How Numbers Work by New Scientist

Author:New Scientist
Language: eng
Format: epub
Publisher: Quercus
Published: 2017-12-27T05:00:00+00:00

Quantum connection

Early in the twentieth century mathematicians made a further daring conjecture: that the Riemann zeros could correspond to the energy levels of a quantum mechanical system. Quantum mechanics deals with the behaviour of tiny particles such as electrons. Crucially, its equations work with complex numbers, but the energy of a physical system is always measured by a real number. So energy levels form an infinite set of numbers lying along the real axis of the complex plane – a straight line rather like Riemann’s zeros.

This line is horizontal rather than vertical, but it is a simple bit of maths to rotate the Riemann zero line and put it on top of the real line. If the zeros then match up with the energy levels of a quantum system, the Riemann hypothesis is proved. Various attempts have been made to do just that in a variety of quantum systems – but as yet without success.

If the Riemann hypothesis can be proved, then, using the mathematics of the zeta function, we should be able to predict the results of many quantum experiments, such as scattering of very high energy levels in atoms, molecules and nuclei. It turns out, too, that the same mathematics applies to any situation where waves, including light waves and sound, bounce around chaotically. So the performance of microwave cavities and fibre-optic cables could be improved, and the acoustics of real concert halls might even profit from the music of the primes.

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