An example is a photon which is emitted by a rotating dipole, and after that absorbed by another rotating dipole, and then re-emitted. The old wave function maybe was vastly diluted, but it becomes concentrated again after the absorption and re-emission.
A photon has the spin-z 1, and can be created as a standalone particle.
How to absorb and re-emit an electron: the semiconductor case
Let us study this process first in a semiconductor where there are bound electrons in valence bands and "free" electrons in conduction bands.
If we excite an electron and it jumps to a conduction band, we produce a pair: an electron and a hole, which behaves somewhat like a positron.
Now we have an interpretation for absorbing and re-emitting an electron. Let us have a free electron wave function which has spread wide in a block of a semiconductor
● -----------------> O -----------------> ●
free electron hole new free electron
The free electron wave function collapse might be this process:
1. The free electron drops to a hole: the free electron is "annihilated with a positron".
2. The hole emits a new electron. A new "pair is produced".
The end result of this process is a new free electron, but no new hole.
Alternatively, we may interpret that in the Huygens principle, the two-phase process above creates a new wave.
e- --------
/
/ e+
----------- e-
The Feynman diagram of the process is like the letter Z.
Why we cannot simply make the wave function of the free electron to collapse? Why should we include a complicated two-phase process?
The reason might be the following: we can create a new, concentrated wave function for an electron if we produce a new pair. But it is not clear if we can do the same trick without pair production - using just the electron wave.
Analogously, we can create a new, concentrated wave function for a photon using absorption and emission. But it is not clear if we can do the same trick without absorption and emission.
In a Feynman diagram, a Green's function is used to create a new electron wave. It is somewhat suspicious if such a wave can be created without the associated positron.
Also, Erwin Schrödinger and others observed that a standard Dirac electron wave packet contains positron components. As if one would not be able to treat the electron as a standalone particle - the positron is always present.
Let us assume that we have an "atom" in a semiconductor. We may have a separate positive charge, a free electron orbits it. It might be that zones of positive charge appear in the semiconductor as the free electron moves. These zones can be interpreted as "positron" wave functions.
The electron in otherwise empty space
The semiconductor might be analogous to empty space. Pair production can be treated as the excitation of the electron from the -511 keV energy state to the +511 keV energy state.
The gyromagnetic ratio 2 of the electron
In our February 23, 2022 blog post we speculated that the gyromagnetic ratio 2 of the electron comes from the fact that we "see" the magnetic field of the associated positron, too.
The spin-z 1/2 of the electron defies imagination: how can an object possess a wave function which seems to cancel itself out after a 360 degree rotation? The hypothesis that a positron is tightly associated with the electron may help us to accept this strange state of affairs.
Conclusions
It might be that the correct way to manipulate the electron wave function is through pair production, and we cannot treat the electron as a standalone particle at all.
In a semiconductor, the system of electrons and nuclei is very complex, and it is not surprising if a free electron and a hole cannot be treated as standalone (quasi)particles.
Richard Feynman considered the hypothesis that positrons are electrons traveling back in time. The semiconductor analogue might be more fruitful: positrons are holes in a semiconductor.
A new question: are electromagnetic waves polarization in the "semiconductor" of the vacuum?
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