Schoolboy error
Light also loses frequency on board the spaceship. With the gamma factor of 2, a 1 MHz radio frequency on board the spaceship, would translate to 2 MHz for the earthbound Observer. So the frequency on board the spaceship is lower than it is for the Earthbound Observer. I was assuming that the frequency on board the spaceship had increased to 2 MHz, but in reality it is the 2 MHz frequency, that has reduced to 1 MHz.
The medium exists
I am now convinced that this medium exists. Particles propagate through the medium. Time dilation and length contraction are simply due to the change of frequency and wavelength.
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