My curiosity was piqued by the title of this article:
“We don’t live in a simulation, or computing works differently outside the Matrix.”
https://boingboing.net/2017/10/03/elon-is-wrong.html
http://advances.sciencemag.org/content/3/9/e1701758
But why wouldn’t physics be different outside the simulation?
I suppose one reason is that for a grandfather simulation—where the simulation’s owners try to learn more about their pre-singularity dark ages by letting others (e.g. us) live through them—it would make sense for the rules inside and outside to be the same.
But generally a simulation must consume fewer resources than the universe it is running within, and corners must, therefore, be cut. A program running on a Minecraft Redstone Turing Machine (https://www.youtube.com/watch?v=1X21HQphy6I) will clearly have fewer resources available than assembler running on the bare metal of a processor. Even ignoring the appalling speed at which it will run, lookup tables and special instructions will make some calculations scale better than others in the simulation…
We already know that the ‘substrate’ our universe runs on, is wildly different from the ‘classical world’ we experience. Some physics like entanglement seems to require access to ‘superuser‘ functions which break our Universe’s laws, e.g. instantaneous communication of state changes between entangled particles. Quantum computation is another example of magic, able to solve ‘classically’ impossible equations in the blink of an eye.
Even if our universe is not a synthetic simulation created for amusement or research, theories like the Holographic Universe suggest reality is far less prosaic than we imagined up until now.
Quantum Computation:
Holographic Universe:
https://phys.org/news/2017-01-reveals-substantial-evidence-holographic-universe.html