Question: does mass increase as you approach the speed of light

Answer: Yes, Then, it was pointed out by Thomson and Searle that this electromagnetic mass also increases with velocity. This was further elaborated by Hendrik Lorentz (1899, 1904) in the framework of Lorentz ether theory. He defined mass as the ratio of force to acceleration, not as the ratio of momentum to velocity, so he needed to distinguish between the mass m L = γ 3 m (\displaystyle m_(L)=\gamma ^(3)m) parallel to the direction of motion and the mass m T = γ m (\displaystyle m_(T)=\gamma m) perpendicular to the direction of motion (where γ = 1 / 1 − v 2 / c 2 (\displaystyle \gamma =1/(\sqrt (1-v^(2)/c^(2)))) is the Lorentz factor, v is the relative velocity between the aether and the object, and c is the speed of light). Only when the force is perpendicular to the velocity, Lorentz's mass is equal to what is now called ``relativistic mass''. Max Abraham (1902) called m L (\displaystyle m_(L)) longitudinal mass and m T (\displaystyle m_(T)) transverse mass (although Abraham used more complicated expressions than Lorentz's relativistic ones). So, according to Lorentz's theory no body can reach the speed of light because the mass becomes infinitely large at this velocity.