Yes, according to the theory of relativity, an object's mass does appear to increase as its speed approaches the speed of light. However, it's important to note that the concept of mass is relative and depends on the observer's inertial reference frame.
In classical Newtonian physics, mass is considered an invariant property of an object, meaning it does not change with velocity. However, in special relativity, as an object's velocity increases, its relativistic mass, also known as its "rest mass," appears to increase from the perspective of an observer in a different inertial reference frame.
This increase in mass is a consequence of the energy required to accelerate an object with mass to higher speeds. As an object moves faster, its kinetic energy increases, and this energy contributes to its total relativistic mass. The relationship between an object's relativistic mass (m), its rest mass (m₀), and its velocity (v) can be described by the equation:
m = m₀ / √(1 - v²/c²)
where c is the speed of light.
It's important to emphasize that the increase in mass is a relativistic effect and is not directly observable by the object itself. From the perspective of an observer moving with the object, its mass remains unchanged. It is only when comparing measurements made by observers in different inertial reference frames that the apparent change in mass becomes apparent.
Therefore, while an object's mass does appear to change depending on the observer's inertial reference frame, it is the relative mass that changes, and the rest mass, which is the mass measured in the object's rest frame, remains constant.