Metric-first and entropy-first surprises
P. Fraundorf
Abstract: Established idea-sets don't update seamlessly. The tension between new and old views of nature is e.g. documented in Galileo's dialogs and now present in many fields. However the science of Bayesian model-selection has made recent strides in both life & physical sciences, in effect suggesting that we look to models which are quantitatively surprised least by present-day observations.
We illustrate the relevance of this to physics-education with a qualitative look at two paradigm-shifts, namely from Lorentz-transform to metric-equation descriptions of motion in space-time, and from classical to statistical thermodynamics with help from Boltzmann's choice-multiplicity & Shannon's uncertainty. Connections of the latter to correlation measures behind available-work, evolving complexity, and model-selection relevant to physics undergrads are also explored.
New strategies are exemplified with Appendices for teachers on: anyspeed traffic-laws & 3-vector velocity-addition, the energy-momentum half-plane lost to finite lightspeed, the modern distinction between proper & geometric accelerations, metric-first kinematics with acceleration & differential-aging, quantifying risk with a handful of coins, effective number of choices, available work in bits, reversible-thermalization of life's power-stream, and choice-multiplicity measures of layered complex-system health.
The applications for log-probability measures in Bayesian statistical inference are even broader than those discussed in the manuscript described here. This is illustrated e.g. by the tabulation below of uses for them discussed in the cross-disciplinary Physics 4305 course on Bayesian Data Analysis for the Sciences at University of Missouri Saint Louis in Fall 2017.
References:
P. Fraundorf (2011/2012) "Metric-first & entropy-first surprises", arXiv:1106.4698 [physics.gen-ph].