Manuscript XX-D@1 · XX-D.tex · section · c83a526d

Relational composition and absence of Y 2

Complete classical coefficient through second order › Relational composition and absence of Y 2 · lines 598–615

The spacetime rod label is obtained by transporting $R_{s}$ from its clock slice. Let $α_{s}$ be the inverse clock-and-rod map and write

α_{s} = x + s α_{1} + \frac{s ^{2}}{2} α_{2} .

At first order,

α_{1}^{0} = u_{1}, α_{1}^{i} = - Y_{1}^{i} .

At second order the clock equation gives

α_{2}^{0} = u_{2} - 2 Y_{1}^{i} \partial_{i} u_{1} .

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