A thought experiment about quantum entanglement

A THOUGHT EXPERIMENT ABOUT QUANTUM ENTANGLEMENT
By Eric CAPRON

Documentation :
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Various surveyor ant experiments

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Abbot, Edwin. Flatland, a Romance of Many Dimensions. 1884.

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Cube 2: Hypercube. Directed by Andrzej Sekuła, Lions Gate Films & Ghost Logic, 2002.

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“Aspect’s

experiment.”

Wikipedia,

Wikimedia

Foundation,

21

April

2023,

1

March

2023,

https://en.wikipedia.org/wiki/Aspect%27s_experiment.
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“Wave

function

collapse.”

Wikipedia,

Wikimedia

Foundation,

https://en.wikipedia.org/wiki/Wave_function_collapse.

Let’s start our thought experiment with a little ant, which we task with walking and surveying
the surface of a sphere. In this case, the surveyor ant moves in a straight line on a sphere until
it goes back to its starting point. Its move determines a line on a sphere, i.e. a circle.

We now replace our ant with a line segment in motion (Flatland-style), the line segment going
back to its starting point. Let’s imagine two identical line segments that we’ll call A and B. The
only difference between them is that A is static and stays at the starting point, while B is mobile
and follows the line around the sphere until it rejoins A.
If A is an observer seeing one end of B moving away, when B has followed the line to the
starting point, A will see the other end of B incoming. Is it possible for A to determine that both
ends belong to the same line segment?

Let’s now place an observer at the center of a 4-dimensional hypercube (as happens in the
movie Cube 2). The observer will see an object disappearing in a face of the cube and
reappearing through the opposite face. Once more, could he determine he is observing the same
object?

In the Aspect’s experiment, the detectors can be considered two opposite faces of a 4dimensional hypercube. What they detect are two ends of a same object.

Let’s suppose that an object in quantum superposition is moving inside a 4-dimensional
hypercube. One end is registered by a detector, the other end by the other detector: this creates
the illusion of two different objects coexisting. When this object decoheres, it ends up in a 3dimensional hypercube. The wave function collapse results in a reduction of one dimension for
the hypercube.

To wrap it up, this hypothesis is a simpler one: it saves us from falling back on local and nonlocal hidden variables, as well as on so-called time travelling particles.

chantal.capron@neuf.fr