It is absolutely necessary, for progress in science, to have uncertainty as a fundamental part of your inner nature.
Richard Feynman
It’s extraordinary what you can buy over the Internet. Today a small pot of radioactive uranium-238 arrived in the post. ‘Useful for performing nuclear experiments,’ the advert assured me. I rather enjoyed the comments from other people who purchased a pot: ‘So glad I don’t have to buy this from Libyans in parking lots at the mall anymore.’ One purchaser wasn’t so happy: ‘I purchased this product 4.47 billion years ago and when I opened it today, it was half empty.’
The uranium is naturally occurring and I’m assured it is safe to have on my desk next to me as I write. The documentation just warns me that I shouldn’t grind it up and ingest it. The packet claims that the uranium is emitting radiation at a rate of 766 counts per minute. It’s kicking out a range of radiation: alpha particles, beta particles and gamma rays. But what the specifications cannot guarantee is when exactly the uranium is going to spit out its next particle.
In fact, current quantum physics asserts that this is something I can never know. There is no known mechanism so far developed that will predict precisely when radioactive uranium will emit radiation. The post-Newtonian physics that I explored in the First Edge implied that theoretically everything in the universe is controlled by and follows a deterministic set of mathematical equations. But at the beginning of the twentieth century a group of young physicists – Heisenberg, Schrödinger, Bohr, Einstein and others – sparked a revolution, giving a new perspective on what we can really know about the universe. Determinism was out. Randomness, it appears, rules the roost.
To understand this unknown requires that I master one of the most difficult and counterintuitive theories ever recorded in the annals of science: quantum physics. To listen to those who have spent their lives immersed in this world talking of the difficulties they have in understanding its twists and turns is testament to the challenge I face. After making his groundbreaking discoveries in quantum physics, Werner Heisenberg recalled how ‘I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?’ Einstein declared that ‘if it is correct it signifies the end of science’. Schrödinger was so shocked by the implications of what he’d cooked up that he admitted: ‘I do not like it and I am sorry I had anything to do with it.’ Nevertheless, the theory is one of the most powerful and well-tested pieces of science on the books. Nothing has come close to pushing it off its pedestal as one of the great scientific achievements of the last century. So there is nothing for it but to dive head first into this uncertain world. Feynman has some good advice for me as I embark on my quantum quest:
I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.
The revolution these scientists instigated is perfectly encapsulated in my attempts to understand what my pot of uranium is going to do next.
Over a long period of time the rate of radioactive decay approaches a constant and on average is very predictable, just like the throw of my casino dice. But according to the physics of the twentieth century there is a fundamental difference between the dice and the pot of uranium. At least with the dice I have the impression that I could know the outcome given enough data. However, there seems to be no way of determining when the uranium will emit an alpha particle. Complete information doesn’t make any difference. According to the current model of quantum physics, it’s completely and genuinely random. It is a counterexample to Laplace’s belief in a clockwork universe.
For someone on the search for certainty and knowledge the revelations of quantum physics are extremely unsettling. There is nothing I can do to know when that pot on my desk is going to emit its next alpha particle? That’s deeply shocking. Is there really no way I can know? There is much debate about whether this is truly something random, something we can never know, or whether there is a hidden mechanism we have yet to uncover that would explain the moment that radiation occurs.
This unknown is related to an even deeper layer of ignorance shrouding the universe of the very small. In order to apply the equations of motion discovered by Newton to calculate the future evolution of the universe, it is necessary to know the location and momentum of every particle in the universe. Of course, practically this is impossible, but discoveries made in the twentieth century hint at a deeper problem. Even if I take just one electron it is theoretically impossible to know both its position and its momentum precisely. Our current model of the very small has a built-in limitation on what we can know: this is called Heisenberg’s uncertainty principle.
While my First Edge revealed that the randomness that is meant to describe the roll of the dice is just an expression of a lack of knowledge, the world of the very small seems to have randomness at its heart: an unknowable dice deciding what’s going to happen to the lump of uranium sitting on my desk beside my casino dice.
I have learnt to cope with the unknowability of the roll of the dice, because deep in my heart I know it is still dancing to the regular beat of Newton’s equations. But I’m not sure I can ever come to terms with the unknowability of my radioactive pot of uranium – something that the theory says is dancing to no one’s beat. The challenge is: will it always remain unknowable, or is there another theoretical revolution that needs to take place akin to the radical new perspective that emerged at the beginning of the twentieth century?
We had the first inklings of this revolution when scientists tried to understand the nature of light. Is it a wave or is it a particle? Newton’s great opus on optics, published in 1704, painted a picture of light as a particle. If you considered light as a stream of particles then the behaviour that Newton described in his book appeared very natural. Take the way that light reflects. If I want to know where a ray of light will emerge when it hits a reflecting surface, then thinking of it like a billiard ball fired at the wall gives me a way to predict its path. The geometry of light made up of these straight lines, Newton believed, could be explained only by thinking of light as made up of particles.
Rivals to Newton’s vision, however, believed that a wave was a much better model for describing the nature of light. There seemed to be too many characteristics of light that were hard to explain if it was a particle. An experiment that English physicist Thomas Young concocted in the early 1800s seemed to be the nail in the coffin for anyone believing in light as a particle.
