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Saturday, July 28, 2018

History's most successful mathematical prediction | Mathematics - Cosmos

This article appeared in Cosmos 79 - Winter 2018 under the headline "History's most successful mathematical prediction" 

The power of physical theory drives us to know the world in ever-finer detail. Paul Davies, Regents' Professor and Director of the Beyond Centre for Fundamental Concepts in Science at Arizona State University explains.

American theoretical physicist Julian Schwinger.
Photo: Historical / Getty Images

When Sir James Jeans proclaimed “God is a pure mathematician!” he was referring to the fact that most basic processes of nature obey elegant mathematical relationships. Science is so successful because theorists can use mathematics to make predictions experimenters can test.

Mathematics has been used to predict the existence of the planet Neptune, radio waves, antimatter, neutrinos, black holes, gravitational waves and the Higgs boson, to give but a few examples.

Sometimes the predictions are breathtakingly precise. Probably the most successful example of the power of physical theory concerns the curious case of the spinning electron.

Long ago Michael Faraday found that moving electric charges generate magnetic fields; an electric current flowing around a coil of wire is the basis of the electric motor. Even a static electron has a magnetic field, on account of the fact that all electrons spin. Every electron has an identical quantity of spin, as it does of charge. This intrinsic rotation serves to turn the particle into a tiny magnet.

Naturally physicists want to know how strong a magnet it is. If the electron is treated as a miniscule rotating ball, the calculation is easy. But the answer is only half of what experimenters measure.

The discrepancy is explained by the intrinsic spin not behaving like an ordinary rotation. To illustrate the difference, imagine a cosmic magician turning the Earth upside down. A further 180-degree turn would restore normality. One 360- degree turn returns it to its initial state.
So far, so obvious. Trouble is, if you rotate an electron through 360 degrees it does not come back to its initial state. Instead you have to rotate it through 720 degrees. 

Experimental physicists can readily perform such a double rotation to check. Going round in circles thus takes on a whole new meaning for electrons. Because of its weird double-take on the surrounding world, the strength of an electron’s magnetism is likewise doubled...

Aristotle said that nature abhors a vacuum. He was right. Nature not only fills the vacuum of space with clouds of virtual particles; it embellishes the properties of electrons with minute adjustments that might forever have gone unnoticed were it not for physicists’ faith in the power of mathematics to describe the world in ever-finer detail. 

Source: Cosmos