Equation 27 · The Atlas That Refuses to Close
What does this equation mean?
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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol u
u is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol Sigma
a spacelike hypersurface and the four-velocity of the observer whose notion of simultaneity represents.
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What the article says around this equation
This construction is not confined to flat spacetime or to elementary particles. Janson and Lopp have recently extended exactly this hypersurface-centroid bookkeeping to a composite quantum particle’s own internal structure in a curved, Schwarzschild-type background, deriving the general-relativistic corrections a multi-particle atom’s centre-of-mass coordinate picks up when the atom itself is used as a clock in an interferometer [ 14 ] . The atlas built here stays in flat spacetime throughout, but the same (u,) bookkeeping is what makes that curved-spacetime extension possible at all.
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