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Equation 1 · Part 2 · How Quantum Foundations and Measurement Actually Work

Symbol t

ρS(t)=TrE[U(t) ρS(0)⊗ρE(0) U†(t)]\rho_S(t) = \mathrm{Tr}_E\big[U(t)\,\rho_S(0)\otimes\rho_E(0)\,U^\dagger(t)\big]
tt

What this part means

t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

…are suppressed at a rate set by how strongly and how many environmental degrees of freedom couple in [ 5 ] . This reduced density matrix ρS(t)\rho_S(t) is what an observer restricted to the system alone can predict with; as t grows, its off-diagonal terms in a preferred (“einselected”) basis decay toward zero, and the state comes to look like a classical mixture of definite outcomes with fixed probabilities [ 5 ] . That is a fact, derived from unitary quantum mechanics plus a specification of the environment, and it…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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