If I shine a light at a screen with a single thin vertical slit cut into the screen, and place a photographic plate beyond the screen to record the light as it emerges, the pattern I observe on the photographic plate is a bright region directly in line with the slit and the light source that gradually tails off to darkness as I move away from this central line. So far this is consistent with a particle view of light, in which small deflections can occur as the particles of light pass through the slit, causing some of the light to fall either side of this bright region. (Even with the single slit, if the slit is small compared with the wavelength of light, there is some wavelike variation in the intensity of the light as you move away from the central bright region, which hints at waves at work.)
The intensity of light recorded on the photographic plate after the light has passed through a single narrow slit.
The trouble for the particle version of light was revealed when Young introduced a second vertical slit into the screen parallel to the first slit. You would have expected to see two bright regions occurring in line with each slit corresponding to the particles of light passing through one slit or the other. But that’s not what Young observed. Instead, there was a whole series of bands of light and dark lines across the photographic plate. Bizarrely, there are regions of the plate that are illuminated if only one slit is open and plunged into darkness if two slits are open. How is it, if light is a particle like a billiard ball, that giving the light more options results in a particle suddenly being unable to reach this region of the plate? The experiment truly challenged Newton’s model of light as a particle.
Light emitted from the left passes through the double-slit screen and strikes the photographic plate on the right. The light and dark bands depicted to the right of the plate represent the interference pattern detected.
It seemed that only a model of light as a wave could explain these bands of brightness and darkness. If I think of a still lake full of water and I throw two stones into the water at the same time, then the waves caused by the stones will interact in such a way that some parts of the waves combine to form a much larger wave and other parts of the waves cancel each other out. If I place a piece of wood in the water, I will see this interaction as the combined waves strike the board. The wave hits the board with a series of peaks and troughs across the length of the board.
The light emerging from the two slits appear to produce two waves that interact in a similar way to the stones thrown into the water. In some regions the light waves combine to create bright bands, while in others they cancel each other out to produce dark bands. No particle version of light could get anywhere near explaining these patterns.
The supporters of the particle theory finally had to throw in the towel in the early 1860s, when it was discovered that the speed at which light travels matched exactly the speed predicted by James Clerk Maxwell’s new theory of electromagnetic radiation based on waves. Maxwell’s calculations revealed that light was in fact a form of electromagnetic radiation described by equations whose solutions were waves of differing frequencies corresponding to different sorts of electromagnetic radiation.
However, there was a twist in store. Just as Young’s experiment seemed to push scientists towards a wave model of light, the results of two new experiments at the end of the nineteenth century could be explained only if light came in packets. That is, if it was quantized.
The first inkling that light could not be wavelike arose from trying to understand the light or electromagnetic radiation being cooked up in the coal-fired furnaces that drove the Industrial Revolution. Heat is movement, but if you jiggle an electron up and down then, because it has a negative charge, it is going to emit electromagnetic radiation. This is why hot bodies glow: the jiggling electrons emit radiation. Think of the electron a bit like a person holding the end of a skipping rope: as the person’s hand goes up and down, the rope begins to oscillate like a wave. Each wave has a frequency which records how often the wave pulses up and down per second. It’s this frequency that controls, for example, what colour visible light will have. Red light has a low frequency; blue light a high frequency. The frequency also plays a part in how much energy the wave contains. The higher the frequency, the more energy the wave has. The other contributing factor to a wave’s energy is its amplitude. This is a measure of how big the waveform is. If you think of the skipping rope, then the more energy you put in, the higher the rope will vibrate. For many centuries scientists used the dominant frequency of the radiation as the measure of the temperature. Red hot. White hot. The hotter a fire, the higher the frequency of the light emitted.
I got a chance to see one of these coal-fired furnaces at work when I visited Papplewick Pumping Station near Nottingham. Once a month they fire up the furnaces for one of their ‘steaming days’. The furnace is housed in a beautifully ornate Victorian building. Apparently the cost of building the station was so far under budget that there were funds left over to decorate the pump house. It feels like a church dedicated not to God but to the science of the industrial age.
The temperature inside the furnace at Papplewick was hitting something in the region of 1000 degrees Celsius. Scientists at the end of the nineteenth century were interested in what the spectrum of frequencies of light looked like inside the furnace for any fixed temperature. A closed furnace can reach a thermodynamic equilibrium where the heat jiggling the atoms causes radiation to be emitted which is then reabsorbed, so none of the electromagnetic radiation is lost.
When the furnace hits equilibrium, what frequencies of radiation do you find inside it? You can think of this as like a lot of my cello strings waiting to be vibrated. The total energy of the vibrating string is a function of the frequency of the vibration and the amplitude of the vibration of the string. Higher-frequency waves need more energy to get them going, but this can be compensated for by creating a wave with lower amplitude. Classically, a fixed amount of energy can theoretically get waves of any frequency vibrating, but the amplitude will be correspondingly smaller as the frequency increases.
A theoretical analysis of the spectrum seemed to indicate that waves of arbitrary frequency would occur in the furnace. And yet when I looked inside the furnace at Papplewick I didn’t get zapped by a load of high-frequency X-rays. But the wave-based theory of electromagnetism predicted that I should. Not only that, if I added up all the contributions of the frequencies inside the furnace at thermal equilibrium, then the analysis based on light as a vibrating wave would lead to the absurd conclusion that the total energy contained in the oven is infinite. The furnace in Papplewick wouldn’t have lasted long if that had been the case.
