The Quantum Mystery

How the experiment with two holes transformed our understanding of the world

John Gribbin

Table of Contents

Cover Page

Copyright Page

Introduction

Chapter One - Holes and Spots

Chapter Two - Enter the Electron

Chapter Three - Particles of Light

Chatper Four - The Experiment With Many Holes

Chapter Five - Waving With Electrons

Chapter Six - The Theoretical Minimum

Chapter Seven - The Most Beautiful Experiment in Physics

Copyright © 2015 by John Gribbin

“[Richard] Feynman was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment, so it's well worth discussing.”

—Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (1999)

Introduction

Richard Feynman said that what he called “the experiment with two holes” contains “the central mystery, indeed the only mystery” of quantum mechanics. The experiment is more formally known as the double-slit experiment, but the more formal language does not make it any less mysterious. In his famous Lectures on Physics, making a comparison with the “classical” physics of Isaac Newton – the laws that apply to things in the everyday world, such as footballs being kicked around – Feynman said of the double-slit experiment that it “is impossible, absolutely impossible to explain in any classical way”, and that it “has in it the heart of quantum mechanics”. In another book, The Character of Physical Law, he wrote, “Any other situation in quantum mechanics, it turns out, can always be explained by saying, ‘You remember the case of the experiment with the two holes? It’s the same thing’.”

I have written about this central mystery before, in books dealing more broadly with quantum physics in all its glory (the terms “quantum physics” and “quantum mechanics” are essentially interchangeable). But from questions I have received from readers of those books, it seems to me that it would be appropriate to devote a short essay solely to the central mystery itself, to explain what Feynman was getting at. I hope this will help you to understand why the experiment with two holes is so mysterious. But you will not find here any definitive explanation of how the quantum world works, although I do offer a possible but speculative suggestion. As Feynman also wrote in The Character of Physical Law, “I think I can safely say that nobody understands quantum mechanics . . . Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will go ‘down the drain’ into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”

So fasten your seat belt and enjoy the ride. The mystery began to unfold early in the nineteenth century, when experiments in England and France proved that even Isaac Newton, the founding father of physics, was not always right about the way the world works.

ONE

Holes and Spots

Isaac Newton published his greatest work, Philosophiae Naturalis Principia Mathematica, in 1687. This laid the foundations of physics, and established his reputation as the greatest “natural philosopher”. Seventeen years later, in 1704, he published another great book, Opticks, setting out his ideas about the nature of light. This described the behaviour of light in terms of streams of tiny particles, bouncing off mirrors, being deflected as they passed through glass, and so on. Thanks in no small measure to Newton’s towering reputation, this became the established model of light, although there was an alternative explanation, describing light in terms of waves, that had been developed by Christiaan Huygens from the Hague. His work had been published in 1690, but was overshadowed by Newton’s later book. Until, that is, the beginning of the nineteenth century.

The “experiment with two holes” was developed by Thomas Young, building from experiments he carried out involving sound waves when he was working in Cambridge in the 1790s. Sound definitely travels as a wave, a physical vibration in the air, or water, or even in a solid. Young was particularly interested in the way these waves can interfere with one another, so that two sound waves may add together to make a particularly loud noise, or cancel each other out to leave a quiet spot. By this time, although Newton’s “corpuscular” model of light still held sway, a few people – notably the Swiss mathematician Leonhard Euler – had developed the wave idea in more detail. Young realised that if light did travel as a wave, then the same sort of interference effects that he had observed in his experiments with sound ought to be detectable with light. So he set out to devise an experiment to test the idea once and for all.

He started out by studying water waves in a shallow container, known as a ripple tank. If a wall with a small hole in it is put across the tank and ripples are made on one side of the wall, they pass through the hole and spread out in a semi-circular pattern on the other side. If a second wall, with two holes, is put in front of these spreading ripples, the ripples disseminate through both holes on the far side of the second wall, and the overlapping ripples produce a characteristic interference pattern. In some places the peaks of the two sets of ripples coincide to make large waves; in other places the peak from one ripple coincides with the trough of another ripple, and the water is hardly disturbed. You can see the same sort of interference pattern if you drop two stones simultaneously into a still pond.

In the early 1800s, Young adapted this experiment to study light. Instead of a ripple tank, he had a darkened room with a source of light (such as a hole in a blind to let in a beam of sunshine) and three screens, which could be made of something as simple as cardboard or paper. A hole in the first screen, or in the window blind, acting as a screen, lets in the light, like the hole in the first wall in the ripple tank letting ripples through. The second screen has two pinholes, or in the classic version of the experiment two parallel razor slits, like the second wall in the ripple tank. Finally, there is a third screen, a blank piece of card or paper for the light from the two holes to fall on. Young found that the light arriving at the final screen did indeed make a stripey pattern of light and shade, an interference pattern proving that light travelled through the experiment as a wave. This is the classic Young’s double-slit experiment.

Young went further. He realised that each colour of light corresponds to a particular wavelength, and by careful measurements he was able to calculate the wavelengths of different colours of light. The wavelengths are tiny – typically about half a millionth of a metre – which is why it took so long, and such careful experiments, to prove that light travels as a wave.

When he described his results to the Royal Society in London in 1803, Young said, “The experiments I am about to relate . . . may be repeated with great ease, whenever the Sun shines, and without any other apparatus than is at hand to every one.” And in 1807 he described the results in detail:

The middle [of the pattern] is always light, and the bright stripes on each side are at such distances, that the light coming to them from one of the apertures must have passed through a longer space than that which comes from the other by an interval which is equal to the breadth of one, two, three, or more of the supposed undulations [wavelengths], while the intervening dark spaces correspond to a difference of half a supposed undulation, of one and a half, of two and a half, or more.

But there were still doubters. In Britain at least, it was almost heretical to suggest that Newton could have been wrong. And many people found it hard to get their heads round the idea that you could make darkness by adding two beams of bright light together. The doubters were finally persuaded by the work of a Frenchman, Augustin Fresnel, who, thanks to the Napoleonic Wars, knew nothing of Young’s work at the time he devised his own experiments. (Fresnel was born in Broglie, Normandy. The name Broglie will come up again in this story!)

Fresnel was an engineer who had an interest in optics, but no opportunity to develop his ideas about light until 1815. He had been a seemingly loyal Republican during the Napoleonic era, but came out as a Royalist when Napoleon was defeated and sent into exile in Elba. During Napoleon’s “Hundred Days” as ruler following his escape from Elba, Fresnel was placed under house arrest at his home in Normandy, with nothing to do but work on his description of light, apparently without knowing anything, at the time, about the work of Young, Huygens or Euler. He worked it all out for himself, from scratch. When Napoleon was finally defeated, Fresnel went back to his work as an engineer, and nothing more might have been heard of his contribution had it not been for the French Academy of Sciences.

In 1817, the Academy, which was aware of Young’s work, but found it hard to believe, offered a prize for the best explanation of the phenomenon of diffraction, which occurs when light gets bent round the corner of a sharp edge, or spreads out from the razor slits in Young’s experiment. Only two people entered the competition. One was apparently a crackpot whose idea was so completely bonkers that the Academy has kept no record of either his name or his proposal. The other was Fresnel.

