Probability, Heisenberg and the Eternal Return

Until the mid-1900s, classical physics reigned supreme. It seemed to explain all the possible phenomena that occurred around us.

Classical physics is deterministic by nature. Newton’s Laws, in absolute space and time, governs the movements of all bodies.

This led mathematician Pierre de Laplace to think of a “computer” or “Laplace demon”. If I know the position and speed of all the atoms in the universe and play on this computer, I can use Newton’s laws to calculate the future position of everything: all bodies in the universe, all collisions, explosions and interactions between particles.

Even more. Newton’s laws are reversible. There is no arrow of time, telling what is past or future. If I film a billiard ball hitting another, and play the film backwards, it’s another possible interaction between bodies.

In this way, Laplace’s computer could calculate the whole future, and the whole past, from the present time.

The traditional calculation of probabilities only reflects our ignorance. In a game of heads or tails, for example, if we knew exactly the interactions of each atom of the coin, of the air, and the forces applied, we could predict the outcome of heads or tails with certainty. We just can’t do it because we don’t know the variables.

Another idea is that of the Eternal Return, by the philosopher Friedrich Nietzsche. If there is a finite number of atoms, they can recombine in a finite way (although the number of combinations is stratospheric, but finite). In an infinite time (and the infinite is very, very large), one day the configuration of all the atoms in the universe will be exactly the same as today. Put this configuration in Laplace’s computer, the whole present will repeat itself in exactly the same way, for countless cycles, for eternity …

A little bit of pop culture: the series “Dark” explores the Eternal Return, with a completely insane story of people traveling to the future and to the past, having children who will be their own parents, meeting their old selves, in cycles that repeats endlessly…

To break the cycle of the Eternal Return, Heisenberg’s Uncertainty Principle.

In the mid-1900s, some cracks in classical physics led to quantum physics, which is the model that best describes the world since then: the blackbody radiation problem, the photoelectric effect, among others.

The Uncertainty Principle is one of the pillars of this new knowledge. It says that it is not possible to know at the same time the position and speed (momentum) of a particle, with more precision than a constant (Planck’s constant). If I know the position, I lose precision at the moment, and vice versa.

To measure a subatomic particle, it is necessary to throw a light, a photon on it. The energy of the photon changes the position and momentum of the particle, so that the observation changes the experiment.

The fact that the observer changes the experiment gives rise to several exoteric interpretations, explored in self-help courses and the like: consciousness alters reality, it is enough to wish that the universe shapes itself accordingly, and so on. Less … One thing is to change a subatomic particle, another thing to change the universe!

Although Werner Heisenberg is a real person, he is perhaps best known today, in pop culture, as the code name of Walter White, from Breaking Bad.

Therefore, nature is probabilistic. At the lowest possible decision level, we will not know exactly where the electron, or the photon, or any other elementary particle is. This can be in an infinity of places, from time to time even crossing barriers of energy impossible to be crossed (which is the principle of the electron tunneling microscope).

In this view there is no space for Laplace’s computer. Even with infinite computing capacity, there are an infinite amount of possibilities for each atom, making the universe not deterministic.

When assuming quantum physics as a pillar of modern science, the Eternal Return is a more distant concept.

And if one day or night a demon sneaks into your loneliest loneliness and says to you: “This life, just as you live now and as you have lived it, you will have to live it yet again and countless times: and there will be no nothing new in it, every pain and every pleasure and every thought and sigh and everything that is indivisibly small and great in your life will return you, and everything in the same order and sequence — and in the same way this spider and this moonlight among the trees, and likewise this moment and myself. The eternal hourglass of existence will always be turned again — and you with it, dust of dust!

Nietzsche in Gaia the science


I’m creating a study group about Quantum Computing, to share news, events and to discuss ideias. It’s in Portuguese.



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Arnaldo Gunzi

Arnaldo Gunzi


Project Manager on Analytics and Innovation. “Samurai of Analytics”. Passionate about Combinatorial Optimization, Philosophy and Quantum Computing.