In recent work a Stern-Gerlach interferometer (SGI) was considered in which a polarized beam of spin-(1/2 particles is split by a Stern-Gerlach apparatus into two partial beams, and then subsequent Stern-Gerlach deflecting magnets are used to reconstitute these two beams into one. In these studies it was shown that when such a coherent polarized beam passed through a SGI, some spin coherence is inevitably lost. In this regard, folk wisdom concerning irreversibility provides something of a guide to the present problem, since we all know that when Humpty-Dumpty had his great fall nobody could put him together again. In the present paper we consider the fate of our spin-(1/2 Humpty-Dumpty when a detector is present that is sensitive to the passage of particles along one trajectory, but not the other. It is not surprising that coherence is destroyed as soon as one is able to tell along which path the atom traveled. However, there seems to be no general agreement about the mechanism of coherence loss. Our conclusion is that the loss of coherence in measurements on quantum systems can always be traced to the dynamics of correlations between the measuring apparatus and the system being observed.
Time-reversal had always been assumed to be a symmetry of physics at the fundamental level. In this paper we will explore the violations of time-reversal symmetry at the fundamental level and the consequence on thermodynamic systems. First, we will argue from current physics that the universe dynamics is not time-reversal invariant. Second, we will argue that any thermodynamic system cannot be isolated completely from the universe. We then discuss how these two make the dynamics of thermodynamics systems very weakly irreversible at the classical and quantum level. Since time-reversal is no longer a symmetry of realistic systems, the problem of how macroscopic irreversibility arises from microscopic reversibility becomes irrelevant because there is no longer microscopic reversibility. At the classical level of a thermodynamic system, we show that the H theorem of Boltzmann is still valid even without microscopic reversibility. We do this by deriving a modified H theorem, which still shows entropy monotonically increasing. At the quantum level, we explicitly show the effect of CP violation, small irreversible changes on the internal states of the nuclear and atomic energy levels of thermodynamic systems. Thus, we remove Loschmidt's objection to Boltzmann's ideas.
Originally conceived as a thought experiment, an apparatus consisting of two Stern–Gerlach apparatuses joined in an inverted manner touched on the fundamental question of the reversibility of evolution in quantum mechanics. Theoretical analysis showed that uniting the two partial beams requires an extreme level of experimental control, making the proposal in its original form unrealizable in practice. In this work, we revisit the above question in a numerical study concerning the possibility of partial-beam recombination in a spin-coherent manner. Using the Suzuki–Trotter numerical method of wave propagation and a configurable, approximation-free magnetic field, a simulation of a transversal Stern–Gerlach interferometer under ideal conditions is performed. The result confirms what has long been hinted at by theoretical analyses: the transversal Stern–Gerlach interferometer quantum dynamics is fundamentally irreversible even when perfect control of the associated magnetic fields and beams is assumed.
The discussion on time-reversal in quantum mechanics exists at least since Wigner's ``Uber die Operation der Zeitumkehr in der Quantenmechanik'' paper in 1932. If and how the dynamics of the quantum world is time-reversible has been the subject of many controversies. Some have seen quantum mechanics as fundamentally time-irreversible, see for example von Neumann, and some have seen in that the ultimate cause of time's arrow and second law behavior. In his best-selling book ``The Emperor's New Mind'', Roger Penrose argues similarly and concludes that ``our sought-for quantum gravity must be a time-asymmetric theory'' [p.351]. Not so long ago, we read yet about another project in Physicalia 26: to extend quantum mechanics into new fundamentally irreversible equations, thus proposing a new theory giving ``... une description fondamentale irreversible de tout systeme physique''.
Loschmidt's paradox asks why macroscopic irreversibility is universal despite the time-reversal symmetry of microscopic dynamics. We argue that irreversibility is not a property of the dynamics but of accessibility: chaotic evolution drives phase-space structure below the quantum resolution scale
ℓℏ, at a critical time
tc=λ−1ln(δ0/ℓℏ), after which the time-reversed microstate exists as a valid solution of Hamilton's equations but cannot be selected by any physically admissible operation. The mechanism operates entirely within the semiclassical regime
tc≤tE, where classical geometry is exact. This provides a dynamical resolution of the Loschmidt paradox.
The quantum foundation is established using a Krylov-complexity framework: we prove that for any
H(t)=H(−t), the quantum Lyapunov exponent satisfies
λLforward=λLbackward. The arrow of time is not in the dynamics. The mechanism predicts sigmoid fidelity decay, logarithmic scaling of
tc with
λ−1, and ensemble-size independence of the inaccessibility threshold -- all consistent with three decades of Loschmidt echo experiments and confirmed in a stadium-billiard simulation reported here. Underlying everything: quantum mechanics conserves information exactly. Entropy, defined as the logarithm of the multiplicity
Ω -- the number of possibilities consistent with the available information -- can only increase when information becomes operationally inaccessible. The second law reflects not a breakdown of microscopic reversibility, but the dynamical inaccessibility of the information required to reverse it.