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Equation 59 · Part 2 · The Atlas That Refuses to Close

Symbol u

Xμ(u,Σ)X^\mu(u,\Sigma)
uu

What this part means

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

Its job in the formula

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

The passage around this formula

The first, the covariant centre of energy, transforms simply as the spatial part of a four-vector under a change of Lorentz frame — exactly the property Xμ(u,Σ)X^\mu(u,\Sigma) was built with above — but its three spatial components fail to commute with each other once spin is present, by an amount proportional to the spin itself. The second, constructed by Newton and Wigner for exactly this purpose and reproduced in Pryce’s classification as a distinct case, has strictly commuting components, [XNWiX_{\mathrm{NW}}^i, XNWjX_{\mathrm{NW}}^j] = 0 , the property any operator called “position” ought to have if it is to support ordinary probability densities and wavefunction localization at all, at the price of…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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