The reason something with mass cannot be accelerated past the speed of light is rooted in the fundamental principles of special relativity. According to this theory, the speed of light in a vacuum is an absolute speed limit for all objects with mass.
In special relativity, it is postulated that as an object with mass approaches the speed of light, its relativistic mass increases, requiring an ever-increasing amount of energy to continue accelerating. At the speed of light, the relativistic mass would become infinite, and it would require an infinite amount of energy to accelerate an object with mass to reach or surpass that speed.
The equation that governs this relationship is:
m = m₀ / √(1 - v²/c²)
Where: m is the relativistic mass of the object, m₀ is the rest mass (mass at rest) of the object, v is the velocity of the object, and c is the speed of light.
As the velocity (v) approaches the speed of light (c), the denominator of the equation approaches zero, resulting in an infinitely large mass.
This concept implies that it is not physically possible to reach or exceed the speed of light for objects with mass. However, it's important to note that particles without rest mass, such as photons (particles of light), always travel at the speed of light in a vacuum. Since they have no rest mass, the equation above does not apply to them.
In summary, the prohibition on accelerating an object with mass past the speed of light arises from the relationship between relativistic mass and velocity described by special relativity. The speed of light acts as an absolute speed limit, while particles without rest mass, like photons, always move at the speed of light in a vacuum.