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arXiv:1304.7850 · Frontiers in Science

Comment on “Entanglement and the Thermodynamic Arrow of Time” and Correct Reply on “Comment on "Quantum Solution to the Arrow-of-Time Dilemma"” of David Jennings and Terry Rudolph

Kupervasser Oleg

Published Jan 7, 2013• 7 citations
arXivHTMLPDF

Abstract

Recently David Jennings and Terry Rudolph published two papers as reaction on Maccone’s paper Quantum Solution to the Arrow-of-Time Dilemma. In these papers, the authors suppose that second law of thermodynamics is not relevant for quantum systems. Unfortunately, these papers did not get relevant reply from Maccone. The reason of this is following. Both Maccone and the above-mentioned authors use thermodynamic law and thermodynamic-like terminology for non-thermodynamic systems, for example, microscopic system of three qubits. However, big size of a system (quantum or classic) is also not an enough condition for a system to be macroscopic. The macroscopic system must also be chaotic and has small chaotic interaction with its environment/observer resulting in decoherence (decorrelation). We demonstrate that for relevant thermodynamic macroscopic quantum systems no objection appears.

DOI
10.5923/j.fs.20120206.13

Related papers

"New Cybernetics and the Application of its Principles in Physics" and "Comment on "Quantum Solution to the Arrow-of-Time Dilemma" of L. Maccone arXiv:0802.0438"

Oleg Kupervasser, Dimitri N. Laikov

The first paper: We describe principles of new cybernetics and use these principles for resolution of basic physical paradoxes. It demonstrates universality of the principles of new cybernetics. The second paper: recent letter by Maccone presents a solution based on the existing laws of quantum mechanics to the arrow-of-time dilemma. He argues that all phenomena in which the entropy decreases must not leave any information (in the observer's memory) of their having occurred because the observer is a part of the whole system. Maccone concludes that quantum mechanics is necessary to his argument, which he believes does not otherwise work in classical mechanics. This Comment consists of four parts. We discuss the basic problems in the first part. This Comment and the previously published Comment by Jennings and Rudolph describes flaws in Maccone's arguments. However, the main argument (erasure of the observer's memory), which was previously formulated in our work and was repeated by Maccone, is correct under the conditions described in this Comment. Moreover, this argument can be used to resolve a reduction paradox (the Schrodinger's Cat paradox) in quantum mechanics. This use is demonstrated in the second part. In the third part, the synchronisation (decoherence) of time arrows is discussed. In the fourth part, the synchronisation (decoherence) of time arrows in quantum gravity is considered.

arXiv:0911.2610•Nov 13, 2009•2 citations

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, 2010•1 citation

A quantum solution to the arrow-of-time dilemma: reply

Lorenzo Maccone

I acknowledge a flaw in the paper "A quantum solution to the arrow of time dilemma": as pointed out by Jennings and Rudolph, (classical) mutual information is not an appropriate measure of information. This can be traced back to the quantum description underlying my analysis, where quantum mutual information is the appropriate measure of information. The core argument of my paper (summarized in its abstract) is not affected by this flaw. Nonetheless, I point out that such argument may not be adequate to account for all phenomena: it seems necessary to separately postulate a low entropy initial state.

arXiv:0912.5394•Dec 30, 2009•3 citations

The Universal Arrow of Time II: Quantum mechanics case

Oleg Kupervasser

This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum mechanics is even a little bit easier: all closed systems of finite volume are periodic or nearly periodic. The proof in quantum mechanics is in many respects similar to the proof in classical Hamilton mechanics - it also uses small interaction between subsystems and impossibility to observe entropy decrease at introspection. However, there are special cases which were not found in the classical mechanics. In these cases one microstate corresponds to a set of possible macrostates (more precisely, their quantum superposition). Consideration of this property with use of decoherence theory and taking into account thermodynamic time arrows will introduce new outcomes in quantum mechanics. It allows to resolve basic paradoxes of quantum mechanics: (a) to explain the paradox of wave packet reduction at measurements when an observer is included in the system (introspection) (paradox of the Schrodinger cat); (b) to explain unobservability of superposition of macroscopic states by an external observer in real experiments (paradox of Wigner's friend); (c) to prove full equivalence of multi-world and Copenhagen interpretations of quantum mechanics; (d) to explain deviations from the exponential law at decay of particles and pass from one energy level to another (paradox of a kettle which will never begin to boil).

arXiv:1106.6160•Jun 30, 2011•3 citations

Comment on "Quantum Solution to the Arrow-of-Time Dilemma"

Hrvoje Nikolić

In this paper we criticize the attempt of Maccone [Phys. Rev. Lett. 103, 080401 (2009), arXiv:0802.0438] to solve the problem of the arrow of time.

