Javaro, every electron 'jiggles.' They are not stationary. The mass of any electron is determined by the amount of space its jiggling takes up. If you heat up your chair, all the atoms are moving faster, and thus the chair, atomically, has 'gained mass'. But as far as you are concerned there is no difference except in what you feel regarding the tempeerature. You see no change in mass.
The Zero Point Energy has been measured as increasing with time. That has been measured by measurements of something called Planck's Constant. The chart showing that in a simple form, but with references, is here:
http://www.setterfield.org/Charts.htm#graphs (it's the middle graph)
This means that there is a reason for the electrons to be taking up more space with their 'jiggling' -- they are becoming more battered by a higher ZPE and thus their motion is more violent. Atomically, this gives them greater mass.
But that does not affect the construction of the atom itself or its electromagnetic properties which cause the binding to other atoms and molecules which eventually make up your chair. It is that combination of atoms and molecules together which must be moved to determine the mass of your chair. The fact that the components on such a small scale may be moving, or jiggling, a little faster or slower does not affect the matter of the entire chair. The amount of matter making up the chair is defined as mass. The amount of movement taking place within that matter does not affect the amount of matter itself, as long as we don't have something like spontaneous combustion!
One way mass measured on the atomic scale is a matter of space -- how much space does that jiggling point-charge take up? That is defined as its mass. There is another way of measuring the mass of an electron, and that has to do with its own total energy. This is a constant, as the jiggling is a result of the battering from the outside by the ZPE.
While the "eneergy mass" stays constant, the "jiggling mass' can increase or decrease without affecting the fact that the atom it is in stays stable, and connected with other atoms (or not) the same way. It is this matter of connections which make up your chair, and you, and not how much any electon is battered by the ZPE.
This is why we have been able to measure the mass of the electron as increasing in terms of volume of space taken up (by the jiggling effect), but that mass as you and I deal with it on a daily basis remains unchanged.
I hope that helps.
Oh, I believe that 'natuurekunde' is a general science course.