Final answer:
In the quantum case, Loschmidt's paradox challenges the time-reversal symmetry observed in classical mechanics. Quantum mechanics introduces probabilities and uncertainties that make the evolution of states non-deterministic, contradicting the reversibility of classical mechanics.
Step-by-step explanation:
In the quantum case, Loschmidt's paradox refers to the apparent time-reversal symmetry in the microscopic laws of nature. According to classical mechanics, the motion of particles is deterministic and reversible, meaning that if we know the initial conditions, we can predict the future and also determine the past. However, in quantum mechanics, the evolution of states is governed by non-deterministic equations (like Schrödinger's equation) that introduce probabilities and uncertainties. This leads to the arrow of time being asymmetrical, which contradicts the time-reversal symmetry observed in classical mechanics.