Equation 49 · Part 7 · How Fast Can a Horizon Learn Which Path You Took?
=
=
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.
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The passage around this formula
The sharper 2026 challenge comes from quantum rather than semiclassical extremality. Biggs and Trezzi study near-extremal charged Reissner–Nordström black holes with quantum fluctuations of the near-horizon geometry. In their electromagnetic single-charge-superposition setup, a spin-induced gap in the black-hole spectrum makes the late-time decoherence rate vanish when the energy above extremality lies below . in their natural-unit conventions. They establish the zero through quartic order in the interaction and conjecture it to all orders for the stated opposite-dipole geometry; above the gap, the quantum-corrected rate remains below the semiclassical prediction [ 8 ] .…
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.