arXiv:0802.0438 · Physical Review Letters

Quantum Solution to the Arrow-of-Time Dilemma

Lorenzo Maccone

Published Aug 17, 2009• 84 citations

Abstract

The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.

DOI: 10.1103/physrevlett.103.080401

Related papers

The Thermodynamic Arrow-of-time and Quantum Mechanics

Lorenzo Maccone

I give an explanation of the thermodynamic arrow-of-time (namely entropy increases with time) within a quantum mechanical framework. This entails giving a solution to the Loschmidt paradox, i.e. showing how an irreversible macro-dynamics can arise from a reversible micro-dynamics. I argue that, in accordance to the reversible dynamics, both entropy-increasing and entropy-decreasing transformations take place, but entropy-decreasing transformations cannot leave any information of their having happened. This is indistinguishable from their not having happened at all. The second law of thermodynamics is then reduced to a tautology: the only transformations that can be seen are those where entropy does not decrease. However, typicality arguments seem to prevent this argument to be used as a complete solution to the arrow-of-time dilemma: it might still be necessary to postulate a low entropy initial state for the system under consideration.

Electronic Notes in Theoretical Computer ScienceFeb 1, 20110 citations

Quantum-Entropy Physics

Davi Geiger, Zvi M. Kedem

All the laws of physics are time-reversible. Time arrow emerges only when ensembles of classical particles are treated probabilistically, outside of physics laws, and the entropy and the second law of thermodynamics are introduced. In quantum physics, no mechanism for a time arrow has been proposed despite its intrinsic probabilistic nature. In consequence, one cannot explain why an electron in an excited state will "spontaneously" transition into a ground state as a photon is created and emitted, instead of continuing in its reversible unitary evolution. To address such phenomena, we introduce an entropy for quantum physics, which will conduce to the emergence of a time arrow. The entropy is a measure of randomness over the degrees of freedom of a quantum state. It is dimensionless; it is a relativistic scalar, it is invariant under coordinate transformation of position and momentum that maintain conjugate properties and under CPT transformations; and its minimum is positive due to the uncertainty principle. To excogitate why some quantum physical processes cannot take place even though they obey conservation laws, we partition the set of all evolutions of an initial state into four blocks, based on whether the entropy is (i) increasing but not a constant, (ii) decreasing but not a constant, (iii) a constant, (iv) oscillating. We propose a law that in quantum physics entropy (weakly) increases over time. Thus, evolutions in the set (ii) are disallowed, and evolutions in set (iv) are barred from completing an oscillation period by instantaneously transitioning to a new state. This law for quantum physics limits physical scenarios beyond conservation laws, providing causality reasoning by defining a time arrow.

arXiv:2103.07996Mar 14, 20212 citations

Focus: A Quantum Arrow of Time

JR Minkel

Real-world events always proceed in the direction of increasing entropy, even though the laws of physics don’t require it. The reason we never see events that reduce entropy is that they cannot leave behind any evidence of having happened, according to a new theory.

Aug 17, 20090 citations

A Quantum Arrow of Time

JR Minkel

FocusAug 1, 20090 citations

Bridging quantum mechanics and thermodynamics: Irreversible correlations as the arrow of time

Xi Ming, Qing-yu Cai

This work investigates the fundamental connection between quantum mechanics and thermodynamics through the concept of the arrow of time. While the second law of thermodynamics identifies the arrow of time with the monotonic increase of entropy in isolated systems, closed quantum systems evolve unitarily and conserve von Neumann entropy, making the origin of irreversibility less apparent. Here we establish a no-go theorem proving that correlations in unknown states of closed quantum systems cannot be universally removed by any physical operation. This result demonstrates that correlation generation is inherently irreversible, providing a microscopic and universal basis for the arrow of time. In thermodynamic settings, this irreversibility ensures that heat flows spontaneously from hotter to colder subsystems, reproducing the Clausius formulation of the second law. More generally, the irreversible growth of correlations explains entropy increase, the approach to equilibrium, and decoherence as observable manifestations of the same principle. Our findings ground a quantum-mechanical foundation for the second law of thermodynamics and demonstrate the universality of the arrow of time.

Annals of PhysicsDec 3, 20251 citation

Comment on `Quantum Solution to the Arrow-of-Time Dilemma' of L. Maccone arXiv:0802.0438

Oleg Kupervasser, Dimitri N. Laikov

A recent Letter by Maccone presents a solution to the arrow-of-time dilemma based on existing laws of quantum mechanics. He argues that all phenomena where the entropy decreases must not leave any information (in the observer's memory) of their having happened, the observer being a part of the whole system. He concludes that quantum mechanics is necessary to his argument, which he thinks does not otherwise work in classical mechanics. This Comment and the previously published Comment of Jennings, Rudolph describes flaws in Maccone's arguments. However, the main argument (observer's memory erasing) previously formulated in the works by one of us (O.K.) and repeated by Maccone is correct under conditions described in this Comment. Moreover, this argument can be used for resolving a reduction paradox (Schrodinger Cat paradox) in quantum mechanics. In part fourth time arrows synchronization (decohorence) is discussed. In part fifth time arrows synchronization (decohorence) in quantum gravity is discussed. This Comment consists of five parts. The first one is written by Oleg Kupervasser and Dimitri Laikov. The second, third, fourth and fifth ones are written by Oleg Kupervasser only.

Apr 30, 20101 citation