In no direction is a 3d slice enough to determine what happens with, say, Maxwell’s equations. This is true in a space-like direction, as in your example, and it is true in a time-like direction, as in the case of an electron and a positron appearing out of the vacuum. Throwing in Newton’s laws isn’t enough to change this. You need to know what governs the creation of particles or what holds together the uniform sphere of charge.
Certainly you need to know those things, but I’m not clear on how that relates to the 3dness of the slice; suppose you add rules like particles can neither be created nor destroyed and spherical charged particles hold together by fiat, doesn’t that solve that problem?
In no direction is a 3d slice enough to determine what happens with, say, Maxwell’s equations. This is true in a space-like direction, as in your example, and it is true in a time-like direction, as in the case of an electron and a positron appearing out of the vacuum. Throwing in Newton’s laws isn’t enough to change this. You need to know what governs the creation of particles or what holds together the uniform sphere of charge.
Certainly you need to know those things, but I’m not clear on how that relates to the 3dness of the slice; suppose you add rules like particles can neither be created nor destroyed and spherical charged particles hold together by fiat, doesn’t that solve that problem?