This assumes that reality is simulated using a grid, and particles are either in that cube or that one.
But that's not the only way to run a simulation - you can make the fundamental particles the building pieces and simulate them - they can move anywhere they want, in any direction, they don't live in a grid.
The only thing that matters is their relationship to the particles near them.
Which follows very nicely from relativity which shows that there is no absolute coordinate system, or absolute energy, only relative distances and relative energy differences.
i.e. like the difference between polar coordinates and rectilinear ones.
Also the simulation doesn't really even have to involve particles. Stephen Wolfram did some interesting writing on concept of our reality / laws of physics emerging from simple computational systems like cellular automaton [0]. Also Eliezer had some interesting points about how a continous interpretation of causal networks gives rise to some concepts we recognize from physics, like space, time and the speed of light binding them together [1].
But that's not the only way to run a simulation - you can make the fundamental particles the building pieces and simulate them - they can move anywhere they want, in any direction, they don't live in a grid.
The only thing that matters is their relationship to the particles near them.
Which follows very nicely from relativity which shows that there is no absolute coordinate system, or absolute energy, only relative distances and relative energy differences.
i.e. like the difference between polar coordinates and rectilinear ones.