The circular number π also appears in physics. British researchers are now coming up with surprisingly quantum physical formulas for this.
3.141592 – these are the first seven digits of the circular number π, the exact value of which has occupied scientists for millennia. While the Babylonians still calculated with 3+1/8 and Archimedes arrived at a value between 3+10/71 and 3+10/70, it was to take until the 18. century to reveal the true character of π: That it is an irrational, even transcendent number that can only be represented in decimal notation as an infinite, non-periodic sequence.
This sounds intriguing, especially when you consider what "infinite" and "non-periodic" actually exists. π must thus, if one codes its digits as letters, contain every ever written text of human knowledge, and all unwritten texts in addition, plus the completely nonsensical letter combinations. It sounds mysterious, almost magical – and therefore π exerts a rough fascination on the layman as well as the scientist.
In fact, π is actually nothing special at all. The mathematician Georg Cantor has shown in 1874 that there are far more transcendent than algebraic (non-transcendent) numbers. The rational numbers that surround us in everyday life are an almost tiny slice of reality that seems so normal to us only because we can grasp it with common sense.
This supposedly exotic character is a property that the circular number has in common with various findings of quantum theory, which also likes to be used to abolish reality and build an infinite variety of possible worlds. What is often forgotten: Mathematics or physics serve as theories for the description of the given world. What you successfully, i.e. verifiably, provide in terms of conclusions is science – the rest is metaphysics or philosophy.
From this point of view a paper is exciting, which appeared now in the Journal of Mathematical Physics. Two physicists from the University of Rochester show for the first time how π can be derived from the rules of quantum physics. In it, the researchers apply Schrodinger’s wave function to the excitation states of a hydrogen atom – and show that in this way a formula for π found by the English mathematician John Wallis in 1655 can be derived, the so-called Wallis product (see picture). Circles play no role whatsoever in the derivation of this concept. This discovery has no practical use. However, according to the researchers, it shows that there are always interesting connections to be discovered between established physics and pure mathematics.