En 1623, Galileo in The Assayer writing : ” We cannot understand [le livre de l’Univers] if one does not first of all endeavor to understand its language and to know the characters with which it is written. It is written in the language of mathematics (…) ”. In doing so, he founds modern physics as split from philosophy, and entirely coming under 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 have passed between the birth of mathematics and its 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 two-way. We might 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 the latter 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 astonishing examples of this intimate relationship is undoubtedly provided by the complex numbers. In the XVIe century, mathematicians have felt the need to add to ordinary numbers an additional number, called i (for “imaginary”), whose main property is to have a negative square: i² = -1. The numbers increased by this imaginary number are called the complexes, and are all in the form a + b·i, like 2 + 3i.
Nothing more abstract then than this fictitious number, since the ordinary numbers all have a positive square (2² = (-2) ² = 4)! And yet, complex numbers have naturally found their use in physics. In the XIXe century they were initially used only as a tool because they simplified the calculations of wave problems. A convenient tool of course, but one that might be dispensed with.
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 – which thirty years of uninterrupted experimental research had gradually brought to light in a disparate manner and to this –, a real surprise awaited the physicists community.
You have 33.86% of this article left to read. The rest is for subscribers only.
