We present a derivation of special relativity based on the quantification of causally-ordered events. We postulate that events are fundamental, and that some events have the potential to influence other events, but not vice versa. This leads to the concept of a partially-ordered set of events, which is called a causal set. Quantification proceeds by selecting two chains of coordinated events, each of which represents an observer, and assigning a valuation to each chain. An event can be projected onto each chain by identifying the earliest event on the chain that can be informed about the event. In this way, events can be quantified by a pair of numbers, referred to as a pair, that derives from the valuations on the chains. Pairs can be decomposed into a sum of symmetric and antisymmetric pairs, which correspond to time-like and space-like coordinates. From this pair, we derive a scalar measure and show that this is the Minkowski metric. The Lorentz transformations follow, as well as the fact that speed is a relevant quantity relating two inertial frames, and that there exists a maximal speed, which is invariant in all inertial frames. Furthermore, the form of the Lorentz transformation in this picture offers a glimpse into the origin of spin. All results follow directly from the event postulate and the adopted quantification scheme.
One of successful applications of the order-theoretic approach to fundamental physics is the recent derivation REF of Lorentz transformations and Minkowski metric of special relativity directly from the consideration of the partial order of events in space-time.
A Derivation of Special Relativity from Causal Sets
arXiv: Mathematical Physics
Mathematics Physics