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Classical Electron-Photon Interaction

October 20, 2011

Start again with the simple Bohr hydrogen model where an electron drops from one non-radiating orbit to another. The amplitude of the electric field in the emitted classical em wave will start at zero, increase to some amount based on the orbits, then decrease back to zero as the electron settles into its final orbit. Since we don’t know why these non-radiating orbits exist, we also don’t know exactly how the amplitude of the emitted em wave behaves. We only know the endpoints are zero. The frequency of the emitted em wave will increase from that of the initial orbit to that of the final orbit. As with the amplitude, the exact instantaneous frequency is not known but the endpoints are.

What effect will this emitted em wave have on a free electron that’s initially at rest? As earlier, let’s place the free electron along the axis of the hydrogen atom and assume axis of rotation remains constant so that the free electron sees an amplitude-modulated, chirped, circularly polarized em wave. The electron is accelerated in a circular path by the rotating electric field, with an orbital radius proportional to the magnitude of the electric field. Simultaneously, the electron is forced downstream by v x B. This longitudinal acceleration is proportional to the rate of change of the amplitude and frequency of the em wave. Note that if both the amplitude and frequency are constant, the longitudinal acceleration will vanish.

What is the overall path of the electron during the interaction? It’s a helix whose radius varies with the amplitude and frequency of the em wave, i.e. from zero to some maximum then back to zero again. The length of the helix depends on the amplitude and frequency of the em wave. It’s important to note that an initially-at-rest electron will return to rest following the passage of the em wave if it doesn’t interact with a third party while under the influence of the em wave. 

Some important notes for this simplified example:

  1. The emitted em wave always has the same amplitude and frequency envelope for a given set of hydrogen orbits.
  2. The emitted em wave’s amplitude decreases as 1/r with distance from the hydrogen atom
  3. The free electron’s path is a limited helix
  4. The free electron’s position is changed by a fixed amount that depends on the distance from the source
  5. The maximum amount of energy available to the free electron decreases with distance
  6. Only a tiny amount of the emitted energy will be intercepted by the free electron.
  7. The free electron will only retain energy from the em wave if it interacts with a third party

Due to #2 and #6, at any reasonable distance from a single hydrogen atom, the classical em wave is billions of times too weak to transfer a photon’s worth of energy to the free electron. Clearly, a classical explanation of the photon effect must depend on energy already contained in the target electron’s environment.

What possible local mechanism will mimic receipt of a photon of energy by the free electron? There is no known classical mechanism … but that doesn’t mean that one doesn’t exist.  In addition, we never experiment with single, isolated electrons but always with collections of them. That enables third party interactions. If the initial conditions are right, individual electrons could be ejected from those collections while under the influence of em waves. That would be where probability and statistics come into the model, not at the low-level individual interaction level.

With so many unknowns in the classical world, it seems premature to discard determinism and switch to the quantum world with all its “weirdness”. From a software perspective, I consider such “weirdness” a bug, not a feature.


From → physics

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