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Equation 51 · Part 4 · Every Crystal Has Its Own Speed of Light

=

vLR=12eJmax⁡v_{\mathrm{LR}} = 12eJ_{\max}
=

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 first verdict is a genuine win for the theory. Every exponent measured is super-linear — ζ\zeta > 1 at seven of the eight points — exactly where the long-range bound says a finite-velocity linear cone is not guaranteed and faster-than-linear growth is required instead, and the propagation outright violates the nearest-neighbour bound vLRv_{\mathrm{LR}} = 12eJmax⁡J_{\max} once α\alpha drops below 1 [ 4 ] . Read against a naive short-range picture, the ion chain is unambiguously non-local. The second verdict tempers the first: the three competing long-range thresholds theory offers — a worst-case bound, a typical-state bound, and a free-particle bound — all sit above α\alpha = 2 , while Richerme’s…

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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.

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Sources cited in the surrounding passage

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