# If Energy can be converted into mass, why can it not be converted into charge?

Probably a silly question, but something that came to mind yesterday. I couldn't find anything when searching.

Why is there an Energy mass equivalence principle but not an Energy charge equivalence principle?

In other words, why do our field theories have a Gauge invariance which allow for charge conservation, but not mass conservation, or why is it that charge has escaped from being a term in the energy mass equivalence? Is it just because we have observed these to be the case and made our field theories around this, or because that's just how the mathematics works out?

• That's just the way the physics/nature works out. – user108787 Oct 22 '16 at 19:59
• Why would it be possible to convert energy into charge? Energy and charge are very different things. – Tanner Swett Oct 23 '16 at 1:57

You're making some category errors in the question. Energy can't be converted into mass, mass is a form that energy can take. In other words, when energy is "converted" into mass it never stops being energy. It's kind of like if I have a mass on a spring hanging vertically in a gravitational field, and I make it start bouncing. The energy moves back and forth from kinetic energy to the gravitational and spring stretch potential energies, and back. At no point in this process do any of these quantities not qualify as "energy". Mass, likewise, is just another way energy can be stored. If you study quantum field theory, you'll even learn that mass is one of the types of potential energies a field can store.

Charge, on the other hand, is about how a particle couples to a force. That gravity couples to mass is simply an observational fact that didn't, necessarily, have to be the case. When that distinction is being made physicists will refer to gravitational mass versus inertial mass. One of the strongest arguments for general relativity is the observed fact that gravity doesn't just couple to mass, it couples directly to energy/momentum in a way that is consistent with Einstein's equations. See: the gravitational lensing (observed many times by gravity from galaxies, galaxy clusters, microlensing, and even stars near the sun during a solar eclipse), gravitational redshift (observed frequency shift of light directed upward), etc.

Charge, on the other hand, is how various fermion fields, like the electron, up, and down fields, couple to the electro-magnetic field.

Note that total energy is conserved, so that which the gravitational field couples to is just as conserved as electric charge.

• +1 your answer is much more precise than my post and you have encouraged me to read more on qft, to see how mass fits in. Your answer is better than my mild rant on speculation , which I now have deleted. – user108787 Oct 22 '16 at 21:10

I believe that this question is still valid through logical deductions because of the fact that charge can be converted to energy using the following equations:

$$E = mc^2$$ $$V = \frac{E}{Q}$$

Therefore according to current physical knowledge, the following should be applied:

$V = \frac{mc^2}{Q}$

Where the variables symbolize the following values:

• $E$ = Energy
• $V$ = Voltage
• $Q$ = Charge
• $c$ = the relative speed of light

I think of it like this, atoms can be ionized, isotopes can decay and other reactions can occur that make atoms release mass from their containing field. This process reduces the mass of that field and causes the release of the energies binding that mass to the field and remove the charge from the field as the mass carries charge with it (either negative, neutral or positive) when being emitted. Using this knowledge we have learned to harness some of those energies directly with current technologies such as batteries.

• Did I get voted down on this because of peoples general feeling towards my other views so do not want my voice heard on mediums such as this, or is it because you believe the above is wrong? I ask this due to the above being scientifically verified and reproducable: #Laws# - Einsteins energy equivalence law is: e = mc squared. - Ohm's law is: V = e / q – Greg Goldberg Jan 24 '17 at 0:30
• Your answer was downvoted because it has technical inaccuracies. – Yashas Feb 17 '17 at 17:08