^
| spin-z
electron cloud
^
|
(======) "generator"
|
v
positron cloud
| spin-z
v
We imagine that the generator is analogous to a classical rotating electric dipole which produces a circularly polarized radio wave.
We first imagine that the electron-positron wave is a classical wave. The generator creates classical "clouds" of positive and negative charge.
The clouds have angular momentum, just like a rotating electric dipole gives up ħ of angular momentum per produced photon.
We assume that the z component of the angular momentum of the cloud is 1/2 ħ per produced elementary charge. The negative cloud and the positive cloud rotate to the opposite directions.
The wave-particle duality
This setup reminds us of the 19th century belief that electricity is some kind of a liquid which can flow. The particle model of electricity came later, when radioactivity was studied around the year 1900.
For electromagnetic waves, people recognize that a strong wave is a classical object whose quantum is the photon. We are very much aware of the wave-particle duality for electromagnetic waves.
On the other hand, we tend to conceive the electron purely as a particle. The classical aspect of an electron cloud is usually forgotten.
"Collapse" of a wave function
Absorption of photons shows that a weak classical electromagnetic wave somehow can "concentrate" its energy into a small spacetime 4-volume and excite, for example, a hydrogen atom.
An analogous process might be that we have a diffuse classical cloud of negative electricity, and the charge "collapses" into a small spacetime 4-volume, to be observed as an electron.
The gyromagnetic ratio 2 in the electron-positron generator
Our generator produces rotating clouds of electricity. The magnetic field of both clouds points to the same direction. Let the magnetic field of the rotating negative cloud be B.
Classically, we can measure a magnetic field strength of roughly 2 B, because the rotating negative and positive charge fields together form a "coil".
One may now ask that if the magnetic field "collapses" into a small spacetime 4-volume, what is its measured strength? Is it the field of a single electron, or double that field?
Empirically, it is double the field. The gyromagnetic ratio of the electron is 2.
Observing a single electron far from the generator
For photons, we have introduced in this blog the "teleportation" model where we conceptually move the rotating electric dipole very close to the absorbing antenna. That is the way to make the energy of the electromagnetic wave to "collapse" into a small spacetime 4-volume.
Similarly, we may imagine that when we measure the magnetic moment of the electron, we are doing it close to the electron-positron generator. That could explain the gyromagnetic ratio when we are observing an isolated electron.
Why we do not observe the electric charge of the positron when we measure an isolated electron?
The teleportation model has a hard time explaining why we measure -e as the charge of the electron, and do not see the positron charge +e around.
The explanation might be that the electric field has sources, while the magnetic field does not have. Let us measure the charge of a certain volume in the classical cloud of the electron-positron generator. We will classically get just the charge of the electrons there. On the other hand, the magnetic field classically is measured as 2 B.
The electron spin 1/2
In the electron-positron generator model, the pair is considered a single object. The summed absolute spin-z of the system is 1 ħ.
Thus, the wave of the pair does return to the same state after a single rotation. There is no problem of destructive interference which would happen if the system would have the spin-z 1/2 ħ.
If Nature has 1 ħ as the smallest possible absolute angular momentum to the z direction of an independent system, then the spin-z 1/2 ħ of the electron and the positron is the logical minimum possible spin. The spin of the photon is 1 ħ because the photon can be created independently from other particles. A single photon is an independent system.
The structure of the electron and the photon
Our new model claims that the "structure" of the electron is the imagined electron-positron generator and its classical electron and positron clouds very close to the generator. The clouds are rotating. That is the origin of the electron spin and angular momentum.
A collapse of the electron wave function teleports the generator very close to the observer.
This is similar to the photon. We claim that the "structure" of the photon is the rotating electric dipole which produces a classical electromagnetic wave. A collapse of the photon wave function teleports the rotating dipole very close to the absorbing system.
To explain the photon spin angular momentum, we do not imagine that the photon is a rotating little ball, or that it does some kind of zitterbewegung. Rather, we think that the photon, in an abstract way, possesses a part of the energy and the angular momentum of the classical electromagnetic wave.
It is a mistake to think that the electron is a tiny classical particle which does zitterbewegung to produce the spin and the magnetic moment. Rather, the electron is a "collapse" of a classical cloud of charge. The properties of the electron reflect the properties of that classical cloud. In this thinking, the classical limit is reflected in the quantum world. One might claim that the classical limit is fundamental and the quantum, the electron, secondary.
Conclusions
Our new model has a similarity to the "pipe" model which we introduced a couple of years ago. The pipe was imagined to connect the electron to the corresponding positron of a pair. In the new model we explain the pipe functionality through the collapse of the wave function and the teleportation model.
We conjecture that if a particle carries a charge which must be conserved, then the particle must have the spin-z 1/2, and the "gyromagnetic" ratio for the corresponding field is 2. We need to check what is currently known about elementary particles.
We still do not understand why the Dirac equation gets the electron spin and the gyromagnetic ratio 2 right. Is it somehow aware of our electron-positron generator?
Does the new model solve the problem of the infinite energy of the electric field of a point particle? If the "particle" is just a quantum of a diffuse field, the problem may not arise.
No comments:
Post a Comment