The substance of a tree is carbon and where did that come from? That comes from the air; it’s carbon dioxide from the air. People look at trees and they think it [the substance of the tree] comes out of the ground; plants grow out of the ground. But if you ask “where does the substance come from” you find out … the trees come out of the air … the carbon dioxide and the air goes into the tree and it changes it, kicking out the oxygen.… We know that the oxygen and carbon [in carbon dioxide] stick together very tight … how does the tree manage to undo that so easily? … It is the sunlight that comes down and knocks this oxygen away from the carbon … leaving the carbon, and water, to make the substance of the tree!
RICHARD FEYNMAN1
THE MASSACHUSETTS Institute of Technology, better known as MIT, is one of the world’s scientific powerhouses. Founded in 1861 in Cambridge, Massachusetts, it boasts nine current Nobel laureates among its one thousand professors (as of 2014). Its alumni include astronauts (one-third of NASA’s space flights were manned by MIT graduates), politicians (including Kofi Annan, former Secretary-General of the United Nations and winner of the 2001 Nobel Peace Prize), entrepreneurs such as William Redington Hewlett, cofounder of Hewlett-Packard—and, of course, lots of scientists, including the Nobel Prize–winning architect of quantum electrodynamics, Richard Feynman. Yet one of its most illustrious inhabitants is not human; it is in fact a plant, an apple tree. Growing in the President’s Garden in the shadow of the institute’s iconic Pantheonesque dome is a cutting from another tree kept at England’s Royal Botanic Gardens, which is a direct descendant of the actual tree under which Sir Isaac Newton supposedly sat when he observed the falling of his famous apple.
The simple yet profound question that Newton had been contemplating sitting under a tree at his mother’s Lincolnshire farm three and a half centuries ago was: Why do apples fall? It may seem churlish to suggest that his answer, one that revolutionized physics and indeed all of science, could be inadequate in any way; but there is an aspect of that famous scene that went unnoticed by Newton and has gone unremarked upon ever since: What was the apple doing up in the tree in the first place? If the apple’s accelerated descent to the ground was puzzling, then how much more inexplicable was the bolting together of Lincolnshire air and water to form a spherical object perched in the branches of a tree? Why did Newton wonder about the comparatively trivial matter of the pull of the earth’s gravity on the apple and overlook entirely the utterly incomprehensible puzzle of the fruit’s formation in the first place?
One factor that might explain Isaac Newton’s lack of curiosity about this was the predominant seventeenth-century view that although the brute mechanics of all objects, including living ones, might be accounted for by physical laws, their peculiar inner dynamic (dictating, among other things, how apples grow) was driven by that vital force or élan vital that flowed from a supernatural source beyond the reach of any godless mathematical equation. But, as we have already discovered, vitalism was blown away by subsequent advances in biology, genetics, biochemistry and molecular biology. No serious scientist today doubts that life can be accounted for within the sphere of science; but there remains a question mark over which of the sciences can best provide that account. Despite the alternative claims of scientists such as Schrödinger, most biologists still believe that the classical laws are sufficient, with Newtonian forces acting upon ball and stick biomolecules that behave like, well, balls and sticks. Even Richard Feynman, one of Schrödinger’s intellectual successors, described photosynthesis (in the passage quoted at the head of this chapter) in strictly classical terms with “sunlight that comes down and knocks this oxygen away from the carbon,” with light acting like some kind of golf club able to whack the oxygen golf ball out of the carbon dioxide molecule.
Molecular biology and quantum mechanics developed in parallel, rather than cooperatively. Biologists hardly attended physics lectures and physicists paid little attention to biology. But in April 2007, a group of MIT-based physicists and mathematicians who worked in a rather esoteric area called quantum information theory was enjoying one of its regular journal clubs (with each member taking a turn at presenting a new paper they had found in the scientific literature) when one of the group arrived with a copy of the New York Times carrying an article that suggested plants were quantum computers (more on these remarkable machines in chapter 8). The group exploded into laughter. One of the team, Seth Lloyd, recalled first hearing about this “quantum hanky-panky.” “We thought that was really hysterical … It’s like, ‘Oh my God, that’s the most crackpot thing I’ve heard in my life!’ ”2 The cause of their incredulity was the fact that many of the brightest and best-funded research groups in the world had spent decades trying to figure out how to build a quantum computer, a machine that could carry out certain calculations much faster and far more efficiently than the most powerful computers available in the world today (since, rather than relying on digital bits of information that are either 0 or 1, it would allow them to be both 0 and 1 simultaneously and therefore be able to pursue all possible calculations at once—the ultimate in parallel processing). The New York Times article was claiming a humble blade of grass was able to perform the kind of quantum trickery that lay at the heart of quantum computing. No wonder these MIT researchers were incredulous. They might not be able to build a working quantum computer but, if the article was right, they could eat one in their lunchtime salad!
Meanwhile, not far from the room where the MIT journal club was laughing its quantum socks off, a photon of light traveling at 186,000 miles per second was hurtling toward a tree with a famous pedigree.
We’ll return to that photon and tree shortly, and how they might be related to the quantum world, but first you need to be introduced to a beautifully simple experiment that highlights just how weird the quantum world really is. While we will go to great lengths to explain as best as we can just what is meant by notions such as “quantum superposition,” nothing really hits the message home better than the famous two-slit experiment, which we will describe here.
What the two-slit experiment delivers is the simplest and starkest demonstration that, down in the quantum world, everything is different. Particles can behave like waves spread out across space and waves can sometimes act like individual localized particles. You’ve already encountered this wave–particle duality: in the opening chapter, as the peculiarity that is necessary to account for how the sun generates its energy; and in chapter 3, where we saw how the wave properties of electrons and protons allow them to seep though energy barriers inside enzymes. In this chapter you will discover that wave–particle duality is also involved in the most important biochemical reaction in the biosphere: the conversion of air, water and light into plants, microbes and, indirectly, all the rest of us. But first we must discover how the outlandish idea that particles can be in many places at once is forced upon us by one of the simplest, most elegant, but most far-reaching experiments ever performed: the experiment that, according to Richard Feynman, “has in it the heart of quantum mechanics.”
