untermensche
Your belief is that direction in spacetime is quantized? In other words, you believe there are only a finite amount of directions leading from a point in spacetime?
You also believe that length is quantized? In other words, you believe there are only certain distances something can travel from a point in spacetime, that are quantized units?
I am just thinking about what a quantized spacetime would even be like and if it is even logical. So if there is something between each point in space, then wouldn't that make that and spacetime continuous? It would be like how the rationals and irrationals need each other to be continuous.
Or, if there is nothing in between any two points in space (or nothing between stuff/ether that is between the 2 points), then wouldn't that also make the universe necessarily continuous? In other words, we say that there is nothing or no numbers between 2 and 2; or less abstractly we would say that there is nothing between my pencil at a point in time and my pencil in that same point in time.
Either way, there would seem to have to be something real that is continuous. Call it space-time-ether that is a fundamental continuum.