How Can I Visualize One Electron?
I'm a total fan of "visual" understanding. If I can't visualize something, I don't feel that I understand it. I need a visual model for how things work. I am a visual person. I'm struggling with this image in my head. The standard "Copenhagen" interpretation of quantum theory says don't even try to visualize the electron. It's impossible.
But in 1928 Paul Dirac wrote a complete equation for the electron. It is a nonlinear first order differential equation describing the electron field. This was before quantization. Dirac still believed that the electron field was physically real and existed everywhere, even in a vacuum. A year later Dirac produced a quantized version of the equation that only describes the probability of "finding" an electron.
Dirac's original field equation is still correct, but it's very hard to visualize the electron field by looking at the equation. Here is Dirac's original equation from Wikipedia.
 |
| Dirac Equation [Wikipedia] |
After 30 years in microelectronics I know that formulas and equations are very powerful but without common sense formulas can predict nonsense. Garbage in - garbage out.
I spent a lot of time modeling MOSFET transistor behavior in silicon semiconductors. 3D modeling and simulation flourished along with computer speed and power. So I looked for computer simulations of Dirac's equation with visual results for single, localized waves. Here is a paper published in 2017. It shows some 1-dimensional plots of the Dirac electron field as a function of time in free space. These are stable solutions of single waves (solitons) standing still (velocity = 0). This is how I visualize one electron.
 |
| From "Solitary waves in the Nonlinear Dirac Equation" by Jes´us Cuevas-Maraver, Nonlinear Sciences, Page 61, 2017 |
So first of all I don't visualize electrons as "points." Apparently in free space they can stand still and just vibrate in a stable way. They don't fly apart or collapse. It looks like they can just sit there and oscillate. What holds it together? I don't know. The illustrations above are only in one dimension versus time, but I can use my imagination to make the images 3D. From these pictures I visualize the electron like a vibrating (oscillating) charged blob. It has some size, mass, location, and oscillation frequency. It also has "spin" but we can't see it in these photos.
It is much more common to simulate captive electrons in an atom. These simulated 2D "orbital" pictures are in every chemistry book. Here is one from Wikipedia.
 |
| Computer simulated pictures of a single electron in a hydrogen atom with various different energies. Atomic orbitals [Wikipedia] |
So I can visualize a single electron as an oddly shaped "atmosphere," smoothly distributed around a relatively tiny planet (the atomic nucleus). The electric charge is smoothly distributed. These charged electron blobs or clouds are stable, unless they are disturbed.
Since 1927 it was known that free electrons have some wave properties (frequency and wavelength). In 1989 Tonomura performed a double slit experiment with electron beams that showed wave interference. Interference is certainly a wave behavior. This agrees with Dirac's wave equation.
So what about "wave-particle duality?" Is an electron BOTH a wave and a particle? Is it sometimes a wave, sometimes a particle, sometimes both?
If we understand Dirac's wave equation to describe real physical waves (not waves of "probability") then we never need to visualize any "particle" behavior.
The Dirac equation can be written in terms of fluid flow describing an incompressible electrically charged magnetic fluid in an external electromagnetic field. This electron "fluid" has a mass density, a charge density, and a spin (angular momentum) density. [Rashkovskiy, 2018].
Compare this electron field with the electromagnetic field. Both have distributed energy, momentum and spin. The big difference is charge density and mass density. Electromagnetic waves spread out in all directions, but electron waves form vibrating blobs. The blobs are charged and repel each other. Every time one of these oscillating blobs goes through a double slit it interferes with itself just like a wave.
Below is a beautiful Youtube video 3D simulation of a single electron confined in various boxes (wells).
Comments
Post a Comment