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A Genevan creates a mathematical language

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Researcher Nicolas Gisin proposes to change the mathematical language spoken by classical physics to make room for indeterminism and offer an open future

Known for his work in quantum cryptography, the Genevan Nicolas Gisin proposes to change the mathematical language used by classical physics. This would allow randomness and indeterminism to enter, thus bringing it closer to quantum physics.

In classical physics, that is Newtonian physics, it is accepted that since the Big Bang, everything is already determined. The mathematical equations are used to explain the evolution of the world which results from these initial conditions in the most precise way possible.

To do this, physicists use the language of classical mathematics, using in particular real numbers, said the University of Geneva (UNIGE) in a press release today.

In a comment published by the journal Nature Physics, Nicolas Gisin, honorary professor in the Department of Applied Physics at UNIGE, proposes to change the mathematical language, so as to no longer have to resort to real numbers.

Another language

“There is another mathematical language, called intuitionism, which refuses the existence of infinity”, enthuses the Geneva physicist, quoted in the press release. “But it was completely crushed by classical mathematical language at the start of the 20th century”.

Instead of real numbers which at the instant T contain an infinite number of decimals, intuitionist mathematics represent these numbers as a random process which takes place over time, one decimal after the other, so that at each instant T, there is only a finite number of decimal places, and therefore a finite quantity of information.

“This resolves the contradiction of classical physics, which uses infinity to explain the finite,” adds the specialist. Another difference between the two mathematical languages: the veracity of the propositions.

Random share

“In classical mathematics, a proposition is always either true or false, according to the principle of the excluded third. But in intuitionist mathematics, a proposition is either true, false, or indeterminate. So there is an accepted element of randomness ”, continues Nicolas Gisin.

This randomness is much closer to our daily experience than the determinism advocated by classical physics. In addition, we also find randomness in quantum physics.

“Some people try to avoid it by all means by involving other variables based on real numbers. But in my opinion, we should not try to bring quantum physics closer to classical physics by trying to eliminate randomness. On the contrary, it is necessary to bring classical physics closer to quantum physics by finally integrating indeterminism into it,” maintains the Geneva physicist.

Too much determinism

“I now consider that we have accepted too many postulates in classical physics and that we have therefore integrated determinism which did not necessarily have to be,” explains Nicolas Gisin.

“On the contrary, if we choose to base classical physics on intuitionist mathematics, it will also become indeterminate, like quantum physics, and will approach our experience, opening up the possibilities of our future”, concludes the researcher. This would not change the research results to date, he said.

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