Fresnel explained diffraction as a wave phenomenon, exactly like the way waves in the water bend around the end of an obstruction such as a jetty. And he backed this up with detailed equations describing the way these waves would move past the edge of an object. It was clearly an idea worth investigating properly, but one member of the committee set up to oversee the prize spotted what seemed to be a fatal flaw. The mathematician Siméon Poisson used Fresnel’s model, and his equations, to calculate what would be seen exactly behind the centre of a small disk, or a little round ball like a lead shot, placed in a beam of light:

Let parallel light impinge on an opaque disc, the surroundings being perfectly transparent. The disc casts a shadow – of course – but the very centre of the shadow will be bright. Succinctly, there is no darkness anywhere along the central perpendicular behind an opaque disc . . . At a distance behind the disc equal to the disc’s diameter, the intensity is already 80 per cent of what the intensity would be if the disc were absent. Thereafter, the intensity grows more slowly, approaching 100 per cent of what it would be if the disc were not present.

To the Academy, this prediction of the model was clearly both nonsense and testable. So they arranged for a simple experiment to be carried out, expecting to prove Fresnel wrong. Instead, they found that light waves bending around the edges of the disc did indeed produce a bright spot, now known as the Poisson spot, exactly in the middle of the shadow cast on a screen by the disc. The Committee duly reported their conclusions to the Academy:

M. Poisson had deduced from the integrals reported by the author [Fresnel] the singular result that the centre of the shadow of an opaque circular screen must, when the rays penetrate there at incidences which are only a little more oblique, be just as illuminated as if the screen did not exist. The consequence has been submitted to the test of a direct experiment, and observation has perfectly confirmed the calculation.

Fresnel (and Young) were right; Newton was wrong. Or was he?

TWO

Enter the Electron

The two main protagonists in the story of the experiment with two holes are light and electrons. Light, of course, has been known about for as long as people have had eyes to see. But electrons were only identified at the end of the nineteenth century.

Their story begins in the 1860s, when physicists were able to take advantage of the revolutionary development of vacuum pumps which could reduce the pressure inside glass tubes (vacuum tubes), eventually to only a few ten-thousandths of the pressure of the air at sea level on Earth.

The breakthrough in developing these vacuum tubes was made in Germany, by Heinrich Geissler, in the late 1850s. This had such a profound influence on the rest of nineteenth-century physics that it is worth spelling out his achievement, which is often neglected or glossed over. Geissler’s vacuum pumps used mercury to make airtight seals around all the pipes, tubes and taps involved in pumping air out of a glass vessel. A glass jar could be connected by tubes to an intermediate vessel (a rubber bulb) with a two-way tap, connected one way to the open air and the other way to a reservoir of mercury. With the tap open to the air, the pressure of the mercury forced air out of the bulb, which was then switched so that air from the jar rushed in to fill the bulb, reducing the pressure in the jar. Repeating the process over and over again drew more and more air out of the jar. Geissler, an expert glassblower, also devised the technique used in sealing wires in to each end of a glass tube before it was going to be evacuated. An electric current could then be made to flow through these evacuated tubes from a negatively charged electrode at one end, called the cathode, to a positively charged electrode at the other end, called the anode. This was the nineteenth-century equivalent of the “atom-smashing” experiments carried out at particle accelerators in the twentieth century, and led to equally profound discoveries, one of them being the electron and another X-rays. None of that would have happened without the vacuum tube.

The German physicist Johann Hittorf was the first person to notice that glowing rays emitted from the cathode in these tubes travelled in straight lines through the vacuum, and in 1876 his compatriot Eugen Goldstein gave them the name “cathode rays”. (The name carried over into the twentieth century, when the picture tubes in TV sets were known as cathode ray tubes.) At first, physicists assumed that these rays were electromagnetic waves similar to light, although as early as 1871 a British electrical engineer, Cromwell Fleetwood Varley, suggested in a paper published by the Royal Society that they might be “attenuated particles of matter, projected from the negative pole by electricity”.

This idea was taken up by William Crookes, working in London with an improved vacuum tube design, which became known as the Crookes tube. When cathode rays struck the glass at the other end of the tube, they made it glow. In the 1870s, Crookes found that if he put a piece of thin metal shaped like a Maltese Cross in the line of fire of the rays it left a sharp-edged shadow in this glow, and that when he put a tiny paddle wheel in the tube the impact of the rays made it turn. This strengthened the evidence for the “corpuscular” nature of cathode rays.

But the situation was not yet clear-cut. In 1894 Philipp Lenard, building on work by Heinrich Hertz, showed that cathode rays could pass right through thin sheets of metal foil without making any detectable holes. This was interpreted as meaning that the rays must be waves, whatever Crookes said, because particles ought to leave a trace of their passage. But this conclusion was based on the assumption that any particles involved must be at least the size of atoms. One person in particular, though, had the chutzpah to consider the possibility that the rays might be made of a stream of particles much smaller than atoms, so tiny that they left no identifiable holes in the foil sheets. This was a huge intellectual leap in the 1890s, and it was made by the British physicist J. J. Thomson, who was always referred to by his initials, not by his full name.

Definitive evidence that cathode rays could not be a form of electromagnetic wave came in 1894, the same year that Lenard was puzzling over those foil experiments, when Thomson, working at the Cavendish Laboratory in Cambridge, showed that they moved much more slowly than light – Maxwell’s equations (see below) had by then established that all electromagnetic radiation moves at the speed of light. But what were they?

In 1895, the French physicist Jean Perrin discovered that a beam of cathode rays could be deflected by a magnetic field. This implied that the beam must be made up of a stream of electrically charged particles, and the direction in which the beam was deflected showed that the particles had a negative charge. He confirmed this by carrying out experiments which showed that when a beam of cathode rays hit a metal plate a negative charge built up on the plate.

At that time, it was still thought that atoms were the fundamental, indivisible building blocks of matter. So it was natural for the German physicist Walter Kaufmann to suggest that the particles in cathode rays must be atoms, from the residual trace of gas in the tubes, which had picked up a negative charge from the cathode in the vacuum tube. Such “charged atoms” are known as ions. Kaufmann devised experiments in which the rays were deflected either by magnetic fields or electric fields, and by measuring how much the beams were bent he was able to work out the ratio of the electric charge to the mass (e/m) for the particles involved. He did this for tubes with different kinds of residual gas in them, and expected to find different values for e/m corresponding to the different masses of the different kinds of atoms. But to his surprise, he always got the same “answer”.

Meanwhile, in England Thomson had come up with a particularly neat version of this kind of experiment, in which the beam was simultaneously deflected one way by a magnetic field and the opposite way by an electric field. By adjusting the strength of the fields so that the effects cancelled out and the beam went in a straight line, he too could measure the ratio e/m. But unlike Kaufmann, he expected to get the same answer every time, because from the outset he thought that he was dealing with streams of identical particles emitted by the cathode, without any influence from the atoms of gas in the tube. Indeed, he used the best vacuum tubes in the world at the time, with the purest vacuum, to minimise the risk of any such influence. He also tried using different metals to make the cathodes used in his vacuum tubes, but always got the same results.

