The equation E=mc^2, where "E" represents energy, "m" represents mass, and "c" represents the speed of light in a vacuum, is a fundamental principle in physics known as the mass-energy equivalence. This equation shows that mass and energy are two different manifestations of the same underlying physical quantity.
For a particle with mass "m" to travel at the speed of light "c" in a vacuum, the equation tells us that its energy would become infinite. This is because as the particle's speed approaches the speed of light, the term "c^2" becomes very large, and to keep the energy "E" finite, the mass "m" would have to approach zero.
The reason why infinite energy is required to accelerate a massive particle to the speed of light is rooted in the principles of special relativity, a theory developed by Albert Einstein. Special relativity shows that as an object with mass accelerates, its energy increases significantly, and as it approaches the speed of light, its energy requirement becomes virtually infinite. This is why massive particles, such as electrons or protons, cannot reach or exceed the speed of light.
On the other hand, particles with zero rest mass, like photons (particles of light), can travel at the speed of light because they have no mass to begin with. Since their rest mass is zero, the equation E=mc^2 reduces to E=0, meaning they can travel at light speed without requiring infinite energy.
In summary, the equation E=mc^2 does contain finite values for particles with mass at speeds much lower than the speed of light. However, as a massive particle's speed approaches the speed of light, the energy required for further acceleration becomes infinitely large, making it impossible to reach or exceed light speed for particles with mass. Only particles with zero rest mass, like photons, can travel at the speed of light.