Z+ ●
^
|
|
e-
As the electron approaches the nucleus, its speed accelerates. The electric field lines of the electron bend and are squeezed closer to each other (just as in the Edward M. Purcell diagram of the electromagnetic wave production).
Since the field lines are now closer to each other, the energy density E^2 has increased and the tension in the field lines has grown.
In our classical model, the field lines tend to "break" if their tension grows large enough.
field line
--------------- + - ----------------
Broken field lines end at small charges which have formed at the loose ends on the line.
This model is like the rubber band model in quantum chromodynamics.
How do the small charges at the ends of broken field lines clump together to form a full new electron and a positron? Our model predicts that a fuzzy spatial distribution of charges will form.
The electron is the quantum of the formed fuzzy charge distribution. A classical model cannot predict the birth of a quantum from a fuzzy distribution.
A quantum model using a Feynman diagram
A quantum model might treat the electromagnetic field as a particle, a single virtual photon, and create the electron and the positron as particles from that photon.
--------- e-
E, p /
virtual ~~~~
photon / \______ e+
e- -----------------------------------
| virtual
| photon q
Z+ -----------------------------------
The Feynman diagram above describes a quantum process. The electron emits a virtual photon which has E >= 1.022 MeV of energy and momentum p. That photon in the classical model would be part of the increased energy and momentum of the electric field of the electron.
The increased energy escapes from the electric field to a new produced pair. We say that electromagnetism is nonlinear in this case because energy can escape to pairs.
If no pair were created, the extra energy and the momentum in the electron's electric field would return back to the electron and propel the electron out of the potential of the nucleus Z+ at the original speed of the electron. The rubber plate model helps to visualize this process. In the approach the plate lags, in the departure the plate is ahead and pulls the electron out of the potential.
But the electron lost energy and momentum in the production of the pair. The electron will exit the potential of the nucleus more slowly, and suffer an extra loss of momentum q, which is marked as the second virtual photon. Actually, q is the combined effect of several processes which transferred extra momentum from the electron to the nucleus.
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