Re: Analyse This!

Ahmed Ouahi, Architect wrote:
More or less reflexively, he dropped into his equations something called the
cosmological constant, which arbitrarily counterbalanced the effects of
gravity, serving as a kind of mathematical pause button.

Books on the history of science always forgive Einstein this lapse, but it
was actually a fairly appalling piece of science and he knew it. He called
it ' the biggest blunder of my life '. "

From today's perspective this was not a blunder at all. Thinking abstractly, one cannot eliminate from the Lagrangian any terms that satisfy the symmetries required of the theory (chiefly general covariance). If one restricts the terms to those with no derivatives higher than the second, and requires linearity in those second derivatives, one obtains the Lagrangian that yields the Einstein field equation, with cosmological constant. It is the simplest non-trivial Lagrangian that obeys the necessary symmetries.

It is, of course, up to experiments to determine the value of the cosmological constant. Until rather recently, the value was "quite small, consistent with zero"; with improved techniques we now measure it to be nonzero. Einstein originally favored zero, because then the Newtonian limit comes out correct; with a very small value, however, deviations from Newtonian mechanics would not be detectable.


Tom Roberts
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