Re:The Simulation Argument and the Simulation Barrier
by matt-attack on Monday November 25, 2019 @11:35AM
(#21629823)
I don't think there are an infinite number of positions. The Planck length [1] essentially defines the smallest unit of length. Similarly, Planck time [2] does the same for time.
Re:The Simulation Argument and the Simulation Barrier
by skizzik on Monday November 25, 2019 @06:26PM
(#21634023)
Your first reference states that the Planck length isn't the smallest unit of length in standard physics: "The Planck length is sometimes misconceived as the minimum length of space-time, but this is not accepted by conventional physics, as this would require violation or modification of Lorentz symmetry." It then states that alternative theories do allow for a minimum length.
Experimental evidence (the Fermi satellite data discussed in the link in the grandparent comment) seems to support standard physics.
For example, if I'm living in a simulation and I move my hand an inch to the left, it occupies an uncountably infinite number of intermediate positions during that motion. A Turing machine can't calculate or even represent all of those positions, since the set of Turing-computable numbers is only countably infinite.
Of course, what I've written above assumes that spacetime is continuous. Is it?
That can be tested by experiment:
https://physics.stackexchange.com/questions/9720/does-the-pl...
According to that link, spacetime shows no sign of discretization down to fourteen orders of magnitude below the Planck length. (The Planck length itself is so small that if an object that size were expanded so as to be a millimeter across, then a proton, at that scale, would be larger than the distance between the sun and Alpha Centauri.)
That suggests to me that while Turing machines can provide useful approximations to the behavior of physical systems, they can't represent or simulate them precisely.