Nonlocality & Solipsism

Classical vs. Quantum States

“What Einstein really seems to have wanted (in modern terms) is a Local Hidden Variable Theory where hidden variables not only exist, but can be localized to specific points in space and are only influenced by things happening close to them” (Aaronson 99).

Einstein yearned for a theory of quantum mechanics that obeyed locality and local realism. Special Relativity implies that information travels at the speed of light or slower, so objects should behave solely according to the conditions of their proximate environment. For instance, the conditions in another galaxy shouldn’t have any instant effects on the behavior of atoms here. As a result, Einstein aspired to formulate a Local Hidden Variable Theory.

In 1963, John Bell proved that all hidden variable theories must have nonlocal characteristics, and so local hidden variable theories were unviable. His results can be demonstrated in the CHSH game.

CHSH Game

If I had more time, I’d show you the game setup myself. Please find it here!

Classically, the intuitive solution turns out to be the best strategy. Always sending the same bits to win when at least one bit of x or y is 0 will result in a win rate of 75%. A table of other possibilities illustrates that all other deterministic strategies are worse. Adding randomness (ex. if Alice sees a 1, flip a coin to determine what to send) only results in a strategy that is a superposition of the best and worse strategies, resulting in <75% success.

However, there’s a better solution exploiting quantum effects! Check it out!

Philosophical Implications

To push against the Copenhagen interpretation of quantum mechanics, Schrodinger designed his famous thought experiment involving poison and an unlucky cat. Lesser known, Wigner contemplated implications of quantum mechanics by querying how the thoughts of two friends interact.

Schrodinger’s and Wigner’s thoughts experiments indicate that the object of measurement (cat or Wigner) experiences only 1 state, whereas the experimenter sees a superposition of possibilities. This seems to indicate that a measurement doesn’t “force” the object to collapse into either state. If it were so, then we would have to relinquish our belief that Wigner is only having 1 thought, and that the only thing we can know is our own state as the experimenter. We’ve tumbled straight into the solipsistic rabbithole, in which we can’t say anything about the real world except ourselves.

Thus, preserving locality seems to entail increasingly solipsistic concessions. It may be simply a matter of taste to decide which is more reasonable: nonlocality or solipsism. Personally though, I’m allergic to solipsism. What do you think?