# Conservation of charge

1. May 17, 2013

### Lokesh Sharma

What will happen to charge on electron if eletron's mass is converted to energy according to Mass-Energy equivalence principle. Would the charge on electron be conserved? If yes, then were would it go as there is no mass now.

2. May 17, 2013

### Staff: Mentor

3. May 19, 2013

### Popper

That's correct. I'd like to comment on your statement mass is converted to energy. This is a very common but very inaccurate statement. It was pointed out a very long time ago that such a conversion is wrong. It was published as A Relativistic Misconception by Roland Eddy, Science, Sept. 1946. pgs 303. A more recent article is Does nature convert mass into energy?, Ralph Baiellein, Am. J. Phys. 75(4), April 2007

Mass is never converted to energy since both mass and energy are conserved in any reacion. The only think that is not conserved is the sum of the proper masses of the particles in the system. Mass-energy conversion can, at best, only refer to the form in which mass and energy takes. For example; an electron can annihilate a positron with resulting in two photons. The mass to begin with is m and the mass which results is also m. The resulting m is a sum of the relativistic masses of the two photons. The conversion which takes place is that rest energy is converted to kinetic energy. I.e. the initial energy is the sum of kinetic energy and rest energy. The energy after annihilation is all kinetic energy.

If you prefer not to think in terms of relativistic mass then it doesn’t matter because the alternate definition of the mass of a system of particles is the magnitude of total 4-momentum of all the particles in the system. That too is constant in time as well as being an invariant quantity.

One last comment: When considering particle reactions keep in mind that its both energy and momentum must be conserved. That's why you can't have a particle with no charge suddenly change into a single photon. Think of this from the initial rest frame of the particle. The total momentum is zero. If it decay ed into a single photon then since a single photon has momentum, the law of conservation of momentum would be violated.

Last edited: May 19, 2013
4. May 19, 2013

### kurros

I don't have access to the first article, but reading the second, it seems very silly to me. Their argument seems to boil down to a claim that "rest energy" is not the same thing as mass. It was only a quick read, but I did not see where they describe what they think mass "actually" is.

One can go around claiming that mass "doesn't exist" and that it is all just QCD binding energy, or Higgs field interactions or whatever, but as definitions go "mass"="rest energy" is a perfectly good one. So to me that paper is silly word games. I will concede that the OP's phrase "mass is converted into energy" can be troublesome since by "energy" here what is really mean is "kinetic energy", not "total energy". Maybe that was the thrust of the article, but it wasn't obviously the case to me.

As for your post, all this talk of "relativistic mass" is also not very helpful I think. I agree strongly with this article on that subject: http://www.worldscientific.com/doi/pdf/10.1142/9789812814128_0003

As for the OP, jedishrfu basically covered it. Electrons cannot just vanish, leaving behind a "disembodied" unit of charge. To "convert their mass into energy", as it were, you need to destroy them with something, and actually only a positron can do this. Actually that is not totally true, a weak interaction could convert said electron into a neutrino, but other charged particles would be involved such that electric charge is still conserved.

Last edited: May 19, 2013