...space and time are defined as sets of urelements...
Hi, Adib. You should be always prepared to assign a number of dimensions and/or space-time metric to these sets. Is it principally possible? If not, then the set of "elements" cannot serve as a model of space or time, because it cannot comprehend all physical attributes of these concepts, assigned so far by another theories. By another words, you should use the definitions of space and time, which are backward compatible with existing concepts/definitions, so they can be reconciled with them on the background of correspondence principle.
What the
urelements are supposed to be from physical point of view? Can we derive something testable from such assignation?
From Aether Wave Theory perspective the definition of space and time is very simple. The causal energy spreading can occur only along surfaces of Aether density gradients in transversal waves. After then the space dimensions are the directions, along which energy spreading occurs. And the time dimensions are the rest directions, which are perpendicular to space dimensions.
For example, the water surface can be considered as a local space-time for mechanical wave spreading. After then the space dimensions are the directions plan-parallel with water surface and the time dimension is the direction perpendicular (normal) to these directions, i.e. the direction of water surface gradient itself. It's easy to comprehend definition and it brings surprisingly high number of testable insight/predictions into Aether model. You can try to explain your definition of space/time on background of my definition, as I suppose, the physically relevant definitions should be always compatible.
