(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, the contribution of rest mass becomes small compared to momentum, and the total energy is approximately:

    E ≈ hc / λ

 Thus:

    m ≈ (1 / c²) * sqrt((hc / λ)² — (hc / λ)²)

In this case, the mass tends to zero, which corresponds to the behavior of massless particles such as photons.

4. Conclusion

— The rest mass of a particle can be expressed in terms of its wavelength and total energy.

— In the high-energy limit, the wavelength fully determines the dynamic mass of the particle.

— This confirms the connection between mass and electromagnetic waves, aligning with the hypothesis that electromagnetic waves play a fundamental role in the structure of matter.

This conclusion can be used for further research and refinement of elementary particle models.

This approach offers a new perspective on the nature of mass and its relationship to electromagnetic processes. A more detailed discussion of this hypothesis and its philosophical implications can be found in the following works:

— (Dzen)

— (Zenodo)