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THE pleasure and pain of quantum theory began when an 鈥渙r鈥� became an 鈥渁nd鈥�. Are the fundamental components of material reality 鈥� the things that make up light, matter, heat and so on 鈥� particles or waves? The answer came back from quantum theory loud and clear: both. At the same time.

Max Planck started the rot back in 1900, when he assumed, purely to make the maths work, that the electromagnetic radiation emitted by a perfectly absorbing 鈥渂lack body鈥� comes in the form of discrete packets of energy, or quanta. In 1905, Albert Einstein took that idea and ran with it. In his Nobel-prizewinning work on the photoelectric effect, he assumed that quanta were real, and all electromagnetic waves, light included, also act like discrete particle-like entities called photons. Work in the 1920s then reversed the logic. Discrete, point-like particles such as electrons also come with a wavelength, and sometimes act like waves.

Physicist Richard Feynman called this 鈥渨ave-particle duality鈥� the 鈥渙nly mystery鈥� of quantum physics 鈥� the one from which all the others flow. You can鈥檛 explain it in the sense of saying how it works, he wrote; you can only say how it appears to work.

How it appears to work is often illustrated by the classic double-slit experiment. You fire a stream of single photons (or electrons, or any object obeying quantum rules) at two narrow slits close together. Place a measuring device at either of the two slits and you will see blips of individual photons with distinct positions passing through. But place a screen behind the slits and, over time, you will see a pattern of light and dark stripes build up, as if each photon were a wave that passed through both slits, diffracted and interfered with itself like ripples encountering an obstacle on a pond.

Mathematically, these sorts of imponderables are described using entities known as wave functions. These depict quantum objects as existing simultaneously in superpositions of all possible states, not just of position, but momentum, energy or any other property you might measure. Each possible state comes with a probability attached reflecting how often you would see it if you made the same measurement many times over 鈥� but you will never know for certain what you will get from any one measurement. Complicating things still further is the uncertainty principle, which says that there are pairs of quantum properties, such as position and momentum, that you can never measure together to an arbitrarily high accuracy.

Layers of weirdness

Then comes the phenomenon of entanglement. Einstein introduced this in a paper he co-authored in 1935 in the spirit of pointing out it couldn鈥檛 be true. It says that if you prepare two quantum particles in the same state and separate them, measurements on the one influence the outcome of measurements on the other. This 鈥渟pooky action at a distance鈥�, in Einstein鈥檚 phrase, has been demonstrated in countless experiments, and is now the basis of emerging technologies such as quantum computing.

Further iterations of the double-slit experiment build new layers of weirdness on top of all this. For instance, you can show that the apparent guise a quantum object takes depends on how you choose to measure it 鈥� even if you only make that choice after it has passed through the slits.

For all these reasons, the only mystery has come to be expressed as the 鈥渕easurement problem鈥�, the centre of a huge, unresolved debate about the nature of quantum reality and our role in it. Erwin Schr枚dinger formulated it best with his notorious thought experiment about a cat in a box that is apparently dead and alive until you decide which one it is.

鈥淭here is a huge, unresolved debate about our role in making reality鈥�

The measurement problem has sucked physicists down many curious wormholes of metaphysical interpretation (see 鈥淵our quick-fire guide to what quantum theory means鈥�, below). But as we will see, no one has yet come up with a particularly convincing explanation of it, or at least one all can agree on. Most probably, the answer to quantum theory鈥檚 only mystery is something no one has thought of yet 鈥� not an 鈥渙r鈥� or an 鈥渁nd鈥�, but a 鈥渘or鈥�.

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