What physics owes to mathematics. Inspired by each other, these two disciplines are intimately linked. In their carte blanche to “Le Monde”, physicists Wiebke Drenckhan and Jean Farago recall how Erwin Schrödinger was surprised to see the imaginary number “i” appear in his fundamental equation.
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| What physics owes to mathematics |
In 1623, Galileo in Il Saggiatore wrote: “One cannot understand [the book of the Universe] if one does not first apply oneself to understanding its language and to knowing the characters with which it is written. It is written in the mathematical language (…)”. In doing so, he founds modern physics as split from philosophy, and entirely within mathematical rationality.
What followed showed how right his intuition, which was also and still remains an act of faith, was: until now, physicists have worked successfully to unveil the mathematical laws governing phenomena, each time presupposing their existence. The millennia that elapsed between the birth of mathematics and their use in physics show in passing that this rapprochement between natural phenomena and the mathematical laws of our human rationality was far from obvious.
The rest of the story was of course a two-way street. One could thus describe in great detail how a large number of theories and mathematical tools, from the Fourier transform to symplectic geometry, were inspired by physics. But in our time when it is often presented stripped of its theoretical apparatus in order to make it more accessible, it is even more useful to recall here to what extent physics has always been closely linked to mathematical science, and cannot do without her.
One of the most amazing examples of this intimate relationship is undoubtedly provided by complex numbers. In the 16th century, mathematicians felt the need to add an additional number to ordinary numbers, called i (for "imaginary"), whose main property is to have a negative square: i² = -1. Numbers augmented by this imaginary number are called complexes, and they all take the form a + b i, like 2 + 3i.
Nothing could be more abstract than this fictitious number, since ordinary numbers all have a positive square (2² = (-2) ² = 4)! And yet, complex numbers have naturally found their usefulness in physics. In the 19th century, they were first used only as a tool because they simplified the calculations of wave problems. A handy tool, certainly, but one that we could perfectly dispense with.What physics owes to mathematics
Abstraction confirmed by reality
On the other hand, when in 1929 Erwin Schrödinger succeeded in synthesizing in the equation which bears his name all the quantum rules
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