The co-discovery of conservation laws and particle families

Abstract

This paper presents an epistemological analysis of the search for new conservation laws in particle physics. Discovering conservation laws has posed various challenges concerning the underdetermination of theory by evidence, to which physicists have found various responses. These responses include an appeal to a plenitude principle, a maxim for inductive inference, looking for a parsimonious system of generalizations, and unifying particle ontology and particle dynamics. The connection between conservation laws and ontological categories is a major theme in my analysis: While there are infinitely many conservation law theories that are empirically equivalent to the laws physicists adopted for the fundamental Standard Model of particle physics, I show that the standard family laws are the only ones that determine and are determined by the simplest division of particles into families.

Discovery of Conservation Laws via Matrix Search

“…Our results show that the MSMS criterion formalizes adequately the goals that scientists seek to achieve in selecting conservation theories: MSMS theories explain why unobserved reactions do not occur [9, Sec.4], they minimize the magnitude of conserved quantities, and by the theorem of Schulte and Drew [17,18], they connect conservation laws with disjoint particle families. In contrast, our algorithmic method for finding MSMS theories was derived from efficiency considerations and does not match how physicists have gone about finding conserved quantities: they started with plausible particle families, derived conservation laws, then checked them against the data [18]. This amounts to using domain knowledge to solve a computationally challenging problem.…”

“…The ability of the MSMS criterion to recover the correct particle families is surprising because the method receives data only about particle dynamics (reactions), not about particle ontology. Schulte and Drew [17,18] provide a theoretical explanation of this phenomenon: It can be proven using linear algebra that if there is some maximally strict conservation law matrix with disjoint corresponding particle families, then the particle families are uniquely determined by the reaction data. Moreover, the conservation matrix corresponding to these particle families is the unique MSMS optimizer (up to changes of sign).…”

Kelly on Ockham’s Razor and Truth-Finding Efficiency

“…Kelly has shown that the analysis can be applied to the use of Ockham's Razor in various idealized empirical problems, including simple curve-fitting cases (Kelly 2007) and isolating causes from correlation data (Kelly 2011). Impressive attempts have also been made to apply it to real cases from science-most notably, Schulte (2008) has applied it to the problem of discovering conservation laws in particle physics. The analysis has not been extended to statistical inference, where the relevant theories only make probabilistic claims about the data, but Kelly…”