If you think that we are a simulation built by a world that has “real” continuous, non-quantized mechanics, there is a simpler explanation. A particle in such a world would take an infinite amount of information to describe. By using quantum mechanics in their simulations, they could create an infinite number of simulations of their world. Supposing that things on the Planck scale of their “real” world (pun!) are unimportant, these simulations would be just as good as their world. They could also build infinitely larger simulated universes out of their real world, and move into them.
(The number of quantized simulations that you could build in a real world is the number of times that the integers fit into the reals.)
The speed of light is also a necessary limit for these simulations; otherwise, velocities could go towards infinity, requiring an unlimited amount of information for a particle.
1) The infinity seems unlikely to be a problem. Our own three-dimensional space can be subdivided into an infinite number of two-dimensional subspaces. That does not mean we would want to move into them, even if we could.
2) My own personal opinion is that all talks about things on the Planck scale, rarely amount to more than a wild speculation, even if we restrict ourselves to our own “unreal” three-dimensional world. I would not presume even to speculate how an additional dimension might affect this problem.
If you think that we are a simulation built by a world that has “real” continuous, non-quantized mechanics, there is a simpler explanation. A particle in such a world would take an infinite amount of information to describe. By using quantum mechanics in their simulations, they could create an infinite number of simulations of their world. Supposing that things on the Planck scale of their “real” world (pun!) are unimportant, these simulations would be just as good as their world. They could also build infinitely larger simulated universes out of their real world, and move into them.
(The number of quantized simulations that you could build in a real world is the number of times that the integers fit into the reals.)
The speed of light is also a necessary limit for these simulations; otherwise, velocities could go towards infinity, requiring an unlimited amount of information for a particle.
Thanks for your comment.
1) The infinity seems unlikely to be a problem. Our own three-dimensional space can be subdivided into an infinite number of two-dimensional subspaces. That does not mean we would want to move into them, even if we could.
2) My own personal opinion is that all talks about things on the Planck scale, rarely amount to more than a wild speculation, even if we restrict ourselves to our own “unreal” three-dimensional world. I would not presume even to speculate how an additional dimension might affect this problem.