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It’s of historical interest only, at this point, but an analysis of an exchange between Albert Einstein and Erwin Schrödinger seems to show how close Einstein came to predicting the dark energy problem.

In this paper, submitted to Arxiv and described at the Arxiv Blog here, Alex Harvey of City University, New York, examines a brief letter-swap between the two – much of it in the layman-impenetrable maths of relativity.

Einstein had created the cosmological constant to account for the state of the universe as he knew it – fixed and unchangeable. Without it, gravity would either cause contraction (if it were too strong) or expansion (if it were too weak) – so Einstein added a term to maintain the state of the universe (and as we know, when Hubble demonstrated the expansion of the universe, Einstein happily wrote the constant off as his biggest mistake).

Before Hubble, however, Schrödinger tried to untangle the possible properties of the cosmological constant.

Einstein – in remarks that foreshadow his later decision to remove the constant from his equations – was, it seemed, unimpressed by Schrödinger’s interpretation. “When I wrote my description of the cosmic gravitational field I naturally noticed, as the obvious possibility, the variant Herr Schrödinger had discussed,” he wrote. “But I must confess that I did not consider this interpretation worthy of mention.”

Where it becomes interesting is how Einstein draws out Schrödinger’s work: it left only the possibilities that the cosmological constant was a fixed number, or variable. The latter, however, he finds deeply problematic: “one not only has to start out from the hypothesis of the existence of a nonobservable negative density in interstellar spaces but also has to postulate a hypothetical law about the space-time distribution of this mass density. The course taken by Herr Schrödinger does not appear possible to me because it leads too deeply into the thicket of hypotheses.”

As Harvey notes, that “thicket of hypotheses” is exactly where physics ultimately landed, once it was demonstrated that not only is the universe expanding (a discovery which caused Einstein to ditch the cosmological constant), but that the expansion seems to be accelerating (which demands a source for the energy driving the acceleration, vindicating Einstein’s original demand for just such a constant). ®

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