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Equation 71 · Part 4 · The Atlas That Refuses to Close

superscript

ωZ≈1.55×1021 rad s−1\omega_Z \approx 1.55\times10^{21}\ \mathrm{rad\,s^{-1}}
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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

set purely by the rest mass. For an electron this is ωZ\omega_Z ≈\approx 1.55×\times10^{21}\ rad s−1\mathrm{rad\,s^{-1}} , an oscillation period of roughly four zeptoseconds in the particle’s own rest frame — a boosted lab observer would clock a longer, time-dilated period by the ordinary factor γ\gamma , coordinate time and proper time parting ways in exactly the usual manner — with an amplitude of order the reduced Compton wavelength ℏ\hbar/(mem_ec) , the same length scale, twice ρM\rho_M for a spin-half particle, that bounded the Møller disk above. Schrödinger first noticed this trembling motion, zitterbewegung, in the Dirac coordinate’s equations of motion; Foldy and Wouthuysen’s 1950 canonical…

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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 surrounding passage

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