At any given temperature there seems to be some cut-off frequency beyond which the waves fail to get going and vibrate. The classical picture is the following. If light is like a vibrating cello string, then the oven should generate waves of all frequencies, the number of waves increasing with the frequency. At low frequency the graph is correct, but as the frequency increases I see the intensity of the radiation at higher frequencies tailing off until beyond some point (which depends on the temperature) no waves of frequency greater than this number are observed.
The frequencies inside a closed oven predicted by classical and quantum models.
In 1900 the German physicist Max Planck took the experimentally observed distribution of frequencies coming out of a furnace like that at Papplewick and came up with a clever idea that would explain how to get the true curve rather than the nonsensical curve produced by a classical cello-string interpretation of light.
He posited that each frequency of electromagnetic radiation had a minimum energy that was required before it got going. You couldn’t just continuously reduce the energy of a wave vibrating at a given frequency and expect it to sound. At some point, as the energy is reduced, the wave would just flatline rather than continuously vibrate at smaller and smaller amplitudes. Indeed, Planck’s model asserted that there wasn’t any continuous behaviour. Each time the energy increased, it went up in quantized jumps. The jumps in energy were very tiny, so they were very hard to observe unless you were looking for them. But once Planck had this assumption in place, the mathematical implications for the intensity of electromagnetic radiation at each frequency corresponded precisely with the observed radiation emerging from the oven.
So perhaps the universe was not the smooth, continuous place that scientists had believed it to be up to the end of the nineteenth century. Even the atomists – those who believed in matter built of basic building blocks – had no idea that the atomist philosophy would apply to things like energy. The implication for my cello string is that if I draw the bow across the string and increase the volume, although your ear hears a gradual and continuous increase in the volume, actually the volume is jumping up in steps. The size of the steps is very small. For any given frequency v, the energy goes up in steps of h × v, where h is called the Planck constant. This number, which controls the steps in energy measured in joule seconds, has 33 zeros after the decimal place before we get the first non-zero digit:
h = 6.626 × 10–34 joule seconds.
At this stage, Planck had no real physical explanation for the steps in energy, but mathematically it was just what was needed to explain the experimentally observed electromagnetic radiation inside an oven like the one at Papplewick. It was Einstein’s explanation of a second experiment that shifted scientists towards thinking of light as a particle rather than a wave. And it was these particles that each had an energy of h × v.
Metals are such good conductors of electricity because there are lots of free electrons that can move through the metal. This means that if I fire electromagnetic radiation at a piece of metal, I can actually kick these electrons off the metal. The energy from the wave is transferred to the electron, which then has enough energy to escape the confines of the metal. This was the key to Thomson’s discovery of the electron described in the previous Edge.
If I think of electromagnetic radiation as a wave, I should be able to increase the energy of the wave until eventually I’ll knock out the electron. The greater the energy in the wave, the more of a kick I give the electron and the faster it speeds off. As I described in the previous section, there are two ways to increase the energy of a wave like my vibrating cello string. One is to increase the frequency of the wave, to vibrate it faster. Do this and sure enough the speed of the electrons that are ejected goes up proportionally. But if I fix the frequency, the other way to increase the energy is to increase the amplitude of the wave, to play it louder. The strange thing is that, despite dialling up the intensity of the wave at a given frequency, the speed at which the electrons are emitted is not affected. What goes up is the number of electrons kicked off the metal.
Furthermore, if I decrease the frequency of the wave while increasing the amplitude, I can keep the total energy constant, and yet there is a point at which I can’t seem to kick out any of the electrons. There are frequencies below which, however loud I play my cello, the energy just doesn’t kick out electrons. In contrast, with a high-frequency wave it doesn’t matter how far down you turn the volume dial, even an extremely low-intensity wave has the power to knock out electrons. What’s going on? How can I explain this strange behaviour, which scientists call the photoelectric effect?
The answer is to change the model. At the moment I’ve been thinking in terms of: wave in, particle out. What if I try: particle in, particle out? Perhaps the particle nature of the outgoing electron is actually the key to how I should view the incoming electromagnetic radiation.
This was Einstein’s great paradigm shift, which he made in 1905, the year many call his annus mirabilis. It is also the year he came up with the special theory of relativity that I tackle in later Edges, and the theory of Brownian motion, which provided the most convincing support for matter made from atoms described in the previous Edge.
Einstein suggested that you should think of electromagnetic radiation or light not as a wave but like a machine-gun fire of tiny billiard balls, just as Newton had suggested. The energy of each individual particle depends on the frequency of the radiation. With this new idea we have a model that can perfectly describe what scientists were experiencing in the lab. Each billiard ball of light will have energy corresponding to the minimum energy that Planck had mathematically introduced to produce his explanation of the radiation in the furnace. Electromagnetic radiation of frequency v should be thought of in Einstein’s model as billiard balls each with energy h × v. The jumps in energy that Planck introduced simply correspond to the addition of more billiard balls of light to the radiation. Einstein called these balls light quanta, but they were renamed in the mid-1920s, and we know them today as photons.
How does this particle model of light explain the behaviour of the electrons being kicked off a metal? Again, think of the interaction like a game of billiards. The photons of light come crashing onto the surface of the metal. If a photon hits an electron, the energy is transferred to the electron and the electron flies off. But the electron needs to receive a certain amount of energy if it is to get kicked off.
