The equation E=mc^2 is a special case of Einstein's theory of relativity, specifically the theory of special relativity. In this theory, c represents the speed of light in a vacuum, which is an absolute constant in our universe. The value of c is approximately 299,792,458 meters per second.
The equation itself relates energy (E) to mass (m) and the speed of light (c). It states that the energy of an object with mass is equal to its mass multiplied by the square of the speed of light. This equation shows that mass and energy are interchangeable, and the conversion factor is the square of the speed of light.
Now, it's important to note that the equation E=mc^2 does not imply that time stops when an object reaches the speed of light. In fact, according to the theory of special relativity, as an object approaches the speed of light, its energy and momentum increase without bound, but it never actually reaches or exceeds the speed of light. Time dilation effects occur as an object's velocity approaches the speed of light, but time does not stop.
The equation E=mc^2 holds true in any frame of reference, including those moving relative to each other. However, the values of energy and momentum may appear different to observers in different frames of reference due to the effects of relative motion and time dilation. This is a fundamental aspect of the theory of special relativity, which takes into account the fact that the laws of physics should be the same for all observers, regardless of their relative motion.
In summary, the use of the speed of light (c) in the equation E=mc^2 is necessary because it is a fundamental constant of nature, and it represents the maximum speed that anything can travel in our universe. The equation is valid in all frames of reference, and it describes the relationship between energy, mass, and the speed of light.