# Why saying that during electron capture the electron is converted to a neutrino?

Parent question: What came first, neutrons or electrons?

This is about electron capture and neutron decay, and what happens to the electron between two such events.

In the parent question, I was told that during electron capture, 1. the final neutron does not contain the electron, and 2. the electron was actually converted to a neutrino.

But the neutrino of the electron capture does not contain the same amount of energy the incoming electron did. So I assumed a part of the electron is stored in the neutron (again, not as Russian dolls).

proton mass 1.672621898(21)×10−27 kg neutron mass 1.674927471(21)×10−27 kg difference 0.002305573×10−27 kg electron mass 0.000910938356(11)×10−27 kg

This is clearly oversimplistic to just compare rest masses, as energy can be in other forms, yet I just add it as an illustration of what I am asking about, because there is more mass in the neutron than in the proton.

So how can someone says the neutrino is the converted electron even though it was rather stripped? Why not say there has been a redistribution of the "reactants"?

• A neutron can absorb a positron in the same way and become a proton. Would you say the proton now has a positron in it? Keeping in mind that a proton has less mass than a neutron. – Chris May 11 at 21:51
• No, but I consider a positron as antimatter, so it doesn't shock me. – Exocytosis May 11 at 22:01
• Actually it even confirms my mental picture in the sense that a positron and electron annihilate each other, so if there was an electron somewhere in the neutron, that would make sense that a positron reduces the neutron to a proton. – Exocytosis May 11 at 22:04
• the electron becomes a neutrino through a W^- boson which then turns an up quark in the proton into a down quark – Triatticus May 11 at 22:16
• @Triatticus: I assume the "which" in your sentence refers to the boson, not the neutrino. – Exocytosis May 11 at 22:55

A simpler point of view.

So how can someone says the neutrino is the converted electron even though it was rather stripped? Why not say there has been a redistribution of the "reactants"?

Elementary particles, and the electron is an elementary particle in the standard model of physics are different than classical particles.

They obey quantum mechanics rules.They do not obey the classical mechanics intuitions.

The particles in the table are characterized by their quantum numbers. Their masses are fixed at the time of the universe we are living in.

These QM rules are :energy , momentum and angular momentum conservation (spins included in the conservation) , conservation of lepton number, baryon number ( all in the table in the link), conservation of charge. And of course the quantum mechanical equations of the state of the system , given by the solution of the appropirate quantum mechanical differential equations. And there are rules of what happens during interactions with the given forces in the interactions.

In electron capture the energy of the electron is absorbed/distributed through the weak force, by the interaction products, but in order to obey lepton number conservation an electron neutrino has to carry the electron lepton number.

All these rules have come out of observations of innumerable data, and the standard model symmetries which carry the quantum number conservation laws in the group structure (SU(3)xSU(2)xU(1) )is still the current model of particle physics.

• Right. But what the neutrino keeps from the electron is just that or so: the lepton number. The other numbers, such as the charge, affect the neutron. So the standard model says the lepton is not the electron anymore but the neutrino, I won't argue with a definition. But there are properties of the electron that, through the boson, are carried elsewhere, if only in the final mass of the neutron. This is discussed further there and I believe it is not a trivial matter (no pun intended): physics.stackexchange.com/questions/479464/… – Exocytosis May 12 at 5:23
• However your answer is the correct one, in the sense that it explains why physicists say the electron is now the neutrino. – Exocytosis May 12 at 5:25

This is a common confusion, see also this answer of mine to a different question where the asker proposed that muons should be viewed as composites of their decay products (electrons and neutrinos).

In quantum field theory, the reactions that can produce a particle or the products of its decay are completely unrelated to its constituent particles (if there are any). The constituent particles are those where modelling the particle as being a bound state of these particles yields the correct behaviour e.g. in scattering experiments. For instance, a hadron like a proton or a neutron can be usefully thought of to be a mess of quarks and gluons - "partons", see this answer by DavidZ to "What's inside a proton?".

Quantum field theory does not yield human-readable interpretations of the process by which these particles turn into others. It predicts a non-zero probability for a proton and an electron to turn into a neutron and a neutrino, and nothing more. It is a meaningless question to ask whether the electron "turned into a neutrino" or "ended up inside the neutron" - neither happened. The neutron is a partonic mess like the proton, the neutrino has no known substructure. The electron is gone, and nowhere to be found.

• Yet apparently a neutron and an electron may react with the electron antiparticle, the positron, while neither the proton or the neutrino will. So it seems reasonable to me to ask what makes the neutron compatible with the electron antiparticle, even more though after it emerged from the combination of a proton with an electron. Now I understand the theory says those are black boxes, my questions are meaningless, yet I don't know how you can be satisfied with this. – Exocytosis May 11 at 22:47
• @Exocytosis What do you mean by claiming that the positron does not react with the proton? Search the web for "proton-positron scattering". Or look at $\beta^+$-decay: A proton decays into a neutron, a positron, and a neutrino. And neither nature nor our models of it care whether we find them "satisfying", they work nevertheless. – ACuriousMind May 11 at 22:55
• I use the verb react as in chemistry. If a proton decays into a positron, they obviously did not react with each other, they are on opposite ends of the reaction. I tried looking for "proton-positron scattering" but my search engine (duckduckgo) doesnt give useful results. Is it different than the positron and proton on opposite ends or not? – Exocytosis May 11 at 23:18
• @Exocytosis It's simple conservation laws that make a "reaction" in your sense between proton and positron imposslble at ordinary energies. Conserving energy, charge and the other quantum numbers, you simply can't make the proton and the positron become something else without providing lots of additional energy like in a collider. – ACuriousMind May 11 at 23:25
• Well actually this is exactly my point. I was writing this question during the meantime: physics.stackexchange.com/questions/479464/… – Exocytosis May 11 at 23:37

Of course ACuriousmind's answer is right, but I would like to add a few things.

