Why some objects, such as water molecule, can have a (large) electric dipole moment without violating time reversal symmetry, while the existence of an electron or neutron electric dipole moment would imply time reversal invariance? Thank you!
Your question could be "is CP (Charge reversal parity reversal) obeyed by water molecules?", because it is the CPT theorem that is used for getting a time reversal asymmetry check for the neutron.
A permanent electric dipole moment of a fundamental particle violates both parity (P) and time reversal symmetry (T). These violations can be understood by examining the neutron's magnetic dipole moment and hypothetical electric dipole moment. Under time reversal, the magnetic dipole moment changes its direction, whereas the electric dipole moment stays unchanged. Under parity, the electric dipole moment changes its direction but not the magnetic dipole moment. As the resulting system under P and T is not symmetric with respect to the initial system, these symmetries are violated in the case of the existence of an EDM. Having also CPT symmetry, the combined symmetry CP is violated as well.
I think the crucial word here is the dipole moment should be permanent in order to find time reversal violation via CPT, i.e. not dependent on the environment.
After all, the universe we observe has mainly baryons, so CP is mainly violated by the matter antimatter asymmetry observed. CP is violated in weak interactions, but the size is not enough to explain the baryon antibaryon asymmetry observed. CP violation ( and consequently time reversal asymmetry) are an ongoing research subject both experimentally and theoretically.
The proper statement is that the electric dipole moment of a neutral object restricted to a single irreducible representation of the rotation group must vanish, if $T$ symmetry holds.
A typical neutron in the lab is in such a state, because the rotational energy levels of nucleons are widely separated, by much greater energies than are available at room temperature. But the rotational energy levels of a typical water molecule are much closer together, so the argument doesn't work. (However, if you really did have a perfectly isolated water molecule brought to its ground state, it really would have no electric dipole moment; its orientation would enter a superposition in which the dipole moment cancels.)