Francisco Flores

Einstein’s 1935 derivation of mass—energy equivalence is philosophically important because it contains both a criticism of purported demonstrations that proceed by analogy and strong motivations for the definitions of the ‘new’ dynamical quantities. In this paper, I argue that Einstein’s criticism and insights are still relevant today by showing how his derivation goes beyond Friedman’s demonstration of this result in his Foundations of Spacetime ¹heories. Along the way, I isolate three distinct physical claims associated with Einstein’s famous equation that are sometimes not clearly distinguished in philosophical discussions of spacetime theory

Interpretations of Einstein’s equation differ primarily concerning whether E = mc2 entails that mass and energy are the same property of physical systems, and hence whether there is any sense in which mass is ever ‘converted’ into energy. In this paper, I examine six interpretations of Einstein’s equation and argue that all but one fail to satisfy a minimal set of conditions that all interpretations of physical theories ought to satisfy. I argue that we should prefer the interpretation of Einstein’s equation that holds that mass and energy are distinct properties of physical systems. This interpretation also carries along the view that while most cases of ‘conversion’ are not genuine examples of mass being ‘converted’ into energy, it is possible that the there are such ‘conversions’ in the sense that a certain amount of energy ‘appears’ and an equivalent of mass ‘disappears’. Finally, I suggest that the interpretation I defend is the only one that does not blur the distinction between what Einstein called ‘principle’ and ‘constructive’ theories. This is philosophically significant because it emphasizes that explanations of Einstein’s equation and the ‘conversion’ of mass and energy must be top‐down explanations.

In this paper I draw on Einstein's distinction between “principle” and “constructive” theories to isolate two levels of physical theory that can be found in both classical and (special) relativistic physics. I then argue that when we focus on theoretical explanations in physics, i.e. explanations of physical laws, the two leading views on explanation, Salmon's “bottom-up” view and Kitcher's “top-down” view, accurately describe theoretical explanations for a given level of theory. I arrive at this conclusion through an analysis of explanations of mass—energy equivalence in special relativity.

Our goal here is to determine the spatial and temporal constraints on communication between two observers at least one of which moves with constant proper acceleration in two-dimensional Minkowski spacetime. We take as a simplified model of communication one observer bouncing a light signal off another observer. Our derivations use only elementary mathematics and spacetime diagrams, and hence are accessible to students taking their first course in special relativity. Furthermore, the qualitative features of our results can be easily explained to non-physics students in courses that discuss special relativity at a ‘conceptual’ level

In Newtonian physics, there is a clear distinction between a "framework theory", a collection of general physical principles and definitions of physical terms, and theories that describe specific causal interactions such as gravitation, i.e., "interaction theories". I argue that this distinction between levels of theory can also be found in the context of Special Relativity and that recognizing it is essential for a philosophical account of how laws are explained in this theory. As a case study, I consider the history of derivations of mass-energy equivalence which shows, I argue, that there are two distinct types of theoretical explanations in physics. One type is best characterized by the "top-down" account of scientific explanation, while the other is more accurately described by the "bottom-up" account. What is significant, I argue, is that the type of explanation a law receives depends on whether it is part of the framework theory or part of an interaction theory. The former only receive "top-down" explanations while the latter can also receive "bottom-up" explanations. Thus, I argue that current debates regarding "top-down" vs "bottom-up" views of scientific explanation can be clarified by recognizing the distinction between two levels of physical theory