Although he could not separate out the e and the m from these experiments, Thomson was led to a profound conclusion. He actually reported his results the other way up, as m/e, and got a very small number for the ratio. The number was much smaller than the equivalent ratio for hydrogen ions, and hydrogen is the lightest element (lightest atom) known. So either the particles he was measuring had a very small mass, much smaller than the mass of a hydrogen atom, or a very large electric charge, or just possibly some combination of these effects. Assuming the same magnitude of electric charge was involved for the cathode ray corpuscles and the hydrogen ions (which we now know to be true), the mass of each corpuscle must be less than one-thousandth of the mass of a hydrogen atom. It meant that there was something smaller than an atom, and that this “something” might have been chipped off atoms in some way.

Thomson reported all this in a lecture to the Royal Institution in London on 30 April 1897. He acknowledged that “the assumption of a state of matter more finely divided than the atom is a startling one”. It was too startling for some of his audience to accept. In his memoirs, Thomson later wrote, “I was told long afterwards by a distinguished colleague who had been present at my lecture that he thought I had been ‘pulling their legs’.” This accurately reflects how surprising, and significant, the discovery was. It marked the beginning of subatomic physics.

Thomson continued to press ahead with his investigation of these corpuscles, and in 1899 he was at last able to measure directly the size of the electric charge they carried. He first investigated the particles emitted by metal surfaces due to the photoelectric effect (more of this shortly), and showed that they had the same e/m (or m/e) as the cathode ray corpuscles, so must be identical to them. Then he measured the electric charge on these photoelectric corpuscles. This involved an experiment in which droplets of water were electrically charged, using these corpuscles, and manipulated using electric fields. Once he knew e, of course, he knew m, because he already knew m/e. So in 1899 he was able to state that the studies of cathode ray corpuscles, which were soon dubbed “electrons”, by the Dutch physicist Hendrik Lorentz, showed that “electrification essentially involves the splitting up of the atom, a part of the mass of the atom getting free and becoming detached from the original atom”. Furthermore, although different elements contain different atoms, all atoms contain identical electrons. This was published in the Philosophical Magazine for December 1899. So at the end of the nineteenth century it was firmly established that light is an electromagnetic wave, and that electrons are charged particles. Thomson received the Nobel Prize, for his work on electrons, in 1906, and was knighted in 1908. But in the twentieth century, everything changed.

THREE

Particles of Light

By the end of the nineteenth century, the wave theory of light was on a very secure footing. The Scot James Clerk Maxwell had come up with a set of equations that together described all known electromagnetic phenomena, and which included a description of electromagnetic waves that move through space at the speed of light – confirming, if confirmation were needed, that light is a wave, and explaining what kind of wave it was. In 1864 he wrote:

It seems we have strong reason to conclude that light itself (including radiant heat and other radiations, if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.

The reference to “other radiations” was prescient. It refers to what we now call radio waves, electromagnetic waves with wavelengths longer than visible light. In the 1880s the German physicist Heinrich Hertz carried out experiments which confirmed the existence of these waves and showed that they move at the speed of light.

Then came a bombshell.

In 1887, while continuing his work with radio waves, Hertz noticed something peculiar. He generated the radio waves by making a spark jump across a gap between two electrodes. The spark produces electromagnetic radiation at visible wavelengths, which is why we can see it, but also at the longer wavelengths we call radio, which is what Hertz was primarily interested in at the time. In one series of experiments Hertz had put the sparking apparatus in a darkened box, so that he could see the sparks more clearly, with a glass window in the side of the box for him to look through. He noticed that, for the same voltage difference across the gap, the sparks could not jump across as big a gap as they could when the apparatus was not in the box. But when he took the glass window away, still keeping the apparatus in the box, the sparks could fly as freely as before. Hertz tried out different windows, with different absorbing properties, to see if they had any similar effect, and concluded that the glass was absorbing ultraviolet light (electromagnetic waves just too short to be seen by human eyes), which somehow encouraged the sparks to fly when they could reach the electrodes. He published the news of his discovery but did not try to explain it. This left the way clear for other researchers, in particular Philipp Lenard, who had worked as an assistant to Hertz, to investigate further.

Lenard was experimenting with cathode rays in the 1890s, as I have mentioned, and followed up the work of Hertz by investigating whether these rays were being produced by the effect of ultraviolet light shining on a clean metal surface. He was able to produce cathode rays which could be bent by electric and magnetic fields in the usual way, and as we have seen Thomson, in a parallel investigation, was able to identify these as streams of the charged particles we now call electrons – I shall use that name for them from now on.

This process of knocking electrons out of a metal surface by shining a light on it is known as the photoelectric effect. Unlike the rays produced in cathode ray tubes, however, the electrons emitted from metal surfaces under the influence of ultraviolet light travelled quite slowly. They could actually be stopped in their tracks and made to fall back by applying a small electrical potential, and the strength of the potential needed to do this made it possible to measure the energy with which the electrons were escaping from the metal. Since all electrons have the same mass, this was equivalent to measuring the speed with which they escaped from the metal. So Lenard was able to measure the energy of the electrons, energy which could only have come from the ultraviolet light shining on them.

In order to measure how the energy of the ejected electrons was affected by the brightness of the light falling on them, Lenard moved his ultraviolet lamp closer to the metal surface. This was the same as using a brighter light, providing more energy for each square centimetre of the metal surface. Lenard expected that the brighter light would give the electrons more energy, and intended to measure how much more energy they gained. To his surprise, he found that the brightness of the light had no effect on the energy of the ejected electrons. When the light was closer to the surface, more electrons were ejected, so they carried away more energy overall, but the energy of each individual electron was the same as it had been when the light was weaker when the lamp was further away. When Lenard changed the wavelength, or frequency, of the light, however, the energy of the ejected electrons was affected. (Frequency is essentially the inverse of wavelength; so shorter wavelengths correspond to higher frequencies.)

In another series of experiments, Lenard discovered that light with a shorter wavelength (higher frequency) gave individual electrons more energy than light with a longer wavelength (lower frequency). A faint light with a high frequency produces only a few electrons, but each of them is very energetic; a bright light with a low frequency produces very many electrons but each of them has a low energy.

These counter-intuitive discoveries were made right at the end of the nineteenth century, just at the time Thomson was analysing the nature of cathode rays and “discovering” the electron. Although the discoveries were clearly important, nobody quite knew what to make of them. But one young physicist, a recent graduate without a university post, struggling to make ends meet with a series of short-term tutoring jobs in Bern, saw something of their significance at once. In May 1901, he wrote to his girlfriend:

I just read a wonderful paper by Lenard on the generation of cathode rays by ultraviolet light. Under the influence of this beautiful piece I am filled with such happiness and joy that that I must absolutely share some of it with you.

The 22-year-old physicist who wrote those words was Albert Einstein. And he was so excited because he knew about some other recent discoveries, concerning the nature of light, which he thought might offer an explanation of what was going on. But for various reasons it would be four years before his explanation of the photoelectric effect was published.