The energy of each incoming photon of light depends only on the frequency of its radiation. If the frequency of the radiation is too low, the energy of each incoming photon is too small to kick out the electron. It doesn’t matter if you turn up the intensity of the radiation: you’re firing more billiard balls at the metal, but each individual billiard ball has the same energy. There is an increased chance of an electron being hit, but since each billiard ball is as impotent as any other, the electron is never going to be kicked off. In the wave model, the electron could sit there absorbing the incoming energy until it had enough to fly off. With the particle model I can kick the electron as many times as I want, but no single kick is going to be enough to knock out the electron. It’s like gently prodding someone with your finger. Lots more gentle prods are not going to cause the person to fall over.
But if the frequency of the incoming radiation is above a certain value, the energy of each billiard ball is enough to kick the electron off if it hits. It’s like replacing hundreds of tiny prods with one huge shove: now the person falls over. Essentially, the ball has enough energy to transfer to the electron, and the resulting energy of the electron is sufficient for it to overcome the forces binding it to the metal. Increasing the intensity of the radiation means firing more balls at the metal and this simply increases the number of electrons that will be emitted. Hence, rather than knocking out electrons with higher speeds, I just see more electrons being kicked off.
The speed of the emitted electron in Einstein’s model will be linearly proportional to the frequency. Interestingly, this relationship had not been observed or previously predicted, so it gave Einstein’s model the perfect characteristic for any good scientific theory: to be able not only to explain what has been seen in the laboratory to date but also to predict some new phenomenon that can be tested subsequently. This was especially important, since many scientists were intensely sceptical of Einstein’s model. Maxwell’s equations, which described electromagnetic radiation in terms of the mathematics of waves, had been so successful that scientists were not going to change their minds without some convincing.
One of the sceptics was American physicist Robert Andrews Millikan. But his attempts to try to disprove Einstein’s model of light as billiard balls of energy ended up confirming Einstein’s prediction that the speed of outgoing electrons would be directly proportional to the frequency of the incoming radiation. Millikan had previously determined the charge on the electron as part of his research and would subsequently coin the term ‘cosmic rays’ after he proved that the radiation being picked up by detectors on Earth was of an extraterrestrial nature. For all this work Millikan received the Nobel Prize in Physics in 1923, just two years after Einstein got his.
It was Einstein’s explanation of the photoelectric effect for which he received his Nobel Prize in 1921. He wasn’t recognized by the Nobel committee for his theory of relativity! Einstein’s ideas gave the particle party a reason to retrieve the towel they’d thrown in a few decades earlier after Maxwell’s revelations. In turn there would be a counter-revolution which revealed that particles such as electrons have characteristics that make them look more like waves than discrete particles. It seemed as if both light and electrons behaved like particles and waves. Everyone was a winner in the new theory that was emerging.
Despite Einstein’s paradigm shift, the experiments that seemed better explained by light as a wave were not invalidated. Weirdly, the circumstances of the experiment seem to dictate which model of light you should use. The wave–particle duality was upon us.
Recall that it was Young’s double-slit experiment that had been the most devastating demonstration of why light is a wave not a particle. The photoelectric effect had rather nicely used the particle nature of the electron to provide convincing support for thinking of electromagnetic radiation as a particle. But did the dialogue work the other way? What if I ask an electron to take part in the Young double-slit experiment? Firing electrons at a screen with two slits turned out to have shocking implications for our grasp on reality.
One of the most curious consequences of quantum physics is that a particle like an electron can seemingly be in more than one place at the same time until it is observed, at which point there seems to be a random choice made about where the particle is really located. And scientists currently believe that this randomness is genuine, not just caused by a lack of information. Repeat the experiment under precisely the same conditions and you may get a different answer each time. It is this uncertainty about position that is ultimately responsible for bits of my uranium suddenly finding themselves located outside rather than inside the pot on my desk.
The quintessential illustration of this repeats Young’s double-slit experiment, but with electrons rather than light. A physicist colleague of mine in Oxford let me come and play in his lab so that I could see with my own eyes the bizarre game these electrons seem to be playing. I’ve read about it so many times, but as Kant once said: ‘All our knowledge begins with the senses.’
I felt compelled to warn my colleague that experiments and I don’t mix well. No one would agree to be my lab partner at school because my experiments invariably went wrong. It was one of the reasons I was drawn to the more theoretical end of the scientific spectrum, where the mess of the physical universe can be kept at bay. But my colleague assured me this experiment was pretty robust.
To start with, we set up a source emitting electrons at a rate that allowed me to record them arriving on the detector plate one at a time. I then placed the screen with two slits between the source and the detector plate. I first observed what happened when one slit was closed. The electrons that passed through the open slit hit the detector plate, and, after sending sufficiently many through, I began to see a pattern emerge.
The region directly in line with the source and the slit saw a high intensity of electrons arriving. As I moved to either side of this central line I still detected electrons arriving, but the number dropped off as I moved further from the central line. The electrons sometimes seemed to be deflected as they passed through the slit, resulting in their paths being bent either side of the central line. Nothing too strange up to this point. But then I opened the second slit.
