Tuesday, May 16, 2017

[nbdfbdlo] Not simulation

I don't think we live in a simulation, because accurate simulation of our universe is extremely difficult.  The story goes, the full quantum treatment with the Schroedinger equation of a single isolated hydrogen atom (1 electron) is relatively easy, but trying to model a helium atom, with 2 electrons, is already so difficult that numerical simulations on our most powerful computers struggle with it.  (This story might be out of date).  The universe, as even one person experiences it, is much more complicated than a single helium atom, and a full quantum treatment is necessary, because a person experiences many quantum effects, e.g., chemical reactions, not falling through the floor.

I suspect that those who speculate that we live in a simulation have never tried computational chemistry or other scientific computer simulations of the real world.  Perhaps they see video games or movies, but likely do not know of the huge amounts of simplifying assumptions made in those products when something only needs to look good enough for entertainment, not be scientifically accurate.

In order to argue we are not in a simulation, we must postulate limits on the computational capabilities of those who might be simulating us.  I suspect simulating our universe is at least NP-complete, probably at least PSPACE-complete.  Research into complexity theory, in our universe, can settle these questions.  We postulate that even in the simulators' universe, it is impossible to build computers to solve those problems in a reasonable amount of time.  Equivalently, but sounding more radical, any universe in which you can build such computers will not be able to sustain life.  (Then again, life, uh, finds a way, even in seemingly difficult environments.)

Simulating our universe is so difficult that it might be easier just to build it for real (in which case, we are again not a simulation).  This echoes one of the biggest potential uses for quantum computers being to do quantum simulations, or, not simulating a microchip in software, but emulating it with an FPGA.

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