Speed of The Cycle
The Speed of Light Rebooted
Maxwell’s Electromagnetic Wave Equation is traditionally read as a three-dimensional wave equation containing a fixed speed of light. An alternative way to read the mathematics is that
Maxwell’s 3D Wave Equation contains a Fixed 3D Speed.
NeoClassical Relativity (NCR) is based on this interpretation of Maxwell’s mathematics.
One of the most iconic images of the last fifty years is on the cover of Pink Floyd’s album “Dark Side of the Moon”; the image is of a prism separating white light into the colour spectrum.
According to physicists, this “dispersion of light” is a consequence of the fact that different frequencies of light travel at different speeds through different mediums.
By contrast, however, according to the same physicists, all frequencies of light travel at the same speed in a vacuum.
So it appears we are being told that in all material mediums different frequencies travel at different speeds; but in a vacuum, they do not!
Moreover, this idea (on the constancy of the speed of all light in a vacuum) was expanded upon in 1905 when Einstein told us that the speed of all light in a vacuum is independent of the speed of the source or that of the observer…
Einstein’s idea was, and still is, difficult to accept because it conflicts so violently with everyday common sense about how speeds are always perceived to be “relative”. But Einstein told us that our common sense about this is wrong.
In, what is now known as “The Theory of Special Relativity”, Einstein effectively tells us that only slow things have speeds that are relative, high-speed things have nonlinear relativity, and the speed of light in a vacuum has no relativity at all.
This is essentially what he said; however, in truth, Einstein didn’t actually use the term “nonlinear”, that little add-on is mine…
In his latter years, Einstein recalled how as a 16-year-old boy he imagined chasing after a light beam. “If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest - though spatially oscillating.”
In other words, when the young Einstein imagined chasing after a light beam he saw it turn into a stationary “standing wave” — a wave that oscillates in time but does not move in space. Einstein believed that this could not be the case because to do so would violate Maxwell’s Wave Equation (for electromagnetic radiation).
He was wrong about that though.
Maxwell’s Wave Equation is no ordinary wave equation. A wave is a moving thing, consequently, all wave equations must include a wave speed (v) which describes the linear distance the wave travels over time. But unlike most wave equations, Maxwell’s Wave Equation does not demand that speed be restricted to one dimension only. In Maxwell’s Wave Equation, the wave speed is actually describing a rate of change of position across all 3-dimensions at the same time; which means that although the speed of light in a vacuum (c) is a fixed quantity, this fixed quantity can be distributed across all 3 dimensions.
This simple observation is the jumping-off point for my upcoming revision of Einstein’s Theory of Special Relativity, and it leads me to the first of two postulates. [Note: the second postulate will be described in my next post]
The first postulate of NeoClassical Relativity is that:
The Speed of Light is a three-dimensional combination of the Speed of Oscillation and the Speed of Linear Travel.
Mathematically, this combination of speeds is described by the “3D Speed Equation”
Equation (1): ______________ c² = v² + u²
{Where, u is the speed of oscillation in two spatial dimensions, and, v is the speed of travel in the third.}
This equation expresses the idea that although the combined speed is a fixed quantity, the distribution of this fixed quantity can vary.
The 3D Speed Equation is an equation for a moving oscillation — and it essentially tells us that
The faster something moves the slower it will oscillate.
And since the measure of how fast something oscillates is given by the frequency of oscillation, this means that different frequencies must travel at different speeds (even through a vacuum)…
[Below is a table of the distribution of c]
The faster something moves the slower it oscillates, and so conversely, the slower a thing moves the faster the oscillation. Thus
As the young Einstein started to catch up with the light, he would have noticed that: as its linear motion was slowing down, its oscillatory motion was speeding up.
Moreover, had he managed to reach the speed of light himself, the beam of light would indeed appear to be oscillating beside him (just like a standing wave) as he had originally thought; but what he had failed to realize was the fact that this stationary oscillating wave would now be oscillating at c.
Now obviously what I’m saying here is in direct conflict with the traditional understanding of the speed of light (as a fixed linear speed). But, in doing so, I’m not totally breaking with Einstein for I agree with his second postulate that the speed of light is a constant for all observers — just not a constant in the way that he thought.
One of the most obvious, and important, consequences of this change in perspective is that although the speed of light in a vacuum (c) is absolute, the nonlinear distribution of this speed means that some portion of (c) is required for oscillation. Consequently…
Nothing, not even light, can travel from A to B at the speed of light because some fraction of the speed is always required for oscillation.
[Note 1: There are a lot of implications attached to this statement, not least of which is related to the idea of so-called “massless particles”. But I will leave this for the moment, and come back to it later in my future revision of Quantum Mechanics…]
Another consequence of the 3D Speed Equation is that it naturally generates a quantity that is ubiquitous throughout Special Relativity…
If we rearrange equation (1) we can generate
Equation (2):_______________ u² = c² - v²
And if we divide across all terms by c squared and then take the square root of both sides we get
Equation (3):__________u/c = SQRT { 1 - (v²/c²) }
{Where SQRT {…} is shorthand for the “square root” of whatever is inside the brackets.}
And this quantity (u/c), or more precisely its inverse (c/u), appears so often in relativity, that it was given its own symbol “gamma”
Equation (4):_______________ γ = (c/u)
The fact that the gamma term is actually intrinsic to the 3D Speed Equation explains why it is so omnipresent in Special Relativity, (and consequently goes a long way to demystifying it)…
[Note 2: In future posts, I am going to use (c/u) rather than (γ) because it makes the mathematics easier to follow…]
© Kieran D. Kelly
This is Post #1 in the series on NeoClassical Relativity Theory
