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