This program simulates a standing-wave of photons, which is created between two perfectly reflective mirrors \(L\) distance apart (in the restframe).

One can let this system move along the x-axis with a relativistic velocity \(\beta =v/c\). The program enables to "stop" the moving standing-wave, so that the distorsion can better be observed. When the wave "moves out" from the screen, it enters again from the left.

Please note that the values entered in the "length" and "velocity" fields will be submitted only when you press the "Enter" key!  By unchecking the "Move" checkbox the moving wave will be stopped, but its "moving shape" will be conserved.

The mathematical background:

The standing-wave is described by the following function (in its restframe):

\begin{equation} \psi (x,t)= A\cdot \sin(\pi\frac{x}{L})\cdot\cos(2\pi f\cdot t) \end{equation}

The frequency and the length are clearly related:

\begin{equation} f=c/\lambda=c/2L. \end{equation}

The "moving" standing-wave is described by performing the following Lorentz transformation:

\begin{equation}  x =\frac{x'-v\cdot t'}{\sqrt{1-\beta^2}} \hspace{5pt} \mathrm{ and }\hspace{5pt}  t=\frac{t'-\beta\cdot x'/c}{\sqrt{1-\beta^2}}  \end{equation}

and substituting them in equation (1).