Lorentz Transformations and Effective Mass in Classical Mechanics:

(Part 2 of 1 to x)

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

25-04-2024

Description: 

This summary explores the derivation of the Lorentz transformation formula and its relationship to the equation E = KE + PE, where kinetic energy (KE) is treated as 'effective mass' (mᵉᶠᶠ) and often misinterpreted as relativistic mass (m′). The Lorentz factor (γ) and velocity-induced forces play key roles in this framework, affecting how kinetic energy is stored within moving objects according to classical mechanics principles. The concept of effective mass is clarified, emphasizing its significance in both classical and modern physics, particularly in understanding mass increase in objects and its implications for system behaviour under various forces. Deformation effects, such as relativistic mass, length contraction, and relativistic time dilation, are discussed, highlighting their connection to velocity-induced external forces and their influence on Lorentz transformations.

Summary:

The Lorentz transformation formula, m′ = m₀/√{1 - (v/c)²}, is derived from the equation E = KE + PE, where PE represents the rest mass m₀. This equation treats kinetic energy KE as 'effective mass' (mᵉᶠᶠ), often referred to as relativistic mass (m′), representing time distortion(t′). The Lorentz factor (γ) is a velocity-dependent factor, involving velocity-induced forces. Objects subject to these forces store kinetic energy (KE) within moving objects according to classical mechanics principles.

Velocity-induced force (F) stores kinetic energy in an object, causing stress and deformation due to changes in atomic and molecular structures. This stored energy is typically represented as the relativistic mass (m′), but it should be denoted as the effective mass (mᵉᶠᶠ). Effective mass is a crucial concept in both classical and modern physics, influencing system behaviour under various forces. It is essential in mechanical systems like piezoelectric actuators for dynamic response and in relativistic physics to explain mass increase in objects.

Deformation results in relativistic mass, length contraction, and relativistic time dilation, which are influenced by velocity-induced external forces. Equations like F = kΔL describe these changes, impacting Lorentz transformations and influencing the effective mass of the object.