Mass of Hydrogen Atom: Proton, Electron, & Binding Energy

[pej.dgr]

It is well established fact that the mass of a ground state hydrogen atom is less than tha sum of the masses of the proton and electron from which it was formed, less by the mass equivalent of the binding energy (13.6 ev).

There are just two hypotheses that agree with the experimental evidence:
(a) All of the mass of the atom (inclusive of the negative potential energy) is localised in the two particles. The mass of each is reduced by (13.6/9.387 x 10^-6)%.
(b) The negative (potential energy) mass is a separate entity external to the particles. The mass of each of these is constant throughout the life of the particle and any interaction with other particles.

The most explicit discussion of these that I have found in the literature is that of Brillouin: “The actual mass of potential energy, a correction to classical relativity”, Proc. Nat. Acad. Sc. 1965; 53; 3; 475-482. He acknowledges that there is no way we can decide between the two by experiment but argues for (b), the “assumption” that the interaction potential energy is a separate entity from the energy of the self fields of the particles, that its mass cannot therefore be localised in the particles, that to dog so is at best a simplifying assumption.

It can fairly be claimed that (a) is conceptually simpler than (b) but almost everyone rejects it in favour of (b). If no one can devise an experiment to decide between the two why is this so?

Phil Gardner

 

[Parlyne]

The problem with your question is that it assumes the particles can actually be localized in the first place. Quantum mechanics makes it pretty clear that they cannot; so, from a physical standpoint at least, it's not clear that there's really a difference between the two viewpoints.

 

[lightarrow]

It is well established fact that the mass of a ground state hydrogen atom is less than tha sum of the masses of the proton and electron from which it was formed, less by the mass equivalent of the binding energy (13.6 ev).

There are just two hypotheses that agree with the experimental evidence:
(a) All of the mass of the atom (inclusive of the negative potential energy) is localised in the two particles. The mass of each is reduced by (13.6/9.387 x 10^-6)%.
(b) The negative (potential energy) mass is a separate entity external to the particles. The mass of each of these is constant throughout the life of the particle and any interaction with other particles.

The most explicit discussion of these that I have found in the literature is that of Brillouin: “The actual mass of potential energy, a correction to classical relativity”, Proc. Nat. Acad. Sc. 1965; 53; 3; 475-482. He acknowledges that there is no way we can decide between the two by experiment but argues for (b), the “assumption” that the interaction potential energy is a separate entity from the energy of the self fields of the particles, that its mass cannot therefore be localised in the particles, that to dog so is at best a simplifying assumption.

It can fairly be claimed that (a) is conceptually simpler than (b) but almost everyone rejects it in favour of (b). If no one can devise an experiment to decide between the two why is this so?

Let's consider a simpler situation: a positronium atom-like configuration, that is an electron and a positron orbiting one around the other. Then they annihilates to form energy in the form of electromagnetic fields. Where do you localize the mass, after the annihilation?