Unified Perspective on Kinetic Energy | Mass Concepts in Classical, Relativistic, and Extended Classical Mechanics
Kinetic Energy and Effective Mass | Energy and Effective Mass | Phase Shift and Time Distortion | Sign of mᵉᶠᶠ in Classical Mechanics | Hooke's Law over Length Contraction | Force, Deformation, and Time Distortion

Justification for Hooke’s Law in Motion Over Relativistic Length Contraction

 

Hooke’s Law provides a more consistent description of mass deformation (ΔL) than relativistic length contraction (L′), which is traditionally derived from velocity-based transformations.

 

Key Issues with Relativistic Length Contraction:

 

1. Assumes purely velocity-dependent deformation: Ignores material stiffness.

2. Linear object assumption: Emphasizes length deformation but ignores cubic volume changes.

3. Neglects acceleration effects: Does not explicitly account for transition from rest to motion.

 

Advantages of Hooke’s Law in Motion:

• Applies across all speed ranges, including low speeds where relativistic effects are negligible.

• Includes acceleration, whereas relativistic transformations assume undeclared competition with deformation mechanics.

 

Since relativistic length contraction lacks a robust material-based justification, Hooke’s Law provides a more physically grounded approach to deformation across all force conditions. This suggests that relativistic transformations should be reconsidered as force-induced mechanical responses rather than purely geometric effects.