Annihilation and potential energy?

[Quantumcorral]

Sorry, brand new here and this may be in the wrong place or very obvious. When matter and antimatter annihilate is the energy released the sum of all their potential energy? does E=MC² only work because of the specifics of our universe, and if the universe were to contain more matter (and therefore gravitation) a given unit of mass would release more energy upon annihilation?

 

[mfb]

Which potential energy?

The released energy is the total energy (mass, kinetic energy, binding energy, ...) of the annihilation partners in their center of energy frame. Potential energies relative to something else do not count - the final products are created at the same position, you don't lose or gain anything there.

and if the universe were to contain more matter (and therefore gravitation) a given unit of mass would release more energy upon annihilation?

No.

 

[Quantumcorral]

but the sum of the mass of the products is lower than the ingredients, so hasn't gravitational potential energy been lost? on a smaller scale is this not also the case with fusion/fission, gravitational potential energy must have been lost, or am I missing something?

 

[Bill_K]

but the sum of the mass of the products is lower than the ingredients, so hasn't gravitational potential energy been lost?

No, potential energy is not involved at all. What happens is that part of the rest mass of the ingredients is turned into kinetic energy of the products.

 

[mfb]

but the sum of the mass of the products is lower than the ingredients, so hasn't gravitational potential energy been lost? on a smaller scale is this not also the case with fusion/fission, gravitational potential energy must have been lost, or am I missing something?

Gravitational potential energy is relevant for energy, and there is no energy lost in the annihilation process.

 

[Quantumcorral]

Gravitational potential energy is relevant for energy, and there is no energy lost in the annihilation process.

sorry but when an object falls on Earth (or elsewhere) isn't the explanation that it converts its GPE into KE, and so if GPE is relevant for KE the do we have:

GPE of static object when 10km high = GPE of moving object 1km high + KE gained in falling + GPE of gained KE at 1km high?

 

[Bill_K]

but the sum of the mass of the products is lower than the ingredients, so hasn't gravitational potential energy been lost? on a smaller scale is this not also the case with fusion/fission, gravitational potential energy must have been lost, or am I missing something?

The point is, that when we write that the gravitational potential energy is mgh, what we really mean is that m is not just the rest mass. Gravity attracts all forms of energy, and m is really the total energy divided by c².

So in the annihilation process, some of the rest mass is converted to kinetic energy but the total energy remains unchanged, and therefore the gravitational potential energy also remains unchanged.

 

[ChrisVer]

Well, sometimes potential plays a role in creation/anihillation. For example in Klein's paradox (if you adjust a constant potential to V>E+m you will have creation/anihhilation out of the energy being in the potential).

The graviational energy in particles is at ultra high good approximation negligible.