Interpretations of Einstein’s Equation E = mc²

Abstract

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 (or vice versa). 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 (or vice versa), 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.

Acknowledgements

I would like to thank James W. McAllister, the editor, and two anonymous referees for their careful and constructive critique of an earlier version of this essay. For her insightful and constructive criticisms on all versions of this essay, I would like to thank Rachel Fern.

Notes

[1] In a recent communication to the author, Lange claims that in his work, he only uses Lorentz‐invariance as a necessary condition. I believe evidence from his text indicates otherwise. However, Lange may now wish to restrict himself to treating Lorentz‐invariance as a necessary condition.

[2] Although seldom noted in textbooks, the full relation E = (m − q) + K is explicitly derived in many ‘purely dynamical’ derivations. See, for example, Mermin and Feigenbaum (1990).

[3] For simplicity, I am assuming we are working with only two dimensions.