two mathematical ways. One involved waves, summed up in the Schrödinger equation. The other involved pure numbers, in the form of arrays called matrices, developed from the work of Werner Heisenberg and Paul Dirac. They gave the same answers, so it was a matter of choice which one to work with; and since most physicists already had some familiarity with wave equations, that was what they chose. In any quantum calculations, however, what you calculate is the relationship between two states of a system, where the system may be an electron, the experiment with two holes, or (in principle) the entire Universe – or anything in between the electron and the Universe. If you have a set of parameters describing the system in state A, you can calculate the probability that it will be in state B after a certain time. But there is nothing which tells you what is going on in between.
Niels BohrGetty Images
The archetypal example is an electron in an atom. Electrons can, for some calculations, be thought of as if (that caveat) they are in orbits which correspond to different amounts of energy. When an atom emits energy in the form of light, an electron disappears from one orbit and appears in another orbit closer to the nucleus of the atom. When an atom absorbs light, an electron disappears from one orbit and appears in one further out from the nucleus of the atom. But it does not move from one orbit to the other. First it is here, then it is there. This is known as a quantum jump (or a quantum leap*). Schrödinger intended his wave mechanics to explain what happens during the leap, but it didn’t, and he said: ‘If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.’ Alas for Schrödinger, it was, and is, here to stay. The matrix approach is more honest, since it does not pretend to try to tell us what is happening between state A and state B, but it provides less solace than the Schrödinger equation.
What was for decades the standard way of looking at the quantum world became known as the Copenhagen Interpretation, because it was vigorously promoted by Niels Bohr, a forceful personality who was based in that city. This name (actually given to the package of ideas by Werner Heisenberg) caused considerable irritation to Max Born, who was not a member of Bohr’s team, and did not work in Copenhagen, but whose ideas about probability were an integral part of the interpretation. Bohr so dominated any discussions about quantum physics at the end of the 1920s that as well as getting his home town recognised in this way he dissed an alternative, completely viable interpretation of quantum mechanics so thoroughly that it was neglected for two decades. I shall present it as Solace 2.
Bohr was essentially a pragmatist who was happy to stick together different bits and pieces of ideas to make a working package without worrying too much about what it all meant. As a result, there is no straightforward, definitive statement of what the Copenhagen Interpretation is, although Bohr came close to such a revelation in a talk he gave at Como, in Italy, in 1927 – long before the interpretation got its name. The conference at which that talk was given was a landmark moment in physics, because it marked the point where physicists were presented with the tools they would require in order to ‘shut up and calculate’, applying quantum mechanics to the solutions of practical problems involving atoms and molecules (for example, chemistry, lasers, and molecular biology) without having to think about the fundamentals of what it all meant.
Bohr’s pragmatic approach extended to his interpretation. He said that we do not know anything except for the outcomes of experiments. These outcomes depend on what the experiments are designed to measure – on the questions we choose to ask of the quantum world (of nature). These questions are coloured by our everyday experiences of the world, on a scale much larger than atoms and other quantum entities. So we may guess that electrons are particles, and build an experiment designed to test this in an obvious way by measuring the momentum of an electron, thinking of the electron as a tiny pool ball. When we do so, lo and behold, the experiment measures the momentum of the electron, confirming our notion that electrons are particles. But a friend of ours has a different idea. She thinks that electrons are waves, and designs an experiment to measure the wavelength of an electron. Lo and behold, her experiment gives a measurement of the wavelength, confirming her notion that electrons are waves. So what, says Bohr. Just because the electron behaves as if it were a particle when you are looking for particles, or as if it were a wave when you are looking for waves, doesn’t mean that it is either, let alone both. What you see is what you get, and what you see depends on what you chose to look for. It is meaningless, according to the Copenhagen Interpretation, to ask what quantum entities such as electrons and atoms are, or what they are doing, when nobody is measuring them – looking at them, if you like.
So far, so pragmatic, and nothing really too alarming. But Bohr quickly takes us into muddy waters. This is where probability comes in. When Schrödinger came up with his wave equation, he thought of it as being a literal description of an electron (or other quantum entity; electrons are the simplest example to use for illustration). To him, an electron was a wave. But Bohr took Schrödinger’s ball and ran off with it, combining it with Born’s ideas on the role of probability to produce a bizarre and troubling concoction which worked (and still works), as far as quantum calculating was concerned, but makes your head hurt when you stop to think about it. The equation that Schrödinger gave us is, on this new picture, to be thought of as a ‘probability wave’, and the chance of finding an electron at any location is determined by ‘the square of the wave function’, essentially by multiplying the equation that describes the wave by itself, at any point. When we make a measurement, or observe a quantum entity, the wave function ‘collapses’ to a point, determined by the probabilities. But although some locations are more likely than others, in principle the electron could appear anywhere that the wave function has spread to. A very simple example highlights the oddity of this behaviour.
Think of a single electron trapped in a box. The probability wave spreads out to fill up the box evenly, meaning that there is an equal chance of finding the electron at any location inside the box. Now drop a partition down the middle of the box. Common sense tells us that the electron must now be trapped in one half of the box. But the Copenhagen Interpretation (CI) says that the probability wave still fills each half of the box and the electron might with equal probability be found on either side of the partition. Now divide the box in two down the centre of the partition. Keep one half-box in your laboratory, and put the other one on a rocket which takes it to Mars. Still, according to Bohr, there is a 50:50 chance of the electron popping up in the box in the lab or the one on Mars. Now open the box in your lab. Either you find an electron, or you don’t. But either way, the wave function has collapsed. If your box is empty, the electron is on Mars; if you have the electron, the other box is empty. This is not
