Variation of Mass with Velocity: A Theoretical and Mathematical Approach

Objectives: The origin of various equations involving variation of mass with velocity is discussed and a new exponential equation is derived. At lower velocities, this equation and the Lorentz equation both give the same results.

Background: The new theory of variability of the speed of light implies that the speed of light was higher in the early universe. It supports the exponential equation which allows superluminal velocity. The perception of an increase in mass with velocity has been increasingly refined by several scientists.

Methods: The various references right from the inception of the concept of variation of mass with velocity are discussed. The basic common point in various equations is that an invalid operation division by zero is involved. Initially, such an equation was initiated by Thomson, and used by following scientists. Thus aspects are theoretically discussed.

Findings: A newly derived equation is exponential in nature and is interpreted in view of existing experimental observations. It does not involve division by zero, hence never predicts that mass becomes infinite when the velocity of a body, . Lorentz has given an equation for transverse mass , where is an undetermined factor or coefficient differing from unity by the quantity of the order . Lorentz's equation (relativistic mass) is experimentally verified with reasonable accuracy up to velocity 0.75 c. Thus Lorentz's equation is confirmed in a limited region. In LHC, the protons have energy and move with a velocity at about , at this velocity the relativistic mass of the proton must be experimentally measured and compared. Then it must be confirmed up to which extent Lorentz's equation is obeyed. In the future, higher velocities are expected thus experimental verification of equations may lead to interesting results. Further, this equation can be applied in early cosmology.

Applications/Improvements: The exponential equation is the first equation that provides an extension of the Lorentz equation in a conceptual and mathematical way. It stresses superluminal velocities at some stages of the formation of the universe. The exponential equation can be checked in experiments in LHC which involve velocities tending to that of light and other experiments.