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Equation 74 · Part 1 · The Atlas That Refuses to Close

Symbol rho_M

ρM\rho_M
ρM\rho_M

What this part means

the twice.

Its job in the formula

rhoMo_M is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

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.

The passage around this formula

…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 transformation is what removes it, by transforming to exactly the representation…

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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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