Dependence of Mass on Wavelength in the Relativistic Limit

Dependence of Mass on Wavelength in the Relativistic Limit

(zenodo.org) Introduction This paper examines the relationship between a particle’s mass and its wavelength based on the relativistic energy equation. In the case of high-energy particles, the rest mass transitions into a change in wavelength, allowing us to derive a mathematical dependence between these quantities. 1. Fundamental Equations The relativistic expression for the total energy of a particle with nonzero rest mass is given by:     E² = p²c² + m²c⁴  where:- E is the total energy of the particle, - p is the particle’s momentum, - m is the rest mass of the particle, - c is the speed of light. According to de Broglie’s relation, momentum is connected to wavelength λ as follows:     p = h / λ where h is Planck’s constant. 2. Expressing Mass Through Wavelength Substituting the expression for momentum into the energy equation, we obtain:     E² = (hc / λ)² + m²c⁴     Solving for mass:     m²c⁴ = E² - (hc / λ)²     m = (1 / c²) * sqrt(E² - (hc / λ)²) 3. High-Energy Limit At high energies,...
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