Be warned, however, that what will be described here will seem impossible, and you may feel certain that there just has to be a more rational way of explaining what is going on. You may be left wondering where the sleight of hand is in what seems to be a magic trick. Or you may assume that the experiment is mere theoretical speculation dreamt up by scientists lacking the imagination to comprehend the workings of nature. But neither of these explanations is correct. The two-slit experiment doesn’t make (common) sense, but it is real and has been performed thousands of times.
We will describe the experiment in three stages; the first two will merely set the scene so that you can then appreciate the baffling results of the third, and main, stage.
First, a beam of monochromatic light (consisting of a single color, or wavelength) is shone on a screen with two narrow slits that allow some of the light to pass through both slits onto a second screen (figure 4.1). By carefully controlling the width of the slits, their distance apart from each other, and the distance between the two screens, we can create a sequence of light and dark bands on the second screen, known as an interference pattern.
Interference patterns are the signature of waves and are easy to see in any wavy medium. Toss a pebble into a still pond and watch as a set of concentric circular waves travel outward from the splash point. Toss two pebbles into the same pond and each will generate its own expanding concentric waves, but where the waves from the two pebbles overlap you will see an interference pattern (figure 4.2). Wherever the peak of one wave meets the trough of another they cancel out, resulting in no wave at those points. This is called destructive interference. Conversely, where two peaks or two troughs meet, they reinforce each other, generating twice the wave: this is called constructive interference. This pattern of wave cancellation and reinforcement can be produced in any wavy medium. In fact, it was the English physicist Thomas Young’s demonstration of interference of light beams in an early version of the two-slit experiment performed over two centuries ago that convinced him and most other scientists that light was indeed a wave.
The interference shown in the two-slit experiment is due first to the way light waves pass through both slits and then spread out, a property of waves known as diffraction, so that the beams emerging from the slits overlap and merge, just as water waves do, before hitting the back screen. At certain points on the screen the light waves emanating from the two slits will arrive in phase, with peaks and troughs marching in step, either because they have covered the same distance to the screen or because the difference in the distance they traveled is equal to a multiple of the distance between their peaks. Where this happens, the crests and troughs of the waves combine to form higher crests and lower troughs: constructive interference. The fused waves create high-intensity light at these points and hence a bright band on the screen. But at other points, the light from the two slits arrives out of phase, at the point where the crest of one wave meets the trough of another. At these points the waves cancel out, resulting in a dark band on the screen: destructive interference. In between these two extremes the combination is neither completely “in phase” nor completely “out of phase” and some light survives. We therefore don’t see a sharp sequence of light and dark bands on the screen but a smooth variation in intensity, between what are known as maxima and minima in the interference pattern. This appropriately wave-like smooth variation in intensity is a key indicator of wave phenomena. One familiar example of this can be found with sound waves: a musician tuning an instrument listens for the “beats”*1 that occur when one note is very close in frequency to another so that as they travel to the musician’s ear they sometimes arrive in phase and sometimes out of phase. This variation in their combined pattern generates an overall sound that periodically rises and falls in volume. This smooth variation in the intensity of the sound is due to interference between two separate waves. Note that these beats are an entirely classical example that requires no quantum explanation.
Figure 4.1: The two-slit experiment, stage 1. When monochromatic light (having a specific wavelength) is shone into the two slits, each slit then acts as a new source of light on the other side and, because of its wave-like nature, the light spreads out (diffracts) as it squeezes through each slit so that the circular waves overlap and interfere with one another, leading to light and dark fringes on the back screen.
Figure 4.2: Constructive and destructive interference of waves.
A key factor in the two-slit experiment is that the beam of light hitting the first screen must be monochromatic (consisting of a single unique wavelength). In contrast, white light, such as that emitted by a normal light bulb, is composed of many different wavelengths (all the colors of the rainbow), so the waves will arrive at the screen in a higgledy-piggledy fashion. In this case, although peaks and troughs will still interfere with one another, the resulting pattern will be so complex and so smeared out that no distinct bands will be seen. In a similar way, although it is easy to generate an interference pattern when we drop two pebbles into a pond, a huge waterfall crashing into the pond generates so many waves that it is impossible to find any coherent interference pattern.
Now for stage two of the two-slit experiment, which we perform not with light but by firing bullets at the screen. The point here is that we are using solid particles rather than spread-out waves. Each bullet must of course pass through one or the other slit, not both. With enough bullets getting through we see that the back screen will have accumulated two bands of bullet holes corresponding to the two slits (figure 4.3). Clearly, we are not dealing with waves. Each bullet is an independent particle and has no relationship with any other bullet, so there is no interference.
Now for stage three: the quantum “magic trick.” The experiment is repeated using atoms instead of bullets. A source that can produce a beam of atoms fires them at a screen with two appropriately narrow slits.*2 To detect the arrival of the atoms, the second screen has a photoluminescent coating that shows up as a tiny bright spot wherever a single atom hits it.
If common sense prevailed at the microscopic level, then atoms should behave like incredibly tiny bullets. We run the experiment first with just the left slit open and see a band of light spots on the back screen behind the open slit. There is a certain amount of spreading of the spots that one might presume to result from some of the atoms bumping off the edges and being deflected rather than going cleanly through the slit. Next, we also open the right slit and wait for the spots to build up on the screen behind it.
If you were asked to predict the distribution of the bright spots and you knew nothing of quantum mechanics, then you would naturally guess that it would look very much like the pattern produced by the bullets; namely, that a band of spots would build up behind each slit, giving two distinct patches of light that are brightest in their center and gradually fade away as we move out—as the atom “hits” become rarer. You would also expect that the mid-point between the two bright patches would be dark, since it corresponds to a region of the screen that is hardest to reach for the atoms, whichever slit they manage to get through.
Figure 4.3: The two-slit experiment, stage 2. Unlike the wave behavior, firing a stream of bullets at the slits shows particle-like behavior. Each bullet that gets through to the back screen must have gone through one or other slit, but not both (assuming, of course, that the middle screen is thick enough to block any bullets that miss the slits). Rather than multiple banded interference, the pattern on the back screen now shows an accumulation of bullets along just two narrow strips adjacent to each of the slits.
But this is not what we find. Instead, we see a very clear interference pattern of light and dark fringes, just like we did with light. The brightest part of the screen, believe it or not, is in the center of the screen: the very patch we would not expect many atoms to be able to reach (figure 4.4). In fact, with the right distance between the slits and the right distance between the two screens, we can make sure that the bright region on the back screen (the area atoms were able to reach with just one slit open) will now be dark (no atoms arriving there) when we open up the second slit. How can opening up another slit, which should only allow more atoms through, prevent atoms reaching certain regions of the screen?
