Why does mass increase when body travels with velocity of light?
Answers
To be rigorous, nothing happens to the mass of a particle when its state of motion with respect to the some observer changes. What we call the “mass” is a so-called relativistic invariant, or a “scalar” quantity, meaning that its value is exactly the same in every reference frame. Suppose you are in a reference frame where the particle is at rest. Then, if you move to a reference-frame (such operation is also know as “boosting”), where the particle moves at a velocity v, then its mass will still be the same as before.
Maybe, what you are referring to, is the fact that, for a free relativistic particle of mass m, one can write its equation of motion as
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where
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This resembles the equation of motion of a classical particle, with the redefinition [Math Processing Error]. However, if one defines the particle mass as the value of the energy when the particle itself is at rest (and also not subject to any external field!), it is a predetermined parameter of the theory, not dependent on the kinematics of the particle.
What we really mean by the substitution [Math Processing Error], is that, for a free particle, we can take account of the effects of having a theory which has Lorentz-invariance (i.e. a “relativistic theory”) by the minimal replacement of the mass with a “fictitious” velocity-dependent mass parameter. This is just an effective point of view, which is very common in many branches of physics.
For example, in Quantum Field Theory, the coupling constant is also a Lorentz-invariant quantity, as every parameter of the theory (included the mass, of course): however, for calculations it is very useful to introduce an effective coupling constant which depends on the kinematic variables, very much as we do for the mass of a particle.
What the theory predicts when the speed of the particle approaches c , is that the effective mass should become infinite, which, since we don’t know how to make sens of this infinity (or even complex numbers, if the speed exceeds c), means that this cannot happen in reality. And, since we observe from experiments that this is true, we conclude that the theory is good.