Noether's theorem is the result, cited in the source dossier, that symmetries in nature lead directly to conservation laws. The dossier invokes it to explain why the time-translation symmetry of physical law implies the conservation of energy, and therefore why the thermodynamics of time crystals matters.
Statement as used in the dossier
The dossier states: "Symmetries in nature lead directly to conservation laws, something which is precisely formulated by Noether's theorem." The basic idea of time-translation symmetry is that a translation in time has no effect on physical laws — that the laws of nature that apply today were the same in the past and will be the same in the future. This symmetry implies the conservation of energy.
Relevance to time crystals
Because time-translation symmetry implies energy conservation, a system that spontaneously breaks that symmetry must do so without violating energy conservation. The dossier asserts that time crystals do not violate the laws of thermodynamics: energy in the overall system is conserved, no thermal energy is spontaneously converted into mechanical work, and the crystal cannot serve as a perpetual store of work. The source's phrase "motion without energy" is used to describe the apparent motion, which does not represent conventional kinetic energy.
Related work
- Spontaneous Time-Translation Symmetry Breaking — the mechanism the theorem constrains.
- Time Crystal — the concept whose thermodynamics the theorem informs.
- energy — the topic guide for conservation and thermodynamics.
Source notes & attribution
- https://rexresearch.com/WilczekTimeCrystals/WILCZEKTimeCrystals.html