Figure 4.4: The two-slit experiment, stage 3. Replacing the bullets with atoms from a source that can fire them at the slits (of course, in each stage the width and separation of the slits are chosen appropriately) we see the wave-like interference pattern appearing again. Despite each atom hitting the back screen at a localized point indicating its particle nature, they cluster together in bands, just as was seen with light. So what is it that is going through both slits at once, and without which we would not see the multiple interference fringes?
Let us see if we can explain what is going on using simple common sense and avoid appealing to quantum mechanics just yet. Suppose that, despite each atom being a tiny localized particle—after all, every atom hits the screen at a single point—the sheer number of atoms involved, all colliding and interacting with one another in a particular coordinated way, produces a pattern with the appearance of interference. After all, we know that water waves are in fact composed of lots of molecules of water that, on their own, would not be expected to be wavy. It is the coordinated motion of trillions of water molecules that produces the wave-like properties, not each molecule individually. Perhaps the atom gun extrudes a coordinated flow of atoms, rather like a wave machine in a swimming pool.
To test the coordinated atom theory, we repeat the experiment, but now send the atoms through one at a time. We fire the atom gun and wait for the appearance of a spot of light on the back screen before firing it again, and so on. Initially, common sense seems to prevail. Each atom that manages to get through the slits leaves just one tiny localized spot of light somewhere on the screen. It seems that atoms leave the gun as bullet-like particles and arrive at the screen as particles. Surely, in between gun and screen they must similarly behave as particles? But now the quantum rabbit comes out of the hat. As the spots, each one recording the arrival of a single bullet-like atom, gradually build up on the screen, the light and dark interference pattern gradually emerges once again. With the atoms now traveling through the instrument one at a time, we can no longer argue that there is any collective behavior of lots of atoms bumping into and interacting with one another. These aren’t like water waves. And here again, we must confront the counterintuitive result that there are places on the back screen where atoms could land when only one of the slits was open and yet are completely dark if the second slit is also open despite its opening providing an additional route for the atom to reach the screen. It seems as though an atom passing through one slit must somehow be aware whether or not the other slit is open, and act accordingly!
To recap, each atom leaves the gun as a tiny localized particle and arrives at the second screen also as a particle, as is evident from the tiny flash of light when it arrives. But in between, as it encounters the two slits, there is something mysterious going on akin to the behavior of a spread-out wave that gets split into two components, each emerging from a slit and interfering with the other on the far side. How else can a single atom be aware of the state (whether open or closed) of both slits at the same time?
Suspecting sleight of hand somewhere, let’s see if we can catch the atoms out by lying in wait behind the slits. This can be achieved by setting up a detector, behind the left slit, say, so that it registers a “signal” (maybe a beep) whenever an atom passes through that slit on its way to the screen.*3 We can also place a second detector over the right slit to catch atoms that pass through that slit. Now, if an atom passes through one slit or the other, we will hear a beep from either the left or the right detector; but if the atom manages to somehow unwrap its bullet-like nature and go through both slits, then both detectors will beep at the same time.
What we now find is that, with each firing of the atom gun that is accompanied by the appearance of a bright dot on the screen, either the left or the right detector beeps, never both. Surely we now have proof at last that the interfering atoms do indeed go through either one slit or the other, but not both simultaneously. But, be patient and keep watching the screen. As lots of individual flashes of light build up and coalesce, we see that what is produced is no longer an interference pattern. In its place are just two bright bands, indicating the collection of a pile of atoms behind each slit, just like we had in the experiment with bullets. The atoms are now behaving like conventional particles throughout the experiment. It is as though each atom behaves like a wave when it is confronted by the slits, unless it is being spied upon, in which case it innocently remains as a tiny particle.
Maybe the presence of the detector is causing a problem, perhaps upsetting the strange and delicate behavior of the atoms going through the slits. Let’s test this by removing one of the detectors, say the detector over the right slit. We can still get the same information from this arrangement because when we fire the gun, hear a beep and see a bright spot on the screen, we will know the atom must have gone through the left slit; when we fire the gun, don’t hear a beep but do see a bright dot, then we’ll know that the atoms must have reached the screen via the right slit. We can now know whether the atoms have gone through the left or right slit, but we are only “disturbing” one of the routes. If the detector itself was causing the problem then we would expect those atoms that triggered the beep to behave like bullets but those that didn’t (and went through the right slit) to behave like waves. Maybe now we’ll see a mixture of a bullet-like pattern (from atoms going through the left slit) and an interference pattern (from atoms going through the right slit) on the screen.
But we don’t. With this arrangement we still don’t see any interference pattern. Only the bullet-like pattern of dots is seen behind each slit on the screen. It seems that the mere presence of a detector that can register the location of an atom is enough to destroy its wave-like behavior, even if that detector is some distance away from the atom’s path through the other slit!
Perhaps the physical presence of the detector over the left slit is sufficient to influence the path of atoms passing through it, rather like a large boulder changing the flow of water in a fast-moving stream. We can test this by switching off the left detector. It’s still there, so we would expect its influence to be pretty much the same. But now, with the detector present but switched off, the interference pattern builds up on the screen once again! All the atoms going through the experiment have gone back to behaving as waves. How is it that atoms behaved as particles when the detector over the left slit was switched on, but as soon as it was switched off they behaved like waves? How does a particle going through the right slit know that the detector over the left slit is switched on or off?
It is at this stage that you have to leave common sense behind. Now we have to confront the wave–particle duality of tiny objects such as atoms, electrons or photons, that behave like a wave when we do not have information about which slit they went through, but like a particle when we observe them. This is the process of observation or measurement of quantum objects that we first met in chapter 1 when considering Alain Aspect’s demonstration of quantum entanglement in separated photons. You will remember that Aspect’s team measured their photons by passing them through a polarized lens that destroyed their entangled state—which is an aspect of their wave nature—forcing them to choose a single classical polarization direction. In a similar way, the measurement of atoms passing through the two-slit experiment forces them to choose whether to go through the left or the right slit.