I think I understand where your confusion lies, and you have come to a cornerstone in QM. This is why QM is a beautiful thing, it is really different from classical mechanics.

Your confusion lies in that you are trying to go from up to down in scale, you are trying to go from bigger to smaller and use the same methodology. You are asking how a certain elementary particle can convert into another elementary particle, the same way a composite particle, or a macro object would convert into another composite particle or macro object.

This is more of a classical view, and it pre-assumes, that everything is made of the same constituents. True, in strong theory this might work, and this way if you want you can explain that every elementary particle can be converted into any other (except if it is forbidden by laws of physics).

Now in our currently accepted theories, SM and QM, this does not work this way. You cannot say that an electron is converted into a neutrino just because they have the same kind of constituents. Both are elementary particles.

You are saying that chemistry works that way and it is true. Only because in chemistry, everything is built up by atoms, chemistry does not go deeper and you can use this classical view of converting chemical elements into another one.

In QM, everything is energy(matter, particles), and in an interaction it is just simply converted into energy, if you will, into other forms of energy (other matter,particles).

This is why in your interaction, you have to look at the whole interaction, the total energy, and that has to stay the same, this is conservation of energy. This is the basic rule that you have to follow.

Let's see electron capture.

Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shell. This process thereby changes a nuclear proton to a neutron and simultaneously causes the emission of an electron neutrino.

There are two types of electron capture:

1. an outer electron replaces the missing electron (the inner one that was absorbed by the nucleus), and an x-ray is emitted (energy equal to the difference between the two shells)

2. auger effect, the energy is not emitted in a form of a photon, but the energy knocks off the outer electron

Now you are saying that you were told in the parent question that the electron is not included in the neutron after the capture. This is not true. The nucleus absorbs the inner electron as energy (not in the form of an electron). The inner electron gets transferred into energy, and that energy gets absorbed by the nucleus.

An electron is defined as an elementary particle, not consisting of anything else, it does not have any internal structure.

The proton in the nucleus is made up of a sea of quarks, antiquarks, gluons, antigluons. This is an ever changing sea, and only if you net them out, will you get three valence quarks. Now yes, these quarks happen to have exactly 1/3 of the EM charge of the electron. And yes, the electron is able as per QM to transfer into energy and interact with the proton, its quarks, antiquarks, gluons, antigluons, and thus convert the quarks so that the remaining quarks will have a different net EM charge (in this case neutral). This is how you get a neutron from a proton (one way to get it).

The neutrino that is emitted during this type of beta decay (yes, electron capture is a type of beta decay), is not a converted electron, and it is not the same as the inner electron that was absorbed by the nucleus in the form of energy.

The laws of physics are so that the total energy must be equal before and after the decay, and if the neutrino was not discovered (in beta decay), the total energy did not add up.

After they discovered the neutrino during beta decays, it became clear, that there must be an elementary particle, that has exactly the energy that was missing from after the decay.

The simplest way to think about it is not classical, but QM. The proton absorbs the electron:

1. all of the EM charge of the electron is absorbed by the proton, that is how it is able to convert into a EM neutral particle, the neutron

2. not all of the electron's kinetic energy (and rest mass converted into energy) is absorbed by the proton to convert into a neutron, it does not need all of the electron's kinetic energy (and rest mass converted into energy), so there must be an excess of energy

To make the neutron stable, this energy needs to be released, and it is released in the form of a neutrino. It needs to be released in a form of particle, that is:

1. EM neutral

2. it's total energy equals the excess energy of the inner electron, that was not needed for the proton to convert into a neutron

So as per QM, the emitted neutrino is not a converted inner electron. The inner electron converts into energy, and part of that energy is released in the form of a neutrino.

The way you are talking about this as chemistry, would suggest that the electron and the neutrino are made up of the same constituents. So far, all experiments fit the theory of SM and QM, showing no internal structure for the electron.

Maybe if string theory proves right, then we will see that the inner electron that is absorbed by the proton, made up of quarks, and the neutrino, will all be made up of the same constituents, then, and only then, will you be able to make this decay look like the classical chemical reactions.

But for now, as per QM, we say that these are all converted into energy, and convert into other forms of matter, particles. The reality is, you are asking how, and we do not know, we do not know how they get converted, we do not really know what really gets converted, and for the theory to work, we call it energy, all matter and particles are convertible to other forms of energy, other types of particles (along the lines of laws of physics).

• you have missed quantum number conservation – anna v May 12 at 3:39
• @Arpad: Excuse me but who are you talking to? It seems I (the asker) agree with everything you say or so, while you write things I disagree with such as "Now you are saying that the electron is not included in the neutron after the capture. This is not true". I do think aspects of the input particles are redistributed into output particles. I wrote in the question here "So I assumed a part of the electron is stored in the neutron". Please see my next question that details my reasoning: physics.stackexchange.com/questions/479464/… – Exocytosis May 12 at 4:56
• @Exocytosis you are correct. You say that "In the parent question, I was told that during electron capture, 1. the final neutron does not contain the electron" So I will edit my answer. – Árpád Szendrei May 12 at 5:06
• @Arpad: ah ok, thanks for clarifying. – Exocytosis May 12 at 5:13