Why is it impossible for objects to move at the speed of light?

The reasoning behind the assertion that it is impossible for objects with mass to move at the speed of light revolves around the concept of the Lorentz factor, which plays a critical role in Einstein's theory of relativity. As an object approaches the speed of light, the Lorentz factor, defined as ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} ), increases significantly.

When the velocity ( v ) of an object approaches the speed of light ( c ), the denominator of the Lorentz factor approaches zero, which causes the Lorentz factor itself to approach infinity. This phenomenon implies that the amount of energy required to continue accelerating the object also skyrockets toward infinity. Therefore, achieving the speed of light would necessitate an infinite amount of energy, which is not attainable in our physical universe for any object that possesses mass.

This principle is foundational to understanding the limitations imposed by relativistic physics on movement and speeds, particularly for massive objects, distinguishing their behavior from that of massless particles, like photons, which can travel at light speed.