Kevin H. Knuth, Newshaw Bahreyni
Everything that is detected or measured is the direct result of something influencing something else. This is the essence of the concept of force, which has become central to physics. By considering both the act of influencing and the response to such influence as a pair of events, we can describe a universe of interactions as a partially-ordered set of events. In this paper, we take the partially-ordered set of events as a fundamental picture of influence and aim to determine what interesting physics can be recovered. This is accomplished by identifying a means by which events in a partially-ordered set can be aptly and consistently quantified. Since, in general, a partially-ordered set lacks symmetries to constraint any quantification, we propose to distinguish a chain of events, which represents an observer, and quantify some subset of events with respect to the observer chain. We demonstrate that consistent quantification with respect to pairs of observer chains exhibiting a constant relationship with one another results in a metric analogous to the Minkowski metric and that transformation of the quantification with respect to one pair of chains to quantification with respect to another pair of chains results in the Bondi k-calculus, which represents a Lorentz transformation under a simple change of variables. We further demonstrate that chain projection induces geometric structure in the partially-ordered set, which itself is inherently both non-geometric and non-dimensional. Collectively, these results suggest that the concept of space-time geometry may emerge as a unique way for an embedded observer to aptly and consistently quantify a partially-ordered set of events. In addition to having potential implications for space-time physics, this also may serve as a foundation for understanding analogous space-time in condensed matter systems.
View original:
http://arxiv.org/abs/1209.0881
No comments:
Post a Comment