Unlike traditional time crystals, which typically operate within quantum realms and require highly specialized environments, this new variant discovered by the NYU physicists exists at a macroscopic scale, visible to the naked eye. The system consists of millimeter-sized styrofoam beads suspended mid-air by an acoustic levitator—a device that uses standing sound waves to counteract gravity. These beads not only hover gracefully but also interact through scattered sound waves, exchanging forces in a manner that shatters classical physical expectations. What makes this discovery revolutionary is that the interactions between the beads defy Newton’s Third Law of Motion, which stipulates that forces always come in equal and opposite pairs. Instead, these levitated particles move nonreciprocally, meaning the forces they exert on each other are unbalanced, with larger beads influencing smaller ones more than vice versa.

The researchers highlight that the simplicity of their experimental setup belies the profound implications it holds for fundamental physics and potential technological advances. The acoustic levitator chamber stands just under a foot tall, presenting a tangible, accessible system to study the dynamics of time crystals outside the opaque quantum domain. Professor David Grier, director of NYU’s Center for Soft Matter Research and the senior author of the study, emphasizes that this accessible model system paves the way for experimentalists and theoreticians alike to explore phenomena at the intersection of classical mechanics, wave physics, and emergent nonreciprocal behaviors.

Central to this discovery is the mechanism by which the particles interact: the scattering of sound waves. Unlike electromagnetic or mechanical forces, whose action and reaction pairs are symmetrical and balanced, sound waves scattered by particles of different sizes create forces of varying magnitude and direction. Larger beads scatter sound waves more effectively, exerting a stronger influence on smaller beads, which respond with lesser reciprocal force. This asymmetry creates a nonreciprocal interaction matrix where the classic rules of balanced force pairs are transcended, allowing for spontaneous oscillations where the beads collectively “tick” in a coordinated rhythm, forging a classical time crystal.

This acoustic nonreciprocity grants the bead ensemble the capacity to maintain persistent, rhythmic motion without energy dissipation—the hallmark of time crystals. Unlike prior examples that rely heavily on quantum entanglement or complex spin interactions, this classical system reveals that nonreciprocal wave-mediated forces alone are sufficient to originate and sustain time crystal behavior. Such findings hold immense promise, suggesting simpler pathways to harness these effects in practical devices and potentially inspiring new architectures for quantum-inspired computing and sensing technologies.

Moreover, this research offers enlightening parallels to biological systems, particularly our intrinsic circadian rhythms governing daily physiological cycles. Many biochemical networks in living organisms are known to operate via nonreciprocal interactions, coordinating complex processes such as metabolism and cellular repair. The NYU team’s findings underscore how physics principles observed in this acoustically levitated crystal resonate with the foundational rhythms of life itself, opening new interdisciplinary dialogues between physics, biology, and materials science.

The experimental protocol utilized standing sound waves to levitate styrofoam particles, carefully tuning wave frequencies and amplitudes to achieve stable suspension. Once levitated, beads began to interact through continuous scattering of sound, dynamically adjusting their mutual positions within the trapped sound field. A series of high-speed imaging frames captured these evolving oscillations, enabling detailed analysis of the collective modes of the crystal. The results definitively demonstrated the spontaneous breaking of time-translation symmetry—a definitive signature of time crystalline order—under entirely classical and macroscopic conditions.

The theoretical underpinnings draw from non-Hermitian physics and active matter frameworks where dissipative processes and nonreciprocal interactions enable new steady-states far from equilibrium. By exploiting acoustic wave scattering, the NYU team has shown that time crystal order does not necessitate quantum ground states or isolation at ultracold conditions, but can arise naturally from classical wave-mediated forces that break reciprocal symmetry. This insight renders the discovery a paradigmatic shift, broadening the landscape of time crystals beyond the confines of exotic quantum materials.

Taken together, these findings mark a new chapter in our understanding of nonequilibrium phases of matter. The implications extend beyond fundamental science, foreshadowing applications that range from advanced metamaterials with programmable mechanical responses to robust time-keeping devices inspired by classical oscillators. The ability to visualize, manipulate, and control time crystal behavior at macroscopic scales could accelerate innovation in precision timing technologies and potentially new paradigms of information processing that leverage wave-mediated interactions.

The study was made possible through support from the U.S. National Science Foundation and represents a collaborative effort involving graduate student Mia Morrell and undergraduate Leela Elliott under the leadership of Professor Grier. Their combined experimental expertise and theoretical insight achieved a milestone, demonstrating that time crystals are not strictly artifacts of quantum mechanics but can be accessible in real-world classical systems through creative harnessing of sound-mediated interactions.

The research was published in the prestigious journal Physical Review Letters, presenting both experimental data and theoretical context that support the formation of nonreciprocal wave-mediated classical time crystals. This work inspires renewed investigation into acoustic metamaterials, topological wave physics, and active matter, as well as potential translation into technology sectors focused on quantum simulation, nonreciprocal devices, and biomimetic systems.

With fundamental physics entering an era where classical and quantum domains interlace through the language of waves and symmetry-breaking, this discovery of an acoustically levitated time crystal heralds exciting new possibilities. As research accelerates, the interplay of sound, motion, and nonreciprocal forces is poised to reveal deeper insights into the fabric of time-dependent order and to inspire technologies that keep pace with the rhythmic precision of nature itself.

