# Surreal numbers, pseudo real numbers, quantum entanglement .pdf

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Surreal numbers, pseudo-real numbers, Quantum entanglement

Bibliography
- Donald Ervin KNUTH, Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics
and Found Total Happiness: A Mathematical Novelette, Addison-Wesley, Professional, 1974
- John Horton CONWAY, On Numbers and Games, 2nd edition, AK Peters, Natick, 2001
- Lisa ROUGETET's thesis, Des récréations arithmétiques au corps des nombres surréels et à la
victoire d'un programme aux échecs: une histoire de la théorie des jeux combinatoires au XXème
siècle, 2014

Webography
- Wikipedia, Quantum entanglement
- Wikipedia, Quantum tic-tac-toe

How to symbolically represent separated states and entangled states by using surreal
numbers and pseudo-real numbers ?
We indicate a separated state with a surreal number: -1/1
The two particles are created at the same time T (on the same day, in surreal numbers theory).
To symbolize time and space, we use series converging towards 0 on the right and the left. For
similar series, on the left and on the right, rate of convergence is identical. Particle detectors are
placed at an equal distance. In the case the detectors lie at different distances, we use different
convergence speeds, therefore series which are not similar.

We indicate an entangled state with a pseudo-real number: 1/-1
The two particles are created when they are detected (contrary to a naive vision of things), but
inside the system, at the same time T, regardless of the detector's distance. A confusion zone
appears between 1 and -1, which we symbolically attribute to a quantum state superposition.

How do we reconcile those two points of view ?
We take into account how the second solution is verified by experience. The infrastructure is
akin to a pseudo-real number in a combinatorial game. What we observe is akin to the first
solution before we interpret the results.
Therefore, the Universe is similar to a combinatorial game with perfect information. It is much
more than a dice game.

Today, we tend to believe that combinatorial game establishes a pedagagogic model of
quantum mechanics. In fact, the exact reverse is true. We must acknowledge this paradigm
reversal.

chantal.capron@neuf.fr

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