# Escape velocity of electron/positron pair

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P: 595
 Quote by xortdsc mass is either constant (invariant mass) or increases with kinetic energy (relativistic mass) check this article: http://hepth.hanyang.ac.kr/~sjs/physics/mass.html so how could it possibly pay the kinetic energy toll with its mass ? It makes no sense.
Does it make sense to you that a hydrogen atom (a system of interacting proton and electorn) has LESS mass than a separate electron and separate proton? If yes, then what's your problem with interacting electron and positron having similarly reduced masses?

 most people here don't seem to understand what i want to do. I don't care how much kinetic energy a electron needs to escape a positron in proximity, but how much energy is needed to create them. Okay, then you keep repeating it is 2 times the (invariant) rest-mass of the electron, but if mass is invariant, where does the kinetic energy come from ?
"Invariant rest mass of electron" refers to a free electron, one which does not interact with other particles.

When e+e- pair is created, these particles ARE interacting (at least at first when they are close to each other). Their rest masses ARE NOT equal to "Invariant rest mass of electron", they are less than that. The remainder is in their kinetic energy.
P: 94
 Quote by mfb No, it is the whole idea to describe the process with classical concepts.
if by "classical concepts" you mean position and momentum, how can any theory get rid of these ? Sure they are only approximations as in reality there are fluctuations all over the place. So what I mean by terms like position/momentum would be rather an average (to smooth the noise present) position/momentum.
Particles are localized in space, a bit unsharp, but still on average you can determine its position, right ?
P: 94
 Quote by nikkkom Does it make sense to you that a hydrogen atom (a system of interacting proton and electorn) has LESS mass than a separate electron and separate proton? If yes, then what's your problem with interacting electron and positron having similarly reduced masses? "Invariant rest mass of electron" refers to a free electron, one which does not interact with other particles. When e+e- pair is created, these particles ARE interacting (at least at first when they are close to each other). Their rest masses ARE NOT equal to "Invariant rest mass of electron", they are less than that. The remainder is in their kinetic energy.
okay that would make sense. so it really is the case that as they approach, mass energy goes down and kinetic energy goes up by equal amounts (so rest mass is converted to kinetic energy) ? Upon annihilation mass would become zero and all energy is stored as kinetic energy which then radiates off as (mass-less) photons...
That would totally explain where the kinetic energy comes from. I can live with that :) Thanks for the enlightenment
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P: 11,617
 Quote by xortdsc if by "classical concepts" you mean position and momentum, how can any theory get rid of these ? Sure they are only approximations as in reality there are fluctuations all over the place. So what I mean by terms like position/momentum would be rather an average (to smooth the noise present) position/momentum. Particles are localized in space, a bit unsharp, but still on average you can determine its position, right ?
I mean concepts like "position and momentum of particles". Quantum mechanics uses position and momentum operators. They are not simple values.
 So what I mean by terms like position/momentum would be rather an average
Those averages don't help for strong interactions, or they can even be ill-defined.

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