When mass increases with velocity, it is important to consider that this is most definitely not an increase in matter. Rather it reflects an increase in energy. The simplest way to start to understand this energy mass is to consider an object's kinetic energy, or the energy associated with an object's movement relative to another object. At speeds approaching that of light the amount of kinetic energy becomes very substantial, yet to an object that is moving at the same speed and in the same direction as the object, it doesn't exist at all. This inconsistency has led some people to disfavor the use of the concept, including Albert Einstein in later life:
of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion.— Albert Einstein in letter to Lincoln Barnett, 19 June 1948 (quote from L. B. Okun (1989), p. 42[1])
Relativistic mass, as it is known, becomes more complex than simple kinetic energy as the speeds involved approach that of light from the perspective of an object's origination and time dilates from the perspective of the object. Forces exist and accrue over different time scales and general relativity uses the mathematical concept of the stress–energy tensor to define the true nature of this mass increase.
The extent to which relativistic mass has properties similar to "rest mass" is extremely complex. It might be too difficult to determine using analytical methods.
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