In Pursuit of the Unknown (49 page)

It's not really a great surprise that matter behaves strangely on the level of electrons and atoms. We may initially rebel at the thought, out of unfamiliarity, but if an electron is really a tiny clump of waves rather than a tiny clump of
stuff
, we can learn to live with it. If that means that the state of the electron is itself a bit weird, spinning not just about an up axis or a down axis but a bit of both, we can live with that too. And if the limitations of our measuring devices imply that we can never catch the
electron doing that kind of thing – that any measurement we make necessarily settles for some pure state, up or down – then that's how it is. If the same applies to a radioactive atom, and the states are ‘decayed' or ‘not decayed', because its component particles have states as elusive as those of the electron, we can even accept that the atom itself, in its entirety, may be in a superposition of those states until we make a measurement. But a cat is a cat, and it seems to be a very big stretch of the imagination to imagine that the animal can be both alive and dead at the same time, only to miraculously collapse into one or the other when we open the box that contains it. If quantum reality requires a superposed alive/dead cat, why is it so shy that it won't let us observe such a state?

There are sound reasons in the formalism of quantum theory that (until very recently) require any measurement, any ‘observable', to be an eigenfunction. There are even sounder reasons why the state of a quantum system should be a wave, obeying Schrödinger's equation. How can you get from one to the other? The Copenhagen interpretation declares that somehow (don't ask how) the measurement process collapses the complex, superposed wave function down to a single component eigenfunction. Having been provided with this form of words, your task as a physicist is to get on with making measurements and calculating eigenfunctions and so on, and stop asking awkward questions. It works amazingly well, if you measure success by getting answers that agree with experiment. And everything would have been fine if Schrödinger's equation permitted the wave function to behave in this manner, but it doesn't. In
The Hidden Reality
Brian Greene puts it this way: ‘Even polite prodding reveals an uncomfortable feature . . . The instantaneous collapse of a wave . . . can't possible emerge from Schrödinger's math.' Instead, the Copenhagen interpretation was a pragmatic bolt-on to the theory, a way to handle measurements without understanding or facing up to what they really were.

This is all very well, but it's not what Schrödinger was trying to point out. He introduced a cat, rather than an electron or an atom, because it put what he considered to be the main issue in sharp relief. A cat belongs to the macroscopic world in which we live, in which matter does not behave the way quantum mechanics demands. We do not see superposed cats.
²
Schrödinger was asking why our familiar ‘classical' universe fails to resemble the underlying quantum reality. If everything from which the world is built can exist in superposed states, why does the universe look classical? Many physicists have performed wonderful experiments showing that electrons and atoms really do behave the way quantum and
Copenhagen say they should. But this misses the point: you have to do it with a cat. Theorists wondered whether the cat could observe its own state, or whether someone else could secretly open the box and write down what was inside. They concluded, following the same logic as Schrödinger, that if the cat observed its state then the box contained a superposition of a dead cat that had committed suicide by observing itself, and a live cat that had observed itself to be alive, until the legitimate observer (a physicist) opened the box. Then the whole shebang collapsed to one or the other. Similarly the friend became a superposition of two friends: one of whom had seen a dead cat while the other had seen a live one, until a physicist opened the box, causing the friend's state to collapse. You could proceed in this way until the state of the entire
universe
was a superposition of a universe with a dead cat and a universe with a live one, and then the state of the universe collapsed when a physicist opened the box.

It was all a bit embarrassing. Physicists could get on with their work without sorting it out, they could even deny there was anything to
be
sorted out, but something was missing. For example, what happens to us if an alien physicist on the planet Apellobetnees III opens a box? Do we suddenly discover we actually blew ourselves up in a nuclear war when the Cuban missile crisis of 1962 escalated, and have been living on borrowed time ever since?

The measurement process is not the neat, tidy mathematical operation that the Copenhagen interpretation assumes. When asked to describe how the apparatus comes to its decision, the Copenhagen interpretation replies ‘it just does'. The image of the wave function collapsing to a single eigenfunction describes the input and the output of the measurement process, but not how to get from one to the other. But when you make a real measurement you don't just wave a magic wand and cause the wave function to disobey Schrödinger's equation and collapse. Instead, you do something so enormously complicated, from a quantum viewpoint, that it is obviously hopeless to model it realistically. To measure an electron's spin, for example, you make it interact with a suitable piece of apparatus, which has a pointer that either moves to the ‘up' position or the ‘down' one. Or a numerical display, or a signal sent to a computer . . . This device yields
one
state, and one state only. You don't see the pointer in a superposition of up and down.

We are used to this, because that's how the classical world works. But underneath it's supposed to be a quantum world. Replace the cat with the
spin apparatus, and it should indeed exist in a superposed state. The apparatus, viewed as a quantum system, is extraordinarily complicated. It contains gazillions of particles – between 10
²⁵
and 10
³⁰
, at a rough estimate. The measurement emerges somehow from the interaction of that single electron with these gazillion particles. Admiration for the expertise of the company that manufactures the instrument must be boundless; to extract anything sensible from something so messy is almost beyond belief. It's like trying to work out someone's shoe size by making them pass through a city. But if you're clever (arrange for them to encounter a shoe shop) you can get a sensible result, and a clever instrument designer can produce meaningful measurements of electron spin. But there's no realistic prospect of modelling in detail how such a device works as a
bona fide
quantum system. There's too much detail, the biggest computer in the world would flounder. That makes it difficult to analyse a real measurement process using Schrödinger's equation.

