decoherenceTime
plain-language theorem explainer
The definition supplies the timescale over which off-diagonal coherences decay for a quantum system coupled to environment E at separation s. Quantum foundations researchers cite it when analyzing pointer state emergence from neutral windows. It is realized as a direct algebraic formula using the reduced Planck constant divided by temperature, interaction strength, and separation squared.
Claim. The decoherence timescale is given by $τ_D(E,s) = ħ / (T_E · g_E · s²)$, where $T_E$ and $g_E$ are the temperature and interaction strength of environment $E$, and $s$ is the separation.
background
Environment is a structure with positive temperature, interaction strength, and a count of degrees of freedom, modeling a macroscopic setting with many particles. In the module on pointer states from neutral windows, pointer states correspond to configurations that locally minimize J-cost; environment interactions drive relaxation to these states on the decoherence timescale.
proof idea
The definition is a one-line algebraic expression that divides ħ by the product of the environment's temperature, its interaction strength, and the square of the given separation.
why it matters
It provides the explicit decoherence timescale that enables classification of systems into quantum and classical regimes in the QFT.Decoherence module. Downstream results include theorems showing decoherence time decreases with coupling strength and number of modes, plus definitions of isClassical and isQuantum based on comparison to measurement time. This fills the QF-003 target for pointer state emergence from neutral windows in the J-cost landscape.
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