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Demystifying arrow of time

Zura Kakushadze

Published Aug 27, 2024• 1 citation
Publisher

Abstract

Demystifying arrow of time. / Z. Kakushadze. Nano Studies. – 2023–2024. – # 23/24. – pp. 99-118. – eng. Scientific discussions of the arrow of time often get quite confusing due to highly complex systems they deal with. Popular literature then often coveys messages that tend to get lost in translation. The purpose of this note is to demystify the arrow of time by stripping off the unnecessary complexities and thereby simplifying the discussion. We do this by providing examples that are exactly solvable and make it easy to see the root cause of the apparent “time-irreversibility”. We also discuss “time-reversal” solutions, where the initial state evolves such that it reaches the state which is the same as the initial state moving backward in time. These solutions are simple enough to be comprehensible to a highschooler. We discuss the arrow of time both in the classical and quantum settings, including in the cosmological context. Ref. 51.

DOI
10.52340/ns.2022.23.24.06

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Demystifying arrow of time. / Z. Kakushadze. Nano Studies. – 2023–2024. – # 23/24. – pp. 99-118. – eng. Scientific discussions of the arrow of time often get quite confusing due to highly complex systems they deal with. Popular literature then often coveys messages that tend to get lost in translation. The purpose of this note is to demystify the arrow of time by stripping off the unnecessary complexities and thereby simplifying the discussion. We do this by providing examples that are exactly solvable and make it easy to see the root cause of the apparent “time-irreversibility”. We also discuss “time-reversal” solutions, where the initial state evolves such that it reaches the state which is the same as the initial state moving backward in time. These solutions are simple enough to be comprehensible to a highschooler. We discuss the arrow of time both in the classical and quantum settings, including in the cosmological context. Ref. 51.
Scientific discussions of the arrow of time often get quite confusing due to highly complex systems they deal with. Popular literature then often coveys messages that tend to get lost in translation. The purpose of this note is to demystify the arrow of time by stripping off the unnecessary complexities and thereby simplifying the discussion. We do this by providing examples that are exactly solvable and make it easy to see the root cause of the apparent "time-irreversibility". We also discuss "time-reversal" solutions, where the initial state evolves such that it reaches the state which is the same as the initial state moving backward in time. These solutions are simple enough to be comprehensible to a highschooler. We discuss the arrow of time both in the classical and quantum settings, including in the cosmological context.
The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory showirreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility?
Uncovering the origin of the arrow of time remains a fundamental scientifc challenge. Within the framework of statistical physics, this problem was inextricably associated with the Second Law of Thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. It remains to be seen, however, whether the irreversibility of time is a fundamental law of nature or whether, on the contrary, it might be circumvented. Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.
Uncovering the origin of the arrow of time remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the second law of thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. It remains to be seen, however, whether the irreversibility of time is a fundamental law of nature or whether, on the contrary, it might be circumvented. Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.
Uncovering the origin of the "arrow of time" remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the Second Law of Thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. This poses a question of whether it is possible to develop protocols for circumventing the irreversibility of time and if so to practically implement these protocols. Here we show that, while in nature the complex conjugation needed for time reversal may appear exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.
Abstract For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time-symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time-reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time-reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversing a time arrow for a given quantum state on the IBM quantum computer. However, the implemented arrow-of-time reversal embraced only the known states initially disentangled from the thermodynamic reservoir. Here we develop a procedure for reversing the temporal evolution of an arbitrary unknown quantum state. This opens the route for general universal algorithms sending temporal evolution of an arbitrary system backward in time.