Pair Production and Mass Energy Equivalence

[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.

Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon (or another neutral boson). For example an electron and its antiparticle, the positron, may be created. This is allowed, provided there is enough energy available to create the pair – at least the total rest mass energy of the two particles – and that the situation allows both energy and momentum to be conserved.

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

The energy of this photon can be converted into mass through Einstein's equation E=mc² where E is energy, m is mass and c is the speed of light. The photon must have enough energy to create the mass of an electron plus a positron.

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.

 

[SpectraCat]

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?

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.

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

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?

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.

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?

 

[LostConjugate]

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?

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.

 

[qsa]

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

You can google.

 

[LostConjugate]

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

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

 

[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?

 

[qsa]

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?

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!

 

[Schr0d1ng3r]

However in pair-production, you turn one boson into TWO fermions, with conservation of angular momentum, so there is no problem there.

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.

 

[LostConjugate]

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.

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

 

[Schr0d1ng3r]

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

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

 

[SpectraCat]

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.

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.

 

[Schr0d1ng3r]

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.

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...

 

[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

 

[SpectraCat]

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...

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.

 

[Schr0d1ng3r]

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.

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