Quantum Theory Cannot Hurt You (7 page)

The first attempt to explain the conundrum was made in Copenhagen in the 1920s by quantum pioneer Niels Bohr. The Copenhagen Interpretation, in effect, divides the Universe into two domains, ruled by different laws. On the one hand, there is the domain of the very small, which is ruled by quantum theory, and on the other there is the domain of the very big, ruled by normal, or classical, laws. According to the Copenhagen Interpretation, it is when a quantum object like an atom interacts with a classical object that it is forced to stop being in a schizophrenic superposition and start behaving sensibly. The classical object could be a detecting device or even a human being.

But what exactly does a classical object do to stop a quantum object from being quantum? Even more importantly, what constitutes a classical object? After all, an eye is just a big collection of atoms, which individually obey quantum theory. This turns out to be the Achilles’ heel of the Copenhagen Interpretation and the reason it has always appeared to many to be a very unsatisfactory explanation of where the everyday world comes from.

The Copenhagen Interpretation divides the universe, arbitrarily, into two domains, only one of which is governed by quantum theory. This in itself is very defeatist. After all, if quantum theory is a fundamental description of reality, surely it should apply everywhere—to the atomic world and the everyday world. The idea that it is a universal theory is, in a nutshell, what physicists believe today.

It turns out we never observe a quantum system directly. We only observe its effect on its environment. This may be a measuring device or a human eye or, in general, the universe. For instance, the light from an object impinges on the retina of the eye and makes an impression there. What the observer
knows
is inseparable from what the observer
is
. Now, if quantum theory applies everywhere, we have a quantum object observing, or recording, another quantum object. The central question can therefore be restated: Why do weird schizophrenic
states fail to impress themselves on, or
entangle
themselves with, the environment, whereas everyday one-place-at-one-time states do? An example may help.

If a high-speed subatomic particle flies through the air, it knocks electrons from any atoms it passes close to. Imagine it was possible to see a 10-centimetre-long portion of its track. And, say in that 10 centimetres the particle has a 50 per cent chance of interacting with one electron, kicking it out of its parent atom.

The particle, therefore, either knocks out an electron or doesn’t knock out an electron. But because the event of knocking out an electron is a quantum event, there is another possibility—the superposition of the two events. The particle both knocks out an electron and doesn’t knock out an electron! The question is: Why, when this event entangles itself with the environment, does it not leave an indelible impression? As luck would have it, it is possible to actually
see
an electron ejection event with an ingenious device known as a cloud chamber.

Clouds form in the air when a drop in temperature causes water droplets to condense out of water vapour. But this process happens rapidly only if there are things like dust particles in the air that act as “seeds” around which water droplets can grow. Now the seed—and this is the key to the cloud chamber’s operation—need not be as big as a dust grain. In fact, it need be only a single atom that has lost an electron—an ion.

A cloud chamber is a box filled with water vapour with a window in its side to look through. Crucially, the water vapour is ultrapure, so there are no seeds about which the vapour can condense. The vapour is held in a state in which it is absolutely desperate to form droplets, but it is frustrated because there are no seeds. Enter a high-speed subatomic particle. Where it knocks an electron out of an atom, a water droplet will instantly grow around the ion. The droplet is small but big enough to see through the window of the cloud chamber if properly illuminated.

So what would you see if you looked through the window? The
answer is of course just one of the possibilities—either a single water droplet or no water droplet. You would never see a superposition of both—a ghostly droplet, hovering half in existence and half out of existence. The question is, what happens in the cloud chamber to prevent it from recording this superposition?

Take the event in which a water droplet forms. It was triggered by a single ionised atom. The same atom exists in the event in which no droplet formed. It just does not get ionised, so no water droplet forms around it. Say, this atom is painted red in both cases to make it stand out (forget the fact that you can’t paint an atom!).

Now, in the event a droplet forms, zoom in on an atom near the red atom. Water is denser than water vapour; the atoms are closer together. Consequently, the atom in question will be closer to the red atom than it is in the event in which no water droplet forms. For this reason, the probability wave representing the atom in the first event only partially overlaps with the probability wave of the same atom in the second event. Say, for example, that their waves only half overlap.

