According to the theory of relativity, the mass of an object does not actually change with respect to its velocity. This idea, often referred to as "relativistic mass," was initially introduced in earlier formulations of relativity but is no longer commonly used or accepted.
In the modern understanding of relativity, mass is considered an invariant quantity, meaning it remains constant regardless of the object's velocity. This is known as "rest mass" or "invariant mass." The rest mass of an object is the mass measured when the object is at rest relative to the observer.
However, what does change with velocity are other observable quantities such as length and time. Length contraction and time dilation are consequences of the theory of relativity.
Length contraction, also known as Lorentz contraction, states that an object in motion appears shorter along its direction of motion compared to its length at rest. As an object's velocity increases, it undergoes a contraction in the direction of its motion. This effect becomes significant as the object approaches the speed of light.
Time dilation, as mentioned earlier, refers to the slowing down of time for an object in motion relative to a stationary observer. As an object's velocity increases, time appears to pass more slowly for that object. This effect is reciprocal, meaning both observers moving relative to each other would perceive the other's clock as running slower.
These effects of length contraction and time dilation arise from the fundamental principles of relativity and have been experimentally confirmed through various experiments and observations, such as the famous Michelson-Morley experiment and measurements of the lifetimes of fast-moving particles in particle accelerators.