The Frequency-Boost Mechanism for Matter Waves and Mass-Energy Equivalence

We present a fundamental derivation of matter waves from the Lorentz transformation of Compton frequency. Starting from the established relations of quantum mechanics and relativity, we show that dividing the rest-energy equation hf_0 = m_0c^2 by the Lorentz factor \gamma directly yields the moving-frame equation hf = mc^2. The difference between these equations reveals that kinetic energy equals the energy of frequency boost h(f - f_0), while their mathematical structure proves the mass-frequency relation dm/df = h/c^2. This frequency-boost mechanism provides a complete physical picture for wave-particle duality, showing that de Broglie waves emerge naturally from Lorentz-transformed internal oscillations