almost inevitable consequence of having underlying rules that show causal invariance. For assuming that around the particle there is some kind of uniformity in the causal network—and thus in the apparent structure of space—taking slices through the causal network at an appropriate angle will always make any particle appear to be at rest. And the point is that causal invariance then implies that the same underlying rules can be used to update the network in all such cases.

But what happens if one has two particles that are moving with different velocities? What will the events associated with the second particle look like if one takes slices through the causal network so that the first particle appears to be at rest? The answer is that the more the second particle moves between successive slices, the more updating events must be involved. For in effect any node that was associated with the particle on either one slice or the next must be updated—and the more the particle moves, the less these will overlap. And in addition, there will inevitably appear to be an asymmetry in the pattern of events relative to whatever direction the particle is moving.

There are many subtleties here, and indeed to explain the details of what is going on will no doubt require quite a few new and rather abstract concepts. But the general picture that I believe will emerge is that when particles move faster they will appear to have more nodes associated with them.

Most likely the intrinsic properties of a particle—like its electric charge—will be associated with some sort of core that corresponds to a definite network structure involving a roughly fixed number of nodes. But I suspect that the apparent motion of the particle will be associated with a kind of coat that somehow interpolates from the core to the uniform background of surrounding space. With different slices through the causal network, the apparent size of this coat can change. But I suspect that the size of the coat in a particular case will somehow be related to the apparent energy and momentum of a particle in that case.

An important fact in traditional physics is that interactions between particles seem to conserve total energy and momentum. And conceivably the reason for this is that such interactions somehow tend to preserve the total number of network nodes. Indeed, perhaps in most

From Stephen Wolfram: A New Kind of Science [citation]