Quantum mechanics does in fact provide us with a perfectly logical explanation of this phenomenon; but it is only an explanation of what we observe—the result of an experiment—not of what is going on when we are not looking. But since all we have to go on is what we can see and measure, maybe it makes no sense to ask for more. How can we assess the legitimacy or truth of an account of a phenomenon that we can never, even in principle, check? As soon as we try, we alter the outcome.
The quantum interpretation of the two-slit experiment is that at any given moment in time, each atom must be described by a set of numbers that define its probabilistic location in space. This is the quantity we introduced in chapter 2 as the wave function. There we described it as being similar to the idea of tracking a crime wave spreading through a city by assigning probabilities to burglaries taking place in different districts. In a similar way, the wave function describing an atom going through the two slits tracks the likelihood of finding it anywhere in the apparatus at any given time. But, as we emphasized earlier, whereas a burglar must have a single location in space and time, and the “crime probability” wave describes only our lack of knowledge of where he actually is, in contrast, the wave function of the atom in the two-slit experiment is real in the sense that it represents the physical state of the atom itself, which really doesn’t have a specific location unless we measure it and is, until then, everywhere at once—with varying probability, of course, so that we are unlikely to find the atom in places where its wave function is small.
So instead of individual atoms going through the two-slit experiment we have to consider the wave function traveling from source to back screen. On encountering the slits, the wave function splits in two, with each half going through one of the slits. Note that what we are describing here is the way an abstract mathematical quantity changes in time. It is pointless to ask what is really going on, since we would have to look to check. But as soon as we try to do so we alter the outcome. Asking what is really going on between observations is like asking whether your fridge light is on before you open the fridge door: you can never know because as soon as you peek you change the system.
The question then arises: When does the wave function “become” a localized atom once again? The answer is: when we try to detect its location. When such a measurement takes place, the quantum wave function collapses to a single possibility. Once again, this is very different from the burglar situation where the uncertainty about his whereabouts suddenly collapsed to a single point after he was nabbed by the police. In that case, it was only our information about the burglar’s whereabouts that was affected by the detection. He was always only ever in one place at any given time. Not so for the atom; in the absence of any measurement, the atom really is everywhere.
So, the quantum wave function calculates the probability of detecting the atom at a specific location, were we to carry out a measurement of its position at that time. Where the wave function is large before measurement, the resulting probability of finding the atom there will be high. But where it is small, perhaps due to destructive wave interference, the probability of finding the atom there when we decide to look will be correspondingly small.
We can imagine following the wave function describing the single atom as it leaves the source. It behaves just like a wave that flows toward the slits, so, at the level of the first screen, it will be of equal amplitude in each slit. If we place a detector on one of the slits, then we should expect equal probabilities: 50 percent of the time we will detect the atom at the left slit and 50 percent of time we will detect it at the right slit. But—and this is the important bit—if we don’t try to detect the atom at the level of the first screen then the wave function flows through both slits without collapsing. Thereafter, in quantum terms we can talk of a wave function describing a single atom that is in a superposition: of its being in two places at the same time, corresponding to its wave function going through both the left and right slits simultaneously.
On the other side of the slits, each separated piece of the wave function, one from the left and one from the right slit, spreads out again and both form sets of mathematical ripples that overlap, at some points reinforcing and at other points canceling each other’s amplitude. The combined effect is that the wave function now has the pattern characteristic of other wave phenomena, such as light. But bear in mind that this now complicated wave function is still describing only a single atom.
At the second screen, where a measurement of the position of the atom finally takes place, the wave function allows us to calculate the probability of detecting the particle at different points along the screen. The bright patches on the screen correspond to those positions where the two parts of the wave function, coming from the two slits, reinforce each other, and the dark patches correspond to those positions where they cancel each other out to generate a zero probability for atoms being detected at these positions.
It is important to remember that this reinforcement and cancellation process—quantum interference—takes place even when only a single particle is involved. Remember that there are regions of the screen that atoms, fired one at a time, could reach with just one slit open but that were no longer reachable when both slits are open. This only makes sense if each atom released from the atom gun is described by a wave function that can explore both paths simultaneously. The combined wave function with its regions of constructive and destructive interference cancels out the probability of the atom being found in some positions on the screen that it would reach if only one slit were open.
All quantum entities, whether fundamental particles or the atoms and molecules composed of these particles, display coherent wave-like behavior so that they can interfere with themselves. In this quantum state they can exhibit all the weird quantum behaviors, such as being in two places at once, spinning in two directions at once, tunneling through impenetrable barriers or possessing spooky entangled connections with a distant partner.
But then, why can’t you or I, ultimately composed as we are of quantum particles, be in two places at once, something that would certainly be extremely useful on a busy day? The answer on one level is very simple: the bigger and more massive a body is, the smaller will its wave-like nature be, and something the size and mass of a human, or indeed anything large enough to be visible with the naked eye, will have a quantum wavelength so tiny as to have no measurable effect. But more deeply, you can think of each atom in your body as being observed, or measured, by all the other atoms around it, so that any delicate quantum properties it might have are very quickly destroyed.
What, then, do we actually mean by “measurement”? We have already briefly explored this question in chapter 1, but we must now take a closer look since it is central to the question of how much “quantum” there is in quantum biology.
For all its success, quantum mechanics tells us nothing about how to take the step from the equations that describe how an electron, say, moves around an atom to what we see when we make a specific measurement of that electron. For this reason, the founding fathers of quantum mechanics came up with a set of ad hoc rules that became an addendum to the mathematical formalism. They are known as the “quantum postulates” and provide a sort of instruction manual on how to translate the mathematical predictions of the equations into tangible properties we can observe, such as the position or energy of an atom at any given moment.
As for the actual process itself whereby an atom instantaneously stops being “over here and over there” and is just “over here” when we look, no one really knows what goes on and most physicists have been happy to adopt the pragmatic view that it “just happens.” The problem is that this requires an arbitrary distinction to be made between the quantum world, where weird stuff happens, and our everyday macroworld where objects behave “sensibly.” A measuring device that detects an electron has to be part of this macroworld. But how and why and when this measurement process takes place was never clarified by the founders of quantum mechanics.
