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I'm reading from PDG the Tests of Discrete Space-Time Symmetries; we have the following row:

  • Time Reversal (T) Invariance $e$ electric dipole moment $< 0.11 \times e^{-28} e\, \text{cm}$, $\text{CL} = 90\%$.

What is the history of experiments like this?

I am guessing that since classical physics is symmetric under time-reversal the margin of error must be very small. Does it measure an error at all? What does it mean this experiment had time-reversal symmetry up to a tolerance ?

Definition from Wikipedia of dipole moment:

The electric dipole moment is a measure of the separation of positive and negative charges within a system; a measure of it's polarity. The SI units for electric dipole moment are Coulomb-meter (C⋅m); however a commonly used unit in atomic physics and chemistry is the Debye (D).

Here are schematics from Wikipedia of what these separations of charge look like:

In fact, there are three symmetries listed:

Which are part of CPT symmetry discussion.

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.

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