If the electrons behaved like classical particles, I would have expected to see two regions of high intensity in line with the two slits, depending on whether the electron passed through the first or second slit. But this wasn’t what I detected. Instead, I saw the interference pattern begin to build up, just as Young did when he shone light at the screen, which was more consistent with the analogy of a water wave passing through the slits and creating two waves that interfere with each other.
As more electrons are detected, the wavelike pattern of interference emerges.
Remember, though, that I’d set the experiment up so that only one electron was passing through the screen at a time. So this wasn’t many electrons interacting with each other in a wavelike manner. This was a single electron doing what a wave usually does. Even more inexplicably, there were regions on the detector plate that were totally devoid of any electrons arriving, despite the fact that with one slit open, electrons could reach this point. What was happening? I had opened another slit, providing several paths to a point on the detector plate, but the extra choice had led to no electrons arriving.
Kant proposed that all knowledge begins with the senses but ‘proceeds thence to understanding, and ends with reason, beyond which nothing higher can be discovered’. So how did scientists distil reason from the strange behaviour of these single electrons passing through the screen?
When it passed through one slit, how could the electron know whether the other slit was open or not? After all, the other slit was some distance away from the slit through which the electron was travelling. It’s not that the electron splits into two and goes through both slits. The extraordinary thing is that I have to give up on the idea of the electron being located at any particular point until it is observed. Rather, I should describe the electron by a mathematical wave function that gives the range of possible locations. This was the revolutionary new viewpoint proposed in 1926 by the Austrian physicist Erwin Schrödinger. The amplitude of the wave encodes the probability that when the electron is observed it will be found in a particular region of space.
A quantum wave: the higher the wave, the more likely it will be to find the electron at this point in space.
You might ask: a wave of what? What is vibrating? In fact, it is a wave of information rather than physical stuff. Just as a crime wave isn’t a wave of criminals but rather information about the likelihood of a crime happening in a particular area. The wave is simply a mathematical function, and a mathematical function is like a machine or computer: you input information, and it calculates away and spits out an answer. The wave function of the electron has as input any region of space, and the output is the probability that you will find the electron in that region. Amazingly, this particle should really be thought of as a piece of evolving mathematics, not a physical thing at all. It is called a wave because the functions describing these probabilities have many of the features of classical wave functions. The peaks and troughs encode information about where the electron might be. The bigger the amplitude of the wave, the more likely you are to find the electron in that region of space.
In the case of the wave describing the behaviour of the electron, when the wave encounters the screen with the double slits it is affected by its interaction with the screen. The result is a new wave whose characteristics produce the strange interference pattern that I picked up on the detector plate. It is at this moment of detection that the electron has to make up its mind where on the plate to be located. The wave function provides the probability of where the electron might appear, but at this moment of detection the dice is cast and probabilities become certainties. The wave is no more, and the electron looks once again like a particle hitting one point on the detector plate. But run the experiment again and each time the electron might appear somewhere else. The more electrons I fire at the screen, as the pattern of detected electrons builds up, the more I see the statistics encoded in the wave appearing. But in any individual case the physics claims I’ll never know where on the plate I’ll find the electron.
The curious thing is that I can return to the original experiment that Young performed with light, but interpret it in the light (if you’ll excuse the expression) of Einstein’s discovery that light is made up of particles called photons. If I turn down the intensity of the light source in Young’s experiment, I can reach a point at which the energy being emitted is so low that it corresponds to firing one photon of light at a time at the double-slit screen.
Just like the electron, when this photon arrives at the photographic plate it shows up as a single point on the plate corresponding to its particle nature. So what’s happened to Young’s interference pattern? Here is the amazing thing. Keep firing photons at the double-slit screen one at a time, and after a period of time the build-up of the pricks of light on the photographic plate slowly reveals the interference pattern. Young wasn’t witnessing a continuous waveform hitting the plate – it was an illusion. It’s actually made up of billions of billions of pixels corresponding to each photon’s arrival being detected. To give you a sense of how many photons are hitting the plate, a 100-watt lightbulb emits roughly 1020 (or 100 billion billion) photons per second.
The wave quality of light is the same as that of the electron. The wave is the mathematics that determines the probable location of the photon of light when it is detected. The wave character of light is not a wave of vibrating stuff like a water wave but a wavelike function encoding information about where you’ll find the photon of light once it is detected. Until it reaches the detector plate, like the electron, it is seemingly passing through both slits simultaneously, making its mind up about its location in space only once it is observed.
It’s this act of observation that is such a strange feature of quantum physics. Until I ask the detector to pick up where the electron is, the particle should be thought of as probabilistically distributed over space, with the probability described by a mathematical function that has wavelike characteristics. And it is the effect of the two slits on this mathematical wave function that alters it in such a way that the electron is forbidden from being located at some points on the detector plate. But when the particle is observed, the dice is rolled and the probability wave has to choose the location of the particle.
I remember the Christmas when I first read about this crazy story of how things could appear to be in more than one place at the same time. Along with the toys and sweets that had been crammed into my Christmas stocking, Santa had also included a curious-sounding book, Mr Tompkins in Paperback, by a physicist called George Gamow. It tells the story of Mr Tompkins’ attempts to learn physics by attending a series of evening lectures given by an eminent professor, but Mr Tompkins always drifts off to sleep mid-lecture.
