In quantum mechanics the time reversal has obviously something to do with the complex conjugation. Let us consider the symmetry operation |αi −→ |α˜i, |βi −→ |β˜i. We can see already from this example that time reversal in quantum mechanics is represented by an antilinear operator, since a linear operator is unable to map a wave function into its complex conjugate. 6:104. doi: 10.3389/fphy.2018.00104 We require that the absolute value of the scalar product is invariant under that operation: |hβ˜|α˜i| = |hβ|αi|. This allows us to avoid of SUSY- supersymmetric quantum mechanics (SUSY QM) [15{17] without any ne-tuning. This is because the emergent SUSY in our case is a property of entire phases of matter and consequently can thus be observed in any member of any of these phases. Featured on Meta “Question closed” notifications experiment results and graduation It was realized by Wigner that in quantum mechanics, time reversal has to be de ned in a very special way di erent from all other symmetries. Elapsed time is not universal – proper time increases differently along different world-lines. Front. (2) is the Schr¨odinger equation for a particle in a magnetic field, i¯h ∂ψ(x,t) ∂t = 1 2m h − i¯h∇ − q c A(x) i2 ψ(x,t). Browse other questions tagged quantum-mechanics wavefunction time-reversal-symmetry or ask your own question. The problem is simplified in quantum mechanics because time is a parameter just as in classical mechanics. Phys. Time reversal operator is anti-unitary: it maps i to i. in the rst textbook presentation of time reversal in quantum mechanics, remarked that \‘reversal of the direction of motion’ is perhaps a more felicitous, though longer, expression than ‘time inversion’" (Wigner 1931, p.325). If this is the case, then the canonical commutation relation between xand pwill remain invariant under time reversal. Here, we review our recent work on this subject [12,13,14], where we argued that an arrow of time can emerge even in very simple quantum systems.We stress the fact that each solution of time-reversal equation of motion can break the time-reversal symmetry if the system is open. The discovery of the violation of these symmetries has been a decisive breakthrough of the quantum field theory, leading to the standard model. Keywords: philosophy of physics, time-reversal invariance, symmetry, arrow of time, quantum mechanics, motion reversal. The charge conjugation, together with the parity symmetry, is not conserved in the weak interaction11,12, just as the time-reversal symmetry. In relativistic theories, it is not possible to simply replace t! Similarly, the quantum analog of Eq. Therefore, we can indeed have, in specific cases, the dynamics that seemingly breaks the time-reversal symmetry. Citation: López C (2018) Seeking for a Fundamental Quantum Arrow of Time: Time Reversal and the Symmetry-To-Reality Inference in Standard Quantum Mechanics. tto define time reversal.