Why Can't We Travel Faster Than Light?

TL;DR Summary
Science fiction is full of warp drives and hyperspace, but Albert Einstein proved that breaking the cosmic speed limit is impossible.
In science fiction, traveling between star systems requires a simple flip of a switch to engage the hyperdrive. In reality, the speed of light—roughly 299,792 kilometers per second (186,282 miles per second)—is the absolute speed limit of the universe.
No object with mass can ever reach or exceed this speed. But why?
E = mc²
The answer lies in Albert Einstein's Theory of Special Relativity, and his most famous equation: E = mc² (Energy equals mass times the speed of light squared).
This equation proves that mass and energy are interchangeable; they are two sides of the same coin. When you accelerate an object, you are giving it kinetic energy. According to Einstein, adding energy to an object also adds to its relativistic mass.
At everyday speeds, like driving a car or launching a rocket, this increase in mass is so infinitesimally small that it is unnoticeable.
The Wall of Infinity
However, as an object approaches the speed of light, its relativistic mass begins to grow exponentially. Because the object is becoming heavier, it requires even more energy to continue accelerating it.
If you tried to accelerate an object with mass to exactly 100% of the speed of light, its mass would become infinite. Therefore, it would require an infinite amount of energy to push it. Since there is not an infinite amount of energy in the universe, it is physically impossible.
Only photons—particles of light—can travel at the speed of light because they possess exactly zero rest mass.
Time Dilation
Special relativity introduces another bizarre consequence: time is not absolute.
As you move faster through space, you move slower through time relative to a stationary observer. If you were a passenger on a spaceship traveling at 99% the speed of light, time inside the ship would pass normally for you. But if you traveled for one year and returned to Earth, you would find that seven years had passed for everyone else.
If you somehow broke the laws of physics and traveled faster than light, the mathematics of relativity dictate that you would travel backward in time, shattering causality (cause and effect) entirely.