Harmonics Theory, Part 6: Many Harmonics

by Ray Tomes

Harmonics Theory Part 6: Many Harmonics

This blog series from FSC Science Director Ray Tomes will share the fundamentals of physics in layman's terms, showing how present theory must inevitably lead to all waves losing energy and forming harmonically related waves. The end result is a very specific detailed structure that matches the observed universe and explains many previously mysterious observations. This series was previously published.

Based on the present understanding of physics, the universe may support large standing waves. Because of the non-linearity of the wave equation, we know that every wave will produce harmonics. In three dimensions these waves will also be standing waves. Taking a brave step from the correct understanding of the work of Wheeler and Feynman the assumption is that there is nothing but these waves. So, forgetting all other known physics we state a single principle:

The Universe consists of a standing wave which develops harmonically related standing waves and each of these does the same.

From this simple principle the pattern of frequencies of the waves formed in the universe can be calculated. For the following calculations the assumption is that there initially exists a single frequency of a universal wave and that frequency will be called 1. We do not need to know 1 what to do the calculations, but it might be 1 cycle per period of about 14 billion years if that helps people to have some idea in their minds. When frequencies of 2 and 3 and other numbers are mentioned that will mean 2 or 3 or more cycles in 14 billion years. Here is a first look at this process of harmonic generation.

This table shows that some harmonics are formed in multiple different ways, while others are formed in only one way. We may look at the 12th harmonic compared to the 11th and 13th. If a harmonic is formed in more ways then, assuming that the energy from each path is equal, it should have more energy in that wave. The situation is actually more extreme than it at first appears, because some of the harmonics going into the 12th harmonic already occurred in multiple ways and so each supplied multiple doses of energy. Altogether the 12th harmonic may be produced in 8 ways which are 12, 6x2, 2x6, 4x3, 3x4, 2x2x3, 2x3x2, 3x2x2. Each of these ways may supply a flow of energy equal to the 11th or 13th harmonic on its own.

To make this strictly true it is necessary that every path is equal. That will be so when the energy flow from any wave to its harmonics is proportional to the energy of the wave itself and proportional to some inverse power of that harmonic number as well. It doesn't matter which inverse power, the consequences are equivalent. This inverse power means that any harmonic mainly loses energy to its second harmonic with less to the third and rapidly diminishing amounts to the higher order harmonics. Such conditions are quite reasonable for a non-linear wave when the non-linearity is not very great. However under very extreme conditions of energy concentration there may need to be some additional elements added to this calculation.

This second look at harmonics generation keeps count of the number of ways in which each harmonic is formed. So as the ways in which the 4th harmonic is formed is found in the totals at the bottom of the table to be 2, that is fed back in at the side to its production of the 8th, 12th and 16th harmonics and so on.

This little table shows the method of calculating how many ways each harmonic can be formed. Once the method is understood, computers can be used to do the same calculations for an extended range of numbers including very large harmonic numbers. Such calculations have been performed for numbers with 50 digits and more, but there is a practical limit because the number of calculations gets very great.