Physical Speed Limits

The speed limit of matter is the speed of light, a speed that can be approached, but not met nor exceeded. What does this speed limit look like in our time-based sparse matrix? Since we've abandoned both the idea of position as well as velocity, it may seem an absurd statement to reason about, however remember that we've simply substituted the idea of objective location for events and the relationships between them.
Consider some particle moving at some speed [1]. A photon leaves the particle (one event X), and at a later point is absorbed by the same particle (another event Y).
  • If the particle's speed is less than the speed of light, it means that the photon could have gone off from X, had another interaction, Z, elsewhere and returned to Y.
  • If the particle's speed is the speed of light, it means that the photon couldn't have had any other interactions, since there's only enough time to go from X to Y.
  • If the particle's speed is greater than the speed of light, it means that the photon leaving X could never arrive at Y [2]. That cell in the matrix must be empty.
[1]"Speed" is an artificial fiction, from the point of view of the sparse event-matrix. It's the result of looking at sequences of interactions in the matrix for a given particle and, after mapping these interactions onto 3D space, estimating the average speed over segments between interactions.
[2]Photons can travel faster than the speed of light [2-1], so this proscription is statistical, not absolute.
[2-1]Cherenkov Radiation ⬈ is caused by particles moving through water faster than the speed of light. How is this possible? It's because the speed of light through water is slower than the speed of light through a vaccuum (as light bounces from one water molecule to the next). Our sparse-matrix representation treats all light as traveling through a vaccuum, the media through which it travels can be encoded in the contents of the matrix.
Three examples of a particle traveling from X to Y, with light making the same journey. In the first, there is enough time for light to have another interaction Z. In the second, it cannot. And in the third, it cannot even make it to the interaction Y.
The third case shows why the speed of light cannot be exceeded: the events left by a faster-than-light particle in our matrix must necessarily be undefined, meaning that our faster-than-light particle doesn't exist.
The second case shows (obliquely) why the speed of light cannot be met: particles traveling at the speed of light cannot participate in outside events, meaning that our matrix cannot hold any evidence of its existence (since the matrix only holds interactions).