The phenomenon we witness every day when ice melts into water is a one-directional process in which the orderly atomic arrangement of a crystal is disrupted by thermal energy and transitions into a disordered fluid. In the change from solid to liquid, the spatial order that the substance once held appears to be lost all at once. However, the universe also contains a strange state of matter that does not follow this common-sense rule—one in which the symmetries of time and space are relinquished at entirely separate moments and through entirely separate mechanisms. This is the non-equilibrium phase of matter known as the "space-time crystal."
A research team from Shanghai Jiao Tong University in China, with Guoqing Liu and Jimin Bai serving as co-first authors and Matteo Baggioli and Jie Zhang as corresponding authors, has created a classical space-time crystal using a tabletop-sized experimental apparatus. The team achieved the world's first direct observation of the melting phenomenon in which this exotic phase of matter loses its structural order, and they revealed that the process unfolds not in a single step but through three distinct stages. Published in the Proceedings of the National Academy of Sciences (PNAS) of the United States, this discovery sheds new light on the concept of phase transitions that physicists have pursued for over half a century.
What Makes This Fundamentally Different from Ice Turning into Water
In ordinary physics, the word "crystal" refers not only to beautiful, light-refracting minerals like quartz and diamond, but more broadly to any state in which atoms or molecules form a regular three-dimensional lattice in space. The property whereby the structure at any given position perfectly overlaps with that at any other position is described as "broken spatial translational symmetry," and it forms a fundamental pillar supporting the world of equilibrium thermodynamics. For decades, physicists have pursued the question of how this spatial crystalline order is lost through melting.
Notably, in the 1970s, physicists John Kosterlitz, David Thouless, Bertrand Halperin, David Nelson, and Robert Young proposed the KTHNY theory, which posits that the melting of a crystal in a two-dimensional plane proceeds through a process of up to two stages, sandwiching an intermediate phase called the "hexatic phase." This theory vividly explained how defects in crystal structure proliferate due to thermal fluctuations, and it later became part of the work recognized by the Nobel Prize in Physics.
While research into spatial order advanced, it was Frank Wilczek—winner of the 2004 Nobel Prize in Physics—who conceived of matter possessing a regular structure in the time direction as well. In 2012, he proposed the concept of a "time crystal," in which a quantum system in its ground state spontaneously moves with a fixed periodicity without any external energy input, thereby breaking time translational symmetry. This is akin to a clock's hands ticking forever at a constant tempo without requiring any external power source, and it sparked fierce debate in the physics community at the time. Subsequently, in 2015, Patrick Bruno, along with Japan's Haruki Watanabe and Masaki Oshikawa, proved that time crystals cannot exist in a thermodynamic equilibrium state.
But physicists did not give up. Building on theoretical developments by Norman Yao and others, experimental teams led by Christopher Monroe and Mikhail Lukin demonstrated between 2016 and 2017 that in a non-equilibrium state driven by continuous periodic external energy input (a Floquet system), it is possible to realize a time crystal that spontaneously oscillates at, for example, a multiple of the input period. Space-time crystals possessing order in both space and time thus became a real phenomenon. However, quantum space-time crystals created using quantum simulators up to this point required extremely low-temperature environments and suffered from the weakness of collapsing within mere microseconds to milliseconds due to decoherence and thermal excitation across the entire system. The best way to understand order is to observe the melting phenomenon in which that order breaks down, but tracking this process in such short-lived quantum systems has proven extremely difficult.
The Time Order Kept by Plastic Discs Dancing All Day on a Vibrating Plate
To tackle this challenge, the research team at Shanghai Jiao Tong University chose a bold approach: bypassing the difficulty of quantum mechanical control and instead using a macroscopic classical mechanical system as an analog model. The apparatus the team built in their laboratory was a flat plate vibrating vertically up and down at a frequency of 100 times per second, or 100 Hz. It resembled experimental setups used to create Chladni patterns, but instead of scattering sand grains onto the plate, the team scattered several hundred special plastic discs, each equipped with six diagonally angled pin-like legs on its underside.
Every time the plate moves up and down, these specially legged discs undergo repeated brief collisions, receiving kicks in random directions from the driving force (active agitation). When the number of discs is small, each simply moves chaotically around the plate. However, when the research team increased the density of discs beyond a certain threshold and packed them tightly together, a remarkable self-organization phenomenon awakened. Numerous discs spontaneously adjusted their positions relative to one another, assembling a beautiful triangular crystal lattice in space. Furthermore, this entire crystal lattice began to rotate in perfect synchrony, as if it were a single rigid body, continuing to circle at an extremely slow tempo of roughly one full rotation every five hours.
What matters here is the gap between the period of the externally supplied vibrational energy and the period of the emergent rotational motion. Even though the vibrating plate strikes the discs up at a short tempo of once every 0.01 seconds, the entire system spontaneously generates its own unique period of approximately 18,000 seconds (5 hours)—1.8 million times longer—beautifully breaking time translational symmetry. The research team confirmed that this classical space-time crystal maintained its state for approximately 86,400 seconds, nearly a full day, even in an experimental environment where physical noise and friction were constantly present. This corresponds to four to five complete rotations, representing a level of stability far exceeding the millisecond-scale persistence typical of conventional quantum systems. With this powerful classical non-equilibrium proxy stage in hand, physicists finally gained a lens through which they could meticulously observe how a space-time crystal comes to the end of its life.
An Experiment Reducing the Filling Fraction Reveals the Independent Collapse of Time and Space
Rather than leaving the space-time crystal in its stable state, the research team deliberately removed discs from the plate a few at a time, lowering the particle filling fraction (density) to artificially induce a melting phenomenon. Whereas in an equilibrium crystal one would raise the temperature to increase thermal fluctuations, in this experiment the team induced the breakdown of order by reducing the frequency of interparticle interactions. Intuitively, one would expect that decreasing the density would cause the overall structural order and the timing of rotation to blur simultaneously, bit by bit, ultimately sliding into a chaotic fluid state.
