Fundamental

by Tim James

  Dedicated to the students of Northgate High School

  ‘No matter how sure scientists think they are, nature has a way of surprising them.’

  Nemesis by Isaac Asimov

  INTRODUCTION The End

  Nature is out of her mind. When you get right down to the fundamental laws of physics, right down to the basement, you find yourself in a realm of craziness and chaos where knowledge and imagination become the same thing.

  This should not come as a surprise of course – you have to question the sanity of a universe which permits the existence of starfish – but even if you are prepared for nature to be eccentric, nothing braces you for quantum physics.

  It began at the end of the nineteenth century when everyone was feeling smug about themselves. We had mapped the stars, isolated DNA and were on the verge of splitting the atom. Our knowledge was nearly complete and it looked as though we were about to witness the grand finale of human achievement: the end of science itself.

  There were obviously a few awkward scientific puzzles nobody had quite solved but they were minor curiosities dangling to one side, like loose threads hanging off a tapestry. It was only when we gave these threads a tug that the whole picture we had been weaving for centuries began to unravel and we were brought face to face with a new picture of reality. A quantum one.

  The Nobel Laureate Richard Feynman once opened a series of lectures on quantum physics by saying: ‘My physics students do not understand it. I do not understand it. Nobody does.’1 These are sobering words to hear from arguably the greatest quantum physicist in history. After all, if someone as brilliant as Feynman could not fold his brain around the topic, what chance do the rest of us mortals have?

  What has to be appreciated, however, is that Feynman was not saying quantum physics is too complicated to understand. He was saying quantum physics is too darn strange.

  Suppose someone told you to picture a four-sided triangle, or to think of a number that is smaller than ten but bigger than a billion. Those instructions are not complicated but you could not easily follow them because they are nonsensical. This is what our journey into quantum physics is going to look like.

  It is a world of four-sided triangles and numbers that do not follow ordinary rules; a place where parallel universes and paradoxes lurk around every corner and objects do not have to pay attention to space or time.

  Unfortunately our brains are not built to handle this kind of madness and the words we have at our disposal are not weird enough to capture nature as she truly is. That is why the physicist Niels Bohr said that when it came to quantum physics ‘language can be used only as poetry’.2

  The mistake a lot of people make is to find the whole thing baffling and decide they are not clever enough to grasp it. Do not be troubled though. Frankly, if you find this subject bizarre and unsettling that puts you alongside the greatest minds in history.

  CHAPTER ONE Glowing with Pride

  SOME LIGHT HISTORY

  Quantum physics began with trying to understand light, something we have been scratching our collective heads over for millennia. The Greek philosopher Empedocles, some time around the fifth century BCE, was the first person to theorise what light is.

  He believed the human eye contained a magical fire-stone, which shone rays outward from our faces, illuminating whatever we wanted to look at.1 A poetic idea, but with an obvious flaw: if our eyes are generating the light we should always be able to see in the dark because our eyes themselves are torches.

  Empedocles was also the guy who gave us the now debunked idea of four elemental substances (fire, water, wind and earth) as well as attempting to explain biological diversity as the result of bodiless limbs crawling around the world until they joined up with each other at random to form animals.

  Really, Empedocles’s job in scientific history was to come up with bonkers ideas everyone else proved wrong. Although in the case of light rays, it took us about thirteen hundred years to realise his mistake.

  It was not until the Arabic scholar Alhazen came along that we finally let go of Empedocles’s notion. Alhazen carried out an experiment in which he dissected a pig’s eyeball and showed that light bounced around inside the cavity the same way it does in a dark room, i.e. light is coming from objects around us and our eyes just happen to intercept their paths.2

  It might seem weird that it took over a thousand years for us to be sure our eyes were not zapping out magical lasers, but those were different times. Back then everyone assumed humans gave objects their purpose for existing, so there was no need for them to have an appearance when they were not being looked at.

  Fortunately, Alhazen’s suggestion that experiment should trump human ego gradually caught on and we decided that light, whatever it was, came from the objects themselves and entered our eyes in straight lines. Cue the Renaissance.

  Arguably, the most influential Renaissance scientist/philosopher was René Descartes, who gave us our next big idea about the physics of light.

  Descartes noticed that when a candle is lit, the illumination can simultaneously reach every corner of a room, the same way a ripple started in the centre of a pond can reach every edge at the same time. Light, he reasoned, was a similar phenomenon; there was an invisible material surrounding us in every direction, which he called plenum, and light was the result of ripples and waves moving through it.3

  The only person to disagree with his plenum-wave idea was Isaac Newton, who chiefly made it his business to disagree with anyone he considered less intelligent than himself (which was basically everyone).

  Newton pointed out that if light was a wave moving through a medium it should bend around an object as it went past, the way a water wave will curve slightly as it goes around a rock. This would give shadows blurry edges, but since they are sharply defined it made more sense to think of light being made of particles, which he called ‘corpuscles’.4

  The corpuscular light theory was inevitably accepted over Descartes’s plenum waves, largely due to Newton’s celebrity status and the fact that he was a bully to anyone who challenged him.

