Top Quark Spin Correlations with the CMS Detector

The differential top quark precision measurements of polarizations and spin correlations presented in this dissertation may potentially lead to breakthroughs in several key areas: observing quantum entanglement and Bell's Inequality violations in a hadronic system, discovering toponium, illuminating supersymmetry, interpreting field theories beyond the Standard Model, and advancing the understanding of electroweak vacuum stability. Additionally, this thesis provides a significantly improved understanding of CMS detector lepton trigger efficiencies, which has greatly enhanced the search for Lorentz invariance violation in top quark events, boosting the sensitivity by greater than a factor of 100. Finally, the thesis includes TCAD simulations that explore the feasibility of using the initial transient induced current, as described by the Ramo-Shockley Theorem, to achieve the picosecond timing precision in silicon pixel detectors needed for four-dimensional tracking.