← All parts of this equation

Equation 117 · Part 1 · The Atlas That Refuses to Close

Symbol delta_ij

δij(u,Σ)=∣Xiμ(u,Σ)−Xjμ(u,Σ)∣ΣρM,\delta_{ij}(u,\Sigma) = \frac{\big|X_i^\mu(u,\Sigma) - X_j^\mu(u,\Sigma)\big|_\Sigma}{\rho_M},
δij\delta_{ij}

What this part means

deltaia_ij is part of the quantity the equation computes from the expression on the right.

Its job in the formula

deltaia_ij is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…two of them evaluated on the same hypersurface Σ\Sigma , δij(u,Σ)=∣Xiμ(u,Σ)−Xjμ(u,Σ)∣ΣρM\delta_{ij}(u,\Sigma) = \frac{\big|X_i^\mu(u,\Sigma) - X_j^\mu(u,\Sigma)\big|_\Sigma}{\rho_M}. the proper spatial separation within Σ\Sigma between the two charts’ answers, normalized by the spin-to-mass length fixed in the first section. δij\delta_{ij} is dimensionless by construction, symmetric, zero exactly when the two charts coincide, and it has now been checked, not merely asserted, in both directions this kind of construction is required to pass: it vanishes as v/c →\to 0 for any spin, and it vanishes as S →\to 0 for any observer…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

The article lists its research sources here.