Tag: wave equations

The physics of the wave equation

The rather high-brow discussions on deep electron orbitals and hydrinos with a separate set of interlocutors, inspired me to write a paper at the K-12 level on wave equations. Too bad Schroedinger did not seem to have left any notes on how he got his wave equation (which I believe to be correct in every way (relativistically correct, too), unlike Dirac’s or others).

The notes must be somewhere in some unexplored archive. If there are Holy Grails to be found in the history of physics, then these notes are surely one of them. There is a book about a mysterious woman, who might have inspired Schrödinger, but I have not read it, yet: it is on my to-read list. I will prioritize it (read: order it right now). 🙂

Oh – as for the math and physics of the wave equation, you should also check the Annex to the paper: I think the nuclear oscillation can only be captured by a wave equation when using quaternion math (an extension to complex math).

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The wavefunction in a medium: amplitudes as signals

We finally did what we wanted to do for a while already: we produced a paper on the meaning of the wavefunction and wave equations in the context of an atomic lattice (think of a conductor or a semiconductor here). Unsurprisingly, we came to the following conclusions:

1. The concept of the matter-wave traveling through the vacuum, an atomic lattice or any medium can be equated to the concept of an electric or electromagnetic signal traveling through the same medium.

2. There is no need to model the matter-wave as a wave packet: a single wave – with a precise frequency and a precise wavelength – will do.

3. If we do want to model the matter-wave as a wave packet rather than a single wave with a precisely defined frequency and wavelength, then the uncertainty in such wave packet reflects our own limited knowledge about the momentum and/or the velocity of the particle that we think we are representing. The uncertainty is, therefore, not inherent to Nature, but to our limited knowledge about the initial conditions or, what amounts to the same, what happened to the particle(s) in the past.

4. The fact that such wave packets usually dissipate very rapidly, reflects that even our limited knowledge about initial conditions tends to become equally rapidly irrelevant. Indeed, as Feynman puts it, “the tiniest irregularities tend to get magnified very quickly” at the micro-scale.

In short, as Hendrik Antoon Lorentz noted a few months before his demise, there is, effectively, no reason whatsoever “to elevate indeterminism to a philosophical principle.” Quantum mechanics is just what it should be: common-sense physics.

The paper confirms intuitions we had highlighted in previous papers already, but uses the formalism of quantum mechanics itself to demonstrate this.

PS: We put the paper on academia.edu and ResearchGate as well, but Phil Gibbs’ site has easy access (no log-in or membership required). Long live Phil Gibbs!