Revisiting Lorentz Transformations: Resolving Scalar-Vector Dynamics Discrepancies

(Part 3 of 1 to x)

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

25-04-2024

Description:

The comprehensive series of studies, collectively titled "Revisiting Lorentz Transformations: Resolving Scalar-Vector Dynamics Discrepancies," delves deep into the intricacies of Lorentz transformations and their interaction with scalar and vector quantities. Building upon previous research that highlighted concerns about mathematical inconsistencies in Lorentz transformations, particularly in reconciling scalar-vector dynamics, this study series aims to provide clarity and resolution.

Beginning with the foundational study "Addressing Contradictions in Lorentz Transformations: Reconciling Scalar-Vector Dynamics," the series identifies discrepancies between theoretical expectations and empirical observations regarding Lorentz transformations. It underscores the need for further examination to reconcile these inconsistencies.

Subsequently, the focus shifts to "Lorentz Transformations and Effective Mass in Classical Mechanics," which elucidates the derivation of Lorentz transformation formulas and their relationship to kinetic energy and effective mass. This study clarifies misconceptions surrounding effective mass and its distinction from relativistic mass, shedding light on its significance in classical and modern physics.

The final instalment challenges previous notions by asserting that phenomena like length contraction, mass change, and relativistic time dilation are not fundamental manifestations but rather consequences of energy transfer induced by the Lorentz factor. It argues that these effects arise from velocity-induced forces acting on moving objects, influencing the kinetic energy stored within them.

Ultimately, the series concludes that while there may not be a mathematical discrepancy in Lorentz transformations, inconsistencies arise in treating phenomena like length contraction and mass change as standalone entities. Instead, they are portrayed as outcomes of energy transfer due to velocity-induced forces, necessitating a re-evaluation of the scalar-vector dynamics within the Lorentz framework.

Summary:

The study (Part 1 of 1 to x), titled 'Addressing Contradictions in Lorentz Transformations: Reconciling Scalar-Vector Dynamics,' suggests that the statements express a valid concern regarding the mathematical consistency of Lorentz transformations, particularly in their interaction with scalar and vector quantities. It indicates that the discrepancy highlighted indicates a need for further examination and clarification to reconcile theoretical expectations with empirical observations.

In response, we aim to examine and clarify to reconcile the theoretical expectations regarding the mathematical consistency of Lorentz transformations:

The subsequent study, (Part 2 of 1 to x), titled 'Lorentz Transformations and Effective Mass in Classical Mechanics,' describes 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 misunderstood as relativistic mass (m′).

The Lorentz factor (γ) and velocity-induced forces play pivotal roles in this framework, influencing how kinetic energy is stored within moving objects based on classical mechanics principles. The concept of effective mass is clarified, underscoring its significance in both classical and modern physics, particularly in comprehending 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, highlight their association with velocity-induced external forces and their impact on Lorentz transformations.

The Lorentz factor (γ), as a velocity-induced force, influences how kinetic energy is stored within moving objects based on classical mechanics principles. Thus, the stored kinetic energy (KE) is treated as 'effective mass' (mᵉᶠᶠ), often misunderstood as relativistic mass (m′).

When a force acts on an object, causing it to move a certain distance in the direction of the force, work is performed on the object. This work leads to a change in its kinetic energy. Kinetic energy (KE) represents the energy an object possesses due to its motion.

In Lorentz transformations, the mechanical force induced by velocity (v) deforms the moving mass, altering the arrangement of its molecules or atoms, and thus storing kinetic energy as structural deformation, which is reversible when the mass ceases moving. Deformation effects, such as relativistic mass, length contraction, and relativistic time dilation, underscore their linkage to velocity-induced external forces and their influence on Lorentz transformations.

A change in energy can generate forces; similarly, force acts on an object, leading to energy transfer, which impacts its motion and the dynamics of objects. Displacement, velocity, position, including force, are all vector quantities.

This study suggests that the Lorentz factor (γ) in Lorentz transformations is often misunderstood regarding its effects on moving objects. It argues that the Lorentz factor is linked to velocity-induced forces acting on objects in motion, resulting in energy transfer and various deformation effects such as "effective mass," which is frequently confused with relativistic mass, length contraction, and relativistic time dilation.

However, the study contends that these deformational effects do not fundamentally alter the rest mass, cause permanent length contraction, or result in proper time dilation. Instead, they are manifestations of energy transfer caused by the Lorentz factor inducing mechanical force, affecting the kinetic energy stored within the moving object. This stored kinetic energy is treated as reversible "effective mass," often misinterpreted as relativistic mass, leading to temporary length deformation misunderstood as length contraction and time distortion misinterpreted as relativistic time dilation.

According to the study, the velocity-induced resultant force in Lorentz transformations is a vector quantity, influencing the kinetic energy stored within moving objects based on classical mechanics principles. This force interacts more with the Lorentz factor than with stored kinetic energy, resulting in alternative and reversible length deformation, effective mass, or time distortion. Consequently, the Lorentz factor induces force as another vector quantity, leading to vector quantity products in the relevant transformations.

Therefore, the study concludes that there is no mathematical discrepancy, as the Lorentz factor induces force as another vector quantity. However, there is indeed inconsistency, as the previous study (Part 1 of 1 to x), titled 'Addressing Contradictions in Lorentz Transformations: Reconciling Scalar-Vector Dynamics,' suggests. It indicates that length contraction, mass change, and relativistic time dilation, as presented in Lorentz transformations, are not proper manifestations of these phenomena. Instead, they are manifestations of energy transfer due to the Lorentz factor inducing mechanical force, affecting the kinetic energy stored within the moving object. This highlights a valid concern regarding the mathematical consistency of Lorentz transformations, particularly in their interaction with scalar and vector quantities, when phenomena like length contraction, mass change, and time dilation—scalar quantities—are treated as real entities. They are not.