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Revista Brasileira de Ensino de Física

Entanglement and the ticking of the clock

Andrea Valdés-Hernández, C. G. Maglione, A. P. Majtey, Angel Ricardo Plastino

Published Jan 1, 2020• 1 citation
Publisher

Abstract

The concept of entanglement is at the heart of quantum physics.It plays a central role in all quantum phenomena involving composite systems.Interestingly, there is an intriguing idea that has attracted considerable attention recently, according to which quantum entanglement may also be essential for understanding the very emergence of time and dynamical evolution.Within this point of view, sometimes referred to as the timeless picture of quantum dynamics, the Universe is regarded as consisting of a clock and a system (or "rest of the Universe") that are jointly in a stationary quantum state, and time evolution arises as an emergent phenomenon rooted at the entanglement between the clock and the system.Here we provide a pedagogical and self-contained exposition, at the upper undergraduate level, of the role of entanglement in this timeless evolution approach to quantum mechanics.In particular, we give a detailed explanation of how the entanglement between the clock and the system is directly and quantitatively related to the average distinguishability between the states of the system at different times.

DOI
10.1590/1806-9126-rbef-2019-0313

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The concept of entanglement is at the heart of quantum physics.It plays a central role in all quantum phenomena involving composite systems.Interestingly, there is an intriguing idea that has attracted considerable attention recently, according to which quantum entanglement may also be essential for understanding the very emergence of time and dynamical evolution.Within this point of view, sometimes referred to as the timeless picture of quantum dynamics, the Universe is regarded as consisting of a clock and a system (or "rest of the Universe") that are jointly in a stationary quantum state, and time evolution arises as an emergent phenomenon rooted at the entanglement between the clock and the system.Here we provide a pedagogical and self-contained exposition, at the upper undergraduate level, of the role of entanglement in this timeless evolution approach to quantum mechanics.In particular, we give a detailed explanation of how the entanglement between the clock and the system is directly and quantitatively related to the average distinguishability between the states of the system at different times.
Entanglement is at the core of quantum physics, playing a central role in quantum phenomena involving composite systems. According to the timeless picture of quantum dynamics, entanglement may also be essential for understanding the very origins of dynamical evolution and the flow of time. Within this point of view, the Universe is regarded as a bipartite entity comprising a clock CCC and a system RRR (or ``rest of the Universe'') jointly described by a global stationary state, and the dynamical evolution of RRR is construed as an emergent phenomena arising from the entanglement between CCC and RRR. In spite of substantial recent efforts, many aspects of this approach remain unexplored, particularly those involving mixed states. In the present contribution we investigate the timeless picture of quantum dynamics for mixed states of the clock-system composite, focusing on quantitative relations linking the clock-system entanglement with the emerging dynamical evolution experienced by the system.
In quantum theory it is possible to explain time, and dynamics, in terms of entanglement. This is the timeless approach to time, which assumes that the universe is in a stationary state, where two noninteracting subsystems, the ``clock'' and the ``rest,'' are entangled. As a consequence, by choosing a suitable observable of the clock, the relative state of the rest of the universe evolves unitarily with respect to the variable labeling the clock observable's eigenstates, which is then interpreted as time. This model for an ``evolution without evolution'' (Page and Wootters, 1983), albeit elegant, has never been developed further, because it was criticized for generating severe ambiguities in the dynamics of the rest of the universe. In this paper we show that there are no such ambiguities; we also update the model, making it amenable to possible new applications.
Time, space and entanglement are the main characters in this work. Their nature is still a great mystery in physics and we study here the possibility that these three phenomena are closely connected, showing how entanglement can be at the basis of the emergence of time and space within closed quantum systems. We revisit and extend the Page and Wootters theory that was originally introduced in order to describe the emergence of time through entanglement between subsystems in a globally static, quantum Universe. In the book, after providing a complete review of the salient aspects of the theory, we establish a connection with recent research on the foundations of statistical mechanics and we propose a new understanding of the thermalization process. Furthermore, we generalize the framework in order describe the spatial degree of freedom and we provide a model of 3+1 dimensional, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe. Finally, via the Page and Wootters theory, the evolution of quantum clocks within a gravitational field is treated and a time dilation effect is obtained in agreement with the Schwarzschild solution.
Abstract Dynamical evolution can be reconstructed within stationary, closed quantum systems by employing the Page-Wootters “timeless approach”. When conditioning upon the state of a “clock” subsystem, the rest of the system regains its time dependence. This mechanism, involving entanglement between the above subsystems has gained much attention during the last few years. After a brief introduction to the topic we will elaborate on a few recent results: The derivation of new time-energy uncertainty relations, emergence of non-Hermitian dynamics when utilizing non-inertial quantum clocks and dynamical nonlocality in quantum time.
Quantum entanglement, a bizarre phenomenon where two or more particles become linked in such a way that they share the same fate, remains one of the most intriguing and debated aspects of quantum mechanics. This research investigates a novel theoretical framework designed to quantitatively analyze the time scale of entanglement propagation, ultimately providing insights into the fundamental nature of this phenomenon and its potential applications across diverse fields. We propose a 'Quantum Entanglement Time Scale' (QET) concept, predicated on the observation of entanglement's propagation as a measurable phenomenon, allowing for precise predictions regarding its temporal evolution. The core mechanism involves a dynamic model integrating quantum measurement and entanglement dynamics, aiming to quantify the rate at which entangled particles can diverge. This work explores the implications of this model for understanding and potentially controlling entanglement, pushing beyond current theoretical limitations and offering a path toward more predictable quantum interactions.
Entanglement of quantum systems refers to the situation where two or more systems interact and the state of the whole system cannot be seen as a superposition of states of the single systems. This feature of quantum dynamics is crucial in many algorithms of quantum communication and quantum information processing and it is a resource for many fascinating applications. Moreover entanglement, as a feature of quantum mechanics, has stimulated in-depth investigation on the value of quantum mechanics itself as a physical theory.