How Einstein proved photons don't exist

According to Einstein's theory, the energy of the photon is E=pc, where p is photon momentum. But since momentum is mass times velocity, p=mv=mc, the equation becomes E=mc^2. And since photons have no mass, it means photons have no energy either. Which means photons don't exist, according to Einstein’s theory. And it is easy to see why Einstein’s theory is incorrect, because he discarded the aether and magically transformed the light wave into a particle. He did so because he could not explain the invariance of the speed of light as a wave in classical physics. But I proved that the speed of light is invariant in classical physics by using Doppler effect, and therefore that the Lorentz transformations which SR relies on are not needed to explain the invariance. The demonstration is quite simple, and is based on the Doppler effect which changes frequency and wavelength for a moving observer/source. Since the speed of the wave is c=flambda, to calculate the speed of light in the ...