Causality and dispersion relations

Our basic observations from daily experiences as well as sophisticated experiments suggest causality in various branches of physics (and beyond). Causality is mathematically reflected in the analyticity of the system's response function, which relates the dispersion of the system to the dissipation. We also observe that the dissipation is related to fluctuations in that system. By surveying introductory elements (and thus mostly undergraduate textbooks) of this relation, the student finds the interrelationship among different sub-disciplines of physics otherwise buried. A pedagogical experiment in class reveals a student's enjoyment in learning through this experience.Our basic observations from daily experiences as well as sophisticated experiments suggest causality in various branches of physics (and beyond). Causality is mathematically reflected in the analyticity of the system's response function, which relates the dispersion of the system to the dissipation. We also observe that the dissipation is related to fluctuations in that system. By surveying introductory elements (and thus mostly undergraduate textbooks) of this relation, the student finds the interrelationship among different sub-disciplines of physics otherwise buried. A pedagogical experiment in class reveals a student's enjoyment in learning through this experience.