From: mk_thisisit
Self-organization refers to the spontaneous arrangement of a many-body system into a regular, ordered structure [00:02:39]. While commonly observed in space, such as in physical crystals like diamonds or table salt [00:02:46], physicists are exploring whether similar phenomena can occur in the time dimension [00:00:17].
Self-Organization in Spatial Crystals
In well-known spatial crystals, self-organization leads to regular structures in space [00:02:51]. When energy is lowered (e.g., by cooling), atoms, due to their interactions, prefer to arrange themselves into a regular structure [00:03:09]. This means that atoms can spontaneously organize into something regular if the right conditions are created [00:05:22].
This phenomenon is tied to the concept of spontaneous breaking of symmetry [00:09:14]. While the equations of quantum mechanics often prefer symmetry, sometimes stationary solutions do not follow this symmetry [00:08:50]. For spatial crystals, instead of a smeared, uniform distribution of atoms (which symmetry might suggest), self-organization leads to a regular, ordered pattern [00:09:10].
Self-Organization in Time Crystals
The concept of self-organization can be extended to the time dimension, leading to time crystals [00:03:18]. A time crystal is a system of many bodies that spontaneously sets itself into periodic motion [00:04:13]. This is distinct from classical periodic motion, such as a clock pendulum, which is an expected regularity [00:04:32]. The key is the spontaneous nature of this periodic motion, especially when it is not directly caused by an external periodic force [00:14:17].
Frank Wilczek, a Nobel Prize winner, first posed the question in 2012 whether a time crystal could be created where a many-body system enters periodic motion in its lowest energy state [00:06:33]. He asked if spontaneous breaking of symmetry could occur with respect to shifts in time [00:09:27], meaning a system with time-independent continuous translational symmetry in time could produce a discrete translational symmetry in time, resulting in periodic motion [00:09:32]. While Wilczek’s initial mechanism was found to be flawed [00:11:14], his brilliant idea spurred new research [00:13:19].
Professor Krzysztof Sacha is credited with the first description of “discrete time crystals” [00:15:31]. His approach involved a multi-body system disturbed by a periodically changing force [00:13:52]. In this scenario, the system begins to evolve periodically with a different period than the driving force, a spontaneous emergence of a new periodic motion [00:14:09]. This type of time crystal has been experimentally realized by groups at the University of Maryland and Harvard [00:15:04].
Self-Organization and the Nature of Quantum Mechanics
The concept of spontaneous symmetry breaking in self-organization highlights a fascinating aspect of quantum mechanics: “certain things that are basically natural they do not exist in quantum mechanics” [00:16:11]. For example, in a system of ultracold atomic clouds, a motion where two clouds bounce alternately, which would be natural classically, does not exist in quantum mechanics for time crystals [00:17:01]. Instead, a different crystal structure emerges in time [00:17:23].
Impact of Observation
This phenomenon is also linked to the impact of observation in quantum mechanics. When a system is described by a wave function, which holds maximum information about the system, observing or measuring a property (like position) changes the quantum state [00:24:45]. This is analogous to Schrödinger’s cat, where the act of observation collapses the superposition of states [00:18:15]. In time crystals, while a “Singer’s cat” theoretical state might exist momentarily, it disappears if any question is asked about the quantum system [00:23:06], leading to the observation of periodic motion with a period different from the driving force [00:23:17]. However, once formed, time crystals are generally robust to repeated observations for certain types of information, not dramatically changing their state [00:22:47].
Primitive vs. Complex Organization
The self-organization seen in both spatial and time crystals is considered a “very primitive self-organization” when compared to the complex organization required for the creation of an organism [00:35:06]. The question of how consciousness arises from matter remains one of the most important unanswered questions in science [00:36:14].
Future Applications
While quantum mechanics begins to describe the world using probabilities, giving a sense of freedom [00:00:54], the field of time crystals is still young in terms of applications [00:26:15]. However, there are potential prospects, similar to how spatial crystals are universally used for their conductivity properties [00:26:40]. Researchers are investigating if time crystals can exhibit analogous properties like conductivity, insulation, or superconductivity in time [00:27:28]. The possibility of building quantum computers using time crystals is also being explored, showing promising theoretical results [00:29:09].