In 2012, the Nobel laureate Frank Wilczek proposed a radical idea: a crystal that repeats not just in space but in time, a phase of matter that spontaneously develops periodic motion, like a pendulum that never stops, without being periodically pushed. The idea was met with intense theoretical scrutiny, and for years it seemed that Wilczek’s “time crystal” might be impossible in thermal equilibrium. But a remarkable series of experiments since 2017 has proven otherwise, first with discrete time crystals in trapped ions and later with continuous time crystals in atom-cavity systems.
Now, researchers at Shanghai Jiao Tong University have taken the next step: they have built a macroscopic, classical spacetime crystal visible to the naked eye, and, for the first time, watched it melt.
The experiment, published in PNAS and led by Matteo Baggioli and Jie Zhang, involves roughly 10,000 3D-printed disk-shaped particles, each the size of a large coin (8.8 millimeters in diameter), sitting on a vibrating aluminum plate about 50 centimeters (20 inches) across. Each particle has six alternately inclined legs, like a tiny rotor, and a marker dot for tracking orientation. When the plate vibrates at 100 Hz (an acceleration of roughly 3 times Earth’s gravity), collisions between the tilted legs and the plate generate active forces that set the particles in motion.
At high density, something extraordinary happens: all 10,000 particles spontaneously synchronize into a single, coherent, rigid-body rotation with a period of approximately 4.7 to 5.5 hours, about six orders of magnitude slower than the 100-Hz drive. The system has spontaneously broken continuous time-translation symmetry: it has chosen a rhythm of its own. The Fourier spectrum shows a sharp peak at roughly 5.5 × 10⁻⁵ Hz, confirming genuine periodic temporal order. The rotation persists for nearly a day, limited only by the apparatus, and survives strong acoustic noise injection. In control experiments with seven smaller replicas, the onset times and rotation directions were random, confirming the spontaneous nature of the ordering.
The three-stage unravelling
The central insight of the paper comes from what happens when the researchers reduce the particle density. By slowly removing particles from the plate (decreasing the packing fraction), they watched the spacetime crystal melt through three distinct stages, a progression never before observed in any spacetime crystal system.
In the first stage, at a packing fraction of about 0.734, the system enters what the researchers call “T-coexistence.” The temporal (time-crystalline) order begins to break down: some regions of the plate continue to rotate coherently while others become time-disordered. Meanwhile, the spatial lattice has already melted from a crystal into a hexatic phase, a state with quasi-long-range orientational order but only weak translational order, a familiar intermediate in the classic two-dimensional melting theory of Kosterlitz, Thouless, Halperin, Nelson, and Young.
In the second stage, at a packing fraction of about 0.709, temporal order is completely lost; no coherent rotation remains. Now spatial order begins its own breakdown, entering what the team calls “S-coexistence”: hexatic domains and fluid domains coexist on the plate.
In the third stage, below a packing fraction of 0.687, all spatial order vanishes, and the system becomes an isotropic fluid of particles undergoing random Brownian motion.
“The most striking finding is that spatial and temporal order decouple, they melt through completely different mechanisms,” said co-first author Guoqing Liu. “The temporal order is destroyed by loss of directional persistence as many-body interactions weaken, while the spatial order goes through the classic KTHNY defect-mediated melting scenario.”
Why this matters
The experiment provides the first complete experimental phase diagram of a spacetime crystal. Prior work had focused on realizing these exotic states of matter; no one had systematically studied how they fall apart.
The decoupling of spatial and temporal symmetry breaking is a fundamental physical insight. It suggests that spacetime crystals, despite their name, are not unitary objects whose order stands and falls together. The two kinds of periodicity, in space and in time, are underpinned by separate physical mechanisms and can be destroyed independently.
“This is a classical system, not a quantum one,” Baggioli noted. “But the principle of symmetry breaking is universal. The fact that we can observe these effects in a tabletop experiment with 3D-printed parts is remarkable.”
The work also opens a new direction: the study of temporal analogs to well-known spatial phases. The hexatic phase, for instance, has a temporal counterpart, a “time hexatic,” that may be observable in the T-coexistence region. The concept of phase diagrams for spacetime crystals is now a concrete experimental pursuit rather than a theoretical abstraction.
A few caveats are worth noting. The rotation in the system is always counterclockwise, an artifact of a small experimental imperfection rather than true spontaneous chirality breaking. The system is a classical, driven, nonequilibrium steady state, it is not a quantum time crystal of the type Wilczek originally envisioned. And the specific melting scenario may depend on the details of the granular system’s dissipation and driving mechanisms.
Nevertheless, the experiment demonstrates that a classical spacetime crystal can be built, observed, and systematically taken apart, a feat that would have seemed like science fiction when Wilczek first proposed the concept 14 years ago.
Source: Liu, G., Bai, J., Baggioli, M. & Zhang, J. “Three-stage melting of a macroscopic continuous spacetime crystal.” PNAS 123(27), e2613063123 (2026). DOI: 10.1073/pnas.2613063123