EDM & Time Reversal: Why Does It Matter?

[kelly0303]

Why for some systems (such as the electron or neutron) the presence of an electric dipole moment (EDM) implies time reversal violation, while for others, such as water molecule, this is not the case? Thank you!

 

[mfb]

A water molecule has an ordered structure in space ("L"-shaped, oxygen at the center). Neutrons and electrons do not.

 

[kelly0303]

A water molecule has an ordered structure in space ("L"-shaped, oxygen at the center). Neutrons and electrons do not.

I am not sure I understand. What does the structure has to do with this? A neutron can be though of a dumbbell, with positive charge at one end and negative at the other (of course the separation is very small, hence why the EDM was not observed experimentally yet). How does the "L" shape of water doesn't violate CP, but the dumbbell shape of neutron does?

 

[mfb]

A neutron can be though of a dumbbell, with positive charge at one end and negative at the other (of course the separation is very small, hence why the EDM was not observed experimentally yet).

Only from very weak effects from CP violation. Otherwise it wouldn't have that shape. Don't take illustrations with quarks too literal.

Chemical bonds have binding angles. Quarks in hadrons don't have fixed positions.

 

[kelly0303]

Only from very weak effects from CP violation. Otherwise it wouldn't have that shape. Don't take illustrations with quarks too literal.

Chemical bonds have binding angles. Quarks in hadrons don't have fixed positions.

Well it's the CP violation the main reason I am asking this question. I know it is due to the weak interactions, but if it wasn't for the weak interaction I wouldn't have asked this questions (and same applies to the electron, so I am not sure what do you mean by quarks illustration). But again, I am not sure why does the shape of the molecule matters. I can take 2 non-conducting hemispheres, having opposite charge and stick them together. I would get a dipole moment without violating parity. I can have almost any shape I want and still get a dipole moment. But these won't violate CP and I am not sure I understand why.

 

[mfb]

But these won't violate CP and I am not sure I understand why.

They will still have some dipole moment from CP violation but it will be completely negligible compared to the dipole moment from the structure. Something the neutron doesn't have because it doesn't have a structure.

 

[kelly0303]

They will still have some dipole moment from CP violation but it will be completely negligible compared to the dipole moment from the structure. Something the neutron doesn't have because it doesn't have a structure.

Yes. My question is, why doesn't the dipole moment not coming from the weak interaction violate CP? I am sure that doing the math and applying the C and P operators for a given system will show that, but I am looking for some more physics insight. For example, I imagine T violation implies that running the movie of an experiment forward and backward, will look differently. So for some reason if I film the electric dipole of a water molecule and run the movie backward I can't tell the difference. But if I do the same with an electron, I would be able. I am not sure why. Thank you!

 

[Vanadium 50]

You're not thinking about the answers you are getting. You are reacting to them.

How do I know? Because only a few minutes pass between an answer and your reaction that you don't understand. There hasn't been enough time for you to think things through. You would be much better served by thinking about the responses you are getting and if you need a follow up to ask something focused and well-posed rather than just shotgunning questions back as fast as you can. You are much, much more likely to reach understanding that way.

 

[kelly0303]

You're not thinking about the answers you are getting. You are reacting to them.

How do I know? Because only a few minutes pass between an answer and your reaction that you don't understand. There hasn't been enough time for you to think things through. You would be much better served by thinking about the responses you are getting and if you need a follow up to ask something focused and well-posed rather than just shotgunning questions back as fast as you can. You are much, much more likely to reach understanding that way.

I am thinking about the answers, I just don't understand. What I understood so far is that water can have an electric dipole without violating CP because it is L-shaped. But I don't understand the physical reason as to why the shape of the molecule (or any object I would build, as mentioned above) would not violate CP, while the neutron does violate CP by having an EDM. Thank you!

 

[vanhees71]

The issue is not whether some state or most importantly the groundstate of the system is symmetric or not but whether the Hamiltonian commutes with the symmetry operator (like in this case $\hat{C} \hat{P}$) or not.

You know this from everyday experience: The matter around us is held together by the strong interaction (binding quarks and gluons together to nucleons and these again to atomic nuclei) and the electromagnetic interaction (forming electrons and atomic nuclei to atoms, molecules, and all kinds of condensed matter). All these interactions obey rotation invariance, but the matter around us doesn't only form spheres but all kinds of objects which are not invariant under rotation. So though the relevant Hamiltonian is rotation invariant the states of the matter around us is not.

Within the Standard Model only the weak interaction violates $\hat{P}$, $\hat{T}$, $\hat{C}$, and also $\hat{C} \hat{P}$ (while $\hat{C} \hat{P} \hat{T}$ must be a symmetry in any local relativistic QFT, and there's no hint of violation of this "grand reflection symmetry" at all).

Now take the neutron, which has a spin and magnetic moment, which is an axial vector. If it has also in addition an electric dipole moment, $\hat{C} \hat{P}$ is broken by the dynamics of the system, because there's no other intrinsic vector than the spin of the neutron. If you take into account only the strong interaction which binds quarks and gluons together to a neutron, this implies that the neutron cannot have an electric dipole moment since the strong interaction is invariant under $\hat{C} \hat{P}$ (which is in a way a problem, because there's no "natural" mechanism to explain this invariance of QCD, the socalled "strong CP problem"). Now there's also the weak interaction, which violates CP symmetry due to a corresponding phase in the quark-mixing matrix. You can predict which electric dipole moment you expect from this symmetry breaking, and it turns out to be very small, some orders of magnitude smaller than the upper bound we can get from measurements of the neutron's EDM.

There's much effort to get more and more accurate bounds of this EDM, because we know that CP symmetry should be much stronger broken than predicted by the Standard Model, because CP symmetry is also needed to explain the matter-antimatter imbalance in the universe, and thus it's quite promising to find "physics beyond the Standard Model" looking for stronger CP violation than predicted by the Standard Model.