During the 1980s and 1990s, physicists came to appreciate what must be happening when an isolated quantum system, such as a single atom in the two-slit experiment, with its wave function existing in its superposition of being in two places at once, interacts with a macroscopic measuring device, say one placed on the left slit. It turns out that detecting the atom (and note here that even not detecting the atom is regarded as a measurement, as that means it must have gone through the other slit) causes the atom’s wave function to interact with all the trillions of atoms in the measuring device. This complex interaction causes the delicate quantum coherence to leak away very quickly and be lost in the incoherent noise of its surroundings. This is the process called decoherence that we have already met in chapter 2.
But decoherence does not need a measuring device to come into effect. It is taking place all the time inside every single classical object as its quantum constituents—the atoms and molecules—undergo thermal vibrations and get buffeted around by all the surrounding atoms and molecules, so that their wave-like coherence is lost. In this way we can think of decoherence as the means by which all the material surrounding any given atom, say—what is referred to as its environment—is constantly measuring that atom and forcing it to behave like a classical particle. In fact, decoherence is one of the fastest and most efficient processes in the whole of physics. And it is because of this remarkable efficiency that decoherence evaded discovery for so long. It is only now that physicists are learning how to control and study it.
Returning to our analogy of throwing pebbles into water, when we threw them into a still pond it was easy to see their overlapping waves interfering with one another. But try throwing those same pebbles into the base of Niagara Falls. The hugely complex and chaotic nature of the water now immediately wipes out any interference pattern generated by the pebbles. This turbulent water is the classical equivalent of the random molecular motion surrounding a quantum system, resulting in instant decoherence. Most environments are, at a molecular level, just as turbulent as the waters at the base of Niagara Falls. Particles within materials are constantly being jostled and bumped around by their environment (other atoms, molecules or photons of light).
At this point we should clarify some of the terminology we are using in this book. We talk about atoms being in two places at once, behaving like spread-out waves and existing in a superposition of two or more different states at once. By way of making things easier for you, the reader, we can settle on a single term that encompasses all these concepts: that of quantum “coherence.” Thus, when we refer to “coherent” effects we mean something is behaving in a quantum mechanical way, exhibiting wave-like behavior or doing more than one thing at the same time. Thus, “decoherence” is the physical process whereby coherence is lost and the quantum becomes classical.
Quantum coherence is normally expected to be very short-lived unless the quantum system can be isolated from its surroundings (fewer jostling particles) and/or cooled to a very low temperature (much less jostling) to preserve the delicate coherence. In fact, to demonstrate interference patterns with single atoms, scientists pump all the air out of the apparatus and cool their equipment down to very close to absolute zero. Only by taking these extreme steps can they maintain their atoms in a quiet quantum coherent state for long enough to demonstrate the interference patterns.
The issue of the fragility of quantum coherence (keeping the wave function from collapsing) is of course the principal challenge to the MIT group whom we met in the opening paragraphs of this chapter, and their colleagues around the world, in their quest to build a quantum computer; and this was why they were so skeptical about the New York Times claim that plants were quantum computers. Physicists come up with all sorts of clever and expensive stratagems to shield the quantum world inside their computers from the coherence-destroying outside environment. So the idea that quantum coherence could be maintained in the hot, wet and molecularly turbulent environment inside a blade of grass was understandably thought to be crazy.
However, we now know that down at the molecular level, many important biological processes can indeed be very fast (of the order of trillionths of a second) and can also be confined to short atomic distances—just the sort of length and timescales where quantum processes like tunneling can have an effect. Thus, although decoherence can never be entirely prevented, it may be kept at bay for just long enough to be biologically useful.
Glance up at the sky for one second and a column of light 186,000 miles long descends into your eye. In that same second, the earth’s plants and photosynthetic microbes harvest the solar light column to make about 16,000 tonnes of new organic matter in the form of trees, grass, seaweed, dandelions, giant redwoods and apples. Our aim in this section is to discover how this first step in the transformation of inanimate matter into nearly all of the biomass on our planet actually works; and our exemplar transformation will be the conversion of New England air into an apple on Newton’s tree.
To see this process in action, we will borrow once again the nanotechnology submarine that we used to explore enzyme action in the last chapter. Once you’ve climbed aboard and flicked the miniaturization switch, you launch the craft skyward, up into the foliage of the tree, where you alight upon one of its expanding leaves. The leaf continues to expand until its farthest edges are lost beyond the horizon and its apparently smooth surface becomes an irregular platform paved with rectangular green bricks pock-marked by paler round blocks, each penetrated by a central pore. The green bricks are called epidermis cells and the round blocks are called stomata: their job is to allow air and water (the substrates of photosynthesis) to pass through the surface of the leaf into its interior. You guide the craft over to the nearest stoma and, when the vessel is only a micron (a millionth of a meter) in length, you lower its prow to dive through the pore and emerge within the green and bright interior of the leaf.
Once inside, you come to rest within the roomy and rather still space of the leaf’s interior, floored by rows of boulder-like green cells and roofed by thick cylindrical cables. The cables are the veins of the leaf, which either carry water from the roots to the leaf (xylem vessels) or transport newly made sugars from the leaf to the rest of the plant (phloem vessels). As you shrink further, the face of the boulder-like cell expands in all directions until it appears to be the size of a football field. At this scale—you are now about ten nanometers tall, or one hundred-thousandth of a millimeter—you can see that its surface is turfed with a ropy mesh of cords, rather like a thick jute rug. This corded material is the cell wall, which is a kind of cellular exoskeleton. Your nanosubmarine is armed with instruments that you use to hack a path down through this ropy rug, revealing a waxy underlay, the cell membrane, which is the final water-impermeable barrier between the cell and its external environment. A closer inspection reveals that it is not entirely smooth, but pockmarked by water-filled holes. These membrane channels are called porins and they are the cell’s plumbing, allowing nutrients in and waste products out. To enter the cell you need only wait alongside one of the porins until it has expanded sufficiently for you to dive into the cell’s watery interior.
Once through the porin channel you can immediately see that the inside of a cell is very different from its exterior. Instead of majestic columns and wide-open spaces, this interior is crowded and somewhat messy. It also looks like a very busy place! The watery fluid filling the cell, known as the cytoplasm, is thick and viscous; in places it’s more like a gel than a liquid. And suspended in the gel are thousands of irregular globular objects that appear to be in a state of constant internal motion. These are protein enzymes, like those we met in the last chapter, responsible for conducting the cells’ metabolic processes, breaking down nutrients and making biomolecules such as carbohydrates, DNA, protein and fats. Many of these enzymes are tethered to a network of cables (the cell’s cytoskeleton) that, rather like chair-lift cables, appear to be pulling numerous cargoes to various destinations within the cell. This transport network appears to emanate from several hubs, where the cables are anchored onto large green capsules. These capsules are the cell’s chloroplasts, within which the central action of photosynthesis takes place.