In his dream world the microscopic quantum world of electrons is magnified up to the macroscopic world, and the quantum jungle Mr Tompkins finds himself in is full of tigers and monkeys that are in many places at the same time. When a large pack of fuzzy-looking tigers attacks Mr Tompkins, the professor who accompanies him in his dreams lets off a salvo of bullets. One finally hits its mark and the pack of tigers suddenly becomes a single ‘observed’ tiger.
I remember being enchanted by this fantasy world and even more excited by the prospect that it wasn’t as fantastic as it appeared. I was beginning to have doubts about the existence of Santa, given that he had to visit a billion children in the course of one night, but the book renewed my faith in the idea. Of course, Santa was tapping into quantum physics. Provided that no one actually observed him, he could be in multiple chimneys at the same time.
To emphasize the peculiar role of observation, if I return to the double-slit experiment and try to sneak a look at which slit the electron ‘really’ passed through by placing a detector at one of the slits, the interference pattern disappears. The act of looking to see which slit the electron passes through changes the nature of the wave function describing the electron. Now the pattern at the detector plate simply shows two regions of light lining up with the two slits – there is no longer any interference pattern. My act of trying to know changes the behaviour of the electron.
Although it is a bit of a cheat, one way to think about this is to imagine an anthropologist observing a previously undiscovered Amazon tribe. To observe is to alter behaviour. It is impossible to observe without interacting in some fashion and changing the behaviour of the tribe. This is even more evident in the case of the electron. To know which slit the electron went through means to ‘look’, but that must involve some sort of interaction. For example, it could be a photon of light bouncing off the electron and returning to a detector. But that photon must impart some change of momentum or energy or change the electron’s position. It can’t interact without some change. But the truth is that this interaction need not be as obvious as a photon bouncing off our electron. It can be more subtle. If I observe whether the electron passes through one slit but don’t detect it, I can infer that it passed through the other slit. But there was no photon bouncing off the electron in this case. This is an interaction-free measurement of the electron’s location.
There is a very strange thought experiment that exploits this act of looking as the electrons pass through the slits in the screen. Suppose I could make a bomb that would be activated by a single electron hitting a sensor. The trouble is that there is no guarantee that the bomb works. Classically, the only way to test this seems to be the rather useless act of firing an electron at the bomb. If it goes off, I know it works. If it doesn’t, then it’s a dud. But either way, after testing, I don’t have a bomb.
The weird thing is that I can use the double-slit experiment to detect working bombs without setting them off. Remember that there were places on the screen where the electron can’t hit if it is really going through both slits at the same time. If I detect an electron at this point, it means I must have been looking and forced the electron to choose one slit or the other. We are going to use this region as the ‘bomb detector region’. Place the bomb’s sensor at the location of one of the slits, and if the bomb is a dud, the sensor won’t activate it. We are making no observations if it is a dud. That means the electron passes through both slits and can’t hit the ‘bomb detector region’.
But what if it isn’t a dud? Well, the sensor will detect the electron if it goes through the slit and set the bomb off. Not much good. But because now I am detecting which slit the electron is going through, it is going through only one slit and has the chance to reach our ‘bomb detector region’. So if I pick up an electron in the ‘bomb detector region’, it must mean the bomb is live. A live bomb is a detection mechanism. Half the time the electron is detected going through the slit where the bomb is located and the bomb goes off. But the other half of the time the bomb detects that the electron passed through the other slit, the interference pattern can’t occur, the electron has the chance to hit the ‘bomb detector region’ and yet the bomb doesn’t explode. The electron has given up information about which slit it passed through but the act of ‘observation’ didn’t involve looking at the electron or hitting it with a photon of light or blowing up a bomb.
The strange implications of the act of observation can also be applied to stop the pot of uranium on my desk decaying. By continually making lots of mini-observations, trying to catch the uranium in the act of emitting radiation, the observations can freeze the uranium and stop it decaying. It’s the quantum version of the old adage that a watched pot never boils, but now the pot is full of uranium.
It was the code-cracking mathematician Alan Turing who first realized that continually observing an unstable particle could somehow freeze it and stop it evolving. The phenomenon became known as the quantum Zeno effect, after the Greek philosopher who believed that because instantaneous snapshots of an arrow in flight show no movement, the arrow cannot be moving at all.
Think of a particle that can be in two states, HERE and THERE. Unobserved, it’s in a mixture of the two, but observation forces it to decide which one. If it decides to be HERE, then after observation it begins to evolve into a mixed state again, but observe it quickly enough and it’s still mostly HERE and will probably collapse into the HERE state again. So by continually observing the particle it never evolves sufficiently into the THERE state to have a chance of being observed THERE. It’s like having two glasses half filled with water, but each time you observe you have to pour the water from one glass into the other, filling it to the brim. After observation you can start to refill the empty glass, but look quickly enough and it’s hardly full and so the easiest thing is to refill the almost full glass again. By looking quickly each time, you ensure the full glass stays full.
My children are obsessed with the science fiction TV series Doctor Who, just as I was as a kid. The aliens we find scariest are the Weeping Angels, stone figurines like those in our local cemetery that don’t move provided you don’t take your eyes off them. But blink and they can move. The theory says that the pot of uranium on my desk is a bit like a Weeping Angel. If I keep observing the uranium, which obviously means a little more than just keeping my eyes on the pot on my desk, I can freeze it in such a way that it stops emitting radiation.
