1. ### Colin Cheng

10
In the process of particle decay (eg carbon-14 ---> nitrogen-14), is there any relations with radioactivity? Is it reversible? ( up quark + 2 x down quark + W positive boson = down quark + 2 x up quark + electron, so that carbon-14 turns to nitrogen-14. Is it possible that down quark + 2 x up quark + W negative boson = up quark + 2 x down quark + ? , so that nitrogen-14 can turn back to carbon-14? If possible, what's that '?' ?

### Staff: Mentor

Yes, that's an example of beta decay.

It's easier to think of this reaction as a neutron emitting an electron and an anti-neutrino as it converts to a proton. Where did you get the W from and where did you lose the neutrino?
Energy is released when C-14 decays to N-14, so that reaction can and does happen spontaneously. In principle the reaction could go the other way, but you'd have to find a way of adding the necessary energy back in: bring an electron, and anti-neutrino, and an N-14 nucleus all together with just the right amount of energy and exactly the right magic conditions. So that mystery "?" is just the energy that escaped in the decay and has to be restored somehow.

In practice, this and other spontaneous decays are about as reversible as a golf ball dropping into the hole - you don't see the ball bounce out again very often.

3. ### Colin Cheng

10
Sorry I don't get it. When a neutron converts to a proton, why are there both electrons and anti-neutrino emitted?

4. ### mathman

6,514
Conservation of charge (electron to balance proton) and conservation of lepton number (anti-neutrino to balance electron).

### Staff: Mentor

Physics cannot answer "why" questions. Our theories are all based on observations, and this is one of the observations.

Sure, not emitting those particles would violate conservation laws, but those conservation laws are based on observations as well.

6. ### ChrisVer

Up to nowadays knowledge, the Leptonic number seems to be conserved ...that's why you need the antineutrino. The deal, at least mathematically, is that you have a symmetry in the standard model which corresponds to that lepton number conservation. There are also some propositions for Leptonic and Baryonic numbers being violated (not conserved), but instead they keep the conservation of their difference... (one such interaction is the proton decay in some GUTs). The symmetries then $U(1)_{L}$ and $U(1)_{B}$ would be broken -I think this can be done through an anomaly- while symmetries like $U(1)_{B-L}$ survive.

Of course when physicist first came across the beta decay they didn't know anything about leptonic numbers etc, they didn't know that the neutrino existed. But the problem was that they got the spectra of the electrons' energies, and they found it that it wasn't a 2 body decay (In two body decay spectra you see 1 peak at a single value of energy). On the other hand, what they saw was a continuum spectrum...
In order to save energy conservation, Pauli introduced a really funny particle to save the day (one that of course is emitted to get the energy needed, but it doesn't interact with others)... 2 decades I think later, the neutrino was finally detected.

(of course physics answers to some "why" questions, answers to "why nature works this way". It's not only observation, otherwise we wouldn't need the confinement problem -we'd say quarks are just staying in there because that's what we see-, we wouldn't need the hierarchy problem-we'd say EW scale is such because that's what we see- and we wouldn't need the strong CP problem-we'd say Θ is so small because that's what we see... Hope you get what I'm trying to say )

But may I ask something about weak decays going backward? For the case where CP symmetry is violated, we also need the T symmetry to be violated....In that case does that mean that the opposite interaction does not occur/is highly supressed?

Last edited: Mar 31, 2014

### Staff: Mentor

Okay, let me rephrase this: physics cannot answer "why" questions on a fundamental level. For every explanation of a phenomenon or theory with a more fundamental theory, you can ask "why is this theory true?". Why do we live in a universe where quantum field theory is useful?

Most of those interactions are decays, where you don't see the opposite reaction anyway. But T violation has been observed in the mixing of B0 mesons (BaBar: arXiv, Belle: arXiv).