Fundamental

by Tim James

  Planck could not believe it at first and even sent his assistant to Switzerland to check if this ‘A. Einstein’ fellow was real and not someone writing under a pseudonym to avoid ridicule.1 When he discovered that Einstein was in fact a genuine human (although a fairly inexperienced one – he did not even have a doctorate) Planck published his paper at once. His ridiculous light-quanta idea might not be so ridiculous after all.

  Einstein’s paper dealt with something called the photoelectric effect. Simply put: when you shine light on a clean piece of metal, electrons on the outside of the metallic atoms can get dislodged and come flying away from the surface.

  The reason it happens is because electrons absorb light and, if the incoming beam is energetic enough, an electron can absorb it and be shaken loose. This is not that surprising in itself, but what is surprising is that not every colour makes it happen.

  Each metal is unique but generally speaking red, orange and yellow lights do nothing to a metal surface, whereas green, blue and violet will cause electron emission. Green, blue and violet light packs more energy than red, orange and yellow so that makes sense, but what is strange is that if you increase the brightness of a red light (until it equals a blue one) nothing happens.

  We measure quantum energy in units called electron-Volts (eV for short) and a red light of 10 eV contains the same amount of energy as a blue light of 10 eV. So how come red and blue light of equal energy do not cause the same effect? Is 10 eV of red not the same as 10 eV of blue? Einstein showed that if you took Planck’s quantum theory seriously, it was not. Ten does not always equal ten.

  AN APPLE IN THE HAND IS WORTH TWO NOBEL PRIZES

  Imagine someone holding an apple in an outstretched arm. If you spray a water pistol at their hand (do not ask why you are doing this, this is how physics analogies work) the apple will stay put until you crank things up to a powerful stream. At this point, the water energy can overcome the hand’s grip and the apple goes flying into the air.

  In the same way, an electron is bound to its atom with a certain amount of energy and as we increase the brightness of the incoming light, we should eventually knock it loose, no matter what colour we’re dealing with. We do not get that result in the lab, however, so once again we need to crumple up our theory and try something new.

  If we consider our red beam and imagine chopping it into little pieces as Planck suggested, each one will contain a certain amount of energy. A beam of blue can be chopped into the same number of pieces, of course, but each one will pack more of a punch.

  Instead of thinking of light energy as a smooth water jet, we need to think in terms of particles. Red light quanta would be akin to something like ping-pong balls. If you fire a ping-pong ball at someone’s hand, the apple will not budge even if you boost the intensity. You can chuck a whole bucket of ping-pong balls at your volunteer but because each interaction between apple and ball is insignificant, nothing ever gets displaced no matter how much light there is.

  By contrast, a quantum of blue light is more like a cannonball. If you fire a single blue particle at your apple holder it will dislodge the apple and probably their hand as well. Pick your volunteer carefully.

  A hundred ping-pong balls might have the same overall energy as a single cannonball but the cannonball is easily going to have more of an impact. Therefore, the total energy of a beam of light is irrelevant if it is split into particles; all that matters is the colour. Which is what we observe.

  According to Einstein, Planck’s quantum theory of light had real physical meaning. It was not just a way of getting us near the answer, it was the literal answer itself. Light was made of particles after all. Soon after Einstein’s proof, the chemist Gilbert Lewis decided these particles ought to have a catchier name than ‘light-quanta’ and started using the word photon (Greek for light), which has now stuck.2

  Both Planck and Einstein received Nobel Prizes for their new approach to light physics in 1918 and 1921 respectively. Gilbert Lewis did not get a Nobel Prize, sadly, but he did have an awesome moustache and is credited with having invented the word ‘jiffy’, so in a way everyone was a winner.

  UM… EINSTEIN? WE HAVE A PROBLEM

  When Einstein proved light was made of particles it was not just confirming Planck’s quantum theory, it was flying in the face of Young’s light waves as well.

  On the one hand, the photoelectric effect and ultraviolet catastrophe could only be explained if light was made of particles. On the other hand, the double-slit experiment shows light has to be a wave in some sort of background medium.

  When two proposed hypotheses clash, scientists resolve the disagreement by carrying out experiments to distinguish them. But what in the name of Newton’s apple-munching ghost do we do when the experiments themselves disagree? This was an unprecedented situation for science so we had to try and find a loophole.

  Perhaps we could explain the results of Young’s double-slit experiment in terms of photons. Is our light source spraying them out like a machine gun and they collide mid-air to generate the zebra pattern?

  The best way to confirm this would be to eliminate the possibility of photons interacting with each other as they fly through the double slits. Rather than spraying them all in one go we should try firing them individually, effectively replacing our machine gun with a sniper rifle.

  Lots of versions of this experiment have been devised over the years but the best, hands down, was the one carried out by Akira Tonomura in 1994 while working for Hitachi.3 The same company that make tanks, refrigerators and massage wands also holds claim to the most precise double-slit experiment ever executed.

  The details of Tonomura’s setup are quite different to the one Thomas Young carried out but they achieve the same goal so for simplicity and convenience I am going to use the same terminology, even though it was not quite as simple as I am going to make it sound.

