Time-translation symmetry

Time

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Time translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval. Time translation symmetry is the hypothesis that the laws of physics are unchanged, (i.e. invariant) under such a transformation. Time translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time translation symmetry is closely connected via the Noether theorem, to conservation of energy.^[1] More formally, we say the equations for a system at times $t$ and $t+\tau$ are the same for any value of $t$ and $\tau$ .

There are many symmetries in nature besides time translation, such as spacial translation or rotational symmetries. These symmetries can be broken and explain diverse phenomena such as crystals, superconductivity, and the Higgs mechanism.^[2] However, It was thought until very recently that time translation symmetry could never be broken.^[3] Time crystals, a newly discovered state of matter, break time translation symmetry.^[4]

Time translation symmetry is guaranteed only in spacetimes where the metric is static: that is, where there is a coordinate system in which the metric coefficients contain no time variable. Many general relativity systems are not static in any frame of reference so no conserved energy can be defined.

Symmetry

Symmetries are of prime importance in physics and are closely related to the hypothesis that certain physical quantities are only relative and unobservable.^[5] Symmetries apply to the equations that govern the physical laws rather than the initial conditions or to themselves and state that the laws remain unchanged under a transformation.^[1] If a symmetry is preserved under a transformation it is said to be invariant. Symmetries in nature lead directly to conservation laws, something which is precisely formulated by the Noether theorem.^[6]

Symmetries in physics^[5]
Symmetry	Transformation	Unobservable	Conservation law
Space-translation	$\mathbf {r} \rightarrow \mathbf {r} +\Delta$	absolute position in space	momentum
Time-translation	$t\rightarrow t+\tau$	absolute time	energy
Rotation	$\mathbf {r} \rightarrow \mathbf {r} '$	absolute direction in space	angular momentum
Space inversion	$\mathbf {r} \rightarrow -\mathbf {r}$	absolute left or right	parity
Time-reversal	$t\rightarrow -t$	absolute sign of time	Kramers' degeneracy
Sign reversion of charge	$e\rightarrow -e$	absolute sign of electric charge	charge conjugation
Particle substitution		distinguishability of identical particles	Bose or Fermi statistics
Gauge transformation	$\psi \rightarrow e^{iN\theta }\psi$	relative phase between different normal states	particle number

Time translation symmetry breaking (TTSB)

Time crystals, a newly discovered state of matter, break time translation symmetry.^[4]

References

^ ^a ^b Wilczek, Frank (16 July 2015). "3". A Beautiful Question: Finding Nature's Deep Design. Penguin Books Limited. ISBN 978-1-84614-702-9.
^ Richerme, Phil (18 January 2017). "Viewpoint: How to Create a Time Crystal". physics.aps.org. APS Physics. Archived from the original on 2 Feb 2017.
^ Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals" (PDF). Physical Review Letters. 117 (9): 090402. arXiv:1603.08001v4. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. ISSN 0031-9007. PMID 27610834.
^ ^a ^b Gibney, Elizabeth (2017). "The quest to crystallize time". Nature. 543 (7644): 164–166. doi:10.1038/543164a. ISSN 0028-0836. Archived from the original on 13 Mar 2017.
^ ^a ^b Feng, Duan; Jin, Guojun (2005). Introduction to Condensed Matter Physics. singapore: World Scientific. p. 18. ISBN 978-981-238-711-0.
^ Cao, Tian Yu (25 March 2004). Conceptual Foundations of Quantum Field Theory. Cambridge: Cambridge University Press. ISBN 978-0-521-60272-3.

External Links

The Feynman Lectures on Physics - Time Translation

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Symmetry

Time translation symmetry breaking (TTSB)

References

See also

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