# Lamb shift and mass

1. Mar 13, 2005

### elas

Lamb shift proved that within an atom the energy level of electrons changes with changes in orbital position. Given that energy and mass are related (or “one and the same” according to some texts) does this mean that within an atom electron mass varies? And if so does this not contradict particle physics teaching that states the electron is the one unchanging particle?
I am confused.

2. Mar 20, 2005

### Creator

Elas, forget Lamb shift for a second. The electron mass is known to change even in fine structure. Fine structure splitting is known to be a relativistic effect. In the hydrogen atom for example Dirac was the first to do a relativistic treatment.
The major contribution to the Hamiltonian is mainly due to the spin-orbit coupling. However, there is an added contribution to the atomic energy due to the variation of the electron's mass with velocity:
H(rel) =$$\frac{p^4}{8mc^2}$$ (I think that's correct value.)

This shift occurs at both fine structure levels by the same amount and so doesn't affect the splitting.

Lamb shift on the other hand is attributable to what is called a 'radiative correction' or the self energy of the electron. It indicates the radiative coupling of the electron to the vacuum field. In QED the electron field causes a polarization of the vacuum, altering the interaction energy slightly.
It's really a measure of the electrostatic polarizability of the virtual vacuum fluctuations.

You bring up an interesting point about the electron's position dependence. However, it is the vacuum polarization that causes the charge, actually the charge to epsilon ratio (actually $$\frac{q}{\sqrt\epsilon_0}$$), to be position dependent, increasing from its 'normal' value but only at very close interparticle separations (below the electron's Compton wavelength).
In actuality it is $$\epsilon_0$$, the dielectric 'constant' of the vacuum, that is not constant afterall. :surprised At close distances its value is altered by the polarized virtual particles surrounding the electron.
It is usually more practical to speak of the position dependence of the alpha structure constant, since it also varies with $$\epsilon_0$$.

Sometimes due to the effective screening of the charge the difference is referred to as 'screened' charge vs. 'bare' charge.
Hope that helps.

Creator

(Modified to include Latex correction).

Last edited: Mar 20, 2005
3. Mar 20, 2005

### arivero

Perhaps it is worth mentioning that there is also the concept of "bare mass".

4. Mar 21, 2005

### elas

Many thanks, this is a detailed reply that I can study and use. It is replies of this quality that enable me to determine whether my way out ideas are right or wrong and that means making progress even if only by eliminating a wrong idea. Fortunately this time it confirms a right idea, if only that were always the case!.

5. Mar 21, 2005

### Creator

Creator

6. Mar 21, 2005

### Antiphon

Elas,

A final note on energy and mass to compliemnt the many fine posts..

Energy and mass really are completely equivalent. If you compress
a spring, the potential energy of the compression will manifest itself as an
equivalent mass. That is, a squeezed spring is a tiny tiny bit heavier than
a not-squeezed one! This means strict conservation of energy is more
general than the classical conservation of mass.