While the experiments have shown similar wave-nature of matter-particles and photons, there are two different formulae for finding Relativistic-increase of energy of massive-particles and photons. This paper presents a unification of the two different formulae, in terms of Doppler-shifts of waves; leading to an insight that the ‘particles-of-matter’ seem to be the ‘standing-waves’; and de-Broglie’s ‘matter-waves’, and ‘quantum-mechanical-waves’ are ‘envelop-variations’ of the actual, more-fundamental waves.
In the framework of Special Relativity and in agreement with the electromagnetic approach used to connect Quantum and Relativistic effects in Bridge Theory, a first order wave-equation able to emulate the wave-particle duality in terms of local electromagnetic interactions is proposed. The equation is able to describe the propagation of a fermion as a de Broglie's wave and simultaneously to characterise the wave in motion with a mass energy as a particle. The solution of the wave-equation proposed is compatible with the de Broglie's idea of an empty pilot wave, carrying information about the dynamical properties of a particle materialising during each local interaction with the observers.