Friction Arises from How Quickly We Measure Quantum Systems

Seiki Saito, from Yamagata University, and colleagues reveal a data-driven framework demonstrating that macroscopic friction does not originate as an inherent property of isolated quantum systems. Friction emerges as a consequence of temporal coarse-graining, or the observer’s timescale for measurement. Utilising the XXZ spin chain model, the framework establishes a key link between microscopic reversibility and macroscopic transport phenomena, highlighting how finite observational resolution dictates the appearance of dissipation and viscosity. Understanding this relationship is crucial for bridging the gap between the deterministic laws governing quantum mechanics and the seemingly irreversible behaviour observed in everyday macroscopic phenomena. The implications extend to diverse fields, including materials science, condensed matter physics, and even our fundamental understanding of thermodynamics.

Extracting governing equations from data using low-dimensional Galerkin projections

Generalised Extended Dynamic Mode Decomposition, or gEDMD, is a powerful data analysis technique akin to identifying repeating patterns within a complex musical piece to reveal its underlying structure. It extracts governing equations directly from experimental data, circumventing traditional modelling approaches by constructing a low-dimensional representation of the system’s behaviour and focusing on key observable quantities. Unlike conventional methods that rely on pre-defined assumptions about the system’s dynamics, gEDMD allows the equations governing the system to emerge directly from the data itself. Galerkin projection, a mathematical tool central to gEDMD, simplifies complex systems by concentrating on observable elements, similar to blurring a detailed photograph to highlight the main subject. This projection technique effectively filters out irrelevant high-frequency modes, reducing the computational cost and improving the clarity of the extracted dynamics. Dr. Peter Zulian and Dr. Samuel Rowley employed gEDMD alongside the Mori-Zwanzig projection to analyse a chaotic XXZ spin-1/2 chain; this system comprised a one-dimensional chain with nearest and next-nearest neighbour interactions defined by parameters J=1.0, ∆=1.0, and J2=0.5. These parameters define the strength of the interactions between spins, influencing the system’s overall behaviour and the emergence of collective phenomena. A random complex vector representing an unpolarised, infinite-temperature ensemble was initialised with a time step of dt for the simulation. The choice of an infinite-temperature ensemble ensures that all possible initial states are equally probable, providing a statistically robust basis for the analysis. This approach avoids mathematical ambiguities inherent in standard Extended Dynamic Mode Decomposition and its reliance on the matrix logarithm, offering a data-driven alternative. The standard EDMD method can be sensitive to noise and numerical errors due to the logarithm operation; gEDMD circumvents this issue by directly extracting the governing equations from the data without relying on this potentially problematic step. The Mori-Zwanzig projection is a crucial component, allowing for the systematic elimination of unobserved degrees of freedom and focusing the analysis on the relevant observables.

Emergent friction and kinematic viscosity linked to observation timescale

A finite observation timescale of Δtcg > 0 was required for macroscopic friction in an isolated quantum system to transition from zero dissipation to positive values, a threshold previously considered insurmountable. This finding challenges the conventional understanding of friction as an inherent property of materials and suggests that it is, instead, a consequence of how we measure the system. Before this point, the system exhibited rapid oscillations around zero, preventing the establishment of genuine macroscopic transport, although elasticity remained intrinsically linked to the system’s unitary dynamics. These rapid oscillations represent the underlying quantum fluctuations that are present even in the absence of external forces. The timescale Δtcg represents the minimum time interval over which the system is observed; if this interval is sufficiently short, the oscillations average out to zero, resulting in zero net dissipation. This data-driven framework reveals that friction and kinematic viscosity are not inherent properties, but emerge from the observer’s temporal resolution. Kinematic viscosity, a measure of a fluid’s resistance to flow, is similarly linked to the observation timescale, indicating that even the transport properties of materials are influenced by the limits of our measurement capabilities.

Mechanical elasticity, represented as c², arises directly from the system’s exact unitary dynamics, maintaining microscopic reversibility. Unitary dynamics ensures that the total probability is conserved, meaning that the system evolves in a deterministic and reversible manner. The analysis of the XXZ spin chain revealed that both friction (γ) and viscosity (ν) initially oscillate rapidly around zero, demonstrating zero net dissipation before any observation timescale is applied. This confirms that, at the microscopic level, the system is not inherently dissipative. Applying a finite observation timescale of Δtcg > 0 allowed the team to pinpoint a crossover point where these oscillations averaged out, establishing positive values for both friction and viscosity. This crossover point represents the threshold at which the observer’s temporal resolution becomes significant enough to detect the emergent friction and viscosity. Genuine macroscopic transport requires this temporal coarse-graining; without it, the system remains in a state of reversible fluctuation. These findings currently focus on a specific chaotic XXZ spin chain model, and further investigation is needed to determine how readily these principles translate to more complex, real-world materials or larger systems. Exploring different materials and system sizes will be crucial for establishing the generality of these findings and their applicability to a wider range of physical phenomena.

Quantum friction emerges as a consequence of measurement limitations

Scientists have long sought to understand how friction arises in isolated quantum systems, a puzzle central to reconciling the microscopic world of reversible physics with the macroscopic realm of irreversible change. This new work offers a compelling, data-driven explanation, demonstrating that friction isn’t a fundamental property, but emerges with observation. It is still important to acknowledge that some physicists maintain a belief in inherent, fundamental irreversibility at the quantum level; this research does not disprove such a principle, but shifts the focus to how we observe it. By demonstrating that friction arises from the limits of our measurement, Dr. Zulian and Dr. Rowley gain a powerful new set of tools for modelling complex quantum systems and understanding energy transfer within them. The ability to accurately model energy transfer is critical for developing new technologies in areas such as energy harvesting and quantum computing.

Macroscopic friction does not pre-exist within isolated quantum systems, but instead arises from the timescale at which observers monitor them. Explicit examination of spin currents revealed a fundamental distinction between elasticity, directly linked to the system’s inherent dynamics, and friction, which requires a finite observation period to emerge. Without applying a minimum observation timescale, Δtcg > 0, systems exhibit reversible fluctuations, preventing the establishment of genuine macroscopic transport. This research provides a new perspective on the nature of irreversibility, suggesting that it is not an intrinsic property of the universe, but rather a consequence of the limitations of our observational capabilities. Further research could explore the implications of this finding for our understanding of the arrow of time and the foundations of statistical mechanics.

The research demonstrated that macroscopic friction does not exist as an inherent property within isolated quantum systems. Instead, friction emerges as a consequence of the finite temporal resolution used when observing these systems, requiring an observation timescale greater than zero. Elasticity, however, is intrinsically linked to the system’s underlying unitary dynamics and preserves microscopic reversibility. The authors extracted these findings from analysis of a chaotic XXZ spin chain using a data-driven framework integrating generalized Extended Dynamic Mode Decomposition with the Mori-Zwanzig projection.