Now take a second atom in the first event. It too will be closer in the first case than in the second. Once again, their probability waves will only half overlap. If we now consider the probability wave representing the two atoms together, it will overlap only one-quarter with the second case, since
¹
/
₂
×
¹
/
₂
=
¹
/
₄
.

See where this is going? Say the water droplet contains a million atoms, which actually corresponds to a very small droplet. How much will the probability wave representing a million atoms in the first event overlap with the probability wave representing a million atoms in the second event? The answer is
¹
/
²
×
¹
/
²
×
¹
/
²
×… a million times. This is an extraordinarily small number. There will therefore be essentially zero overlap.

But if two waves don’t overlap at all, how can they interfere? The answer is, of course, they cannot. Interference, however, is at the root of all quantum phenomena. If interference between the two events is impossible, we see either one event or the other but never the effect of one event mingling with the other, the essence of quantumness.

Probability waves that do not overlap and so cannot interfere are said to have lost coherence, or to have
decohered
. Decoherence is the ultimate reason why the record of a quantum event in the environment, which always consists of a lot of atoms, is never quantum. In the case of the cloud chamber, the “environment” is the million atoms around the ionised/nonionised atom. In general, however, the environment consists of the countless quadrillions of atoms in the Universe. Decoherence is therefore hugely effective at destroying any overlap between the probability waves of events entangled with the environment. And since that’s the only way we can experience them—what the observer
knows
is inseparable from what the observer
is
—we never directly see quantum behaviour.

They came from far and wide to see it—the river that ran uphill. It
flowed past the fishing port, climbed through the close-packed houses,
before meandering up the sheep-strewn hillside to the craggy summit
overlooking the town. Startled seagulls bobbed on it. Excited children
ran beside it. And at picnic tables outside pubs all along the river’s lower
reaches, daytrippers sat transfixed by this wonder of nature as beer crept
steadily up the sides of their beer glasses and quietly emptied itself onto
the ground.

Surely, there is no liquid that can defy gravity like this and run uphill? Remarkably, there is. It’s yet another consequence of quantum theory.

Atoms and their kin can do many impossible things before breakfast. For instance, they can be in two or more places at once, penetrate impenetrable barriers, and know about each other instantly even when on different sides of the Universe. They are also totally unpredictable,
doing things for no reason at all—perhaps the most shocking and unsettling of all their characteristics.

All of these phenomena ultimately come down to the wave-particle character of electrons, photons, and their like. But the peculiar dual nature of microscopic objects is not the only thing that makes them profoundly different from everyday objects. There is something else: their
indistinguishability
. Every electron is identical to every other electron, every photon is identical to every other photon, and so on.
1

At first sight this may not seem a very remarkable property. But think of objects in the everyday world. Although two cars of the same model and colour appear the same, in reality they are not. A careful inspection would reveal that they differ slightly in the evenness of their paint, in the air pressure in their tires, and in a thousand other minor ways.

Contrast this with the world of the very small. Microscopic particles cannot be scratched or marked in any way. You cannot tattoo an electron! They are utterly indistinguishable.
2
The same is true of photons and all other denizens of the microscopic world. This indistinguishability is truly something new under the Sun. And it has remarkable consequences for both the microscopic world and the everyday world. In fact, it is fair to say that it is the reason the world we live in is possible.

Recall that all the bizarre behaviour in the microscopic world, such as an atom’s ability to be in many places at once, comes down to interference. In the double slit experiment, for example, it is the interference between the wave corresponding to a particle going through the left-hand slit and the wave corresponding to the particle going through the right-hand slit that produces the characteristic pattern of alternating dark and light stripes on the second screen.

Recall also that if you were to set up some means of determining which slit each particle goes through—enabling you to distinguish between the two alternative events—the interference stripes disappear because of decoherence. Interference, it turns out, happens only if the alternative events are
indistinguishable
—in this case, the particle going through one slit and the particle going through the other slit.

In the case of the double slit experiment, the alternative events are indistinguishable just as long as nobody looks. But identical particles, such as electrons, raise the possibility of entirely new kinds of indistinguishable events.