The work on light which Einstein saw as providing an insight into the photoelectric effect had been published by the German physicist Max Planck at the end of 1900, only a few weeks before Einstein wrote that excited letter. It actually came just after Lenard made his discoveries concerning the photoelectric effect. Planck had been seeking an explanation for the way light is emitted from a hot object. This is known as “blackbody radiation”, because an object that is perfectly black and absorbs all electromagnetic radiation when it is cold also radiates a distinctive “perfect” spectrum of light when it is hot. In this sense, the Sun is a good example of a “black body”. This is not the place to go in to all the details, which I have covered before, in particular in my book In Search of Schrödinger’s Cat. What matters is that Planck had found that the observed spectrum of this kind of radiation can only be explained if light is emitted or absorbed by atoms in little packets of energy. The energy E of one of these packets, he found, is related to its frequency, denoted by the Greek letter nu (ν), by the simple equation E = hν, where h is a number now known as Planck’s Constant.

In 1900, Planck knew perfectly well that light is a wave, and did not think that this new equation had any physical significance. He thought of it as a kind of mathematical trick, a heuristic device needed to make the equations describing blackbody radiation work. Looking back from 1931, he wrote in a letter to a colleague, “I can characterise the whole procedure as an act of despair . . . a theoretical interpretation had to be found, at any price.”

Einstein’s insight, which he obviously had as soon as he read Lenard’s paper, was that the energy packets required to explain the character of the blackbody spectrum might be real physical entities, little particles of light. He was well aware of the revolutionary implications of this idea, given the implications of the double-slit experiment, and he spent years working out a detailed physical model of what was going on, alongside the day job he got at the Swiss Patent Office and a few other pieces of scientific work, including the special theory of relativity. Like the special theory, his paper on what became known as light “quanta” was published in 1905, coincidentally, the year that Lenard received the Nobel Prize for his work on cathode rays. In some ways, the paper is even more impressive than the paper on the special theory, and Einstein fully deserved the Nobel Prize which he received for this work – not for relativity theory! – in 1922 (it was actually the 1921 prize, held over for a year). But in order not to frighten his readers, Einstein chose a seemingly innocuous title for his paper: “On a Heuristic Point of View Concerning the Production and Transformation of Light”. He was pretending it was just a mathematical trick; but the contents of the paper suggested otherwise.

Einstein used the statistical techniques of thermodynamics to work out how light quanta would behave and combine in large numbers to give the appearance of a smooth continuum. Early on in the paper, he spelled out a clear indication of how this conflicted with the wave model of light. If light is a wave, then you could turn it down fainter and fainter, and always detect a wave. But:

According to the assumption considered here, in the propagation of a light ray from a point source, the energy is not distributed continuously over ever increasing volumes of space, but consists of a finite number of energy quanta localised at points of space that move without dividing, and can be absorbed or generated only as complete units.

In other words, if you had a very sensitive detector looking at the light from a very faint source, you would detect each light quantum arriving as a separate entity, with gaps in between them where nothing was detected. This is exactly what astronomers today see when they use such detectors to study light from very distant galaxies. The light quanta, which would later be called photons, arrive one at a time, slowly building up an image on the detector.

After taking his readers through the necessary mathematics, Einstein then presents his bombshell: “Monochromatic radiation of low density . . . behaves thermodynamically as if it consisted of mutually independent energy quanta.”

He is saying that the “graininess” of light is an intrinsic property of the light itself, not an illusion caused by the way light interacts with atoms of matter. And it is only after making this clear that Einstein moves on, in the 1905 paper, to look at the implications of all this for the photoelectric effect. The simple explanation, once you have accepted the earlier parts of the paper, is that each light quantum carries a certain amount of energy, corresponding to the frequency, in line with Planck’s equation. It gives up all of that energy to a single electron. So all light quanta with the same frequency (that is, the same colour) release electrons with the same energy. In Einstein’s words, “the simplest conception is that a light quantum transfers its entire energy to a single electron”. A brighter light simply produces more quanta (photons) with the same energy, so it releases more electrons with the same energy, not electrons with more energy.

There was one small snag. Einstein’s calculations, which predicted how much energy should be associated with each frequency of light, were more accurate than Lenard’s measurements because there was some range of experimental errors in his measurements of the energy carried by the escaping electrons. So Einstein’s cautious conclusion was that: “As far as I can tell, this conception of the photoelectric effect does not contradict its properties as observed by Mr Lenard.”

But it did contradict almost everything that had been known about light for the previous hundred years, and the implication that light might not really be a wave was so shocking that at first the paper was largely ignored. The one person who really sat up and took notice of it was an American, Robert Millikan, who became aware of the work a couple of years after it was published. And he only took notice because he thought the whole idea was preposterous, and set out to prove Einstein was wrong, essentially by carrying out more accurate measurements of the kind Lenard had pioneered. He measured the energies of the photoelectrons at different temperatures, using different metals, and with different wavelengths of light. In 1916, he admitted defeat. His superbly accurate experiments convinced him that Einstein was right. But he was not pleased. He grudgingly wrote:

The Einstein equation accurately represents the energy of electron emission under irradiation with light [but] the physical theory upon which the equation is based [is] totally unreasonable.

Looking back from 1949, in an article he wrote for the Reviews of Modern Physics, Millikan said, “I spent ten years of my life testing that 1905 equation of Einstein’s and contrary to all my expectations I was compelled in 1915 to assert its unambiguous verification in spite of its unreasonableness.”

Unreasonable or not, thanks to Millikan’s confirmation of his prediction the work earned Einstein his Nobel Prize. So by 1922, it was established that light quanta were real. The situation was baffling. Some experiments, notably the double-slit experiment, continued to show that light is a wave. Some experiments, such as the photoelectric effect, showed that light is a stream of particles. And as you may have noticed, a curious feature of those particles is that their energy depends on their frequency, or wavelength. How can a particle have a wavelength? What was going on? But at least, while light seemed increasingly mysterious, at the beginning of the 1920s there was no doubt that electrons were particles. Except, that is, in the mind of a French physicist who was getting to grips with his Ph.D. research, after having his career interrupted by military service during the First World War. To see how his ideas panned out, we need to take a step back in time to look at some seemingly independent research involving X-rays and crystals.

FOUR

The Experiment With Many Holes

X-rays had been discovered in 1895 – another result of the invention of the vacuum tube. While studying cathode rays, the German physicist Wilhelm Röntgen had detected a new kind of ray being emitted from the glowing spot where the cathode rays struck the glass wall of the vacuum tube. He dubbed them “X” rays, because he did not know what they were, and the name stuck. As with cathode rays, at first nobody knew whether these “rays” were waves or particles. But in 1912 Max von Laue and his colleagues at the University of Munich found that when they fired a beam of X-rays through a crystal of copper sulphate and on to a photographic plate, it produced a distinctive pattern of spots on the photograph. This was exactly what would be expected if a wave was being diffracted in a more complicated version of the double-slit experiment – an experiment with many holes. A crystal of copper sulphate is made up of an array of atoms at the corners of a regular grid, with the atoms separated by regular intervals.