Subject of Research: Physics – Classical and Quantum Time Crystals, Nonreciprocal Wave-Mediated Interactions, Acoustic Levitation

Article Title: Nonreciprocal Wave-Mediated Interactions Power a Classical Time Crystal

News Publication Date: 6 February 2026

Web References: DOI: 10.1103/zjzk-t81n

References: Physical Review Letters (Journal)

Image Credits: NYU’s Center for Soft Matter Research

Keywords

Crystals, Particle physics, Condensed matter physics, Time crystals, Acoustic levitation, Nonreciprocal interactions, Wave-mediated forces, Classical time crystal, Symmetry-breaking, Active matter, Physics experiments

Recently, a pioneering team at TU Wien has addressed a longstanding enigma surrounding these discrepancies. Delving deep into computational quantum chemistry, the researchers identified a surprising source of error: the once-revered coupled-cluster method, widely regarded as the gold standard for predicting molecular interactions, systematically overestimates the binding energies in large, highly polarizable molecules. This discovery emerged after careful comparison with quantum Monte Carlo simulations, an alternative approach that probabilistically explores possible electron configurations to identify energetically favorable states.

Quantum Monte Carlo methods operate by sampling a vast landscape of electron arrangements, retaining those that minimize the overall energy. This stochastic approach, although computationally expensive, is renowned for its accuracy and has served as a benchmark for validating less demanding techniques. Conversely, the coupled-cluster method approximates electron correlation by starting from a low-energy reference state and incrementally adding corrections from higher-energy configurations. While this method offers high accuracy and greater computational efficiency, subtle deviations from Monte Carlo results had long puzzled scientists.

The breakthrough by TU Wien’s team, led by Tobias Schäfer, Andreas Irmler, Alejandro Gallo, and Prof. Andreas Grüneis, stemmed from a meticulous analysis of these deviations. They established that the coupled-cluster’s overestimation of binding energies was systemic, particularly pronounced in larger molecules where electron polarizability and collective effects become significant. To correct this, the team developed an enhanced variant of the coupled-cluster approach that fine-tunes the treatment of electron correlation in such complex systems. Notably, this refinement achieves improved accuracy aligning closely with Monte Carlo results without imposing prohibitive computational costs.

Accurately capturing van der Waals forces in large molecules is far from an academic exercise; it is imperative for the investigation of biological systems, materials engineering, and the ever-expanding frontier of renewable energy technologies. Molecules comprising dozens or even hundreds of atoms challenge computational resources due to the exponential growth of possible electron configurations. As Alejandro Gallo points out, even cutting-edge supercomputers reach practical limits, necessitating approximation methodologies that balance precision and scalability.

The implications of this advancement are vast. In pharmaceutical science, for example, understanding how drugs crystallize and how molecules interact within complex matrices influences efficacy and stability. Similarly, in materials research, the accurate prediction of molecular interactions underpins the design of nanostructures and energy storage solutions, such as hydrogen adsorption materials critical for future fuels. Van der Waals forces, although relatively weak compared to covalent bonds, dictate many essential supramolecular assemblies and phase behaviors, making their precise computation indispensable.

Beyond traditional computational chemistry, the enhanced coupled-cluster variant paves the way for improved training data feeding artificial intelligence models. These AI systems increasingly assist in predicting molecular properties and behavior, accelerating the discovery of novel materials and therapeutics by screening vast chemical landscapes virtually. Reliable quantum chemistry data remain foundational for calibrating these models, ensuring their predictions translate faithfully to real-world behavior.

This new breakthrough exemplifies the dynamic nature of scientific progress, where even established “gold standard” methods must be continually scrutinized as research demands grow in complexity and precision. Prof. Andreas Grüneis emphasizes that bridging the gap between ultimate theoretical accuracy and practical usability unlocks fresh potentials for innovation. The TU Wien group’s findings remind the scientific community of the necessity to reassess foundational tools regularly, fostering methodological evolution alongside technological advances.

In essence, this work refines one of the central pillars of computational chemistry, enhancing our ability to simulate molecular interactions across diverse disciplines. The corrected coupled-cluster approach not only reconciles longstanding computational discrepancies but also fortifies the predictive frameworks that underpin modern scientific discovery. As molecular systems scale up in size and function, such methodological breakthroughs will be increasingly essential to decode nature’s complexities and engineer solutions addressing global challenges.

The future of molecular modeling now appears brighter. With improved tools to understand van der Waals forces accurately, researchers can push the limits of material design and drug development with greater confidence. As computational methods converge in precision and efficiency, the interplay between theory, simulation, and experiment will deepen, driving innovation in ways previously constrained by computational uncertainties. TU Wien’s contribution stands as a pivotal step in this transformative journey.

Subject of Research: Computational Methods for Modeling Van der Waals Interactions in Large Molecular Systems
Article Title: Understanding discrepancies in noncovalent interaction energies from wavefunction theories for large molecules
News Publication Date: 14-Oct-2025
Web References: https://doi.org/10.1038/s41467-025-64104-8
Image Credits: TU Wien

Keywords

Van der Waals forces, quantum chemistry, coupled-cluster method, quantum Monte Carlo, molecular interactions, computational chemistry, electron correlation, molecular modeling, large molecules, materials science, pharmaceutical development, renewable energy