The simplest case was the man standing on a negative plane manipulating an electron.
The man inside a positively charged box was a very different scheme.
We can now present the new version of the energy-momentum relation for a static external electric field and an electron in it:
E^2 = p^2 + (m + b |V|)^2,
where b can be calculated by considering the distribution of the electric field energy when we move the electron.
The field energy density for a static electric field is E_V^2, where E_V is the electric field strength.
The Poynting vector is one method of calculating the energy flow in the electric field when we move the electron a little bit. The momentum of the energy flow tells how much extra inertia the electron gets from the field.
If metals are present, they affect the electric field change greatly and may dominate the calculation of b. The method of the "mirror electron" shows that m + b |V| is actually 2m inside a metal shell if the electron moves slowly.
Since the hydrogen atom does not present a different spectrum inside a metal shell, the orbital frequency of 10^18 Hz is too fast for mirror electrons to take part in action. Or, the quantum mechanical fact that the atom is in its ground state bans all energy-consuming interaction with the environment.
We should calculate the inertial mass of the electron in the hydrogen atom. Since the electric fields of the proton and the electron partially cancel each other out, our first guess is that the inertial mass is slightly less than 511 keV. The inertial mass depends on the distance from the proton. Close to the proton, we need to decide how close to each particle we let the field to extend. As is well known, the electric field energy is infinite for a point particle, and the integral may diverge.
The system electron-proton is a dipole. Most of the field energy is concentrated to a cigar-shaped area which surrounds the particles. That area determines the inertial mass of the electron.
____________
/ \
| e- p |
\____________/
Since the hydrogen atom does not present a different spectrum inside a metal shell, the orbital frequency of 10^18 Hz is too fast for mirror electrons to take part in action. Or, the quantum mechanical fact that the atom is in its ground state bans all energy-consuming interaction with the environment.
We should calculate the inertial mass of the electron in the hydrogen atom. Since the electric fields of the proton and the electron partially cancel each other out, our first guess is that the inertial mass is slightly less than 511 keV. The inertial mass depends on the distance from the proton. Close to the proton, we need to decide how close to each particle we let the field to extend. As is well known, the electric field energy is infinite for a point particle, and the integral may diverge.
The system electron-proton is a dipole. Most of the field energy is concentrated to a cigar-shaped area which surrounds the particles. That area determines the inertial mass of the electron.
____________
/ \
| e- p |
\____________/
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