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Equation 47 · Part 4 · Every Crystal Has Its Own Speed of Light

=

γ=(1−vd2/ceff2)−1/2\gamma = (1 - v_d^2/c_{\mathrm{eff}}^2)^{-1/2}
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The second surprise is the one that keeps the inversion honest. Carlos Barceló and Gil Jannes proved in 2008 that an interferometer built entirely out of the same quasiparticles it uses to measure — its splitters, its mirrors, its rulers all made from the emergent medium rather than from anything outside it — cannot detect the drift after all, because the binding fields holding its own arms together obey the same emergent wave equation as the signal racing through them, and the arms contract by exactly the factor γ\gamma = (1 - vd2v_d^2/ceff2c_{\mathrm{eff}}^2)^{-1/2} needed to cancel the timing shift [ 9 ] . That result is not this paper’s discovery — it is Barceló and Jannes’ theorem, cited here at…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.