Symbol ddotx^mu
ddotu is part of the quantity the equation computes from the expression on the right.
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Why this formula appears here
Snell’s law, in other words, is not an independent fact about glass. It is what falls out of a single global stipulation — least time — applied to one path among infinitely many. Pierre-Louis Maupertuis generalized the same move to all of mechanics in the 1740s, proposing that nature always acts by the smallest possible “action,” and Euler, Lagrange, and Hamilton spent the following century turning that guess into the working machinery of classical physics: a moving body’s entire trajectory falls out of minimizing one integrated quantity over the whole path, not from adding up forces moment to moment. General relativity is this idea pushed as far as it goes. Einstein’s field equations recast…
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Symbol Gamma^mu_αβ
Gammu_αβ is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Symbol ẋ^α
ẋ^α has a dot, marking the rate of change of the underlying indexed quantity with respect to the article’s time variable.
Read this term in its guide →Symbol ẋ^β
ẋ^β has a dot, marking the rate of change of the underlying indexed quantity with respect to the article’s time variable.
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Equation 4 · Einstein & Evolution
Physics Optimizes, Evolution Satisfices: Two Kinds of Perfection
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Snell’s law, in other words, is not an independent fact about glass. It is what falls out of a single global stipulation — least time — applied to one path among infinitely many. Pierre-Louis Maupertuis generalized the same move to all of mechanics in the 1740s, proposing that nature always acts by the smallest possible “action,” and Euler, Lagrange, and Hamilton spent the following century turning that guess into the working machinery of classical physics: a moving body’s entire trajectory falls out of minimizing one integrated quantity over the whole path, not from adding up forces moment to moment. General relativity is this idea pushed as far as it goes. Einstein’s field equations recast…
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