The pattern the German team found could only be explained as a result of the X-rays being diffracted as they passed through the gaps between the atoms in the crystal. Eventually, it was established that X-rays are electromagnetic waves like light, but with shorter wavelengths (higher frequency). Which, of course, meant that they too could be “explained” in terms of streams of photons, like Einstein’s description of light! But in 1912 nobody except Einstein accepted that interpretation of the behaviour of light, so that puzzle still lay in the future when two British physicists, the father and son team of William and Lawrence Bragg, put von Laue’s discovery to practical use.

William Bragg’s involvement is particularly interesting because it demonstrates the importance of one of the most powerful rules in science, and the correct scientific approach to understanding the world. Before he heard about von Laue’s work, William Bragg was a firm advocate of the idea that X-rays were made up of a stream of particles, just as cathode rays had been shown to be made up of a stream of electrons. But when he saw experimental evidence that X-rays were waves, he changed his mind. The fundamental rule of science is that if an idea conflicts with experiment then it is wrong. It sounds trite, but lesser scientists than Bragg sometimes find it hard to give up their cherished ideas even in the face of conflicting experimental evidence.

William Bragg worked at Leeds University, while Lawrence was based in Cambridge. When they got together to discuss von Laue’s discovery they realised that they could go one better than the German team. Von Laue had identified the pattern of spots in his photographs as a diffraction pattern, but he had not been able to use the information in the pattern to work backwards and determine the exact structure of the crystal that was making the pattern. The Braggs decided that if they could work out the rules that applied to this kind of diffraction, and the way the pattern would change if X-rays with different wavelengths were used, it would be possible to work out the structure of a crystal by accurate analysis of the pattern of spots produced by diffraction. But this would need a set of theoretical rules, and a way to measure the wavelengths of the X-rays being used.

This led to a natural division of labour. Lawrence Bragg concentrated on the theoretical side, working out the relationship that predicted exactly where the spots would appear on a photograph produced when X-rays of a certain wavelength passed through a crystal with atoms that had a certain spacing at a certain angle. William Bragg developed an instrument (a spectrometer) to measure the wavelengths of X-rays. Together, they had everything they needed. They, or rather, William, put the package of ideas to the test in a series of experiments involving different crystals. It worked both ways. If you knew the wavelength of the X-rays, you could use the diffraction pattern to work out the structure of the crystal; if you knew the structure of the crystal, you could use the diffraction pattern to work out the wavelength of the X-rays. This became one of the most important scientific tools of the twentieth century, used most famously to work out the structure of DNA, the molecule of life, from X-ray diffraction images obtained by Rosalind Franklin, at King’s College in London.

The Braggs published all their work together, culminating in a book, X Rays and Crystal Structure, which appeared in 1915. The previous year, von Laue had received the Nobel Prize in physics for his discovery of the diffraction of X-rays by crystals. In the year the book was published, Lawrence Bragg was serving in the British Army in France. While he was there, he heard that he and his father had together been awarded the Nobel Prize for 1915 for their studies of crystal structure using X-rays. There were many features of these awards that extend beyond their scientific importance. In successive years, a German and a British team had each been awarded the prize for related work, while the two countries were at war. Lawrence Bragg, then aged twenty-five, was the youngest person to receive the prize, and this was the only occasion that a father and son shared the award for their joint work. But before very long, another son of a Nobel-prizewinning father would receive his own prize, as a result of experiments which brought the wave-particle puzzle out fully into the open. It was those experiments, also involving diffraction with many holes, that were inspired by the work of the Frenchman Louis de Broglie.

FIVE

Waving With Electrons

Louis de Broglie made one of those inspired leaps that are both truly profound and yet so simple that it leaves other people wondering, “why didn’t I think of that?” Einstein’s explanation of the photoelectric effect in terms of light quanta saw those quanta as real particles, which carried energy, related to their wavelength, or frequency, by the equation E = hν. But real particles also have a property called momentum, which physicists denote by the letter p, since m is reserved for mass. In the course of developing his special theory of relativity, Einstein also came up with an equation for the momentum of a photon, which is simply p = E/c, where c is the speed of light. It was de Broglie who put the two equations together and said that in that case the momentum of a photon is related to its frequency by the equation p = hν/c. Or, since wavelength, denoted by the Greek letter lambda, l, is simply the speed of light divided by the frequency, for light quanta p = h/l. This curious equation relates a fundamentally particle property, momentum, to a fundamentally wave property, wavelength. Weird enough for photons. But de Broglie didn’t stop there. His inspired leap was to say that this equation must apply to any particle that has momentum, which means any particle. and to any wave which has wavelength, which means any wave. In particular, it must apply to electrons. Electrons should have a wavelength which could be measured by the same diffraction techniques used to study X-rays.

De Broglie presented his big idea in his Ph.D. thesis in 1924. His baffled Ph.D. supervisor, Paul Langevin, sent a copy to Einstein to ask what he thought of it. Einstein endorsed the idea with the comment, “I believe that it involves more than a mere analogy.” So de Broglie got his Ph.D., and the experimenters set out to test the idea.

Some experiments, in fact, had already been hinting at the wave-particle relationship, without anyone realizing it. Clinton Davisson was an American researcher who, in the early 1920s, had been looking at the way electrons bounce off a nickel surface. In 1926, he was on a visit to Britain, where he attended a lecture given by the German physicist Max Born. Born described de Broglie’s idea and its implications, then, to Davisson’s surprise, pointed out that the results of some of the scattering experiments carried out by Davisson and already published matched up with what would be expected if de Broglie was right. As soon as he was back in the USA, Davisson and his colleagues adapted their experiment to make a proper test of the electron wave theory.

The wavelength to be measured is predicted by turning de Broglie’s equation round to read l = h/p. Planck’s constant, h, is a very small number, so the predicted wavelength is unmeasurably tiny except for very small particles such as electrons, which have correspondingly small momenta. Davisson and his colleague Lester Germer used an experimental setup which echoed the way the Braggs had worked with X-rays a decade earlier. The electrons they used were in effect boiled off from a hot wire, and then manipulated with electric fields to produce a beam of particles with a known momentum directed at a nickel surface. The piece of nickel was mounted in such a way that it could be rotated and tilted so that the electrons struck it at different angles, and an electron detector could be moved to different places around the nickel to measure the intensity of the beam of electrons being scattered at different angles. It was the experiment with many holes, but carried out with electrons instead of X-rays. Early in 1927, the American team had clear evidence for a pattern of peaks and troughs in the intensity of the scattered radiation which exactly matched Bragg’s law for waves diffracted by a crystal lattice. So they were able to work out the wavelength of this radiation using Bragg’s law. It matched the wavelength predicted by de Broglie’s equation.