However, the reality the research team observed followed a far more complex path than that intuition suggested. The melting process of the space-time crystal separated into three completely distinct physical stages, each with its own independent critical point for space and time. The transitions recorded in each phase eloquently testified to the independence of physical symmetries.
First, in Stage 1, even though the spatial order of the triangular arrangement across the entire crystal lattice remained perfectly intact, the timing of synchronized rotation in localized patches (regions) began to go out of sync. This was a state in which islands of particle groups unable to keep up with the rhythm emerged within the overall rigid-body rotation. Next, in Stage 2, as the filling fraction was further reduced, even though the geometric crystal lattice formed by the discs was still maintained across most of the region, the overall synchronized five-hour rhythm collapsed entirely, and only the temporal order dropped to zero. The research team identified the strange state that emerged at this stage as a fluid-like crystal state in which only spatial order remained (an intermediate phase resembling a fluid-space-time-crystal phase or fluid-hexatic phase). Finally, in Stage 3, the particle arrangement itself broke down, the triangular crystal lattice disassembled, and the system transitioned into a completely disordered fluid.
Why do the orders of time and space melt apart in this way? Through detailed analysis, the research team pinpointed that the physical mechanisms driving the breakdown of the two symmetries are fundamentally different. The loss of temporal order (the synchronized rotational rhythm) stemmed from the weakening of many-body interactions—collisions and repulsions between particles—as density decreased, which in turn caused the force maintaining a consistent rotational direction (directional persistence) to decay. In contrast, the collapse of spatial order (the crystal lattice arrangement) was driven by an entirely different mechanism: topological defects—misalignments generated within the crystal—propagating and proliferating throughout the lattice. Here lies proof that the rules governing space and the rules governing time function in a completely independent manner in a non-equilibrium state.
Where the New and Old Melting Models Position Non-Equilibrium Phase Transitions and Crystal Physics Today
The fact of "separated three-stage melting" demonstrated by the Shanghai Jiao Tong University team dramatically expands our previous physical understanding of the process by which matter loses order. To clarify the differences between conventional equilibrium thermodynamics and the melting model observed in this classical non-equilibrium system, a quantitative comparison of the conditions and collapse characteristics of both is organized below.
| Comparison Item | Conventional Equilibrium Crystal Melting (Old) | 2D KTHNY Theory Melting (Intermediate) | Non-Equilibrium Space-Time Crystal Melting in This Study (New) |
|---|---|---|---|
| Target of order | Spatial order only | Spatial order (position/orientation) only | Spatial order and temporal order (space-time crystal) |
| Main driving variable | Temperature (thermodynamic energy) | Temperature (increased thermal fluctuation) | Particle filling fraction (density of non-equilibrium many-body interactions) |
| Number of transition stages | 1 stage (direct solid-to-liquid transition) | Up to 2 stages (via intermediate hexatic phase) | Clear 3 stages (separated collapse of temporal and spatial order) |
| Collapse mechanism | Breaking of interatomic bonds by thermal energy | Dissociation and proliferation of topological defects | Decay of directional persistence (time) and defect propagation (space) |
| Persistence time/scale | Stable (thermodynamic equilibrium state) | Stable (thermodynamic equilibrium state) | Classical macroscopic system maintained for approximately 86,400 seconds (about 1 day) at room temperature |
What emerges from this comparison is the physical reality that the breaking of symmetry in the non-equilibrium space-time crystal phase behaves as an independent dimension rather than as an extension of conventional spatial order. As the KTHNY theory suggested, when a two-dimensional crystal melts, a "hexatic phase" appears in which positional order is lost first while only orientational order remains. This study extends that concept into the time direction, showing that a "temporally disordered phase"—in which only the temporal rhythm vanishes while the spatial structure remains firmly assembled—actually exists. This marks the moment when a new boundary line, at the intersection of space and time in the non-equilibrium regime, was added to the map of phase transitions that physicists have constructed over decades.
Unresolved Phase Changes Extending from Classical Mechanical Simulations to Quantum Many-Body Systems
This research result demonstrates that the dynamics of space-time crystals—previously accessible only through theoretical calculations or extremely short-lived quantum simulators—can now be directly and visibly verified using a macroscopic classical system. However, beyond this new frontier opened by the research team, numerous unverified questions still remain.
The biggest question is whether the classical three-stage melting scenario confirmed in the laboratory using plastic discs can be applied as-is to genuine quantum many-body systems governing the microscopic world of atoms and electrons. In quantum mechanical space-time crystals, quantum entanglement and interference effects are deeply involved in interparticle interactions, and quantum fluctuations exist that differ from those in classical active particle systems. Whether temporal order and spatial order still collapse separately at completely distinct critical points in this quantum world, or whether quantum effects create a pathway that somehow couples the collapse of both, remains a question that has not been fully settled either theoretically or experimentally.
Furthermore, while this observation was limited to a two-dimensional plane on a flat plate, how topological defects propagate in complex three-dimensional spatial geometries, and how they interfere with long-period synchronized rhythms, also remains an unknown territory. In the conclusion of the paper, Jie Zhang and colleagues on the research team state that this approach using macroscopic classical systems has opened a path toward exploring new phases exhibiting spontaneous breaking of space-time symmetry. How does the matter that makes up our world create order under extreme non-equilibrium conditions, and how does it relinquish that order? The challenge of unraveling the universal physical laws hidden behind these questions has only just had its first door opened.