Defining Light Speed

For the fun of it, given Fourier,

$F_{ f }[f(x)]=F(f)=\int_{-\infty}^{\infty} { f(x).e^{ -i2\pi fx } } dx$

as

$f.\lambda=c$

$f.x=\cfrac{c}{\lambda}x$

If we denote inertia in time as

$m_t=\cfrac{1}{c}$ and

$n_\lambda=\cfrac{x}{\lambda}$

the number of wavelengths in a distance $x$.  The expression,

$f.x = \cfrac { n_{ \lambda  } }{ m_{ t } }$

where $\cfrac{n_\lambda}{m_t}$ is the number of wavelength per unit inertia in the time dimension.

$f$ stretches $x$ into spacetime, $fx$.  When measured in units of wavelength, $\lambda$, the expansion of spacetime is weighted by its inertia in time, $m_t=\cfrac{1}{c}$.

Furthermore, if the time and space dimensions are equivalent, that $f.x$ is a square, then

$m^2=c.n_\lambda$

$c=\cfrac{m^2}{n_\lambda}$

or

$n_\lambda=\cfrac{m^2}{c}$

where $m^2$ is a complete square of a rational number of our choosing.  If we define $c$ to be a complete square too,

$c=b^2$

where $b$ is rational, then

$n_\lambda=\cfrac{m^2}{b^2}$

$n_{\lambda}$ is always rational, provided spacetime, $fx$ stretches uniformly, equally in both $f$ and $x$ directions, that both time and space dimensions are equivalent.

$c=299792458$ is a complete square of rational number $\cfrac{17314515817660047984}{10^{15}}$

approximately...