Think of a teenage boy who plans to go out clubbing with his girlfriend, who happens to have an identical twin sister. Unbeknown to him, his girlfriend decides to stay in and watch TV and sends her twin in her place. Because the two girls appear identical to the boy (although they are not of course identical at the microscopic level), the events of going clubbing with his girlfriend and going clubbing with his girlfriend’s sister are indistinguishable.

Events such as this one, which are indistinguishable simply because they involve apparently indistinguishable things, have no serious consequences in the wider world (apart from allowing identical twin girls to run rings around their boyfriends). However, in the microscopic world, they have truly profound consequences. Why? Because events that are indistinguishable—for any reason whatsoever—are able to interfere with each other.

Take two atomic nuclei that collide. Any such collision—and this particular point will have to be taken on trust—can be looked at from a point of view in which the nuclei fly in from opposite directions, hit, then fly back out in opposite directions. In general, the in and out directions are not the same. Think of a clock face. If the nuclei fly into the collision point from, say, 9:00 and 3:00, they might fly out toward 4:00 and 10:00. Or 1:00 and 7:00. Or any other pair of directions, as long as the directions are opposite each other.

An experimenter could tell which direction the two nuclei ricochet by placing detectors at opposite sides of the imaginary clock face and then moving them around the rim together. Say the detectors are placed at 4:00 and 10:00. In this case, there are two possible ways the nuclei can get to the detectors. They could strike each other with a glancing blow so that the one coming from 9:00 hits the detector at 4:00 and the one coming from 3:00 hits the one at 10:00. Or they could hit head on, so that the one coming from 9:00 bounces back almost the way it came and hits the detector at 10:00 and the one coming from 3:00 bounces back almost the way it came and hits the detector at 4:00.

The directions of 4:00 and 10:00 are in no way special. Wherever the two detectors are positioned, there will be two alternative ways the nuclei can get to them. Call them events A and B.

What happens if the two nuclei are different? Say the one that flies in from 9:00 is a nucleus of carbon and the one that flies in from 3:00 is a nucleus of helium. Well, in this case, it is always possible to distinguish between events A and B. After all, if a carbon nucleus is picked up by the detector at 10:00, it is obvious that event A occurred; if it is picked up by the detector at 3:00, it must have been event B instead.

What happens, however, if the two nuclei are the same? Say each is a nucleus of helium? Well, in this case, it is impossible to distinguish between events A and B. A helium nucleus that is picked up by
the detector in the direction of 10:00 could have got there by either route, and the same is true for a helium nucleus picked up in the direction of 4:00. Events A and B are now indistinguishable. And if two events in the microscopic world are indistinguishable, the waves associated with them interfere.

In the collision of two nuclei, interference makes a huge difference. For instance, it is possible that the two waves associated with the two indistinguishable collision events destructively interfere, or cancel each other out, in the direction of 10:00 and 4:00. If so the detectors will pick up no nuclei at all, no matter how many times the experiment is repeated. It is also possible that the two waves constructively interfere, or reinforce each other, in the direction of 10:00 and 4:00. In this case, the detectors will pick up an unusually large number of nuclei.

In general, because of interference, there will be certain outward directions in which the waves corresponding to events A and B cancel each other and certain outward directions in which they reinforce each other. So if the experiment is repeated thousands of times and the ricocheting nuclei are picked up by detectors all around the rim of the imaginary clock face, the detectors will see a tremendous variation in the number of nuclei arriving. Some detectors will pick up many nuclei, while others will pick up none at all.

But this is dramatically different from the case when the nuclei are different. Then there is no interference, and the detectors will pick up nuclei ricocheting in all directions. There will be no places around the clock face where nuclei are not seen.

This striking difference between the outcomes of the experiment when the nuclei are the same and when they are different is not because of the difference in masses of the nuclei of carbon and helium, although this has a small effect. It is truly down to whether collision events A and B are distinguishable or not.

If this kind of thing happened in the real world, think what it would mean. A red bowling ball and a blue bowling ball that are repeatedly collided together would ricochet in all possible directions.
But everything would be changed merely by painting the red ball blue so the two balls were indistinguishable. Suddenly, there would be directions in which the balls ricocheted far more often than when they were different colours and directions in which they never, ever ricocheted.

