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Equation 4 · Part 2 · Physics Optimizes, Evolution Satisfices: Two Kinds of Perfection

Symbol Gamma^mu_αβ

x¨μ+Γαβμx˙αx˙β=0\ddot{x}^\mu + \Gamma^\mu_{\alpha\beta}\dot{x}^\alpha\dot{x}^\beta = 0
Γαβμ\Gamma^\mu_{\alpha\beta}

What this part means

Gammama^mu_αβ is part of the quantity the equation computes from the expression on the right.

Its job in the formula

Gammama^mu_αβ is part of the quantity the equation computes from the expression on the right.

The passage around this formula

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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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