# Mass, Charge, Energy relation

1. Mar 8, 2012

### TMSxPhyFor

Hi All

A question that bothering me and I can't find answer for:

a charged particle in empty space will generate an electromagnetic field that has energy density and can be described by Energy-Momentum Tensor.

A non charged particle at rest also has energy due to mass energy equivalence.

so the total energy of our universe will be bigger if the particle is charged?!

if that true please explain why there is no kind of charge/energy equivalence like for mass.
But if that wrong, please explain from where our field gets the "extra" energy that it "radiates" (i.e photons)

2. Mar 8, 2012

### tiny-tim

Hi TMSxPhyFor!

The energy-due-to-mass of all the particles in the universe adds up.

But the energy-due-to-charge of all the particles in the universe mostly cancels.

If there are two equal and opposite charges close together, the energy-due-to-charge is almost zero after a very short distance.

3. Mar 8, 2012

### TMSxPhyFor

I understand that you are talking about dipoles , but I mean if we imagine abstract empty universe with just one charged particle....

4. Nov 9, 2013

### dineshb

equivalence of energy and charge

Hello
I have had the same question regarding the possible equivalence between energy and charge. I recently published a paper on charge energy equivalence.
Let me know if you have found any definitive answer to this question.

db

5. Nov 9, 2013

### WannabeNewton

What kind of equivalence are you looking for? In general relativity, (non-gravitational) energy-momentum density is codified in a symmetric tensor $T_{ab}$ whereas charge density and 3-current density are codified in a 4-vector $j^a$ (the energy-momentum tensor and 4-current density respectively) so clearly they are not even the same objects!

However there is a relationship between $j^a$ and $T_{ab}$ when the latter represents the energy-momentum density of an electromagnetic field $F_{ab}$. In such a case, $T_{ab}$ is given by $T_{ab} = \frac{1}{4\pi}(F_{ac}F_{b}{}{}^{c} - \frac{1}{4}g_{ab}F_{de}F^{de})$ and one can easily show that $\nabla^a T_{ab} = F_{ab}j^a$ using Maxwell's equations $\nabla^a F_{ab} = -4\pi j_b$ and $\nabla_{[a}F_{bc]} = 0$. This is nothing more than the general relativistic version of Poynting's theorem.

Indeed, we have that $\nabla^a T_{ab} = \frac{1}{4\pi}(F_{b}{}{}^{c}\nabla^aF_{ac} + F_{ac}\nabla^a F_{b}{}{}^{c} - \frac{1}{2}F_{ac}\nabla_bF^{ac}) \\= -F_{bc}j^{c} + \frac{1}{8\pi}(F_{ac}\nabla^a F_{b}{}{}^{c} + F_{ac}\nabla^{c}F^{a}{}{}_{b} - F_{ac}\nabla_bF^{ac}) = F_{ab}j^{a}$
as desired.

6. Nov 10, 2013

### dineshb

Hello,
without getting into general relativity, I would like to get an equivalence between charge quantity of a particle like electron and its total energy in a rest frame. similar to what e=mc^2 for a particle with m mass.
further, this should be able to extend to an energy-momentum relation, as in the case of a mass particle, where E^2=(mc^2)^2 + (pc)^2.

7. Nov 10, 2013

### WannabeNewton

Oh, certainly there exists something of that nature but not exactly as you have posed it. See here: http://en.wikipedia.org/wiki/Electromagnetic_mass

Check out Schwartz "Principles of Electrodynamics" pp.200-203 for a discussion/derivation of the electromagnetic mass.

8. Nov 10, 2013

### dineshb

Hi,
well, when it comes to E=mc^2, the energy is a function of the mass quantity but not based on its structure. However the one that you have pointed out is not just a function of the charge associated with the particle, but also with its structure terms like radius.
If you have little time, you could go through this paper that I published, titled "On the Planck Scale Potential Associated with Particles" and give your feedback.
https://www.researchgate.net/profile/Dinesh_Bulathsinghala/?ev=prf_highl [Broken]
thanks

Last edited by a moderator: May 6, 2017