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Quantum theory is slippery, but there are ways to bring its inner secrets into the light

If quantum theory works as it should, Schroedinger's cat can never be seen in its weird mixed state, half-dead and half-alive. That's reassuring, since we know from experience that cats are not unworldly quantum beings. But then what does the indeterminate state of Schroedinger's cat actually mean?

Niels Bohr's cardinal principle in dealing with quantum theory was to concentrate wholly on what you could see. He saw no point in getting agitated about the seemingly impossible or contradictory nature of intermediate states that are, by definition, unobservable. Sounds eminently sensible, except that you can't do without those strange intermediate states. Unobservable they may be, but they must exist in some sense?

In 1996, researchers at the National Institute of Standards and Technology in Boulder, Colorado, succeeded in creating what they described as a "Schroedinger cat" atomic state - a single atom that was, for a time, in two places at once. This was an atom that was "half-here, half-there", you might say. But if such a state, according to the rules, can't be observed, how did the researchers prove they had made it?

Chris Monroe and his colleagues took a single atom of beryllium, knocked out one electron to create an ion, and trapped it with laser beams. Beryllium usually has four electrons, two of which orbit the nucleus in the outermost "shell". Remove one of these and you are left with a lone electron in the shell farthest from the nucleus. Electrons and atomic nuclei both have a property called spin, as was discovered in the 1920s. The electron's state is called "up" or "down," depending on whether its spin is aligned with or opposite to the nucleus's spin. Because either possibility is equally likely, the outermost electron is in a "half-up, half-down" quantum state.

Those two atomic states, however, have slightly different energies. By using separate lasers precisely tuned to those energies, the researchers nudged the two states in opposite directions. The up part goes one way, the down part the other. This ingenious arrangement translates the "half-up, half-down" state of the atom into a "half-here, half-there" state, in which the two halves of the atom's quantum state become physically separate, ending up as far as 80 nanometres apart. Not a huge distance, perhaps, but considerably bigger than the atom itself.

Since Monroe's team couldn't have seen the atom in two places at once how did they know they'd pulled off such a feat? They nudged the two states apart and then back together in such a way that the two halves of the atom's quantum state ended up combined slightly differently than if the atom had remained undisturbed. It was this tiny difference, a measure of the separate journeys the "up" and "down" halves had taken, that could be observed.

To be absolutely pedantic about it, you can't say that the team actually detected the Schroedinger cat-state of the beryllium atom. It's more a matter of inferring its presence from observations that turned out as quantum theory predicted. You may think this is a bit of cheat. But remember you are trying to demonstrate the existence of something that by definition can't ever truly be seen.

Other striking demonstrations of fundamental quantum phenomena have stemmed from recent technical wizardry - the ability to manipulate individual atoms or groups of atoms and keep them trapped with lasers or magnets. In 1995, another group of physicist created what's known as a Bose-Einstein condensate. They cooled a collection of a few thousand rubidium atoms to within a whisker of absolute zero, just 200 billionths of a degree above it in fact, and all the atoms fell into lock step - a single quantum state encompassed them all.

The essence of this achievement is simple. Normally, when atoms are jiggling around, bumping into each other, exchanging energy back and forth, they occupy different and ever-changing quantum states. But there is one state out of all the possible quantum states which has absolutely the least amount of energy, and if you could somehow extract enough energy from a group of atoms, they would all fall into this "ground state". Einstein and the Indian physicist S. N. Bose foresaw this possibility as far back as the 1920s.

There's one little corollary - only bosons particles with whole- number quantities of spin - can fall into a Bose-Einstein condensate. Particles with half-number spins (12, 32, 52,...) are called fermions, and obey something called the Pauli exclusion principle, which says that no two fermions can simultaneously occupy the same quantum state. A collection of fermions must always fill up different quantum states, beginning with lowest-energy state and working upwards.

That, incidentally, is why white dwarfs exists. A white dwarf is the dying ember of a star like our own Sun that has finally spent its nuclear fuel. It is tiny, not much bigger than the Earth, but extremely dense, because gravity has squeezed its atoms so close together that all their electrons move freely throughout the whole core of the star. Because electrons are fermions, Pauli's exclusion principle prevents gravity from compressing the star any further. The white dwarf shrinks only to the point where the electrons fill up the available quantum states as compactly as possible. Only if the star is so massive and its gravity so strong that electrons and protons merge into neutrons can the star shrink any further. Even a neutron star has its limits, because neutrons are also fermions, and the size of a neutron star, like that of a white dwarf, is determined by a contest between quantum theory and gravity.

Rubidium atoms are bosons, however, and the 1995 experiment did persuade a collection of these atoms to discard their individuality and behave as one. All these experiments - from the Bose-Einstein condensate, and the Schroedinger-cat beryllium ion, to entangled EPR particles and the double-slit experiment - illustrate in different ways how a single quantum state can reign supreme over an extended region of space. They are just examples of non-locality, the pre-eminently non-classical feature of quantum mechanics. Non-locality may never be as directly observable as a dyed-in-the-wool classical physicist would like, but its consequences are inescapable. Experiments in the past few years prove beyond a shadow of a doubt that quantum mechanics really is as strange as it is different.