Although Turing first suggested the idea as a theoretical consequence of the mathematics, it turns out that it is not just mathematical fiction. There have been some experiments in the last decade that have demonstrated the real possibility of using observation to inhibit the progress of a quantum system.
Quantum physics seems to imply that there are multiple futures for the electron in my double-slit experiment until I observe it, and then the roll of some unknown quantum dice determines which one of these futures it will be. I suppose I can come to terms with the fact that I will not know the future until it becomes the present. After all, if I pick up my casino dice with the intention of throwing it three times, then there are 6 × 6 × 6 = 216 possible futures that the dice can realize. My act of throwing the dice picks out one of these 216 possible futures, just as observing the electron determines one of its many possible locations. But another twist on the double-slit experiment has the frightening implication that the past isn’t uniquely determined either.
Indeed, I seem to be able to alter the past by my actions in the present. There is a way to look and see which slit the electron went through long after it has passed through the screen. The observation device can be put up just before the electron is about to hit the detector plate. Let’s call the observation device the ‘slit observer’.
Suppose I set up the double-slit experiment on a cosmic scale. I put my electron-emitting device on one side of the universe and the double-slit screen just in front of it. I place my detector plate on the other side of the universe. In this way it will take many years for the electron to traverse space and finally hit the detector plate. So when the electron passes through the screen with the double slit, it won’t know whether I am going to observe it with my ‘slit observer’.
The decision whether to insert the ‘slit detector’ in the path of the particle in AD 2016 can alter what the particle did in 2000 BC.
If, years later, I do use the ‘slit observer’, it means that many years earlier the electron must have passed through one slit or the other. But if I don’t use the ‘slit observer’, then years earlier the electron must have passed through both slits. But this is weird. My actions at the beginning of the twenty-first century can change what happened thousands of years ago when the electron began its journey. It seems that, just as there are multiple futures, there are also multiple pasts, and my acts of observation in the present can decide what happened in the past. As much as it questions knowledge of the future, quantum physics asks whether I can ever really know the past. It seems that the past is also in a superposition of possibilities that crystallize only once they are observed.
The interesting point for me – one that is often missed – is that up to the point of observation, quantum physics is totally deterministic. There is no question of what the nature of the wave equation is that describes the electron as it passes through the slits. When he came up with his theory in 1926, Schrödinger formulated the differential equation that provides this completely deterministic prediction for the evolution of the wave function. Schrödinger’s wave equation is as deterministic in some sense as Newton’s equations of motion.
The probabilistic character and uncertainty occurs when I observe the particle and try to extract classical information. The highly non-classical and bizarre new feature is this discontinuous shift that seems to happen when the wave is ‘observed’. Suddenly the determinism seems to vanish and I am left with an electron randomly located at some point in space. Over the long term the randomness is described by information contained in the wave function, but in each individual instance there seems no mechanism that scientists have identified that lets me determine in this particular experiment where the electron will be located. Is this really what is going on? Is the location of the electron something I will never truly be able to predict before I make the observation?
Once I make an observation or measurement there is this strange jump which locates the particle at one particular coordinate. But immediately after the observation, the evolution of the particle is described by another wave function until the next measurement and the next jump. Schrödinger hated these discontinuous changes in behaviour: ‘If all this damned quantum jumping were really here to stay, then I should be sorry I ever got involved with quantum theory.’
We should be careful not to over-egg the role of humans here. Worms too can presumably collapse the wave function. But it is not just living creatures that are doing the measuring. There are particles on the other side of a potentially lifeless universe that are interacting with inanimate objects, causing the wave function to collapse into making a decision about the properties of the particle. This interaction is as much an act of observation as my experimental investigations in the lab. The universe is flooded with radiation that shines a light on anything it encounters. Is this why on the whole the universe appears classical and not in a constant state of uncertainty? This is related to an idea physicists call decoherence.
I am having real trouble getting my head around this idea of observation marking a divide between a deterministic electron described by a wave function and an electron that suddenly has a location determined purely by chance. The whole thing seems crazy. Nonetheless, there is no denying that it works as a computational tool. As the physicist David Mermin is reputed to have said to those who, like me, are unhappy with this unknown: ‘Shut up and calculate.’ It is the same principle as the theory of probability applied to the throw of the dice. The dice may be controlled by Newton’s equations, but the theory of probability is the best tool we have for calculating what the dice might do.
But even though I’m meant to shut up, I can’t help feeling that the objections are valid. The equipment I use to make a measurement is a physical system made up of particles obeying the laws of quantum physics as much the single electron I’m trying to observe. And me too! I’m just a bunch of particles obeying quantum laws. Surely even the observer, whether a photographic plate or a person, is part of the world of quantum physics and is itself described by a wave function. The interaction of the wave function of the electron and the observer should still be described by a wave. After all, what constitutes an ‘observation’ or ‘measurement’?
And if the equipment and observer and the particles passing through slits are all described by a wave function, then isn’t everything deterministic? So suddenly the randomness disappears. Why are physicists happy to say the act of observation collapses the wave function when frankly there is a mega-wave function at work describing all the particles at play – the electron, the equipment, me. Where’s the dividing line between the quantum world of probability and the classical world of certainties? This dualistic vision of a microscopic quantum world and a macroscopic classical world all seems a bit suspicious. Surely the whole shebang should be described by a wave equation. The whole thing is highly unsatisfactory, but the truth is that most physicists just take Mermin’s advice and get on with it. My colleague Philip Candelas tells a story of how a promising young graduate student, for whom everyone had high hopes, suddenly dropped out of sight. When Candelas investigated what had happened, he discovered the reason. A family tragedy? Illness? Debts? None of these. ‘He tried to understand quantum mechanics.’
