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Equation 60 · Part 2 · The Atlas That Refuses to Close

Symbol X_NW^j

[XNWi,XNWj]=0[X_{\mathrm{NW}}^i, X_{\mathrm{NW}}^j] = 0
XNWjX_{\mathrm{NW}}^j

What this part means

XNX_NWjW^j is part of the quantity the equation computes from the expression on the right.

Its job in the formula

XNX_NWjW^j is part of the quantity the equation computes from the expression on the right.

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 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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