Why does mass of a body vary with velocity?

Answer 1

Here's one way of looking at it: you have to consider the problem from two different frames of reference. Let's set one as a spaceship accelerating at some speed above 0.5c. The other will be a rest frame, the inertial frame from which the ship departed. Each frame contains an identical clock. Each clock, tested before separation, ticks off identical seconds. If I send the ship out and back at high acceleration, then compare the elapsed time on both clocks, I will find that the times vary. Seconds on the moving clock were stretched when compared with those of the rest clock, though time appeared to pass normally on the ship. Consider all of this in terms of fuel consumption. From my frame of reference within the ship, all clocks run normally, so I register a constant fuel consumption for what I expect to be constant acceleration. But from the external (rest) frame, I can calculate that the moving clock has stretched each second in proportion to each increase in speed by the Lorenz time dilation factor, so I record the ship's fuel consumption as being stretched over longer and longer intervals as the ship accelerates. In fact, what is perceived in the ship as constant fuel usage appears to be decreasing usage from the rest frame. It will take longer and longer intervals (or an increasing rate of fuel consumption) to accomplish each increasing increment of velocity as the same amount of energy is expended over increasing intervals. From the ship, I see progressively smaller increases in velocity from the same rate of fuel expenditure. By any method of measurement, this equates to an increase in mass. It appears to take progressively more energy to accelerate the ship by any given increment.