I guess I have forgotten Feynman’s advice that he gave those who, like me, were trying to become quantum initiates: ‘Do not keep saying to yourself, if you can possibly avoid it, “But how can it be like that?” because you will get “down the drain”, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.’
That said, there are a number of ways in which people have tried to overcome this apparently in-built uncertainty. One is the hypothesis that, at the point of observation, reality splits into a superposition of realities. In each reality the photon or the electron is located in a different position so that the wave in some sense doesn’t collapse but remains, describing the evolution of all these different realities. It’s just that, as conscious beings, we are now stuck in one of the realities and are unable to access the other realities in which the photon or electron ended up somewhere else on the photographic plate.
This is a fascinating attempt to make sense of the physics. It is called the ‘many worlds’ interpretation and it was proposed in 1957 by American physicist Hugh Everett. The interesting thing for me is whether we could ever know that these many worlds are out there and existing simultaneously with our own. No one has yet come up with a way to test or probe these other worlds – if they exist. The theory posits that there is just one single wave function which describes the evolution of the universe in an entirely deterministic manner. It is back to Newton and Laplace, but with a new equation.
The trouble for us is that as part of this wave function, we are denied access to other parts of it. It traps us inside, confined to one branch of reality, and it may be an in-built feature of our conscious experience that we can never experience these other worlds. But could I still use my mathematics to analyse what is happening on the other branches? I observe the electron at this point on the detector plate, but I know that the wave function describes what is happening on all the other branches of reality. I can’t see those, but I can at least describe them mathematically. Of course, just as the electron exists in many worlds, so do ‘I’ – there are copies of me on the other branches witnessing the electron hitting other regions of the detector plate.
This model of reality is very intriguing, seeming to impact directly on what we understand by consciousness. I shall return to the question of consciousness in my Sixth Edge, but my current Edge already raises the interesting question of whether it might be related to the behaviour of this wave function. Why am I aware of only one result of the electron hitting the plate? Is my conscious awareness of what is happening around me some version of the electron hitting a plate? Is the equipment in my skull unable to process multiple worlds? I look out of the window, and the photons emitted from the house opposite enter my eye and are detected on my retina. Why can’t I sometimes look out and see house numbers 14 and 16 swapped over?
This attempt to reconcile what is going on involves trying to explain that the jump caused by the act of observation is not real but just something going on in the mind. We perceive a jump, but that isn’t what is really happening. This sort of explanation, though, raises the question of what it is we are trying to do when we give a scientific explanation of the world.
What is science? How do we attempt to navigate our interaction with the universe? It is only by measuring and observing that we know anything. Mathematical equations can tell us what to expect, but it’s just a story until we measure. So it’s curious that our only way to ‘know’ anything about the universe is to observe and make particles and light make up their mind about where and what they are doing. Before that, is it all just fantasy? I can’t measure an entire wave function, I can only know it mathematically. Is a quantum wave function part of the universe that we can never know because how can we truly know without measuring? At which point it collapses. Perhaps it’s just greedy to believe that I can know more than I can measure. Hawking has certainly expressed such a view:
I don’t demand that a theory correspond to reality because I don’t know what it is. Reality is not a quality you can test with litmus paper. All I’m concerned with is that the theory should predict the results of measurements.
My real problem with the current mainstream interpretation of quantum physics is that if you run the double-slit experiment twice, set up with exactly the same conditions, the outcome can be different each time. This goes against everything I believe in. It is why I was drawn to mathematics: the certainty of a proof that there are infinitely many prime numbers means I’m not suddenly going to get finitely many prime numbers next time I check. I believed that ultimately science was made up of similar certainties, even if we as humans might not ultimately have access to them. I throw my dice and the mathematics of chaos theory I recognize means I may never be able to calculate the final outcome of the throw of the dice. But at least the mathematics says that if I start the throw in the same place it will end up with the same face pointing up. But now the physics developed in this Edge fundamentally questions whether this is the case.
Probability for the dice is an expression of lack of information. In quantum physics it’s not about the physicist’s ignorance of the complete picture. Even if I knew everything, probability and chance remain. According to current interpretations of quantum physics, different outcomes of the roll of the dice really can result from the same starting point, the same input.
Some would question if it makes sense to talk about setting up the experiment and running it again with exactly the same conditions – that in fact it is an impossibility. Locally you might get the conditions exactly the same, but you have to embed the experiment in the universe, and that has moved on. You can’t rewind the wave function of the universe and rerun it. The universe is a one-time-only experiment which includes us as part of its wave function. Each observation changes the wave function of the universe and there’s no going back.
But what if reality is random and not as deterministic as I might want? Feynman in his Lectures on Physics states: ‘At the present time we must limit ourselves to computing probabilities. We say “at the present time”, but we suspect very strongly that it is something that will be with us forever – that it is impossible to beat the puzzle – that this is the way nature really is.’
It looks like the truly random thing sitting on my desk is not the casino dice I picked up in Vegas but the little pot of uranium I bought over the Internet.
