Clarification of Concepts in Relativistic Mass, Energy, and Length Contraction:

Soumendra Nath Thakur

December, 26, 2024

The notion of "variation in mass with velocity" is addressed as a misunderstanding. The research framework "Relativistic Mass and Energy Equivalence: Energetic Form of Relativistic Mass in Special Relativity" does not discuss any variation in rest mass. Instead, it introduces the concepts of effective mass and apparent mass as energetic constructs. These terms describe variations in energy, not mass, and do not imply changes to the invariant rest mass.

The idea that particles such as neutrons, protons, and electrons behave as "looped waves in the medium of space" is speculative. Unlike massless photons, massive particles remain stationary within gravitationally bound systems unless influenced by external forces. Their behaviour cannot be directly associated with the relationship E=hf, as this applies to electromagnetic waves. For massive particles, E=mc² governs the conversion of rest mass into energy through nuclear processes and does not involve motion or conversion into pure frequencies.

The assertion that "The change in frequency affects the mass through E=hf" reflects a misconception. E=hf pertains to electromagnetic waves and describes variations in electromagnetic energy rather than mass. It is distinct from E=mc², and the equivalence between hf and mc² does not apply.

Similarly, the suggestion that "the change in wavelength is the cause of length contraction" conflates unrelated concepts. Object length is not analogous to wavelength. Relativistic length contraction is a distinct phenomenon that can be compared to classical mechanics length deformation under Hooke's law. However, the relativistic model relies on the Lorentz factor and often omits classical considerations such as material stiffness and acceleration, potentially leading to less precise predictions than classical deformation theory.

In the relativistic framework, relativistic mass is expressed as m = γm₀, where γ = 1/√(1 − v²/c²). This relativistic mass is an energetic quantity distinct from proper (rest) mass, which remains invariant.

The study emphasizes that no variation in inertial mass is proposed. Instead, the variability of effective mass and apparent mass as energetic forms is central to describing the dynamics of energy systems within the scope of Extended Classical Mechanics.