The Theory of Relativity

Y'know..I almost, kinda understand a couple parts of that equation. Scary...

The Theory of Relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word "relativity" is sometimes used in reference to Galilean invariance.
The theory of relativity enriched physics and astronomy during the 20th century. When first published, relativity superseded a 200-year-old theory of mechanics elucidated by Isaac Newton. It changed perceptions.
For example, it overturned the concept of motion from Newton's day, into all motion is relative. Time was no longer uniform and absolute, as related to everyday experience. Furthermore, no longer could physics be understood as space by itself, and time by itself. Instead, an added dimension had to be taken into account with curved space-time. Time now depended on velocity, and contraction became a fundamental consequence at appropriate speeds.
In the field of microscopic physics, relativity catalyzed and added an essential depth of knowledge to the science of elementary particles and their fundamental interactions, along with introducing the nuclear age. With relativity, cosmology and astrophysics predicted extraordinary astronomical phenomena such as neutron stars, black holes, and gravitational waves.
Albert Einstein‘s theory is known as the Theory of Relativity because its core principle is that the speed of light in a vacuum is always the same, relative to the observer. This is totally unlike the speed of anything else.
If you are driving along the motorway at 100km/hr and the car in the next lane is doing 120km/hr, you will observe it gaining on you at 20 km/hr. If this keeps up for an hour the other car will end up 20 kilometers ahead of you. Similarly, if the car in the next lane is doing 80 km/hr, it will appear to be going backwards at 20 km/hr, compared to you. But light, along with other forms of electromagnetic radiation such as radio waves and X-rays, doesn’t work that way.
No matter how fast you’re going, any beam of light appears to be travelling away from you at the same speed: 300,000 km/second. If you’re travelling at 50,000 km/second, and someone who is stationary switches on a lamp, the beam of light travels past you at 300,000 km/second, not at 250,000 km/second as you might expect. And yet, if the stationary person measures the speed, they also find that it travels away from them at 300,000 km/second. Weird!
How can this be? Bizarrely, as things move faster they get shorter and their time travels more slowly. So the observer moving at 50,000 km/second is measuring the light’s speed with a shorter ruler and a longer second. No wonder the light seems to travel the same number of kilometers each second, if the moving observer’s kilometers and seconds are different from those of the stationary observer.
At small speeds, the difference is not much. If you’re on a bus travelling at 100 km/hour, the bus gets shorter by less than a millionth of a millimeter, and its time slows down by the same proportion. Not enough to notice! But the effects predicted by Einstein’s Theory of Relativity have been repeatedly measured with larger objects and distances (such as planets orbiting the sun) and with objects travelling at high speeds (such as subatomic particles).

Another part of Einstein’s theory states that mass and energy are equivalent, and it provides a formula to convert from one to the other. This is Einstein’s famous equation “E equals m c squared”, where E is energy, m is mass (at rest), and c is the speed of light.
Any time you liberate energy, you are also reducing mass. When you discharge a battery, the electricity is generated by chemical changes inside the battery. These chemical reactions leave the battery slightly lighter than it was when it was fully charged, and the battery gets heavier again when you charge it up! Again, the difference is very small. Only a tiny proportion of the battery’s mass is converted into energy.
When you accelerate an object, it gets heavier. The faster an object goes, the heavier it gets. This is totally counter-intuitive, but it really happens. The energy used to accelerate the object doesn’t just disappear into nothingness; it reappears as increased mass of the object being accelerated.
This is why it’s impossible for anything to travel faster than the speed of light. As the speed of an object approaches the speed of light, it gets exponentially more massive (“heavier”). It would become infinitely massive at the speed of light, but of course you can never get that fast because it becomes harder and harder to accelerate the object as it gets faster and more massive.
This is a very informal explanation of the theory of relativity. The effects are so small at everyday speeds that we aren’t aware of them, but the theory is readily verifiable by experimentation.
Einstein’s theory points tantalisingly towards some kind of deeper understanding of the essential nature of time, gravity, energy and matter. Many scientists have spent a lot of time trying to unify these into an all-encompassing “theory of everything” but so far without success.