# Pair Production and Mass Energy Equivalence

1. Jul 21, 2011

### LostConjugate

Hello,

In a previous discussion of Pair production I was shocked by what I heard and I have some questions from the general explanation of the subject.

So you can make fermions out of bosons? You can make rest mass out of energy?

Does this mean that not just relativistic mass, but also rest mass is just energy?

These are claims that are always shot down immediately anytime they are made around here with rest mass being implied as something more than energy, something mystical and intrinsic.

2. Jul 21, 2011

### SpectraCat

The restriction prohibiting conversion of fermions to boson (under normal low-energy conditions) is about 1-to-1 conversion of bosons to fermions (or vice-versa). This is not allowed because it violates (at least) angular momentum conservation. However in pair-production, you turn one boson into TWO fermions, with conservation of angular momentum, so there is no problem there.

What makes you think that there is no conversion between rest-mass and energy? We see it all the time. Look at the atomic mass of iron for example ... the mass there is significantly lower than the summed mass of the component nucleons. This is because of the extremely high binding energy in the iron nucleus (remember it is the end-point of the stellar fusion cycle, neglecting novae.) That energy was released upon formation of the nucleus, and so the nucleus appears lighter than the sum of its nucleon masses, with the difference corresponding precisely to the binding energy according to E=mc2.

Furthermore, pair-production is just the reverse of electron-positron annihilation. Do you object to that on the grounds that rest mass can't be converted into energy?

I guess I don't really understand what your question/issue is here. Can you provide links to threads where the objections you are citing were raised?

Last edited: Jul 21, 2011
3. Jul 21, 2011

### LostConjugate

Thanks Spectra,

The posts are so far back I don't know. I stopped speaking of Mass as Energy and vice-versa years ago because people would flip on the subject.

I will keep this post as reference or pair production as reference in the future.

The question for me now is

What you say makes sense about a single boson creating two fermions, the spins add up and the whole idea seems intuitive. Why can't we explain all physics in terms of bosons only and treat fermions as a special state of bosons?

Why do we even need to propose an electron field if electrons can be broken down into photons into electromagnetic fields.

4. Jul 21, 2011

### qsa

Have you ever hear about "electromagnetic mass" theory by lorentz. Even today there are people who tried to prove it experimentaly in scotland. I will dig up that info for you lf you want. Basically photons in cavity.

Last edited: Jul 21, 2011
5. Jul 21, 2011

### LostConjugate

I had not heard of it but am looking at it now.

6. Jul 21, 2011

### LostConjugate

Why is the mass of an electron always the same? What is special about this specific spectrum that massive particles have? What makes the electromagnetic wave suddenly stick and become a massive particle at these specific energies?

7. Jul 21, 2011

### qsa

too many theories "conjectures" have been proposed not only to describe them but also how their interaction arises and if rest mass is indeed constant and under what conditions. it will take too much time to list them and describe what is what. some even say they are little black holes!!

8. Jul 21, 2011

### Schr0d1ng3r

Isn't it supposed to be TWO photons into an electron and a positron? It still conserves angular momentum, and it's what has been used in every example that I've seen. I could be wrong on this though, I haven't done a whole lot with pair production.

9. Jul 21, 2011

### LostConjugate

The spin of a Photon is 1 and the spin of an Electron is 1/2. I guess the spin needs to add up, I think it is because a quantum state must describe the process and so there is addition of angular momentum involved. Since the spin is intrinsic you can't just say it was lost as energy somewhere.

1 = 1/2 +1/2

10. Jul 21, 2011

### Schr0d1ng3r

So the electron and positron both have spins of +1/2?

11. Jul 21, 2011

### SpectraCat

I don't know about that ... pair-production is usually (only?) observed near nuclei, because interaction with the nucleus is required to conserve linear momentum. I suppose that it might be correct to think of the interaction with the nucleus as being a second photon, but I have never seen it described or calculated that way. The equation I am used to is: $\gamma\rightarrow_{nucleus}~~e^+~+~e^-$, where the "nucleus" subscript on the arrow is often omitted. My main point is that the production of an even number of fermions from bosons at least has the possibility to conserve angular momentum, while the production of a single fermion from boson(s) must violate angular momentum conservation.

12. Jul 21, 2011

### Schr0d1ng3r

Oh, I think I get it now. We only briefly covered pair production/annihilation last year (and I do remember it having to be near a nucleus), but I guess I didn't quite grasp it.

What then would you say is going on here:

http://hendrix2.uoregon.edu/~imamura/123cs/lecture-7/pair_production_and_annihilation.jpg

It seems like it is showing two incident photons there...

13. Jul 21, 2011

### LostConjugate

It looks like you can create particle / anti-particle pairs from any particle by localizing the particle within a distance smaller than hbar/mc.

This pdf on page 8 (marked page -5-) refers this concept to poping particle anti-particle pairs out of the vacuum. This implies that the vacuum is where particles come from and that the energy was only a means to access the particles.

http://www.damtp.cam.ac.uk/user/tong/qft/one.pdf

14. Jul 21, 2011

### SpectraCat

That is an example of a theoretically possible (by time reversal symmetry I believe) two-photon interaction to induce pair production. Because there are *two* photons, you can theoretically satisfy momentum conservation without interacting with a massive body. However, the cross section for the photon-photon interaction is tiny .. this isn't precisely my field of study, so I might have missed it, but I am not aware of such an event (pair-production from two photons in free space) ever being experimentally observed.

15. Jul 21, 2011

### Schr0d1ng3r

Ahhhhh, ok. THAT'S where I was getting mixed up. Thanks, you helped a lot :D