  Newton would have been aghast, therefore, to hear the results of an experiment carried out by a man named Thomas Young, which showed the opposite conclusion, seventy years after his death. By that, I mean the experiment was carried out seventy years after Newton’s death. Thomas Young did very few experiments after his own.

  THE TALENTED MR RIPPLE

  Thomas Young possessed one of the most remarkable minds of the eighteenth century. He is probably best known for translating the Rosetta stone and thus becoming the first modern man to decipher Egyptian hieroglyphs. He was also the first person to recognise colour receptors in our eyes, wrote several books on medicine, spoke fourteen languages, played a dozen instruments and developed our modern theory of elasticity.5

  The experiment of his that really caused waves for light theory (pun very much intended) was one he performed in 1803, known as the double-slit experiment.

  Let’s go back to the idea of waves moving across a pond for a moment. Imagine a regular pulse of waves moving over a calm liquid surface and passing through a barrier with a gap in it. As these waves waft to the other side of this gap they fan out slightly – a process we call diffraction.

  The reason they spread out is because the edge of a wave dissipates its energy to the surrounding water. Viewed from above, we get a pattern looking like the one below, where wave peaks are drawn as solid lines and wave troughs are dashed:

  Now let’s try it with two gaps in our barrier instead. The same thing will happen, only this time we see two waves diffracting through at the same time, eventually to the point where they overlap and mix together. Viewed from above it looks like this:

  In some places you can see the waves
are crossing over perfectly, with a peak from one wave meeting a peak from the other, leading to a mega-peak in the surface of the water. In between these mega-peaks we get the opposite effect, where the waves are out of sync and peak meets trough. In those spots the waves cancel out, leaving hardly any wave at all.

  If we were to place a screen at the end of the pond now, the mixed up waves would strike it in alternating patches of mega-peak and cancelled-out nothingness. Looking at this screen head on (rather than top down) the pattern left by our waves appears like this:

  We are looking here at the effect of waves interfering as they diffract through a double slit, creating a pattern of alternating high intensity and low intensity on the other side. A phenomenon we call wave ‘superposition’.

  What Thomas Young then did was to replicate this wave superposition pattern, only with light beams instead of water. By shining a candle through two slits in a wall, Young ended up creating alternating zebra stripes of light and shadow on his detector screen, similar to the pattern left by mixing water waves:

  If light is made of particles as Newton insisted, they ought to shoot through the two slits and hit the wall in one big mush on the other side. The zebra pattern we actually get can only be explained if light is, in some way, wavelike.

  Newton’s sharp-edged-shadow objection still held some sway, but now that he was dead a few people were daring to question his teachings. If you look at the boundary of a shadow really closely you actually do get blurry edges: they’re just small and easy to miss. This cannot be explained with a particle theory but can be explained as a wave bending around the object.

  The material carrying these waves, which Descartes had called plenum, was given a fancier name – luminiferous aether – and the nature of light was finally settled.

  Descartes’s idea was definitely ahead of its time but it was not accepted until there was experimental proof. This is a powerful reminder that you cannot put Descartes before the horse. I’m almost sorry for that joke. Almost.

  CATASTROPHE OF THE CENTURY

  By the time the 1900s rolled around, nobody was questioning what light was made of any more. Young had settled it. There were a few things that did not add up though, the most notable being what happened when light interacts with a hot object and in order to understand this mystery, we’re going to have to talk about hosepipes.

  Imagine a hosepipe whose spout is plugged into the bottom of a box. When we switch the hose on, the box will gradually fill with water until it cannot hold any more. But suppose we cut three holes into the lid – one small, one medium, one large.

  When we switch the hosepipe on this time, the water will fill up as usual, but then begin pouring out of the holes in the top. Clearly we’ll get the most water coming from the biggest hole and only a meagre trickle coming from the smallest. This would be a slightly pointless contraption to build, but there is nothing difficult going on. We pump water in at the bottom, it spills out of holes at the top.

  This is a fairly good way of visualising why an object glows as it gets hotter. As any object warms, the heat energy gets absorbed and absorbed until the object has taken enough, at which point it begins leaking back out in the form of light.

  The hosepipe in the analogy represents heat being applied to the object and the holes stand for different types of light that can be emitted. The smallest hole represents infrared (too low in energy to see), the middle hole represents visible (red through violet) and the largest hole represents ultraviolet (too high in energy to see).

  Dark-coloured objects tend to do this heat–light conversion process most efficiently since they absorb all the energy hitting them, and thus a theoretically perfect heat-absorber is called a ‘black body’ in physics jargon (even if it is not literally a black object).