arXiv:0912.1947•Dec 10, 2009•1 citation

Quantum chaos and the arrow of time

Nilakash Sorokhaibam

We show that quantum chaotic many-body systems possess the thermodynamic arrow of time in the thermodynamic limit. Berry's conjecture in quantum chaotic systems and equivalence of ensembles imply the Kelvin statement of the second law of thermodynamics at leading order in perturbation theory. We verify this result using numerical calculations. We also show that this gives rise to new constraints on the off-diagonal terms in eigenstate thermalization hypothesis (ETH) statement. We call the new constraints collectively as ETH-monotonicity. These constraints arise because pure entropic consideration is not enough for the emergence of the thermodynamic arrow of time.

arXiv:2212.03914•Dec 7, 2022•0 citations
Recently David Jennings and Terry Rudolph published two papers as reaction on Maccone’s paper Quantum Solution to the Arrow-of-Time Dilemma. In these papers, the authors suppose that second law of thermodynamics is not relevant for quantum systems. Unfortunately, these papers did not get relevant reply from Maccone. The reason of this is following. Both Maccone and the above-mentioned authors use thermodynamic law and thermodynamic-like terminology for non-thermodynamic systems, for example, microscopic system of three qubits. However, big size of a system (quantum or classic) is also not an enough condition for a system to be macroscopic. The macroscopic system must also be chaotic and has small chaotic interaction with its environment/observer resulting in decoherence (decorrelation). We demonstrate that for relevant thermodynamic macroscopic quantum systems no objection appears.
The first paper: We describe principles of new cybernetics and use these principles for resolution of basic physical paradoxes. It demonstrates universality of the principles of new cybernetics. The second paper: recent letter by Maccone presents a solution based on the existing laws of quantum mechanics to the arrow-of-time dilemma. He argues that all phenomena in which the entropy decreases must not leave any information (in the observer's memory) of their having occurred because the observer is a part of the whole system. Maccone concludes that quantum mechanics is necessary to his argument, which he believes does not otherwise work in classical mechanics. This Comment consists of four parts. We discuss the basic problems in the first part. This Comment and the previously published Comment by Jennings and Rudolph describes flaws in Maccone's arguments. However, the main argument (erasure of the observer's memory), which was previously formulated in our work and was repeated by Maccone, is correct under the conditions described in this Comment. Moreover, this argument can be used to resolve a reduction paradox (the Schrodinger's Cat paradox) in quantum mechanics. This use is demonstrated in the second part. In the third part, the synchronisation (decoherence) of time arrows is discussed. In the fourth part, the synchronisation (decoherence) of time arrows in quantum gravity is considered.
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.
I acknowledge a flaw in the paper "A quantum solution to the arrow of time dilemma": as pointed out by Jennings and Rudolph, (classical) mutual information is not an appropriate measure of information. This can be traced back to the quantum description underlying my analysis, where quantum mutual information is the appropriate measure of information. The core argument of my paper (summarized in its abstract) is not affected by this flaw. Nonetheless, I point out that such argument may not be adequate to account for all phenomena: it seems necessary to separately postulate a low entropy initial state.
This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum mechanics is even a little bit easier: all closed systems of finite volume are periodic or nearly periodic. The proof in quantum mechanics is in many respects similar to the proof in classical Hamilton mechanics - it also uses small interaction between subsystems and impossibility to observe entropy decrease at introspection. However, there are special cases which were not found in the classical mechanics. In these cases one microstate corresponds to a set of possible macrostates (more precisely, their quantum superposition). Consideration of this property with use of decoherence theory and taking into account thermodynamic time arrows will introduce new outcomes in quantum mechanics. It allows to resolve basic paradoxes of quantum mechanics: (a) to explain the paradox of wave packet reduction at measurements when an observer is included in the system (introspection) (paradox of the Schrodinger cat); (b) to explain unobservability of superposition of macroscopic states by an external observer in real experiments (paradox of Wigner's friend); (c) to prove full equivalence of multi-world and Copenhagen interpretations of quantum mechanics; (d) to explain deviations from the exponential law at decay of particles and pass from one energy level to another (paradox of a kettle which will never begin to boil).
We show that quantum chaotic many-body systems possess the thermodynamic arrow of time in the thermodynamic limit. Berry's conjecture in quantum chaotic systems and equivalence of ensembles imply the Kelvin statement of the second law of thermodynamics at leading order in perturbation theory. We verify this result using numerical calculations. We also show that this gives rise to new constraints on the off-diagonal terms in eigenstate thermalization hypothesis (ETH) statement. We call the new constraints collectively as ETH-monotonicity. These constraints arise because pure entropic consideration is not enough for the emergence of the thermodynamic arrow of time.