A Derivation of Special Relativity from Causal Sets

We present a novel derivation of special relativity based on the information physics of events comprising a causal set. We postulate that events are fundamental, and that some events have the potential to receive information about 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. Events can be projected onto each chain by identifying the earliest event on the chain that can be informed about the event. In this way, each event can be quantified by a pair of numbers, referred to 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. All results follow directly from the Event Postulate and the adopted quantification scheme.Comment: 19 pages, 7 figures. v2 includes corrections to derivation of Lorentz transformation, and a discussion of the origin of spin 1/

A Potential Foundation for Emergent Space-Time

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an observer can consistently quantify events and their relationships to one another. The result is a potential foundation for emergent space-time.Comment: The paper was originally titled "The Physics of Events: A Potential Foundation for Emergent Space-Time". We changed the title (and abstract) to be more direct when the paper was accepted for publication at the Journal of Mathematical Physics. 24 pages, 15 figure