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Equation 46 · Every Crystal Has Its Own Speed of Light

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v2/c2∼10−8v^2/c^2 \sim 10^{-8}

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v2v^2

Symbol v^2

The square of v: multiply v by itself.

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c2c^2

Symbol c^2

The square of c: multiply c by itself.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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The magnitude is the first surprise. In a driven or flowing lattice, the cone speed along the drift is ceffc_{\mathrm{eff}} + vdv_d in one direction and ceffc_{\mathrm{eff}} - vdv_d in the other, so the anisotropy between the along-drift and transverse directions is δ\delta c/c ≃\simeq vdv_d/ceffc_{\mathrm{eff}} — first order in the drift velocity, not the crushing second-order v2v^2/c2c^2 ∼\sim 10^{-8} that made the 1887 experiment so demanding to run and so easy to see nothing in. At a tenth of the cone speed, the anisotropy is ten percent — a signal any competent interferometer would catch on its first pass, the mirror image of the historical null result. Such anisotropies are not a fiction of the model:…
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The magnitude is the first surprise. In a driven or flowing lattice, the cone speed along the drift is ceffc_{\mathrm{eff}} + vdv_d in one direction and ceffc_{\mathrm{eff}} - vdv_d in the other, so the anisotropy between the along-drift and transverse directions is δ\delta c/c ≃\simeq vdv_d/ceffc_{\mathrm{eff}} — first order in the drift velocity, not the crushing second-order v2v^2/c2c^2 ∼\sim 10^{-8} that made the 1887 experiment so demanding to run and so easy to see nothing in. At a tenth of the cone speed, the anisotropy is ten percent — a signal any competent interferometer would catch on its first pass, the mirror image of the historical null result. Such anisotropies are not a fiction of the model: ultrasonic measurements already resolve a field-angle-dependent sound velocity in the Weyl semimetal tantalum arsenide, a real, measured anisotropic cone speed in exactly the material family the paper’s own census uses for its Weyl-semimetal row [ 13 ] .

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