13 research outputs found
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