This fact, that events involving identical particles in the microscopic world can interfere with each other, may seem little more than a quantum quirk. But it isn’t. It is the reason why there are 92 different kinds of naturally occurring atoms rather than just 1. In short, it is responsible for the variety of the world we live in. Understanding why, however, requires appreciating one more subtlety of the process in which identical particles collide.

Recall the case in which the nuclei are different—a carbon nucleus and a helium nucleus—and consider again the two possible collision events. In one, the nuclei strike each other with a glancing blow, and in the other they hit head on and bounce back almost the way they came. What this means is that, for the nucleus that comes in at 9:00, there is a wave corresponding to it going out at 4:00 and a wave corresponding to it going out at 10:00.

The key thing to understand here is that the probability of an event is not related to the height of the wave associated with that event but to the square of the height of the wave. The probability of the 4:00 event is therefore the square of the wave height in the direction of 4:00 and the probability of the 10:00 event is the square of the wave height in the direction of 10:00. It is here that the crucial subtlety comes in.

Say the wave corresponding to the nucleus that flies out at 10:00 is flipped by the collision, so that its troughs become its peaks and its peaks become its troughs. Would it make any difference to the probability of the event? To answer this, consider a water wave—a series of alternating peaks and troughs. Think of the average level of the water
as corresponding to a height equal to zero so that the height of the peaks is a positive number—say plus 1 metre—and the height of the troughs is a negative number—minus 1 metre. Now it makes no difference whether you square the height of a peak or the height of a trough since 1 × 1 = 1 and –1 × –1 also equals 1. Consequently, flipping the probability wave associated with a ricocheting nucleus makes no difference to the event’s probability.

But is there any reason to believe that one wave might get flipped? Well, the 10:00 collision and the 4:00 collision are very different events. In one, the trajectory of the nucleus hardly changes whereas in the other it is turned violently back on itself. It is at least plausible that the 10:00 wave might get flipped.

Just because something is plausible does not mean it actually happens. True. In this case, however, it does! Nature has two possibilities available to it: It can flip the wave of one collision event or it can leave it alone. It turns out that it avails itself of both.

But how would we ever know about a probability wave getting flipped? After all, the only thing an experimenter can measure is the number of nuclei picked up by a detector which depends on the probability of a particular collision event. But this is determined by the square of the wave height, which is the same whether the wave is flipped or not. It would seem that what actually happens to the probability wave in the collision is hidden from view.

If the colliding particles are different, this is certainly true. But, crucially, it is not if they are identical. The reason is that the waves corresponding to indistinguishable events interfere with each other. And in interference it matters tremendously whether or not a wave is flipped before it combines with another wave. It could mean the difference between peaks and troughs coinciding or not, between the waves cancelling or boosting each other.

What happens then in the collision of identical particles? Well, this is the peculiar thing. For some particles—for instance, photons—everything is the same as it is for identical helium nuclei. The waves that correspond to the two alternative collision events interfere with
each other normally. However, for other particles—for instance, electrons—things are radically different. The waves corresponding to the two alternative collision events interfere, but only after one has been flipped.

Nature’s basic building blocks turn out to be divided into two tribes. On the one hand, there are particles whose waves interfere with each other in the normal way. These are known as bosons. They include photons and gravitons, the hypothetical carriers of the gravitational force. And, on the other hand, there are particles whose waves interfere with one wave flipped. These are known as fermions. They include electrons, neutrinos, and muons.

Whether particles are fermions or bosons—that is, whether or not they indulge in waveflipping—turns out to depend on their spin. Recall that particles with more spin than others behave as if they are spinning faster about their axis (although in the bizarre quantum world particles that possess spin are not actually spinning!). Well, it turns out that there is a basic indivisible chunk of spin, just like there is a basic indivisible chunk of everything in the microscopic world. For historic reasons, this “quantum” of spin is
¹
/
₂
unit (don’t worry what the units are). Bosons have integer spin—0 units, 1 unit, 2 units, and so on—and fermions have “half-integer” spin—
¹
/
₂
unit,
³
/
₂
units,
⁵
/
₂
units, and so on.