Map-Based Dynamics in Flat Space

Law 1: Non-interacting objects follow paths of extremal aging (e.g. maximum traveler time τ) through spacetime, predicated by nature's command on small size-scales to explore all paths. Such commands on the macro-scale in flat spacetime predict that energy (γ m c2) and momentum (m w) will be constants of a non-interacting object's trajectory. Rates of change of these quantities are therefore useful for tracking interactions.
Law 2: Local eyes may see interactions as mediated by rates of momentum exchange per unit map-time i.e. by frame-variant forces F. The net sum of these forces relates to the proper-acceleration alpha experienced by the object via:
Here γt = Sqrt[1+(wt/c)2] where wt is the proper-velocity transverse to the force direction, and the unit-vector il along the force direction turns toward the velocity line & away from acceleration when velocities both perpendicular and parallel to the acceleration direction are large compared to lightspeed c. For electromagnetic forces, a dual set of fields tracks deviations from F = m α.
Law 3: Conservation of momentum across interactions means that for every transfer of momentum from one object to another, there is an equal and opposite transfer from the other back to the first. Likewise for energy transfers.
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