Loschmidt's paradox-II: Quantum Decoherence

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Loschmidt's paradox highlights the conflict between time-symmetric dynamics and the observation of irreversible processes. The discussion centers on how time-asymmetric quantum decoherence arises from time-symmetric quantum mechanics. It posits that while the universe's wave function is time-reversible, our perception of irreversibility stems from selective observation and the inherent choices we make in interpreting superpositions. The analogy is drawn to the second law of thermodynamics, suggesting that specific initial conditions and coarse-graining lead to time-asymmetry. This exploration emphasizes the relationship between quantum mechanics and thermodynamic principles in understanding entropy and irreversibility.
Dmitry67
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So if you remember, Loschmidt's paradox is about "Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics" ( http://en.wikipedia.org/wiki/Loschmidt's_paradox )

My question is, how time-assymetric Quantum Decoherence emerges from time-symmetric Quantum Mechanics?

P.S. I don't think weak CP violation (which leads to T-symettry violation) plays any role in it.
 
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Isn't it simply that the wave-function of the universe/multiverse as a whole is time reversible, even though we can inspect it from a basis in which each part is not reversible? In other words, there's nothing preventing the SE from back-evolving a superposition of "observed dead cat" plus "observed live cat" into "haven't yet opened the box"; apparent asymmetry arises from our (self-centred) choices to ignore/drop part of the final superposition.

(And classicaly, there is no paradox in time-symmetric laws predicting that if the universe had low entropy at its lower bound of time then it will have entropy increasing with time.)
 
Dmitry67 said:
My question is, how time-assymetric Quantum Decoherence emerges from time-symmetric Quantum Mechanics?
Essentially, the same way how time-asymmetric second law of thermodynamics emerges from classical time-symmetric equations of motion:
Special initial conditions + coarse graining -> time-asymmetry
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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