Editing T-symmetry (section)

===Electric dipole moments===
{{Main|Electron electric dipole moment}}
This has an interesting consequence on the [[electric dipole moment]] (EDM) of any particle. The EDM is defined through the shift in the energy of a state when it is put in an external electric field: {{nowrap|Δ''e'' {{=}} d·''E'' + ''E''·δ·''E''}}, where ''d'' is called the EDM and δ, the induced dipole moment. One important property of an EDM is that the energy shift due to it changes sign under a parity transformation. However, since '''d''' is a vector, its expectation value in a state |ψ⟩ must be proportional to ⟨ψ| ''J'' |ψ⟩, that is the expected spin. Thus, under time reversal, an invariant state must have vanishing EDM. In other words, a non-vanishing EDM signals both ''P'' and ''T'' symmetry-breaking.<ref>{{cite book|last1=Khriplovich|first1=Iosip B.|last2=Lamoreaux|first2=Steve K.|title=CP violation without strangeness : electric dipole moments of particles, atoms, and molecules.|date=2012|publisher=Springer|location=[S.l.]|isbn=978-3-642-64577-8}}</ref>

Some molecules, such as water, must have EDM irrespective of whether '''T''' is a symmetry. This is correct; if a quantum system has degenerate ground states that transform into each other under parity, then time reversal need not be broken to give EDM.

Experimentally observed bounds on the [[neutron electric dipole moment|electric dipole moment of the nucleon]] currently set stringent limits on the violation of time reversal symmetry in the [[strong interactions]], and their modern theory: [[quantum chromodynamics]]. Then, using the [[CPT invariance]] of a relativistic [[quantum field theory]], this puts [[CryoEDM|strong bounds]] on [[strong CP violation]].

Experimental bounds on the [[electron electric dipole moment]] also place limits on theories of particle physics and their parameters.<ref>{{cite journal|last1=Ibrahim|first1=Tarik|last2=Itani|first2=Ahmad|last3=Nath|first3=Pran|title=Electron EDM as a Sensitive Probe of PeV Scale Physics |date=12 Aug 2014 |arxiv=1406.0083|doi=10.1103/PhysRevD.90.055006|volume=90|issue=5|journal=Physical Review D|page=055006|bibcode=2014PhRvD..90e5006I|s2cid=118880896}}</ref><ref>{{cite journal|last1=Kim|first1=Jihn E.|last2=Carosi|first2=Gianpaolo|title=Axions and the strong CP problem|journal=Reviews of Modern Physics|date=4 March 2010|volume=82|issue=1|pages=557–602|doi=10.1103/RevModPhys.82.557|arxiv = 0807.3125 |bibcode = 2010RvMP...82..557K }}</ref>