March 6, 2020

Answered by: Jonathan Gorard

How can your models be Lorentz invariant?

Lorentz covariance, as well as the far stronger condition of general covariance, is one of the many consequences of the principle of causal invariance, i.e. the requirement that all branches of the multiway system should yield causal networks that eventually become isomorphic as directed acyclic graphs. Since each possible foliation of a causal graph into discrete spacelike hypersurfaces corresponds to a possible relativistic observer (and therefore, in the case of spatially flat hypersurfaces, to a possible inertial reference frame), and because each such foliation also defines a particular updating order for the underlying spatial hypergraph, the condition of causal invariance necessarily ensures that the orderings of timelike-separated updating events are always preserved across all inertial reference frames, even though the orderings of spacelike-separated updating events are not. This is precisely the statement of Lorentz covariance.