13/04/2018

For Einstein, the principle of physics lies in mathematics.

Reproduction of Marcelo Viana's column in Folha de S. Paulo.

In 1905, Albert Einstein (1879-1955) published seven research papers that became landmarks in the history of science. One of them, entitled "On the Electrodynamics of Moving Bodies," founded the theory of (special) relativity, which revolutionized our understanding of space and time.

But this theory did not satisfy the great German physicist because it did not take into account the phenomenon of gravitation. In a work published in 1907, Einstein identified what needed to be done to obtain a more comprehensive theory, which he called general relativity. But it took him eight years to complete the task, which only happened at the end of 1915.

Why? What happened during all this time?

It's a myth that Einstein was a bad student in mathematics. In fact, his grades in algebra and geometry were even better than in physics.

But it's true that when he was young he didn't have much appreciation for mathematics. "My interest in the study of nature was undoubtedly greater. And, when I was a student, I wasn't yet convinced that a deep understanding of the basic principles of physics depended on sophisticated mathematical methods."

He only came to understand and appreciate this after years of scientific work. "Of course, experience remains the ultimate criterion for the usefulness of a mathematical construct. But the creative principle resides in mathematics," he said.

The scientific revolution initiated by Galileo Galilei (1564-1642) and Isaac Newton (1642-1726) had provided an extraordinarily accurate description of many phenomena in nature. But, at the end of the 19th century, a serious challenge arose, posed by the theory of electricity and magnetism.

The mathematical formulation of this theory, due to the Scottish physicist James Clerk Maxwell (1831 – 1879), states that the speed of light (in a vacuum) is always the same, approximately 300,000 km per second.

Now, according to traditional physics, when a passenger on a moving train points a flashlight forward, the light rays should have a higher speed relative to the ground than if the flashlight were pointed backward, because in the first case the speed of the train is added to the speed of light, while in the second it is subtracted.

The difference is small compared to the phenomenal speed of light, but it can be measured, especially if a faster vehicle is used instead of a train—for example, planet Earth.

This is what American physicists Albert Michelson (1852-1931) and Edward Morley (1838-1923) did in 1887, and their experiment proved Maxwell right: the speed of light is exactly the same in both directions!

This showed that Galilean-Newtonian physics was at odds with reality and needed to be modified. The new theory was proposed, almost simultaneously, by Einstein and the French mathematician Henri Poincaré (1854-1912), whose main work on this subject ("On the Dynamics of the Electron") was also published in 1905.

In fact, some crucial ideas had already been published by Poincaré years earlier, in works that Einstein had access to.

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