  The whole thing is described adequately by a simple equation called the Rayleigh–Jeans law and it works as a good approximation, especially at cold to moderate temperatures. But when things get blazing hot, something really odd happens.

  Logically, most of the light emitted from a hot object should emerge in the form of ultraviolet because it’s the highest energy light (the biggest hole in our box analogy). What actually happens is that almost all the light comes out of the object with a medium value.

  You get a little infrared and a little ultraviolet, but most of the light emitted from a hot object splurges out as yellow/orange, which does not make any sense. It would be like filling our box with water and having it all spout out from the middle hole, rather than the big one.

  In fact, the real situation is even more perplexing than our three-hole analogy, because real light can have any energy it likes, rather than being limited to only three types. A more accurate picture might be to imagine a slit cut along the top of the box and finding water gushing from the middle of the slit only, somehow ignoring the edges.

  The physicist Paul Ehrenfest referred to this conundrum as a ‘catastrophe of the ultraviolet’6 and it has ever since been referred to in physics books as the infamous ‘ultraviolet catastrophe’.

  What we have in this situation is a mismatch between theory and experiment, and in science it’s always the theory that has to change. You do not get to tell an experiment what results it should produce, so if your theory does not predict the data you actually get, it’s goodbye to your theory.

  The catastrophe arose because we apparently had some incorrect ideas about how light energy works but nobody could have guessed that slightly rethinking those ideas would put us on a path to the quantum revolution. Although the man who came up with the answer was not trying to do anything so radical. He just wanted a cheap light bulb.

  BEFORE PLANCKING WAS A THING

  Max Planck was the youngest of six children and graduated high school in 1875, a year ahead of his classmates. He applied to study physics at the University of Munich but the man who considered his application, Professor P. von Jolly (genuine name), tried to dissuade him because physics was almost complete and it would be a waste of Planck’s intellect.7

  Despite Jolly being so serious, Planck did not back down and insisted he be allowed to study the course he wanted. He did not care if he discovered anything new because he was not concerned with legacy. He just wanted to understand how the world worked and would not take no for an answer. Planck did not bend.

  Jolly was so impressed with this dogged attitude that he decided to admit Planck after all and he soon became one of the most revered figures on the European physics circuit. His lectures were allegedly so popular people would cram shoulder to shoulder to hear him speak and there are reports of punters fainting from the heat and everyone else ignoring them so Planck could finish what he was saying.

  It was this reputation that brought him to the attention of the German Bureau of Standards, which asked if he would help in its quest to provide Germany with electric streetlighting. Electricity was all the rage in other countries but it was expensive and they wanted to figure out the most efficient way of getting it done. Planck accepted the invitation gladly and set to work analysing the relationship between heat and light for a hot bulb.8

  The filament of such a bulb is effectively a ‘black body’. As it heats up from the inside the outer surface absorbs all the energy and re-emits it as light, mostly of the visible variety. As it gets hotter, however, it does not start producing the kinds of light predicted by the Rayleigh–Jeans law, so Planck decided to invent a new law, one in which he thought of light energy as a kind of gas.

  In a gas, you’ve got a group of particles flying about at random and as they collide their heat gets shared out. By sheer chance some particles will have a low energy and some will have a high energy, but most of them will converge on an average value – what we call the temperature.

  Planck realised that this distribution of energy matched what he was seeing in his light-bulb experiments. As we heat an object the emitted light hovers around a middle energy value with a few beams coming out at the high and low ends. Planck t
herefore proposed that energy gets shared among beams of light the same way heat gets shared among particles in a gas.

  The only catch is that the gas–heat phenomenon only happens because a gas is split into particles. If Planck’s idea was to work then light would have to be made of particles too.

  He called these tiny granules of light ‘quanta’ from the Latin word quantitas, which means quantity, and carried on with his work unperturbed.

  To be clear, Planck was not sincerely claiming light was made of particles – that would be absurd. He was just pulling a silly maths trick, largely out of desperation, to make his results sensible. Everyone knew light was a wave moving through the luminiferous aether due to Young’s experiment; we had got rid of Newton’s corpuscle idea a long time ago.

  As far as Planck was concerned, light quanta were a halfway answer not to be taken seriously. So naturally, when he received a research paper proving they were real things he was stunned. Stiff as a plank in fact.

  CHAPTER TWO Bits and Pieces

  DOCTOR WHOM?

  Planck had largely forgotten about his light-particles idea by 1905 and was working as a senior editor for Annalen der Physik, one of the most prestigious physics journals in the world. Being in that role meant he got a lot of quack suggestions delivered to his in-tray, most of which he discarded.

  The essay he received in March of that year, claiming that light really was made of particles and it wasn’t just a fudge to make the numbers work, seemed like another lunatic idea at first. It came from an unknown twenty-six-year-old amateur physicist from Switzerland who boasted a qualification for teaching high school and little else. Yet the physics in the paper was not only flawless, it solved another puzzle people had been trying to answer for years.