You propel the submarine through the viscous cytoplasm. Progress is slow, but you eventually arrive at the nearest chloroplast. It lies beneath you like a huge green balloon. You can see that it, like the enclosing cell, is bounded by a transparent membrane through which great stacks of green coin-like objects are visible. These are the thylakoids and they are packed full of molecules of chlorophyll, the pigment that makes plants green. Thylakoids are the engines of photosynthesis that, when fueled by photons of light, can bolt carbon atoms (absorbed from the carbon dioxide in the air) together to make the sugars that will go into our apple. To get a better view of this first step in photosynthesis, you steer the craft through one of the pores in the chloroplast membrane toward the topmost green coin of the thylakoid stack. Having reached your destination, you switch off the craft’s engine, allowing the vessel to hover above this powerhouse of photosynthetic action.
Below you lies just one of the trillions of photosynthetic machines that manufacture the world’s biomass. From your vantage point you can see that, as we discovered when examining enzyme machinery in the last chapter, although there are plenty of the billiard-ball-like turbulent molecular collisions going on all around you, there is also an impressive degree of order. The membranous surface of the thylakoid is studded with craggy green islands forested with tree-like structures terminating in antennae-like pentagonal plates. These antennae plates are light-harvesting molecules called chromophores, of which chlorophyll is the most famous example, and it is these that perform the first crucial step of photosynthesis: capturing light.
Probably the second most important molecule on our planet (after DNA), chlorophyll is worth a closer look (figure 4.5). It is a two-dimensional structure made up of pentagonal arrays of mostly carbon (gray spheres) and nitrogen (N) atoms enclosing a central magnesium atom (M), with a long tail of carbon, oxygen (O) and hydrogen (white) atoms. The magnesium atom’s outermost electron is only loosely bound to the rest of the atom and can be knocked into the surrounding carbon cage by absorption of a photon of solar energy to leave a gap in what is now a positively charged atom. This gap, or electron hole, can be thought of in a rather abstract way as a “thing” in itself: a positively charged hole. The idea is that we regard the rest of the magnesium atom as remaining neutral while we have created, through the absorption of the photon, a system consisting of the escaped negative electron and the positive hole it has left behind. This binary system is called an exciton (see figure 4.6) and can be thought of as a tiny battery with positive and negative poles capable of storing energy for later use.
Figure 4.6: An exciton consists of an electron that has been knocked out of its orbit in an atom, together with the hole it leaves behind.
Excitons are unstable. The electron and its hole feel an attractive electrostatic force pulling them together. If they recombine, the solar energy of the original photon is lost as waste heat. So, if the plant is to harness its captured solar energy, it has to transport the exciton very rapidly to a molecular manufacturing unit known as the reaction center, where a process called charge separation takes place. Essentially, this involves stripping an energetic electron completely from its atom and transferring it to a neighboring molecule, rather like the enzymatic action we observed in the last chapter. This process creates a more stable chemical battery (called NADPH) than an exciton that is used to drive the all-important photosynthetic chemical reactions.
But reaction centers are usually quite distant, in molecular terms (nanometer distances) from the excited chlorophyll molecules, so the energy has to be transferred from one antenna molecule to another within the chlorophyll forest to reach the reaction center. This can happen thanks to the tightly packed nature of the chlorophyll. Molecules neighboring the one that has absorbed the photon can themselves become excited, effectively inheriting the energy of the initially excited electron, which is then transferred to their own magnesium atom’s electron.
The problem, of course, is which route this energy transfer should take. If it heads in the wrong direction, randomly hopping from one molecule to the next in the chlorophyll forest, it will eventually lose its energy rather than delivering it to the reaction center. Which way should it turn? It doesn’t have very long to find its way to its destination before the exciton expires.
Until recently, it was thought that this energy-hopping from one chlorophyll molecule to another was haphazard, essentially adopting the search strategy of last resort, known as a random walk. This is sometimes referred to as a “drunken walk” because it resembles the path taken by an intoxicated drinker exiting a bar, wandering this way and that until he eventually finds his way home. But random walks are not a very efficient means of getting anywhere: if the drunk’s home is far away, he may well wake up the following morning in a bush on the other side of town. An object engaged in a random walk will tend to move away from its starting point by a distance proportional to the square root of the time taken. If in one minute a drunk has advanced by one meter, then after four minutes he will have advanced by two meters and after nine minutes, only three meters. Given this sluggish progress, it is not surprising that animals and microbes seldom use a random walk to find food or prey, only resorting to the strategy if no other options are available. Drop an ant onto unfamiliar ground and as soon as it encounters a scent, it will abandon a random walk and follow its nose.
Possessing neither nose nor navigation skills, the exciton energy was thought to advance through the chlorophyll forest via the drunkard’s strategy. But such a picture didn’t make much sense, as this first event in photosynthesis is known to be extraordinarily efficient. In fact, the transfer of captured photon energy from a chlorophyll antenna molecule to the reaction center boasts the highest efficiency of any known natural or artificial reaction: close to 100 percent. Under optimal conditions, nearly every energy parcel absorbed by a chlorophyll molecule makes it to the reaction center. If the path taken were a meandering one, nearly all of them, certainly most of them, should get lost. How this photosynthetic energy can find its way to its destination so much better than drunkards, ants or indeed our most energy-efficient technology has been one of the biggest puzzles in biology.
The senior author on the research paper3 that sparked the newspaper article that had the MIT journal club laughing their quantum socks off was a naturalized American, Graham Fleming. Born in Barrow in the north of England in 1949, Fleming now heads a group at the University of Berkeley in California that is acknowledged as one of the world’s leading research teams in this field, using a powerful technique with the impressive title of “two-dimensional Fourier transform electronic spectroscopy” (2D-FTES). 2D-FTES can probe into the inner structure and dynamics of the tiniest molecular systems by targeting them with highly focused short-duration laser pulses. The group has performed most of its work studying not plants, but a photosynthetic complex called the Fenna–Matthews–Olson (FMO) protein that is made by photosynthetic microbes called green sulphur bacteria, found in the depths of sulphide-rich bodies of water such as the Black Sea. To probe the chlorophyll sample, the researchers fired three successive pulses of laser light into the photosynthetic complexes. These pulses deposit their energy in very rapid and precisely timed bursts and generate a light signal from the sample that is picked up by detectors.
