Agemoz's Physics Blog

There’s a clickbait title if there ever was one! Nevertheless, as I worked on an iterative Schroedinger solver for the three elementary particle (u,d,u) proton case, it became immediately obvious that even if you ignore strong force, gluon masses, and the Higgs boson interactions within a proton, the proton has to have a lot more mass than an electron. Here’s why I think that:

Every physics freshman level student goes through the exercise of solving the Schroedinger equation for a hydrogen atom, yielding solutions that are quantized and form 3D probability distributions for each energy eigenstate. Quantization of these solutions are entirely dependent on the boundary conditions that apply, which for the hydrogen atom include the width of the potential energy quantum well. We also require real solutions and that the probability distribution go to zero at infinite distance, but the one that gives us quantization of the probability distribution shells (s, p, etc) is the physical width of the quantum well potential energy.

The proton is heavy, so we assume that the electron moves about a center-of-mass point that doesn’t move, which yields sinusoidal solutions whose frequencies are essentially integer multiples of the width of the electron-proton charge quantum well.

When I began work on the iterative Schroedinger solver, it immediately became clear that the quantum well width for the three-particle u,d,u case is a whole lot smaller, thus yielding sinusoidal wavelengths that also were much smaller by about a factor of 20 or so. Here is a comparative picture of the electron-proton quantum well vs. the u,d,u proton quantum well:

This has direct implications for the required mass of the proton (three particles rather than one, and each particle has to have at least 20 times as much mass). It’s so interesting to discover that the u,d,u three-particle Schroedinger solution requires much more mass for a proton than an electron–at least a factor of 40 to 60–even if there is no strong force, no massive gluons, and no Higgs boson, only charge potential.

Agemoz

Tags: physics, quantum, quantum theory, special relativity

This entry was posted on June 15, 2022 at 3:47 pm and is filed under Physics. You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.