Harmonics Theory, Part 3: Nonlinearity of Waves

by Ray Tomes

Harmonics Theory: Nonlinearity of Waves, Part 3

This new 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.

Non-linearity of Waves

When Maxwell produced his equations, they were what are called linear equations. This means that when one wave and another meet, they can travel right through each other without any interaction, just as if the other wave was not there. This is a necessary condition for light, because if we look at the Moon, we are not obstructed in seeing it by the light of the Sun traveling across the path that we look through. So the linearity of light's behavior is acceptable for this reason.

However light does some other things that are quite different. Firstly, we can see it. That proves that it didn't just pass through our eye without interacting, it quite clearly did interact. In fact we know that most solid things obstruct light completely, or at the very least refract it. We can add to this behavior that Einstein correctly predicted from General Relativity that light is bent by gravity, and twice as much as is expected by Newton's theory.

Einstein's result gives us a big clue, because it shows that gravitation, a very weak force compared to the charge forces that hold matter together, can affect light if there is a big enough concentration of matter, even totally trapping light in the extreme limit of a black hole.

Although physicists refer to Einstein's equations as bending space, they do not do the same thing with respect to the refraction of light by matter such as glass. It is unreasonable to refer to light that is refracted in different substances as being a change in velocity while referring to the bending of light by massive objects as a change in the metric of space. These two behaviors should be seen as different aspects of the same thing. Different to be sure, because the one case is due to gravity and the other due to charge forces.

These interactions show quite clearly that in the presence of matter light is behaving as if it is non-linear. Perhaps it is the case that light is always really non-linear, but that under common circumstances the non-linearity is so slight as to go unnoticed. In fact, experiments with powerful lasers confirm that very concentrated light can interact with itself without the presence of matter.

This is a very important conclusion, because it is only possible for light and matter to be united in being made of the same stuff if that stuff allows both the interactions and the apparent non-interactions that we observe. Light, and Maxwell's electromagnetic equations are non-linear. This is true even though some physicists have been taught otherwise. It is true in general relativity, because the equations show that energy, be it matter or light, affects the metric or warping of space. This accepted conclusion that Maxwell's equations under general relativity form a non-linear system is very important for understanding the behavior of the universe.