Greg Engel, the lead author on the paper, spent the entire night stitching together the data generated from signals covering a time of fifty to six hundred femtoseconds,*4 to produce a plot of their results. What he discovered was a rising and falling signal that oscillated for at least six hundred femtoseconds (see figure 4.7). These oscillations are akin to the interference pattern of light and dark fringes in the two-slit experiment; or the quantum equivalent of the pulsating sound beats heard when tuning a musical instrument. This “quantum beat” showed that the exciton wasn’t taking a single route through the chlorophyll maze but was instead following multiple routes simultaneously (figure 4.8). These alternative routes act a bit like the pulsed notes of the almost in-tune guitar: they generate beats when they are nearly the same length.
Figure 4.7: The quantum beats seen by Graham Fleming and his colleagues in their 2007 experiment. What is important is not the irregular shape of the oscillations—it’s the fact that there are oscillations at all.
But remember that such quantum coherence is very delicate and extraordinarily difficult to maintain. Was it really feasible that a microbe or plant was able to beat the heroic efforts of the brightest and best of MIT quantum computing researchers to keep decoherence at bay? This was indeed the bold claim made in Fleming’s paper, and it was this “quantum hanky-panky,” as Seth Lloyd described it, that raised the hackles of the MIT journal club. The Berkeley group was suggesting that the FMO complex was acting as a quantum computer to find the quickest route to the reaction center, a challenging optimization problem, equivalent to the famous traveling salesman problem in mathematics, which, for travel plans involving more than a handful of destinations, is solvable only with a very powerful computer.*5
Despite their skepticism, the journal club set Seth Lloyd the task of investigating the claim. To everyone’s surprise at MIT, the conclusion of Lloyd’s scientific detective work was that there was indeed substance to the Californian group’s claims. The beats that Fleming’s group had discovered in the FMO complex were indeed a signature of quantum coherence, and Lloyd concluded that the chlorophyll molecules were operating a novel search strategy known as a quantum walk.
The advantage of a quantum walk over a classical random walk can be appreciated by returning to our slow-moving drunk and imagining that the bar he leaves has sprung a leak and that water is pouring out of its door. Unlike our inebriated drinker, who must choose a single route, the waves of water escaping from the bar advance in all possible directions. Our drunken walker will soon find himself overtaken, as the watery wave advances through the streets at a rate simply proportional to the time taken, not its square root. So if at one second it had advanced by one meter, then after two seconds it will have covered two meters and after three seconds, three meters, and so on. Not only that, but because, like the superposed atom in the two-slit experiment, it travels by all possible routes simultaneously, some part of the wave front will definitely encounter the drunkard’s home well in advance of the inebriated wanderer himself.
Fleming’s paper caused its own wave of surprise and consternation that traveled well beyond the journal club at MIT. But some commentators were quick to point out that the experiments were conducted with isolated FMO complexes cooled to 77 K (a chilly −196°C): clearly far colder than any temperature compatible with plant photosynthesis or even life, but low enough to keep that pesky decoherence at bay. How relevant were these chilled bacteria to anything that goes on in the hot and messy interiors of plant cells?
It soon became clear, however, that quantum coherence was not limited to cold FMO complexes. In 2009, Ian Mercer at University College Dublin detected quantum beating in another bacterial photosynthetic system (or photosystem for short) called the Light Harvesting Complex II (LHC2), which is very similar to a plant photosystem, but at the normal ambient temperatures in which plants and microbes normally perform photosynthesis.4 Then, in 2010, Greg Scholes of the University of Ontario demonstrated quantum beating in the photosystem of a group of aquatic algae (which, unlike the higher plants, lack roots, stems and leaves) called cryptophytes, which are extraordinarily abundant, to the extent that they are responsible for fixing as much atmospheric carbon (that is, extracting atmospheric carbon dioxide) as higher plants.5 Around the same time, Greg Engel demonstrated quantum beating in the same FMO complex that he had studied in Graham Fleming’s laboratory, but now at much higher, life-supporting, temperatures.6 And just in case you might think this remarkable phenomenon is restricted to bacteria and algae, Tessa Calhoun and colleagues from Fleming’s laboratory in Berkeley recently detected quantum beating in another LHC2 system, this time from spinach.7 LHC2 is present in all higher plants and contains 50 percent of all the chlorophyll on the planet.
Before moving on we will describe briefly just how the solar-derived exciton energy is used, as Feynman described, to knock “this oxygen away from the carbon … leaving the carbon, and water, to make the substance of the tree”—or apple.*6
After enough energy arrives at the reaction center, it causes a special pair of chlorophyll molecules (called P680) to spit out electrons. We will be learning a bit more about what goes on within the reaction center in chapter 10, as it is a fascinating place that may house another novel quantum process. The source of these electrons is water (which, remember, is one of the ingredients in Feynman’s description of photosynthesis). As we discovered in the last chapter, the capturing of electrons from any substance is called oxidation, and it is the same process that takes place during burning. When wood burns in air, for example, oxygen atoms pull electrons from carbon atoms. The electrons in the outer orbit of carbon are fairly loosely attached, which is why carbon burns easily. However, in water they are held very tightly: photosynthesis systems are unique in that they are the only place in the natural world where water is “burnt” to yield electrons.*7
So far, so good: we now have a supply of free electrons thanks to the energy delivered by the excitons in chlorophyll. Next, the plant needs to send these electrons where they can be put to work. They are first captured by the cell’s designated electron transporter, NADPH. We met a similar molecule, NADH, briefly in the last chapter, where it was involved in ferrying electrons captured from nutrients, such as sugars, to the respiratory chain of enzymes in the cell’s energy organelles, the mitochondria. If you remember, the captured electrons delivered to the mitochondria by NADH then flowed down a respiratory chain of enzymes as a kind of electric current that is used to pump protons across a membrane, and the resulting backflow of these protons is used to make the cell’s energy carrier, ATP. A very similar process is used to make ATP in plant chloroplasts. NADPH feeds the electrons it is carrying into a chain of enzymes that similarly pumps protons out of the chloroplast membrane. The backward flow of these protons is used to produce ATP molecules, which can then go on to power lots of energy-hungry processes in the plant cell.
