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In classical mechanics, kinetic energy represents an effective mass (mᵉᶠᶠ) when an inertial mass (m) is in motion or subject to a gravitational potential difference, where mᵉᶠᶠ<m.
When two inertial reference frames initially share the same motion and direction relative to each other, they are indistinguishable in their observations of physical phenomena. However, if these frames separate in the same direction, they must acquire different velocities. This necessity of velocity change highlights the role of acceleration in achieving their separation.
Despite acceleration being fundamental to transitioning between different inertial reference frames, it is not explicitly considered in the Lorentz factor or relativity, even though it plays a crucial role in transitioning from v₀ to v₁. This raises important questions about its implications in both classical mechanics and relativistic Lorentz transformations.
During the formulation of the Lorentz factor:
γ = √(1 - v/c)²
or relativistic time dilation:
Δt′ = t₀/√(1 - v/c)²
it was acknowledged that Newton’s second law:
F = ma
induces a force (F) that influences velocity-dependent relativistic transformations. This force leads to deformations in moving objects, affecting relativistic mass, length contraction, and time dilation.
For example, Hooke’s Law:
F = kΔL
describes such deformations, suggesting that Lorentz transformations incorporate force-induced structural changes that impact the effective mass of an object.