This thought experiment has interesting properties : - actually you can’t move diagonaly without moving one time ahead and then one time aside, because there is no common edge between the first one and the latter. For example, the square "2" has no common edge with the square "0", so you are forced to travel through a "1" to reach "2" from "0". - in a non-grid space (let’s say "like ours"), the energy to travel on a pure diagonal is equal to the square root of 2, not just 2, but it’s not a problem because you can do it, you don’t need a common edge. In your model, since you don’t have common edges in diagonal, you can’t. - in relativity theories, time has its own dimension: in your thought experiment, this means that you cannot travel at the same time in space AND in time because that would make you travel in diagonal. But in relativity, in a way, time IS space: if you travel far away, you also travel "late" away. - also in relativity theories, objects are not spinning, but they are travelling in straight lines: the space itself is distorted, and that makes thinking that objects are spinning. 343
In your thought experiment, object could not actually spin in universe due to the rigid grid, so you will have to render forces another way. So, this implies, in your model, that gravity cannot make things accelerate or turn. So we can simply reject it.
So, with all these elements, I would say that you can’t travel faster than light, but you may just choose between travelling through space or through time at the speed of light, but not both at the same time, by steps of one. But actually this is enough, because 1 square of space = 1 square of time, so you have a perfect equivalence between them. That means that, at the speed of light, if you travel only in space, then time doesn’t flow FOR YOU ONLY. In an instant, you have reached the other part of the universe… But the people you left have aged equivalently to what you travelled. If you travel back, also in one instant, you will find your friends older… Except if they have travelled only through time, and not space, at the same speed, and one time forward, ONE TIME BACKWARD. Edit: you need to ignore the speed cone for that last thing to be possible (or you won’t be able to move backward in time…).
If you want to have deeper thoughts about it, you’ll have to make more hypotheses, like: - is it possible to travel backward in time like it is in space? (in our world, as far as I know, it is not) - is it possible to exchange time for space "freely"? (neither possible) - is it possible to travel in diagonal for "2", not for "square root of 2"? - what is your model for gravity? - do you have a special model for the other forces? 781