Meanwhile, on the other side of the Atlantic Ocean, George Thomson, the son of J. J. Thomson, was also following up the ideas presented by Born in his recent lecture. Thomson was based in Aberdeen, where he applied a very different technique to the investigation of electron waves. Thomson placed thin sheets of gold foil, between one ten-thousandth and one hundred-thousandth of a millimetre thick, in vacuum tubes (essentially the same as cathode ray tubes), and fired his beams of electrons straight at the foil. On the other side of the foil, a photographic plate recorded the arrival of the electrons, after they had been deflected by the atoms of gold in the foil. The plates were then developed to study at leisure. At about the same time that the Davisson–Germer experiment was producing results, Thomson was finding that the pattern of spots produced on his photographic plates was a diffraction pattern. In a subtle addition he proved that the spots were being made by the electrons, not by some other radiation, by bending the electron beam with electric fields and monitoring the way the pattern shifted. The wavelengths he measured in this way matched the predictions of de Broglie’s equation to within 1 per cent.

The fact that two completely different experiments had independently confirmed the accuracy of de Broglie’s equation at exactly the same time meant that physicists were quick to accept the reality of wave-particle duality, as it became known, even though they did not understand how the world could be like that. Davisson and Thomson shared the Nobel Prize for their work in 1937, and in his Nobel lecture Davisson highlighted this: “That streams of electrons possess the properties of beams of waves was discovered early in 1927 in a large industrial laboratory in the midst of a great city, and in a small university laboratory overlooking a cold and desolate sea . . . Discoveries in physics are made when the time for making them is ripe, and not before.”

One of the most striking aspects of this particular discovery highlights the mysterious nature of the quantum world. J. J. Thomson received the Nobel Prize for proving that electrons are particles. He lived to see his son, George Thomson, receive the Nobel Prize for proving that electrons are waves. Both of them were right; both awards were justified. And in the mid-1920s, two “explanations” of the quantum world were developed, one theory based on particles, the other theory based on waves. Again, both theories were right. Either one could be used to predict (correctly) the outcomes of experiments involving atoms, electrons and light, and either one could be used to “explain” how things like atoms, electrons and light behave. But still nobody knew how atoms, electrons and light could be like that, and this led to some very strange ideas about what was going on.

SIX

The Theoretical Minimum

I don’t intend to delve into the details of quantum theory here. I’ve done that before. But it is worth providing the minimum amount of quantum theory that you need in order to appreciate just how mysterious the central mystery of quantum mechanics is. It all started with the work of Werner Heisenberg, in Germany, in the mid-1920s.

This was just before the work of Davisson and Thomson, so it was natural for Heisenberg to think in terms of electrons as particles. The particular problem that puzzled quantum physicists at the beginning of the 1920s concerned the way in which atoms interact with light. The image they had was of electrons “in orbit” around the central nucleus of an atom. But it was clear that the electrons were only allowed to occupy certain orbits, corresponding to certain energies – a better term than “orbit” is, indeed, “energy level”. An electron could absorb a photon with a particular frequency, corresponding to a specific amount of energy, and jump up an energy level, or it could fall down from one level to another and emit the corresponding photon. All this “quantum jumping” matched the discoveries concerning the interaction of light with matter made by Planck and by Einstein. But how did the quantum jumping work? What happened to the electron between energy levels?

The physicists at the University of Göttingen, where Heisenberg worked, realised that there was no way of knowing what was going on between energy levels, since no experiment ever observed this. You could make a measurement which showed the electron in one energy level, or quantum state, and you could then make another measurement which showed it in a different quantum state. You could even detect the photon it had emitted as a result of the transition. But it seemed to be meaningless to ask what was going on when the system was not being observed. Heisenberg spotted that the key to observations of this kind is that they always involve two measurements, the before and after states. So he worked out a set of mathematical rules to describe the relationships between pairs of observable quantum stares. This turned out to involve mathematical entities known as matrices, which are like two-dimensional numbers. This is a little like the way the way that the squares on a chess board can be identified using the symbol pairs a1, a2 and so on right through to h7 and h8. One table (one matrix) describes the before state of a quantum system, another matrix describes the before state of another quantum system, and the way they interact can be described using mathematical techniques, such as the matrix equivalent of multiplication, to produce a third matrix which describes the after state of the system. This work was made easier for the Göttingen team because matrices had long been known to mathematicians, who had worked out all the rules describing their behaviour without ever dreaming that they might be put to this practical use.

The mathematical details, however, do not matter here. What matters is that Heisenberg and his colleagues found that by using this technique they could correctly predict the results of experiments involving things like electrons. The idea of orbits seemed to be dead, replaced by the idea that electrons occupied energy levels like rungs on an invisible ladder, and could make the transition from one rung to another instantaneously, without passing through any intermediate state. This successful package of ideas, essentially complete by the end of 1925, became known as matrix mechanics. But how could this be squared with de Broglie’s suggestion that electrons are waves? At the end of 1925, the experiments confirming that de Broglie was right had not been carried out, so there was still leeway for doubt. But one physicist not only took de Broglie’s idea seriously, but jumped off from it to develop another successful description of the quantum world.

Erwin Schrödinger was working in Zürich at the end of 1925, when he decided to see if he could find a way to describe the behaviour of electrons in atoms in terms of waves. The basic idea was very simple, and involved the image of an electron wave forming a circle around an atomic nucleus, with an exact number of wavelengths, to make a kind of stationary orbit. Different numbers of wavelengths would correspond to different orbits, at different distances from the nucleus, and there could be no “in between” orbits because these would not correspond to a whole number of wavelengths. Different energy levels would correspond to different wavelengths, just as different notes on a plucked guitar string correspond to different wavelengths. But what was needed was a wave equation for the electron, which could be used to calculate which orbits were allowed, and the energy levels associated with them. Schrödinger found such an equation, the equivalent for electrons of Maxwell’s equations for electromagnetic radiation, during an intense burst of work at the end of 1925. This led to a series of scientific papers published in 1926, starting with one that appeared in the journal Annalen der Physik in March that year. Like matrix mechanics, Schrödinger’s wave mechanics correctly predicted the outcomes of experiments involving quantum entities.

At the beginning of 1925, physicists had no satisfactory theory of quantum mechanics. At the end of 1926, they had two. And both were right.

There was one other idea that went in to those theories – probability. It had become clear from experiments that events in the quantum world are not precisely determined but follow probabilistic rules. The archetypal example is radioactive decay. This happens when an unstable atom – strictly speaking, its nucleus – spits out an electron, or some other particle, and in the process is converted into an atom of another element. Ernest Rutherford and his colleagues had shown that in a lump of radioactive material half of the atoms “decay” in this way in a certain time, called the half-life. Each radioactive element has its own characteristic half-life. In the next half-life, half of the rest (a quarter of the original sample) decay, and so on. But there is no way to tell which individual atoms will decay first. Any particular atom may decay at once, or not for a very long time. This kind of behaviour is seen across the quantum realm and obeys precise rules of probability worked out in no small measure by Einstein. So probability had to be incorporated into any quantum theory developed either from matrix mechanics or from wave mechanics.

Although both versions of quantum mechanics are equally valid, Schrödinger’s version was the one that became popular as a practical tool used by everyday physicists to solve practical problems, because physicists were used to dealing with waves and thought that they understood them; but matrix mechanics continued to interest theorists with a more abstract concern for the fundamentals of quantum theory. Wave mechanics, with the addition of the probability rules, developed by the end of the 1920s into what became the standard version of quantum theory, known as the Copenhagen Interpretation because its leading proponent, Niels Bohr, worked in that city. The Copenhagen Interpretation worked, in the sense that if you plugged the appropriate numbers in to the equations you could do calculations and make accurate predictions about the outcome of experiments. But it made no sense at all if you thought about it. For fifty years, most physicists did not think about it, they just calculated.

