Editing Arrow of time (section)

=== Quantum arrow of time ===
Quantum evolution is governed by equations of motions that are time-symmetric (such as the [[Schrödinger equation]] in the non-relativistic approximation), and by [[wave function collapse]], which is a time-irreversible process, and is only physically real in explicit collapse interpretations of quantum theory, such as the [[ Diósi–Penrose model]], the [[Ghirardi–Rimini–Weber theory]], or the [[Transactional interpretation]], which uses the direct-action or "absorber" theory of fields. 

The conventional approach is to assume that [[quantum decoherence]] explains irreversibility and the second law of thermodynamics, thus claiming to derive the quantum arrow of time from the [[Entropy (arrow of time)|thermodynamic arrow of time]]; however this is a matter of some debate, since the underlying dynamics is assumed to be unitary and thus reversible.
<ref name="Kastner 2014">Kastner, R. E. (2014). ‘Einselection’ of pointer observables: The new H-theorem? Stud. Hist. Philos. Mod. Phys. 48, 56-58.</ref> 
A conventional account of decoherence is to say that following any particle [[scattering]] or interaction between two larger systems, the relative [[phase (waves)|phases]] of the two systems are at first orderly related, but subsequent interactions (with additional particles or systems) make them less so, so that the two systems become decoherent. Thus decoherence is a form of increase in microscopic disorder{{snd}} in short, decoherence increases entropy. Two decoherent systems can no longer interact via [[quantum superposition]], unless they become coherent again, which is normally impossible, by the second law of thermodynamics.<ref name="Schlosshauer">Schlosshauer, M. (2005). Decoherence, the measurement problem, and interpretations of quantum mechanics. Reviews of Modern physics, 76(4), 1267.</ref> In the language of relational quantum mechanics, the observer becomes entangled with the measured state, where this entanglement increases entropy. As stated by [[Seth Lloyd]], "the arrow of time is an arrow of increasing correlations".<ref name = wolchover >{{cite magazine |url=https://www.wired.com/2014/04/quantum-theory-flow-time/ |title=New Quantum Theory Could Explain the Flow of Time |first=Natalie |last=Wolchover |magazine=Wired |date=25 April 2014 |via=www.wired.com}}</ref><ref name="iqoqi">Univ of Bristol [https://scitechdaily.com/time-reversal-phenomenon-in-the-quantum-realm-not-even-time-flows-as-you-might-expect/ (26 Nov 2021) Time-Reversal Phenomenon: In the Quantum Realm, Not Even Time Flows As You Might Expect] Lead: Professor Caslav Brukner: "quantum systems can simultaneously evolve along two opposite time arrows — both forward and backward in time".</ref>

However, under special circumstances, one can prepare initial conditions that will cause a decrease in decoherence and in entropy. This has been shown experimentally in 2019, when a team of Russian scientists reported the reversal of the quantum arrow of time on an [[IBM]] [[quantum computer]], in an experiment supporting the understanding of the quantum arrow of time as emerging from the thermodynamic one.<ref name="nature">{{cite journal |author=Lesovik |first1=G. B. |last2=Sadovskyy |first2=I. A. |last3=Suslov |first3=M. V. |last4=Lebedev |first4=A. V. |last5=Vinokur |first5=V. M. |date=13 March 2019 |title=Arrow of time and its reversal on the IBM quantum computer |journal=Nature |volume=9 |issue=1 |page=4396 |arxiv=1712.10057 |bibcode=2019NatSR...9.4396L |doi=10.1038/s41598-019-40765-6 |pmc=6416338 |pmid=30867496 |s2cid=3527627}}</ref> By observing the state of the quantum computer made of two and later three [[Superconducting quantum computing#Qubit archetypes|superconducting qubits]], they found that in 85% of the cases, the two-qubit computer returned to the initial state.<ref name="phys">{{cite web |url=https://phys.org/news/2019-03-physicists-reverse-quantum.html |title=Physicists reverse time using quantum computer |publisher=[[Phys.org]] |date=13 March 2019 |access-date=13 March 2019}}</ref> The state's reversal was made by a special program, similarly to the random [[microwave background]] fluctuation in the case of the [[electron]].<ref name="phys"/> However, according to the estimations, throughout the [[age of the universe]] (13.7&nbsp;billion years) such a reversal of the electron's state would only happen once, for 0.06&nbsp;[[nanoseconds]].<ref name="phys" /> The scientists' experiment led to the possibility of a [[quantum algorithm]] that reverses a given [[quantum state]] through [[complex conjugation]] of the state.<ref name="nature"/>

Note that quantum decoherence merely allows the appearance of quantum wave collapse (based on the vanishing of diagonal elements of the density matrix); it is a matter of dispute whether the collapse itself actually takes place or is redundant and apparent only. While the theory of quantum decoherence is widely accepted and has been supported experimentally at the level of the applicable density matrix, the conventional theory's inability to predict actual measurement outcomes via non-unitary collapse remains. That is, the density matrix obtained from standard unitary-only decoherence (without actual collapse) is an improper mixture that cannot be interpreted as reflecting a determinate measurement outcome. Thus the arrow of time question continues to be addressed by way of explicit collapse approaches.<ref name="Kastner 2017">Kastner, R. E. (2017). On Quantum Collapse as a Basis for the Second Law of Thermodynamics, Entropy 19(3)106.</ref>