But the actual carbon fixation process, the capture of carbon atoms from carbon dioxide in air and their use to make energy-rich organic molecules like sugars, takes place outside the thylakoid, though still within the chloroplast. This is performed by a big bulky enzyme called RuBisCO that is probably the most abundant protein on earth as it has to do the biggest job: making nearly all the world’s biomass. This enzyme bolts the carbon atom pulled from carbon dioxide onto a simple five-carbon sugar molecule called ribulose-1,5-bisphosphate to make a six-carbon sugar. To achieve this feat it makes use of the two ingredients it has been supplied with: electrons (delivered by NADPH) and a source of energy (ATP). Both ingredients are the products of the light-driven processes of photosynthesis.
The six-carbon sugar made by RuBisCO immediately breaks down into two three-carbon sugars that are then bolted together in lots of different ways to make all of the biomolecules that make an apple tree, including its apples. The inanimate New England air and water have, with the help of light and a sprinkling of quantum mechanics, become the living tissue of a New England tree.
By comparing photosynthesis in plants with the respiration (burning our food) that takes place in our own cells, discussed in the last chapter, you can see that, under the skin, animals and plants are not so different. The essential distinction lies in where we, and they, get the fundamental building blocks of life. Both need carbon, but plants obtain it from air whereas we get it from organic sources, such as the plants themselves. Both need electrons to build biomolecules: we burn organic molecules to capture their electrons, while plants use light to burn water to capture its electrons. And both need energy: we scavenge it from the high-energy electrons that we obtain from our food by running them down respiratory energy hillsides; plants capture the energy of solar photons. Each of these processes involves the motion of fundamental particles that are governed by quantum rules. Life seems to be harnessing quantum processes to help it along.
The discovery of quantum coherence in warm, wet, turbulent systems such as plants and microbes has come as a huge shock to quantum physicists, and a great deal of research is now focused on working out precisely how living systems protect, and utilize, their delicate quantum coherent states. We will be returning to this puzzle in chapter 10, where we will examine some very surprising possible answers that may even help physicists, such as those MIT quantum theorists, to build practical quantum computers that could work on your desk, rather than in your deep freeze. The research is also likely to inspire a new generation of artificial photosynthetic technologies. Current solar cells are loosely based on photosynthetic principles and are already competing with solar panels for a share of the clean energy market, but their efficiency is limited by losses during energy transport (at best about 70 percent efficiency compared to the near 100 percent efficiency of the photon energy capture step in photosynthesis). Bringing biology-inspired quantum coherence to solar cells has the potential to greatly increase the efficiency of solar energy and thereby deliver a cleaner world.
Finally in this chapter, then, let us take a moment to consider the significance of what we have added to our understanding of what is special about life. Consider again those quantum beats that Greg Engel first saw in his FMO complex data, which show that particles move within living cells as waves. There is a temptation to think of these as laboratory-bound phenomena with no significance outside biochemical experimentation. But subsequent research has demonstrated that they do indeed exist in the natural world too, inside leaves, algae and microbes, and that they play a role, possibly a crucial one, in building our biosphere.
Still, the quantum world appears very strange to us and it is often claimed that this strangeness is a symptom of a fundamental split between the world we see around us and its quantum underpinnings. But in reality there is only a single set of laws that govern the way the world behaves: quantum laws.*8 The familiar statistical laws and Newtonian laws are, ultimately, quantum laws that have been filtered through a decoherence lens that screens out the weird stuff (which is why quantum phenomena appear weird to us). Dig deeper and you will always find quantum mechanics lurking at the heart of our familiar reality.
What’s more, certain macroscopic objects are sensitive to quantum phenomena; and most of these are living. We discovered in the last chapter how quantum tunneling inside enzymes can make a difference to whole cells; and here we have explored how the initial photon-capturing event responsible for putting most of the biomass on the planet appears to be dependent on a delicate quantum coherence that can be maintained for biologically relevant lengths of time within the warm but highly organized interior of a leaf or microbe. Once again we see Schrödinger’s order from order capable of capturing quantum events, and what Jordan termed amplification of quantum phenomena into the macroscopic world. Life seems to bridge the quantum and classical worlds, perched on the quantum edge.
We next turn our attention to another essential process for our biosphere. Newton’s apple tree wouldn’t have been able to make any apples if its blossom hadn’t first been pollinated by birds and insects, particularly bees. But the bees had to find the apple blossom; and they did so using another capability believed by many to be driven by quantum mechanics—the sense of smell.
*1 These are fluctuations in volume—a kind of pulse—created by two notes that are almost the same frequency and thereby nearly in tune. This use of the term “beat” should not be confused with the more common use of “beat” in music to mean its rhythm.
*2 The slits do indeed need to be very narrow and very close together. In the experiments carried out in the 1990s the screen was a sheet of gold foil and the slits were of the order of a single micrometer (a thousandth of a millimeter) wide.
*3 We assume here that the detector has 100% efficiency and will definitely fire if an atom passes through the slit it is watching, and yet does not interfere with the path of the atom. Of course, in practice this is not possible since we unavoidably disturb the passage of the atom through the act of observation, as we are about to see.
*4 A femtosecond is one millionth of one billionth of a second, or 10-15 seconds.
*5 The traveling salesman’s problem is to find the shortest route passing through a large number of cities. This is described mathematically as an NP-hard problem: that is, one for which no shortcut to a solution exists, even in theory, the only way to find the optimal solution being a computationally intensive, exhaustive search of all possible routes.
*6 In fact, Feynmann’s description is actually incorrect, as oxygen is not knocked away from the carbon in photosynthesis.
*7 When we say the “burning of water” we of course do not mean that water is a fuel like coal, but rather we are using the term loosely to denote the molecular process of oxidation.
*8 We should add a qualification here since quantum mechanics cannot so far account for the gravitation force, as general relativity (which is how we understand gravity) appears to be incompatible with quantum mechanics. Unifying quantum mechanics and general relativity to construct a quantum theory of gravity remains one of the greatest challenges confronting physics.
