Being several hundred miles away from my girlfriend for the summer is torture. And while I get to play with animals once in a while at work, the heat is killing me. So I am trying to live inside my brain to endure all of the natural disasters which I seem to be magnetized to. One of the problems I’ve been contemplating is the pixelation of spacetime.
A long time ago, a greek philosopher named Zeno of Elea proposed that the distance between any two points is infinitely divisible. This would mean that to get anywhere we would have to take an infinite amount of steps. He concluded that space, motion, and existence are illusions. But wait, there’s hope! Modern science believes that spacetime is not infinitely divisible.
The revelation did not come in response to Zeno, but with a little playing around with physics. Towards the end of the 19th century, Max Planck invented Planck units in a straightforward manner. He took all of the known constants in physics: G, h, c, Kb, and Ke, to determine the precise size of a single unit of spacetime. A Planck unit is 1.6 x 10-35 meters, and 5.4 x 10-44 seconds. But this solution also causes tremendous problems.
When I first heard about spacetime pixelation, I was struck by the fact that at that level, geometry must be essentially like an atari video game. As an observer magnifies inwards, clean lines break into jagged staircases. The Euclidian sense of circles and triangles was laughable, and even fractal patterns would break down.
Secondly, it confuses me whether matter conducts or wades through spacetime. I feel it is a scientific assumption that spacetime is the medium in which matter exists. Matter is of course, just a form of energy; but we really have no idea why matter behaves in such super complex ways.
Assuming that energy and particles conduct within the medium of spacetime, it follows that particles simply exist within a Planck unit, and no motion within that unit is possible, or else it would be further divisible. Instead, motion is a conductive transfer from one pixel to another.
Futhermore, the arrangement of spacetime in relation to itself troubles me. Does it form a cubic lattice, as we artificially impose on it? Or does it form a chaotic mass, as gumballs in a jar slide into various patterns? What lies between spacetime?
According to relativity, spacetime is quite flexible, and can warp under gravitational stress, so how would one measure the change in that subjective unit, when it is the basis of our reality? I suppose that the irrationality of the smallest building blocks is necessary in order to compose the rational world. Just as mathematics is built of irrational assumptions.