Even so, we do have some understanding of how our classical world emerges from an underlying quantum one. Let's start with a simple version, a ray of light hitting a mirror. The classical answer, Snell's law, states that the reflected ray bounces off at the same angle as the one that hit. In his book
QED
on quantum electrodynamics, the physicist Richard Feynman explained that this is not what happens in the quantum world. The ray is really a stream of photons, and each photon can bounce all over the place. However, if you superpose all the possible things the photon could do, then you get Snell's law. The overwhelming proportion of photons bounce back at angles very close to the one at which they hit. Feynman even managed to show why without using any complicated mathematics, but behind this calculation is a general mathematical idea: the principle of stationary phase. If you superpose all quantum states for an optical system, you get the classical outcome in which light rays follow the shortest path, measured by time taken. You can even add bells and whistles to decorate the ray paths with classical wave-optical diffraction fringes.

This example shows, very explicitly, that the superposition of all possible worlds – in this optical framework – yields the classical world. The most important feature is not so much the detailed geometry of the light ray, but the fact that it yields only
one
world at the classical level. Down in the quantum details of individual photons, you can observe all the paraphernalia of superposition, eigenfunctions, and so on. But up at the human scale, all that cancels out – well, adds together – to produce a clean, classical world.

The other part of the explanation is called decoherence. We've seen
that quantum waves have a phase as well as an amplitude. It's a very funny phase, a complex number, but it's a phase nonetheless. The phase is absolutely crucial to any superposition. If you take two superposed states, change the phase of one, and add them back together, what you get is nothing like the original. If you do the same with a lot of components, the reassembled wave can be almost anything. Loss of phase information wrecks any Schrödinger's cat-like superposition. You don't just lose track of whether it's alive or dead: you can't tell it was a cat. When quantum waves cease to have nice phase relations, they decohere – they start to behave more like classical physics, and superpositions lose any meaning. What causes them to decohere is interactions with surrounding particles. This is presumably how apparatus can measure electron spin and get a specific, unique result.

Both of these approaches lead to the same conclusion: classical physics is what you observe if you take a human-scale view of a very complicated quantum system with gazillions of particles. Special experimental methods, special devices, might preserve some of the quantum effects, making them poke up into our comfortable classical existence, but generic quantum systems quickly cease to appear quantum as we move to larger scales of behaviour.

That's one way to resolve the fate of the poor cat. Only if the box is totally impervious to quantum decoherence can the experiment produce the superposed cat, and
no such box exists
. What would you make it from?

But there's another way, one that goes to the opposite extreme. Earlier I said that ‘You could proceed in this way until the state of the entire
universe
was a superposition.' In 1957 Hugh Everett Jr. pointed out that in a sense, you have to. The only way to provide an accurate quantum model of a system is to consider its wave function. Everyone was happy to do so when the system was an electron, or an atom, or (more controversially) a cat. Everett took the system to be the entire universe.

He argued that you had no choice if that's what you wanted to model. Nothing less than the universe can be truly isolated. Everything interacts with everything else. And he discovered that if you took that step, then the problem of the cat, and the paradoxical relation between quantum and classical reality, is easily resolved. The quantum wave function of the universe is not a pure eigenmode, but a superposition of all possible eigenmodes. Although we can't calculate such things (we can't for a cat, and a universe is a tad more complicated) we can reason about them. In
effect, we are representing the universe, quantum-mechanically, as a combination of
all the possible things that a universe can do
.

The upshot was that the wave function of the cat does not have to collapse to give a single classical observation. It can remain completely unchanged, with no violation of Schrödinger's equation. Instead, there are two coexisting universes. In one, the cat died; in the other, it didn't. When you open the box, there are correspondingly two yous and two boxes. One of them is part of the wave function of a universe with a dead cat; the other is part of a different wave function with a live cat. In place of a unique classical world that somehow emerges from the superposition of quantum possibilities, we have a vast range of classical worlds, each corresponding to one quantum possibility.

Everett's original version, which he called the relative state formulation, came to popular attention in the 1970s through Bryce DeWitt, who gave it a more catchy name: the many-worlds interpretation of quantum mechanics. It is often dramatised in historical terms: for example, that there is a universe in which Adolf Hitler won World War II, and another one in which he didn't. The one in which I am writing this book is the latter, but somewhere alongside it in the quantum realm another Ian Stewart is writing a book very similar to this one, but in German, reminding his readers that they are in the universe where Hitler won. Mathematically, Everett's interpretation can be viewed as a logical equivalent of conventional quantum mechanics, and it leads – in more limited interpretations – to efficient ways to solve physics problems. His formalism will therefore survive any experimental test that conventional quantum mechanics survives. So does that imply that these parallel universes, ‘alternate worlds' in transatlantic parlance,
really
exist? Is another me typing away happily on a computer keyboard in a world where Hitler won? Or is the set-up a convenient mathematical fiction?

There is an obvious problem: how can we be sure that in a world dominated by Hitler's dream, the Thousand Year Reich, computers like the one I'm using would exist? Clearly there must be many more universes than two, and events in them must follow sensible classical patterns. So maybe Stewart-2 doesn't exist but Hitler-2 does. A common description of the formation and evolution of parallel universes involves them ‘splitting off' whenever there is a choice of quantum state. Greene points out that this image is wrong: nothing splits. The universe's wave function has been, and always will be, split. Its component eigenfunctions are
there
: we imagine a split when we select one of them, but the whole point of
Everett's explanation is that nothing in the wave function actually changes.