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: , 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.
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 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 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.