  In his experiment, Tonomura’s beam emitter could be modified from high to low brightness, firing photons towards two slits. A detector screen was set up on the other side made from a material that illuminated when struck, creating a pinprick of light wherever each particle landed.

  When a whole bunch of light was fired at the slits, as Young did in his original, Tonomura got the expected zebra pattern, but when he dialled down the intensity to one photon at a time he got something seriously weird.

  For the first few minutes nothing interesting happened. Each photon shot toward the slits and hit the detector screen seemingly at random. But as he watched, the pattern of dots started to build up in ribbons like this… look familiar?

  That should not be possible because each particle is being fired individually. The zebra pattern requires a photon going through one slit to mix with another photon coming from the other slit. If each photon is fired individually, it should not have anything to mix with. How are the photons creating an interference pattern when there is nothing for them to interfere with? Are the photons somehow going through both slits at the same time?

  QUANTUM PANTS

  I remember once pulling a pair of pyjama pants out of the laundry and being confused because I was apparently wearing them at the same time. For a few seconds I stood in bewilderment, believing myself to be the owner of quantum pants, capable of existing in a pants superposition of location.

  It was then pointed out to me that I own two pairs of the same pants and had simply never noticed before. In my defence, I was thinking about quantum physics at the time and in quantum physics you never go for the simple explanation. The simple explanation never works.

  The double-slit experiment shows that light can act like a particle at the point of being fired from an emitter but it can act like a wave when it goes through the slits.

  In terms of ‘classical physics’ – the physics of Isaac Newton where everything behaves sensibly – particles and waves are distinct things. Quantum theory was starting to blur that boundary.

  ZIGGY SAYS IT’S COMPLICATED

  As Einstei
n was collecting his Nobel Prize in Sweden, a young Danish physicist and football enthusiast4 named Niels Bohr was taking quantum theory and applying it to whole atoms.

  Atoms are made of particles called protons, which cluster in a central nucleus, and electrons, which hum around the outside like bees swarming a nest. (NB: neutrons, which also reside in the nucleus, had not been discovered at this point.)

  It was known that light coming off a glowing atom did so at values unique to that type of atom. Hot iron emits different frequencies to hot nickel, for example, and conversely, it absorbs different light colours shone upon it. Previously this had been difficult to explain because light was thought to be a smooth wavy substance but once we learned that a beam of light was sometimes made of particles with specific energies it became possible to explain its interactions with matter. Photon energies come in specific values, so it stood to reason that electron energies did so as well.

  In Bohr’s quantum theory of the atom, electrons are not considered to be zipping around a nucleus at random. Instead, they travel across the surface of invisible spheres at specific distances. Bohr called these spheres ‘electron shells’, although he obviously should have called them ‘Bohrbits’.

  Bohr’s atom was a three-dimensional version of a solar system and it is the popular picture of an atom people still draw today. The difference between electrons and planets, however, is that planets can travel around the sun at any distance they like. Gravity exerts a force at every point in space and decreases smoothly as you recede, so any orbit distance is allowed provided you move at the correct speed to avoid being sucked in.

  Quantum electron shells are different. Electrons are not allowed to take any energy at will because energy is chunked into specific values (we say it is quantised).

  A low energy electron will be fixed on a shell close to the nucleus but, if it absorbs a photon, it gets a boost and can orbit on a shell further out. Given that the distances between shells are fixed, only certain energy jumps are permitted and thus only certain beams of light will interact with certain atoms.

  Suppose the distance between two shells is a 20-eV jump. If an electron absorbs a 20-eV photon it can thus make the jump perfectly. But if we were to fire a 19-eV photon at the atom, nothing can happen. A 19-eV jump is not permitted so the photon will carry on right through as if the atom were not there.

  This means electrons cannot exist at intermediate energy values between shells. So when an electron absorbs a photon and transitions to a higher shell it does not pass through the no-man’s-land between. It apparently snaps from the inner shell to the outer one instantly, in what is called a ‘quantum leap’. I am not saying the electrons teleport between shells… but it looks an awful lot like it.

  A quantum leap is an electron disappearing from one shell and reappearing on the next, simultaneously absorbing a photon in the process (if gaining energy) or releasing one (if losing it). Ironically, in everyday use the term ‘quantum leap’ tends to mean a huge change, but it actually refers to the smallest change it is literally possible to make.

  Bohr was not sure why electrons orbited at certain energies and quantum leapt between them but it explained what he wanted so he jammed a bunch of ideas together and decided not to worry about it.

  In essence, Bohr made a collage out of existing physics ideas like a child stealing fabrics from their parents’ linen cupboard and taping them together to form a sincere but ugly picture. And, since nobody else was doing any better, everyone just accepted it and stuck it to their refrigerators.

  PHYSICS IS NEVER BOHRING

  Quantum leaping, however, does explain something else pretty crucial. Protons exert an attractive pull on their electrons. It is this pull that electrons have to overcome in the photoelectric effect we saw earlier. We call the attractive property of a particle its ‘charge’ and it comes in two varieties arbitrarily named positive (for protons) and negative (for electrons). Particles with the same charge repel like similar ends of a magnet, while particles possessing opposite charges attract.

