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Equation 146 · Part 2 · The Bend an Elevator Cannot Fake

superscript

diag(−Ω2,−Ω2,0)\mathrm{diag}(-\Omega^2,-\Omega^2,0)
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Even a network that has cleared every check above owes one more: any fictitious, non-curvature contribution to a naive second difference has to be ruled out on its own terms, not merely assumed absent. A uniformly rotating platform’s centrifugal potential, -12\tfrac12|Ω\boldsymbol\Omega×\timesr\mathbf r|^2 , has a nonzero Hessian too — for rotation about the z -axis, diag(−Ω2,−Ω2,0)\mathrm{diag}(-\Omega^2,-\Omega^2,0) — but that Hessian is exactly constant across any laboratory-scale network, tied to a rotation axis independently known from astrometry to extraordinary precision, and entirely absent from the trace-free, 2:{-1}:{-1} , 1/r3r^3 -falling pattern a genuine point-like or spherical mass produces. A real…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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