Equation 13 · A Horizon Is a Toll Booth, Not a Loophole
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol H
H is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol pi
pi is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
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What the article says around this equation
where H is the mean energy in the evolving state and is the ground-state energy of H [ 2 , 1 ] . Inverting this gives a maximum rate of orthogonal state changes per unit proper time, 2( H-)/ , and Giovannetti, Lloyd, and Maccone showed that for a periodic evolution this rate integrates cleanly: a system with mean energy H- above its ground state can pass through at most
Sources cited in the article section
- [3] Quantum Limits to Dynamical Evolution ↗
- [5] Ultimate Physical Limits to Computation ↗
- [4] Energy-Time Uncertainty Relation for Driven Quantum Systems ↗
These citations give research context. Read each source to check which claims it supports.
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