Thursday, August 25, 2011

Bell's Theorem: We're Not In a Simulation

Bell's theorem is the one that predicts quantum entanglement. (If you're not already familiar, go here to learn about it.)

The point for this post is that Bell inequalities have repeatedly been shown to be violated, which means that there are no local hidden variables.

The implication is that quantum mechanics is at the "bottom" of reality; the implication for the simulation argument that I constantly decry as meaningless yet can't seem to keep myself from writing about (most recently here and here) is that we are not in a simulation. No local hidden variables means no concealed causally-upstream inputs.

This is what many simulation-worriers have told us to look for, and if QM is complete (as Bell's theorem suggests) they're not there, period. What we really need is a fully generalizable, formal argument as to whether hidden variables are in principle detectable from inside such a system. When I add cells to a game of Conway's life that's already running, is it just the equivalent (from the gliders' viewpoint) of particle pairs popping into existence? Too bad Turing didn't read more Descartes.

The reality-skeptic's counterargument of course (for example, from Robin Hanson) is that every time we do such experiments, the simulators get ontological do-overs to conceal their dastardliness, i.e. the rules of the simulation are changed briefly, and/or they make us forget, etc. etc. etc. Of course this is the same as saying that if we are in a simulation, we could never know (asking how we could know for sure if we are in a simulation is at least as interesting a twist on this question, which is usually asked in terms of how we could know we're not. That is, what could I do to trick someone else into thinking they're in a simulation when they're not?)

All of this again raises the question of why the simulators would care if we found out. When I'm playing Conway's life, if one of the gliders becomes sentient and figures out it's on my computer, it doesn't much matter to me. What are they going to do, spell out dirty words on the screen next time I check the playing field? Also, it often pays to be suspicious of any science that claims to have solved the universe, even if there is a rigorous argument supporting this. To argue by analogy: would Newton have been able to show, had he rigorously pursued it mathematically, that his own theories were NOT at the bottom?

In closing, just in case, please meet me at La Jolla Shores tomorrow to spell out dirty words.

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