Quantum wonders: The Hamlet effect


A WATCHED pot never boils.” Armed with common sense and classical physics, you might dispute that statement. Quantum physics would slap you down. Quantum watched pots do refuse to boil – sometimes. At other times, they boil faster. At yet other times, observation pitches them into an existential dilemma whether to boil or not.

This madness is a logical consequence of the Schrödinger equation, the formula concocted by Austrian physicist Erwin Schrödinger in 1926 to describe how quantum objects evolve probabilistically over time.

Imagine, for example, conducting an experiment with an initially undecayed radioactive atom in a box. According to the Schrödinger equation, at any point after you start the experiment the atom exists in a mixture, or “superposition”, of decayed and undecayed states.

Each state has a probability attached that is encapsulated in a mathematical description known as a wave function. Over time, as long as you don’t look, the wave function evolves as the probability of the decayed state slowly increases. As soon as you do look, the atom chooses – in a manner in line with the wave function probabilities – which state it will reveal itself in, and the wave function “collapses” to a single determined state.

This is the picture that gave birth to Schrödinger’s infamous cat. Suppose the radioactive decay of an atom triggers a vial of poison gas to break, and a cat is in the box with the atom and the vial. Is the cat both dead and alive as long as we don’t know whether the decay has occurred?

We don’t know. All we know is that tests with larger and larger objects -including, recently, a resonating metal strip big enough to be seen under a microscope – seem to show that they really can be induced to adopt two states at once (Nature, vol 464, p 697).

The weirdest thing about all this is the implication that just looking at stuff changes how it behaves. Take the decaying atom: observing it and finding it undecayed resets the system to a definitive state, and the Schrödinger-equation evolution towards “decayed” must start again from scratch.

The corollary is that if you keep measuring often enough, the system will never be able to decay. This possibility is dubbed the quantum Zeno effect, after the Greek philosopher Zeno of Elea, who devised a famous paradox that “proved” that if you divided time up into ever smaller instants you could make change or motion impossible.

And the quantum Zeno effect does happen. In 1990, researchers at the National Institute of Standards and Technology in Boulder, Colorado, showed they could hold a beryllium ion in an unstable energy configuration rather akin to balancing a pencil on its sharpened point, provided they kept re-measuring its energy (Physical Review A, vol 41, p 2295).

The converse “anti-Zeno” effect – making a quantum pot boil faster by just measuring it – also occurs. Where a quantum object has a complex arrangement of states to move into, a decay into a lower-energy state can be accelerated by measuring the system in the right way. In 2001, this too was observed in the lab (Physical Review Letters, vol 87, p 040402).

The third trick is the “quantum Hamlet effect”, proposed last year by Vladan Pankovic of the University of Novi Sad, Serbia. A particularly intricate sequence of measurements, he found, can affect a system in such a way as to make the Schrödinger equation for its subsequent evolution intractable. As Pankovic puts it: to be decayed or not-decayed, “that is the analytically unsolvable question”

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