Analysis: The concept of Relativistic Lorentz Transformation and Time Dilation.

Soumendra Nath Thakur
14-05-2024

The Lorentz factor (γ) is a velocity-dependent concept that quantifies the changes in time, length, and mass for objects in motion relative to an observer at rest. At the start of a journey, both the object and the observer are at rest, with their kinetic energies (KE) being zero. As the object accelerates to achieve its desired velocity, the Lorentz factor does not directly account for this acceleration process. However, classical mechanics states that as the object accelerates, its mass remains constant, and the force required to accelerate it increases linearly with its mass.

As the object accelerates, its kinetic energy (KE) increases, which is directly proportional to the square of the velocity (v). This increase in KE is due to the addition of effective mass (mᵉᶠᶠ) to the inertial mass (m). Effective mass represents the kinetic energy (KE) of the object, and the total mass experienced by the object becomes (m + mᵉᶠᶠ), contributing to the sensation of heaviness as long as there is an acting force on the object.

Piezoelectric accelerometers empirically demonstrate the concept of effective mass (mᵉᶠᶠ), which accounts for the kinetic energy response to applied forces or accelerations. This validates the concept of effective mass in practical applications where the response of the accelerometer to external forces or accelerations is crucial.

The Lorentz factor (γ) comes into play once the object reaches its desired velocity and is in motion relative to the observer. At this point, the object's energetic state reflects its motion, and the object has kinetic energy (KE) due to its velocity.

The Lorentz transformation, which describes relativistic effects on time, length, and mass for objects in motion, does not directly account for acceleration. Classical mechanics handles acceleration dynamically, but the Lorentz transformation's failure to address acceleration highlights a gap in its applicability, especially in situations where acceleration is crucial. This highlights the need for a more comprehensive theoretical framework that integrates relativistic effects with dynamic processes for a more accurate depiction of physical phenomena.