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William & Mary
[PAST EVENT] High Energy Physics/Mathematical Seminar
June 4, 2014
11am
Abstract:
Anything that is measured is the result of something influencing something else. An act of influencing and the response to that influence form a pair of events. A collection of such events along with a binary ordering relation form a partially ordered set (also called a causal set). We introduce an apt quantification scheme through distinguishing a chain of events, called observer, to quantify events in the partially-ordered set and show how space and time followed by Minkowskian form arise as a consequence of such consistent quantifications. The change of frame from one observer into another results in the Lorentz transformations. Moreover, basic geometrical concepts such as dimension, directions, subspace and even the Pythagorean theorem originated in this framework. Thus all aspects of Special Relativity as well as a discrete version of the most fundamental Euclidean geometry's definitions are derived in this picture from apt quantification of a partially-ordered set of events.
Anything that is measured is the result of something influencing something else. An act of influencing and the response to that influence form a pair of events. A collection of such events along with a binary ordering relation form a partially ordered set (also called a causal set). We introduce an apt quantification scheme through distinguishing a chain of events, called observer, to quantify events in the partially-ordered set and show how space and time followed by Minkowskian form arise as a consequence of such consistent quantifications. The change of frame from one observer into another results in the Lorentz transformations. Moreover, basic geometrical concepts such as dimension, directions, subspace and even the Pythagorean theorem originated in this framework. Thus all aspects of Special Relativity as well as a discrete version of the most fundamental Euclidean geometry's definitions are derived in this picture from apt quantification of a partially-ordered set of events.