Equation 71 · The Atlas That Refuses to Close
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol omega_Z
omeg is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
superscript
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.
See an illustrated explanation →How to interpret it
Its accuracy depends on the assumptions and range of use described in the article.
What the article says around this equation
set purely by the rest mass. For an electron this is 1.5510^{21}\ , 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 , coordinate time and proper time parting ways in exactly the usual manner — with an amplitude of order the reduced Compton wavelength /(c) , the same length scale, twice 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…
Read the full surrounding passage
set purely by the rest mass. For an electron this is 1.5510^{21}\ , 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 , coordinate time and proper time parting ways in exactly the usual manner — with an amplitude of order the reduced Compton wavelength /(c) , the same length scale, twice 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 in which the position operator is the Newton–Wigner operator and the oscillating term is absorbed into the difference between and [ 3 ] .
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
Return to The Atlas That Refuses to Close