At the heart of the Copenhagen Interpretation lay the idea that the wave equation Schrödinger had found did not actually describe a kind of smeared-out electron; after all, we never see (detect) anything except a whole electron. Instead it was interpreted as a “wave of probability”. The intensity of this probability wave at a particular spot was a measure of the likelihood (probability) of finding an electron at any spot, so in diffraction experiments, for example, the electrons congregated in places where the probability wave was strongest. Bohr said that it was meaningless to ask where an electron – or any other quantum entity – was when nobody was looking at it (when it was not being measured), and all you could say was that it was somewhere in the region occupied by the probability wave. Then, when you made a measurement, the wave collapsed and the electron appeared at a point. When you stopped looking, the probabilities took over again, and next time you looked the electron might appear somewhere else. The probabilities could tell you where it was likely to appear, but never where it was certain to appear. Thus idea of the “collapse of the wave function” was at the heart of the Copenhagen Interpretation, and Schrödinger hated what had been done to his equation. He hated it so much that he dreamed up a famous thought experiment to demonstrate how ridiculous the whole package of ideas was.

Schrödinger’s thought experiment concerned a hypothetical cat in a sealed room (through an error in translation, this became known as the “cat in a box” experiment, but no box is actually involved). He asked us to imagine this cat in comfortable surroundings with everything it needed in the way of food, water and a nice bed to sleep on. But the imaginary room also contains what he called a “diabolical device” – a sample of radioactive material linked to a container of poison. If the radioactive sample decays, the poison is released, killing the cat. According to the quantum rules, there will be a time when there is a precise 50:50 chance that the material has or has not decayed. But the wave function cannot collapse one way or the other until it is measured. Schrödinger pointed out that at that moment, before the measurement has been made, the poison has both been released and not been released, and the cat must, according to the Copenhagen Interpretation, exist in what is known as a superposition of states, being both dead and alive at the same time. This is clearly nonsense, but it is what the Copenhagen Interpretation says.

Hardly surprisingly, while the average quantum mechanics were happy to shut up and calculate, a minority of physicists worried about this, and tried to find other explanations for what is going on – other “interpretations” of quantum mechanics. This did not prove difficult. Several other explanations were found, all of which satisfy the requirement of enabling physicists using them to correctly predict the outcomes of experiments. Like the underlying theories of matrix mechanics and wave mechanics, these interpretations are all equally valid, and you can use whichever one you feel comfortable (or least uncomfortable) with. I have described the main contenders in my book Schrödinger’s Kittens, so here I will just give a flavour of my own favourite variation on the theme. But in its own way, it is just as strange as the Copenhagen Interpretation.

The version I like best is called the Many Worlds Interpretation, or MWI. It happens to be the version Schrödinger himself preferred, although when he mentioned it in a talk in Dublin in 1952 it had not yet been given that name. The MWI says that instead of the quantum world existing in an uncollapsed superposition of states until somebody looks at it, every possible outcome of every possible quantum choice really takes place, across a range of possible worlds, often referred to as parallel universes. This neatly resolves the Schrödinger’s cat puzzle. Instead of a cat that is both dead and alive at the same time, we have two universes, one containing a dead cat and the other containing a live cat. By opening the door to the sealed room and looking inside, you are not causing the wave function to collapse, but merely finding out which of those realities you inhabit – while your Doppelgänger in the universe next door is simultaneously finding out which universe they inhabit.

This does not, as is often mistakenly suggested, imply that at the moment of truth the universe splits into two, one with a dead cat and one with a live cat. The idea is that there always were two universes, in one of which the cat died while in the other it lived. There is no collapse and no splitting, at the admittedly considerable expense of invoking an infinite number of alternate realities that we can never communicate with. But as I am the first to admit, none of the quantum interpretations is perfect.

One of the reasons I prefer the MWI to the Copenhagen Interpretation can be seen by looking at another bizarre idea, the so-called “delayed choice” experiment. Unlike the Schrödinger’s cat “experiment”, although this one also started out as a thought experiment, it now really has been carried out.

By the 1970s, physicists knew from experiments that if a light source was turned down so low that only one photon at a time emerged, and those individual photons were fired one at a time through the experiment with two holes, they still combined to build up an interference pattern on a screen, as if each photon had somehow passed through both holes and interfered with itself on the way through the experiment. This didn’t seem too surprising for waves described by Maxwell’s equations, and I won’t go into all the details since this kind of experiment lies at the heart of the much more surprising central mystery, discussed in the next chapter. Physicists also knew that if they set up a system to monitor the passage of the photons through the experiment, in effect looking to see which slit the photons were going through, the photons did indeed behave like particles, going through just one slit or the other, with no interference pattern building up. In the language of the CI, the wave function collapsed when they looked at it. That is strange enough, compared with the way things are in the everyday world. But the American physicist John Wheeler then pointed out something stranger still.

Wheeler contended that in particular it ought to be possible to place the monitoring detectors in the gap between the two slits and the detector screen, so that they “looked at” the photons after they had passed the slits, but before they arrived at the screen. In an echo of the Schrödinger’s cat thought experiment, the Copenhagen Interpretation, the favoured version of quantum theory, said that before the choice is made the entire experiment exists in a superposition of states, one possible reality corresponding to waves passing through both slits, the other corresponding to particles passing through one slit or the other, and that by detecting the photons in flight we could “collapse the wave function” into one version of reality. But this means that what is happening at the slits depends on a measurement made after the photons have passed the slits, like an influence extending backwards in time. It became known as Wheeler’s “delayed choice” experiment.

If you think this is crazy, you are in good company. Like the cat experiment, this was intended to demonstrate the absurdity of quantum theory. Unlike the cat experiment, however, in the 1980s experiments were actually carried out which seemed to show this effect at work. In those experiments, beams of laser light were split in two and then recombined to make an interference pattern. Detectors that could be switched on and off very rapidly were placed in the paths of the beams; they could be switched by a computer program in only 9 billionths of a second. But the distance travelled by the light beams was 4.3 metres, and this took them 14.5 billionths of a second at the speed of light. An automated system “decided” at random whether to switch the detectors on, after the beam had been split. In a long run of experiments, the results were clear-cut. With the detectors off, there was interference. With the detectors on, no interference. The state of the detectors had decided what was happening to the light beams a few billionths of a second earlier, when they passed the beam splitter.

