Why is mass not conserved in special relativity?

[QuantumDefect]

Hi everyone,
A couple days ago in chemistry we talked about nuclear chemistry. This of course is about halflifes, different types of decay, ect. I was surprised when I learned that an electron and a proton combine to create a neutron (electron capture). Now a couple days ago I was reading these forums, someone said an electron can get really close to the nucleus but something happens to the electron so it doesn't fly into the nucleus. Can someone tell me why this decay can happen? and why it creates a neutron? I know neutrons are nuetral particles but the thing that I am wondering is if a proton, made up of two up and one down quark, combines with an electron to create a neutron that has two down quarks and one up quark. Does one of the up quarks combine with an electron to create a down quark? Sorry if this is a stupid question, I have yet to take the Quantum Mechanics class required for my major, but to me this is a question that won't stop bugging me. Thank you guys for the replies.

 

[Janitor]

Take a quick look at this website: http://www.egglescliffe.org.uk/physics/particles/parts/parts1.html

Scroll down to the diagram with the caption "Feynman diagram for beta decay." The process of electron capture is very similar. Then look at the two Feynman diagrams below that one. They show what is happening at the level of quarks. A virtual W particle is a key to the process.

 

[QuantumDefect]

Ok, bare with me but when these two particles hit( proton and W- virtual particle) they create a neutron.
They give an equation: d->u+W-
where an W- virtual particle and an up quark interact which changes the quarks "flavor" to a down quark. This still does not explain the electrons role in this interaction. Does the electron give off this W- particle and vanish? or does it become the W- particle?

 

[Janitor]

In electron capture you can think of the electron as turning into a W and a neutrino. The W conserves the charge of minus one that the now-deceased electron had, and the neutrino conserves the lepton number of one that the electron had. This process can't take place for an electron in empty space since the W is much more massive than the electron, but it can take place in the massive environment of a nucleus. The neutrino leaves the scene, and the W quickly finds a quark and changes its flavor.

 

[QuantumDefect]

So the laws of Quantum Mechanics give weigh to General Reletivity in massive environments such as a neutron star? And how can the W particle be more massive than the electron it was made out of? It makes sense in the view of String theory but how do physicist that do not accept string theory, explain the greater mass of the W particle? And also can you explain to me my other question which was why does quantum mechanics allow the electron to interact with the nucleus, if the electron can't go into it? Or have you answered that question and I am not quick enough to spot it or have I answered it myself in the first sentence?

 

[Janitor]

As far as "how can the W particle be more massive than the electron it was made out of?" goes, the best I can do is some hand-waving about how an isolated electron can decay very briefly into other things, even if doing so violates mass/energy conservation, via the uncertainty principle. The decay products have to be re-absorbed, so to speak, very quickly, to re-constitute the electron. But when the electron is close to some other particle, such as a quark, processes can happen which "use" one or more of the decay particles, and the process becomes "real", i.e. observable, if it does not, in comparing final particles to initial particles, violate mass/energy conservation. I know this does not sound very convincing. Maybe somebody else here can make it sound more plausible.

You say that the electron cannot go into the nucleus. But I think a more careful statement would be that at any time the electron has some small but nonzero probability of occupying the nucleus.

For now I will pass on your questions about general relativity and string theory.

 

[jtolliver]

In special relativity mass is not conserved. The mass is the magnitude of the energy-momentum vector, which is conserved. In relativity you cannot even add the masses of two particles. That is if E_1^2 - p_1^2=m_1^2 and E_2^2 - p_2^2=m_2^2 that does not in general mean that (E_1 + E_2)^2-(p_1+p_2)^2=(m_1 + m_2)^2. A two particle system can only be thought of as having a specific mass(which is the sum of the masses of the particles) when they are moving in approximately the same direction in space-time(this is true in the classical approximation where all particles are moving forward in time, but not moving much in space). Only when the masses can be added does conservation of mass even make sense.