Cosmological Constant Λ vs. Massive Gravitons: A Case Study in General Relativity Exceptionalism vs. Particle Physics Egalitarianism

Abstract

The renaissance of General Relativity witnessed considerable progress regarding both understanding and justifying Einstein’s equations. Both general relativists and historians of the subject tend to share a view, General Relativity exceptionalism, which emphasizes how General Relativity is novel and unlike the other fundamental interactions. But does some of the renaissance progress in understanding and justifying Einstein’s equations owe something to an alien source, namely, particle physics egalitarianism, which emphasizes how similar General Relativity is to the other fundamental interactions? If so, how should the historiography of gravitation and Einstein’s equations reflect that fact? Two areas of renaissance progress can be considered very briefly (gravitational waves and the question of energy and the justification of Einstein’s field equations in terms of particle physics) and one in detail: the longstanding confusion over the relation between Einstein’s cosmological constant Λ and a graviton mass, confusion introduced in 1917 with Λ.

Regarding gravitational waves, General Relativity exceptionalism discouraged trusting the linear approximation, in which the existence of gravitational radiation is evident, whereas particle physics egalitarianism encouraged such trust. While general relativists differed on this issue in the 1950s, the rare particle physicist seriously involved, Feynman, was among those who invented the sticky bead argument that largely resolved the controversy. Regarding the justification of Einstein’s equations in terms of particle physics, the spin 2 derivations of Einstein’s equations provided considerably support of the view that Einstein’s equations correctly describe gravitation.

The idea of a graviton mass has a nineteenth-century Newtonian pre-history in Neumann’s and Seeliger’s long-distance modification of gravity, which (especially for Neumann) altered Poisson’s equation to give a potential e ^−mr∕r for a point mass, improving convergence for homogeneous matter. Einstein reinvented the idea before introducing his faulty analogy with Λ. This confusion was first critiqued by Heckmann in the 1940s (without effect) and by Trautman, DeWitt, Treder, Rindler, and Freund et al. in the 1960s, and especially more recently by Schücking, but it has misled North, Jammer, Pais, Kerszberg, the Einstein Papers, and Kragh. The error is difficult to catch if one has an aversion to perturbative thinking, but difficult to make if one thinks along the lines of particle physics. Λ contributes predominantly a zeroth order term to the field equations (a constant source), whereas a graviton mass contributes a linear term. Nonperturbatively, massive spin 2 gravity is bimetric. The Λ-graviton mass confusion not only distorted the interpretation of Einstein’s theory, but also obscured a potentially serious particle physics-motivated rivalry (massless vs. massive spin 2). How could one entertain massive spin 2 gravity if Λ is thought already analogous to the Neumann-Seeliger scalar theory? Massive spin 2 gravity would encounter problems within particle physics in the early 1970s, which have been substantially resolved in recent years (though new problems have arisen). Other authors manage to avoid confusing Λ with the Neumann-Seeliger long-range decay but fail to recognize that the latter, with the physical meaning of a graviton mass, provides an interesting case of unconceived alternatives.

In sum, both the interpretation and the justification of Einstein’s equations owed some of their renaissance progress to particle physics egalitarianism. Historiography, like physics, is best served by overcoming the divide between the two views of gravitation.