Relax  with Quantum  Theory

This was Richard Feynman, speaking about quantum theory. It pays to take his warning seriously. By the time you finish this book, you will understand the most extraordinary implications of a truly extraordinary theory. But if you try to picture it in familiar ways you will come hopelessly unstuck. The quantum world really is different, and the only way to come to grips with it is to suspend disbelief. So open your mind and become a genius in your own lunchtime.
ONCE upon a time, Newton prevailed, and the world was a safe place for all of us. When you hit a plain, old-fashioned billiard ball, you could predict how fast it would move and in what direction. And when the billiard ball came to rest, you knew exactly where it was. These simple notions seemed obvious, necessary even. Most people believed that for physics to work, it had to be based on such solid and unshakable foundations.

Then on 19 October 1900, physicist Max Planck made a ground-breaking presentation to the German Physical Society. Planck was a sober man and, at 42, a little long in the tooth for a revolutionary. But his discovery was to turn the classical physics of the billiard ball on its head. What he described was an answer to an old question: Why does the colour of radiation from any glowing body change from red to orange and ultimately to blue as its temperature increases? Planck found he could get the right answer by assuming that radiation, like matter, comes in discrete quantities. And he called his little packets of energy "quanta" from the Latin for amount. At the time, Plank seems to have imagined that some deeper explanation of these quanta would emerge.

But it rapidly became clear that the "quantisation" of energy -- dividing it up into individual pieces -- was actually a new and fundamental rule of nature. The classically trained Planck didn't like this conclusion one bit. He resisted it to his dying day, prompting his famous lament that new scientific theories supplant previous ones not because people change their minds, but simply because old people die.

It's not surprising that Planck was unsettled by the implications of quantum theory. If you accept its conclusions nothing is what it seems, or what common sense and Newtonian physics lead you to believe. Things change when you look at them. Objects behave in unpredictable ways.

Take the uncertainty principle, which emerges inevitably from quantum theory. According to this, you can never measure anything as accurately as you'd like. Or to put it another way, measurements affect the thing you're trying to measure. Then there is the notion of wave-particle duality, which says that an electron, for example, may sometimes act like a wave and sometimes like a particle. What all these ideas seem to suggest is that physical objects -- even reality itself -- are not at all what everyone had supposed.

How do such grandiose and alarming conclusions follow from the seemly innocuous statement that energy is divided up into quanta? The American physicist Richard Feynman liked to use a simple and compelling example. Think of light reflected from a mirror. No mirror is perfect, so perhaps 95 per cent of the light bounces off the mirror's surface, while the other 5 per cent passes through, or is absorbed or otherwise lost.

In pre-quantum days, no problem. When light hit a mirror it was seen as a continuous stream of energy: most bounced off the mirror's surface but a fraction streamed through. But Planck recast light as a torrent of quanta -- called photons. Because each photon is indivisible, it must either be reflected or absorbed in its entirety. You can't have 95 per cent of a photon going one way and the rest going somewhere else. But then, to understand what a mirror does to light, you must conclude that 19 out of every 20 photons bounce off the surface while the rogue photon goes its own way. Who decides what each individual photon should do?

Here lies the revolution. Quantum theory says that what happens to any individual photon is genuinely and inescapably unpredictable. It has a 95 per cent chance of being reflected, and a 5 per cent chance of being transmitted or absorbed, and that's all there is to it. There's nothing about any photon, no secret property or hidden clue, that can tell you any more precisely than that what it will do. The unpredictability is innate.

Here's another example. If you rotate your Polaroid sunglasses in front of your eyes, you'll see changes in the amount of light getting through them. Light (as James Clerk Maxwell had shown in 1864) is a type of electromagnetic wave, and the waves can be polarised, like a skipping rope that's made to go up and down or side-to-side, or anything in between. Sunglasses tend to let through vertically polarised light but block the horizontally sort, the source of most glare and reflections.

But a single photon of light coming at your sunglasses has only two options: to pass through or not. What will it do? Again, the best you can do is to know those probabilities. You can't ever predict exactly what any individual photon is going to do.

In the old days of classical physics, you might have wanted to predict what a billiard ball would do when it ran into another billiard ball or the side of the table. To do that, you would need to know its mass, speed and direction, perhaps also at what rate it is spinning, its hardness or springiness when hit, and so on. You might call this list of properties the classical "state" of the billiard ball, and the better you knew its state the better you could predict its behaviour. But quantum theory throws all that out of the window. You can only describe the "quantum state" of a photon in terms of its probabilities. And the probabilities change, depending on what you plan to do with the photon. A photon headed for a mirror will be reflected or transmitted when it gets there. But if the same photon were heading towards a polarising screen, you would need to describe it in a different way. For the classical billiard ball, one set of properties -- mass, speed and the like -- will tell you everything you need to know about it, under every circumstance. But the quantum state of a photon -- now that's a different matter.

You can see why physicists of the old school found quantum theory confusing, alarming and quite possibly dangerous. It seems as if the photon has no reliable properties of its own, and only reluctantly acquires them as a sort of conspiracy between it and the measuring device. The nature of reality it implies recalls Gertrude Stein's comment about the unremarkable city of Oakland, California: "There's no there there."