  Charge has been known about since the days of Benjamin Franklin and his lightning-kite experiment (a real experiment by the way, not an urban legend).5 What charge actually is gets complicated (we’ll find out in Chapter Twelve) but whether you know what causes charge or not, it raises a good question: if electrons have the opposite charge to protons and are attracted to them, how come they do not spiral towards the nucleus, shrinking the atom? Why are atoms not doomed?

  Bohr’s answer was that this would violate the principle of quantum energy. An electron on the lowest shell, nearest the nucleus, is on the bottom rung of the energy ladder. If it were to start drifting inward it would be taking all sorts of values that are not permitted.

  The only way to lose energy once you’re on the innermost shell would be to step off the ladder altogether and simply stop existing. Electrons might desperately want to move towards the nucleus but the principle of quantum energy is deeper than the law of charge attraction.

  KINGS OF THE ELECTRON

  At about the time quantum theory was beginning to germinate in Europe, the undisputed don of particle physics was the British physicist J. J. Thomson – the man who showed that electrons had a negative charge, as well as discovering them in the first place.

  Today, Thomson’s ashes are buried next to those of Isaac Newton and, at Cambridge University, the physics department is located on J. J. Thomson Avenue. Oh, and he was knighted. And he got a Nobel Prize. As did six of his students.

  But did he invent quantum pants?

  Discovering the electron and its properties was Thomson’s crowning glory. He had demonstrated their existence by deflecting arcs of electricity and measuring how much the arcs weighed. Since electricity had a mass, it was evidently made from particles that did as well.

  When he originally announced this discovery on 30 April 1897, several people came up to him at the end of the lecture to congratulate him on having pulled off a successful hoax.6 Nothing could be smaller than an atom, surely?

  Electrons are real though, make no mistake. Two thousand times lighter than the smallest atom, hydrogen, but real nonetheless. Thomson originally wanted to call them corpuscles in honour of Newton, and the American physicist Carl Anderson wanted to call them negatrons7 (which we can all agree is the best name imaginable) but electron caught on instead.

  Among Thomson’s many notable students were Ernest Rutherford, who discovered the atomic nucleus, and Niels Bohr, who showed that electrons had to orbit this nucleus in shells.

  The most revolutionary discovery made by one of Thomson’s students, however, was that electrons were not particles all the time. They sometimes had wave behaviour just like photons. A discovery made by George Thomson, J. J.’s son.

  George was interested in light being sometimes a particle and sometimes a wave, so he decided to see if the same thing could be achieved with electrons.

  If electrons had wave properties, they were obviously very small waves to have gone undetected for so long. In order to diffract electrons through a double-slit experiment, he would therefore need a tiny double slit (smaller waves need a smaller separation between slits), which is not an easy thing to build.

  To get around the problem, he obtained some celluloid film like the kind used in movie cameras because in this substance, atoms are spaced in rows at regular intervals resembling a double slit on the atomic scale, and he fired a beam of electrons through it.

  Sure enough, the beam on the other side split into the zebra pattern, meaning the electrons had to be interfering with each other like waves. (NB: electrons are actually the particles Tonomura used in his experiment from earlier, but I felt that if I announced electrons were waves at that point in the chapter it would have caused mass panic, rioting and the end of civilisation as we know it. So I lied.)

  Turns out electrons, which everyone knew to be particles, could be superpositioned and diffracted like waves of light. Nobel Prize for George.

&nb
sp; It’s sort of brilliant that J. J. Thomson won a Nobel Prize in 1908 for proving electrons were particles and then his son got one in 1937 for proving they were not. I like to imagine awkward Christmas dinners at the Thomson household with J. J. and George sitting opposite each other, both wearing scowls and colourful paper hats, casually polishing their prize medals while Mrs Thomson sits uncomfortably between them. ‘Anyone for plum pudding, dears?’

  CHAPTER THREE Aristocrats, Bombs and Pollen

  THE DUKE OF DUALITY

  I remember many years ago, in the hazy days of my youth, attending a university interview and being sat in front of four distinguished scientists who asked what I knew about quantum theory. Foolishly, I had mentioned it in my application letter so they wanted to grill me and take me down an energy shell or two.

  I reeled off a bunch of facts about waves and particles, trying to make it look like I knew my stuff, until one of them raised her hand to halt my waffle and asked very gently, ‘So, is an electron a particle or a wave?’ before sitting back to watch me flounder. I am not bitter about this experience at all, but in fairness she was asking me an unanswerable question.

  The mystery of electrons and photons behaving in different ways is called ‘wavevparticle duality’ – a term coined by the French nobleman Louis Pierre Raymont, 7th Duke of de Broglie (Louis de Broghie for short). Louis served in the military during the First World War and insisted on getting an education afterwards in both history and physics, which he thought crucial for understanding the past and future of humanity.

  By the time he was in his twenties, quantum theory was the big thing in science, so he decided to write his thesis on this central enigma. Was it possible that things in the universe were neither particle nor wave and only took these forms depending on which experiment we performed? Did electrons and photons somehow hop back and forth between the two states? Could our feeble chimp-brains even handle what nature is really doing at the quantum level?