You might not be too worried about a few billionths of a second between friends. But then Wheeler administered the coup de grâce. Astronomers know of systems called gravitational lenses, in which light from a quasar billions of light years away is bent by gravity to follow two or more paths around an intervening galaxy. This produces multiple images of the quasar in our telescopes. This is the cosmic equivalent of a beam-splitting experiment. The light bending is not so precise as in the splitting of laser beams in the lab, and this tends to blur out the images, which makes carrying out an interference experiment using them impossible with existing technology. But technology is always advancing and some day such an experiment may be possible. This will present an awesome prospect. Light from two gravitationally lensed images of the same quasar could be brought together and combined, allowing for the possibility of interference. If there is interference, it ought to be possible to turn it off by placing a detector in the beam of one of the images to monitor the passage of the photons. Then, there will be no interference. Turn the detector off, and interference will be restored. That is what quantum theory (at least, the CI) says. But turning the detector on or off will mean collapsing the wave function of the light all the way back to the source, in a quasar on the other side of the Universe, a billion or more years ago. The light may have taken a billion years to reach us, but it’s as if the entire Universe “knows” in advance what some astronomer on a mountain top on Earth today, or in an observatory on the far side of the Moon some time in the 22nd century, is going to do a billion years later.

That, surely, is enough theory to be going on with. Perhaps more than the minimum you really need. Time to get back to the certainty of experiments, where the central mystery of the quantum world can be laid bare by studying the behaviour of electrons in the laboratory, without contemplating the nature of the cosmos.

SEVEN

The Most Beautiful Experiment in Physics

There is something peculiar about light, which provides a get-out clause for anyone who thinks that the strange events described in the previous chapter might not apply to “real” particles. Photons travel, of course, at the speed of light. And the special theory of relativity tells us that time runs slower for moving things, to the point that it actually stands still for things moving at the speed of light. To a photon, time stands still, so everything along its flight path happens at once – so maybe it is not so surprising that it knows “in advance” what experiments are going to be carried out. (If you change the frame of reference from our perspective to that of the photon, then relativity theory tells us that space intervals shrink to zero along the line of flight, so it is still true that to a photon everything happens at once, because it is all in the same place.) Could the same sort of thing actually happen for particles like electrons, which move much more slowly than light? Yes, it can. Like photons, electrons seem to “know” about the whole of an experimental setup, including its future and its past. And this is brought out most clearly by electron-based versions of the experiment with two holes.

The first versions of the electron double-slit experiment didn’t literally use a double slit, but a device called an electron interferometer. In this device, a beam of electrons, boiled off from a hot wire like the ones used by Davisson and Germer, is fired past a thin wire lying at right angles to the beam. In early experiments using this technique, the (very) thin wires required were made by coating fibres from spiders’ webs with gold. The wire is negatively charged, so it repels the negatively charged electrons in the beam. The apparatus is carefully designed to be symmetrical, so that half of the electrons go one way round the wire, and half go the other way (or, in the language of the CI, there is a 50:50 chance of any individual electron going one way or the other). After the beam has been split in this way, it encounters a positively charged wire, which pulls the two halves of the beam back together and allows them to interfere. A detector like a TV screen then records the arrival of the electrons in the usual way, with the bonus that each time an electron hits the screen it make a spot which persists, so that an increasingly dense pattern builds up while the experiment is running, and this build-up can even be recorded to play back later.

If electrons behaved like the kind of “particles” we are familiar with – cricket balls, perhaps – you would expect that balls that went one way round the wire would combine to make a blob on one side of the screen, while balls that went the other way round the wire would combine to make another blob on the screen, with the two blobs perhaps overlapping. But that is not what happens. It should be no surprise to you by now to learn that the pattern that is produced on the screen is an interference pattern, just like the pattern produced by light in the Young’s slit experiment. A beam of electrically charged particles is displaying wave properties. But this is just the beginning.

What happens if, instead of firing a beam containing many electrons through the experiment, you fire electrons through one at a time, and watch the pattern that builds up on the detector screen? That is exactly what the Italian physicists Pier Giorgio Merli, Gian Franco Missiroli, and Giulio Pozzi did in 1974, using a slightly more sophisticated beam splitting device, called an electron biprism, which gave them more subtle control over what was happening to the beam; but the principle was exactly the same.

Their detector was so sensitive that it could record the arrival of a single electron, and the team’s control of the electron beam was so subtle that they were able to fire electrons through the experiment one at a time. Each electron made a tiny spot of light on the screen. As more electrons were fired through, one at a time, what looked at first like a random pattern of spots built up on the screen. But as more and more electrons went through the apparatus, the spots built up and merged to make a clear pattern of stripes – the familiar interference pattern for waves. These fringes began to be clear after several thousand electrons had arrived at the screen, but then the spacing of the fringes made it possible to work out the wavelength of the electrons involved, which exactly matched the wavelength calculated using de Broglie’s equation.

This experiment made several things clear. First, the interference pattern is not a result of the combined effect of many particles acting to produce a wave, in the way that many molecules of water combine in the sea to produce a wave. The interference pattern is produced by the accumulation of single events, separated from one another in time and in space – the flight path of the electrons was 10 metres long, so they followed one another like aircraft taking off from Heathrow. Each electron is in some sense behaving as a wave, and they are not interacting with one another in flight. Secondly, electrons are seen to be exhibiting both particle-like properties and wave-like properties in the same experiment, although not at the same time. It would be mysterious enough if pure waves sent through the experiment one at a time combined with one another to make an interference pattern, but the “waves” in the Italian experiment both start and finish their journeys as particles! And all this happens without there being any physical interaction between the electrons and the apparatus between the source and the detector – unlike light, which is physically affected by the two slits in Young’s experiment.

Although the Italian team completed this work in 1974, and published it in the American Journal of Physics in March 1976, it received so little attention at the time that when I was writing In Search of Schrödinger’s Cat, in 1983, I had not heard of it, and none of the people I discussed the book with mentioned it to me. I only became aware of single-electron double-slit diffraction, as it is rather clumsily called, when a Japanese team, headed by Akira Tonomura, carried out a similar experiment and published its results in 1989, also in the American Journal of Physics (the editors of the journal seem to have been unaware that they had published the Italian team’s paper thirteen years earlier). The Japanese version is superficially more impressive, because the improvements in technology since the early 1970s enabled them to produce a more dramatic movie of the build-up of the interference fringes. But both experiments convey the same message.

Belatedly, the importance of that message began to sink in to the consciousness of the physics community. 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 in 2013, the experiment became even more beautiful, when it was carried out using two actual slits, which could be opened and closed at will.

A key step towards this ultimate double-slit experiment was taken by Giulio Pozzi and his colleagues in 2008. They devised an experiment in which electrons could be fired one at a time through two genuine, 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 repeated the experiment, no interference was observed.

It’s worth thinking about this a bit. If electrons are particles, they can only go through one slit or the other. How does an electron going through one slit “know” whether the other slit is open or not? This question doesn’t arise in the electron biprism version of the experiment, because in that experiment both “channels” are always open. So Pozzi and his colleagues had taken a significant step forward. The experiments by Pozzi were the first to use nano-fabricated slits in a wall.

Their success encouraged another group, on the other side of the Atlantic Ocean, to go one step further. After several years of work, in 2013 a team headed by Dutch-born Herman Batelaan announced the results of what is the definitive single-electron double-slit diffraction experiment. They 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 a 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: (https://www.youtube.com/watch?v=hv12oB_uyFs ).

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 set-up 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.

This is exactly what Richard Feynman had predicted 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 famous 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.