Can quantum particles really communicate over vast distances in an instant, or are we missing something?

Neither Max Planck nor Albert Einstein, who between them brought photons into the world, was ever completely happy about what they had done. Planck came up with the idea of little packets of light, but was reluctant to believe they were real objects rather than just mathematical devices that made life easier for physicists.

Einstein had a different problem. He had no difficulty picturing light as a rain of tiny bullets that could literally knock electrons loose from their atoms. He used that idea, in fact, as the basis for a simple explanation of the photoelectric effect, in which light shining on certain metals generates an electric current. Later, he even argued that it made good sense to think of light as a "gas" of photons not unlike a conventional gas of physical atoms.

What really bothered Einstein was that, if photons were real objects, an undesirable element of probability crept into physics. And Einstein, revolutionary though he was, remained a strict classicist in one respect: he believed unswervingly in cause and effect. If you know all the properties and characteristics of any object, in other words, you ought to be able to predict exactly what it will do in any situation.

Quantum theory, by contrast, can only ever give the probability that something might happen. When a stream of photons falls on the lens of Polaroid sunglasses, some will go through and some will not. But there is no way you can predict exactly what any individual photon will do. You can only know the chances of one result or another.

Quantum theory upset Einstein because it gave him nothing better to grapple with than frustrating probabilities. In 1936, he got together with Boris Podolsky and Nathan Rosen to create the "EPR paradox". It's ironic that the spooky EPR connection has now been used in the lab to teleport photons, because the original reason for inventing the EPR paradox was to show that one of the implications of quantum theory was so unacceptable that it must be wrong or incomplete in some respect. What the EPR trio couldn't accept was the idea that measuring a photon in one place could have an instantaneous physical consequence somewhere else -- all because quantum measurements are about probabilities.

The original EPR argument has been recast in many different forms, but let's stick with photons for now. Suppose you entangled a pair of photons polarised at 90 degrees to each other. You can't know what the polarisations are until you measure them; they could be vertical, horizontal or any angle in between. All you do know for sure is that they are perpendicular to each other. You send these photons off in different directions. At some point as they shoot off into the distance the photons will run into polarising filters you've cunningly put in their path.

Suppose one photon passes straight through a vertically aligned filter. It must be vertically polarised, so its partner must be horizontally polarised. The second photon would therefore pass through any horizontal filter in its way, but not through a vertical filter. So far so good. One photon is vertically polarised, the other is horizontally polarised, so they are at right angles as they should be, and all's well with the world.

Not quite. Until the first photon hits the filter, you have no idea whether it will go through or not. And for that matter, the photon doesn't know, what sort of filter it is going to hit until it gets there. Since you know nothing about either photon's individual polarisation until you make a measurement, you only know that the odds of it going through are fifty-fifty, no matter what angle the filter is set at. So the second photon can't know what the first photon will do until it actually does it. Yet the actions of the first photon determine the actions of the second. The second photon has to get some sort of tip-off from the first, even though they are physically a long way from each other.

What's more, this tip-off has to be instantaneous, because it has to work even if the two photons hit their filters at exactly the same time. It's impossible to predict what either photon will do, and yet the two of them must act in concert so that their polarisations have the correct relationship to each other. This is the crux of the spookiness that Einstein, Podolsky, and Rosen took such exception to. It arises precisely because the results of quantum measurements are uncertain or indeterminate until they are actually made.

The story would be different if the polarisations of the two photons were somehow fixed at the outset, even though we don't know what they are. The results of any polarisation measurements would still be fifty-fifty either way, because you have no prior knowledge of what the photons will do when they get to the filters. But from the photons' perspective, everything is predetermined: each photon is in a definite state, so the fact that the two measurements come out as they do is the result of prearrangement, not of a spooky communication.

This is what the classically minded Einstein seized on. It's like saying that a billiard ball headed your way is either red or blue, but you don't know which until you actually look at it. That's an entirely different proposition from saying that the billiard ball is neither red nor blue until you look at it, and it only becomes one colour or the other at the moment you see it.

The argument, in other words, was that if photons' polarisations are truly not determined until they are measured, then the paired EPR photons have to conspire with each other in some instantaneous way in order to guarantee that simultaneous measurements on them come out right. That seemed absurd! Much more sensible, Einstein and his friends believed, was the notion that quantum theory is incomplete, and that each photon has some secret property that, if only you knew it, could tell you what the result of a polarisation measurement would be.

All well and good, except . . . how would you find out the photon's secret except by making the very measurement whose result it is supposed to help you predict? Which rather spoils the point. Most physicists agree that the EPR conundrum is indeed something of a puzzle. But does it mean that quantum theory is wrong, or just hard to understand? What would be the point of giving photons extra properties if there is no independent way of finding out what they are, especially when they don't seem to make jot of difference to the outcomes of experiments?

In the words of the physicist John Bell, who generally sympathised with Einstein's disquiet over quantum theory, the EPR paradox is one of those questions that most physicists feel they will fully understand if they can ever spare twenty minutes to think about it. But in the meantime, why worry?

