| This research is about seeking laws of physics and geometry from order. Anything that is measured is the result of something influencing something else. An act of influencing and the response to such influence form a pair of events. A collection of such events along with their binary ordering relation of influence which forms a partially ordered set or a poset for short, also called a causal set. We introduce an apt quantification scheme by distinguishing a chain of events which we use to model an observer to quantify events in the partially ordered set and show how space and time followed by the Minkowskian form arise from such consistent quantifications. The change of frame from one observer into another results in the Lorentz transformations. Moreover we show how the basic concepts in Euclidean geometry such as direction, dimension, subspaces and even geometric shapes originate in this framework. Thus a discrete version of the most fundamental of Euclidean geometry's definitions and postulates can be derived from apt consistent quantification of a partially-ordered set of events. This suggests that geometry itself is not fundamental, rather it is derived from the quantification of the partially-ordered set of events. |
