Okay, I should be peeling beets right now
Happy Thanksgiving!
I am solidly of the opinion that if you charge an ideal capacitor you will increase its mass.
I am specifically talking about the mass of the electric field, created when electrons are moved from one plate to the other, with no net change in the number of particles that make up the capacitor. The total number of protons, neutrons, and electrons remains exactly the same, but the electrons are moved into a different _higher energy_ arrangement, and the total mass of the capacitor (including its electric field) increases.
However I do not believe that the above statement is experimentally verifiable given the current state of technology.
As I mentioned in my previous post, we have direct measurement of change in mass for nuclear reactions. IMHO this is applicable evidence, because a nuclear reaction is simply a re-arrangement of nucleons in the potential fields that they create; in other words the difference in mass of Deuterium versus Helium is caused by a change in potential energy of the protons and neutrons relative to each other. A change in electron potential energy should also create a change in mass.
We know that electromagnetic waves are attracted by gravity. (This was one of the earliest experimental tests of Einstein's work, measuring how the path of light bends around the sun.) As far as we know, gravity always works in both directions: if a mass attracts a light beam, then the light beam has to attract that mass. But I doubt that the experiment could be run in the reverse direction. Additionally, I doubt that we could measure the change in gravitational attraction created by a charged capacitor.
I think that the most practicable experiment that might be made is to use an extremely high resolution mass spectrometer to measure the mass of different chemicals. For example, if you could measure the mass of Carbon, Oxygen, and Carbon Dioxide with sufficient resolution, then you would be able to directly detect any change in mass associated with the 'heat of formation' of the CO2. I did a quick calculation; such an experiment would need to be able to resolve mass differences of about 1 in 10^14. I don't believe that any hardware even comes close to this resolution.
I did find a relevant discussion among professionals in the field, directed toward educators:
http://www.newton.dep.anl.gov/askasci/phy00/phy00950.htm
http://www.newton.dep.anl.gov/askasci/chem03/chem03641.htm
Note the difference in answers in the first archive, and the way things converge in the second archive. I especially like the last answer of the second archive, which boils down to: "All the things that we can measure suggest that when you put energy into a system, that system becomes more massive...but for the low energies of chemical reactions this mass change is too small to measure. The only reason that we believe that such low energy changes are associated with mass change is because it is simpler to believe that low energy changes will be consistent with high energy changes, but until we actually make the measurement this is just a good guess. Also the idea that simply re-arranging the atoms should change the mass bugs me."
-Jon
P.S.
Calculation notes:
The 'atomic mass unit' is currently believed to be 1.660538782(83) ? 10^27 kg. ('Believed to be' because it is _defined_ as 1/12 the mass of a Carbon-12 atom, and that is open to measurement uncertainty.)
The speed of light is defined to be 299792458 m/s
The energy associated with a single AMU is thus 1.49241783 * 10^-10 J
The 'standard enthalpy of formation' of Carbon Dioxide is -393.52 kJ/mol.
The number of molecules in a mole is 6.02214179(30) ? 10^23
The energy released when 1 atom of carbon reacts with 2 atoms of oxygen is thus approximately 6.53*10^-22 J ( I say approximately because 'standard enthalpy' is defined in terms of standard conditions and I don't know if that really applies when talking of a single molecule.)
So the energy change of this chemical reaction (making CO2 from C and O) is something like 4*10^-12 AMU