Weird quantum connections won't let you break Einstein's ultimate speed limit. But they will help you keep a secret

The EPR paradox would be truly alarming -- as opposed to just puzzling -- if you could dabble with the spooky communication between the two particles to transmit an instantaneous message. If you could somehow choose the outcome of a measurement at your end, you would simultaneously engineer the outcome at the other end because of the way the two particles are entangled. The spooky connection would then let you send a message immediately to someone light years away. That would spell big problems for relativity theory, which strictly forbids any meaningful signals from travelling faster than the speed of light.

But Einstein can rest easy. This stratagem won't won't work because the result of your measurement can only ever be a fifty-fifty shot. You have no control over what is measured at your end, let alone the other.

That's not quite the end of the story, though. It's true you can't use the spooky connection to beat the speed of light, but you can use it to send ultra-secure coded messages. Not only that, but quantum theory actually lets you know if a spy has tried to tamper with your message.

Mathematicians have devised a variety of codes that depend on the use of a "key"--a number known only to the person sending a message and the recipient. Here's how it works. The sender transforms a written message into a set of binary digits, then scrambles the digits by applying a mathematical transformation using the key. The recipient receives the scrambled signal, undoes the mathematical transformation using the key, and thereby reconstructs the original message. Simple.

But there is a weak spot in this system. Both parties must decide on a key and then keep it absolutely secure. The key can be any random sequence of numbers, however, and that's where quantum theory can help. To exchange secret messages, Alice and Bob first set up a device that spits out entangled pairs of photons polarised the same way--either horizontally or vertically. One photon from each pair goes to Alice, and the other to Bob. To detect the photons, Alice and Bob each have a vertically polarised filter. If Alice sees a photon coming through her filter she knows that Bob has seen one too; if she doesn't see one, he won't either. Counting a detection as a "1" and a miss as a "0," both Alice and Bob record the same random string of binary digits which becomes their key to encode messages.

Now suppose a spy realises what Alice and Bob are up to, and inserts his own vertically polarised filter along the path to Alice's detector. The eavesdropper sneakily intercepts the information en route to Alice, and figures out the key. To cover his tracks, every time a photon passes through his filter he sends Alice an identical, vertically polarised photon which she naturally enough sees and records. If no photon goes through the spy's filter, he doesn't send one to Alice, so she can't pick one up. The upshot of this subterfuge is that the spy can intercept the photons to capture the key without either Alice or Bob knowing that their security has been breached.

With a slightly more complicated system, however, Alice and Bob can construct a key that's not only random, but is also immune to interception. If someone is poaching their photons, no matter how carefully, they would know about it. This time, our two protagonists opt for polarising filters that they can set either vertically or at 45 degrees. Every time a photon comes along, Alice and Bob set their filters randomly in either position. If, as will happen by chance half the time, they set their filters at the same angle, the situation is as before: when one sees a photon, so does the other.

But what if the filters are set at 45 degrees to each other? Suppose Alice's filter is vertical, and she sees a photon. Bob's photon must then be vertically polarised too. So what will happen when it encounters a filter set at a 45 degree angle? Classically, in such a case, the intensity of a beam of vertically polarised light would be cut in half. Translated into quantum terms, that means each photon in the beam must have a fifty-fifty chance of passing through. So Bob may or may not pick up the vertically polarised photon. It's a fifty-fifty guess.

Setting their filters at random each time, Alice and Bob measure a series of EPR photon pairs. Afterwards, they tell each other how their filters were set each time, by shouting across the rooftops if need be. If they both chose the same setting, they know they must have got the same result, and they can use the information to create a secret key. When their settings were different, neither can say what the other must have seen, so they ignore those results.

This may seem like a big step backwards. It has taken twice as many measurements to establish the key, since half of the measurements are thrown away. But here's the advantage: an eavesdropper cannot intercept the photons without giving himself away. A spy who wanted to insert his own detector to intercept Alice's photons would have to guess each time whether to set the filter vertically or at 45 degrees. If he guesses right he can pass on a counterfeit photon to Alice and no one will be any the wiser. But if he guesses wrong, he will send on the wrong type of photon to Alice. Alice will still detect photons and record results, but she and Bob can run statistical tests on their measurements that will betray the presence of a spy. This works because the photons Alice and Bob see are linked by the spooky EPR correlation, and eavesdropping destroys that link. In effect, the EPR correlation is now between Bob and the spy, and a quite different non-quantum correlation is introduced between the spy and Alice. The statistical tests tell Alice and Bob whether their EPR connection was preserved during the photon exchange, and hence whether their key is secure.

What all this means is that Alice and Bob can tell the world everything they are doing, except their own individual results for every measurement. They can set their cipher key without sending any sensitive information from one place to another, and they will know immediately if a spy has tried to crack their code.

A few years ago, Richard Hughes and colleagues at Los Alamos National Laboratory in New Mexico set up a system on a 14-kilometre optical fibre network that actually creates a secret cryptographic key. They haven't capitalised on their achievement for any nefarious purpose. At least, not as far as anyone can tell...