###### By Emily Levesque, University of Washington

## There is no one more famous in the field of physics than Albert Einstein: a brilliant scientist who revolutionized the world of science with that infamous equation, E = mc^{2}. But what exactly did Einstein do that was so revolutionary? How did he develop his famous theory of relativity, and how did it change our understanding of how space, time, light, and gravity work?

### A Mathematical Genius?

Albert Einstein was born in Germany in 1879 and spent much of his childhood in Munich, where his father and uncle ran a company that manufactured electrical equipment. From an early age Einstein had a particular enthusiasm for math, working his way through algebra and geometry textbooks on his own. By his early teens, he’d moved on through calculus and developed a strong interest in physics. To Einstein, mathematics was the perfect language for describing and understanding nature.

Einstein is sometimes imagined as a bit one-sided, a reputation that might come from his reportedly failing an entrance exam for the Swiss Federal Polytechnic School in Zurich. It also fits with an often-deployed stereotype that mathematical geniuses may be strong in one area but deficient in another.

Einstein, however, also developed early interests in philosophy and music; he was a classically trained violinist and kept up his playing throughout his entire life, describing himself as thinking and daydreaming in terms of music. Like physics, music has deep mathematical roots.

### Working at a Patent Office

Einstein’s passion for math and physics did not, unfortunately, translate into a teaching position after he finished his studies—at least not right away. In need of a job, he began working at a patent office in Bern while he continued studying science and philosophy and doing theoretical physics research for his PhD.

Much of his patent work was focused on new technologies with electricity and clocks; combined with the work that his father and uncle did making electrical equipment, this likely sparked one of Einstein’s first ground-breaking discoveries: special relativity.

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### Special Theory of Relativity

Einstein’s special theory of relativity grew out of some apparent contradictions between two of the foundational pillars of physics: Newtonian mechanics and electromagnetism. These two topics are taught side by side at universities around the world, and usually make up the first year of a physics student’s college education but taken together they don’t quite seem to get along.

To understand why, let’s look at a basic principle of special relativity. The first is that the speed of light is always the same. Imagine a baseball player standing on the pitcher’s mound and throwing a 90-mile-an-hour fastball to home plate. We know exactly how fast the ball was moving: 90 miles an hour. Now, let’s put that same pitcher on the back of a train moving 40 miles an hour. If he throws his fastball straight off the back of the train, the ball is really only moving 50 miles an hour—Newtonian mechanics tells us that you have to subtract the speed of the train to measure the ball’s true velocity.

### Newtonian Mechanics and the Laws of Electromagnetism

Building on the same example, let’s give our pitcher a flashlight. If he shines a flashlight from the pitcher’s mound to home plate, the light is moving at the speed of light, about 186,000 miles per second. But, what happens when the pitcher is standing on the moving train? According to Newtonian mechanics, we might imagine the light as little individual particles and picture those particles slowing down by 40 miles an hour.

However, according to the laws of electromagnetism, that light is acting like a wave with a constant unchangeable speed: the speed of light. The length of that wave might be stretched by the speed of the train—a phenomenon known as redshift—but the speed of the wave is unchanged.

Obviously, both answers can’t be right, and they’re not: light will leave the train-riding pitcher’s flashlight at 186,000 miles per second, regardless of how fast the train is moving. But why? Newtonian mechanics did just fine at predicting the behavior of the baseball, so why did it get the light so wrong?

### Laws of Physics Must Stay Constant

Other research in the late-19th century had tested and proven the theories of electromagnetism, showing light acting like a wave, but what made light special? Why couldn’t Einstein settle on a definitive answer?

Einstein devised his special theory of relativity to reconcile these two seemingly-at-odds theories. He declared that the speed of light must be constant, and that relativity must be a fundamental tenet of physics. Relativity, simply stated, says that the laws of physics must stay the same everywhere. ‘Everywhere’ here refers to what we call different ‘frames of reference’.

### E = mc^{2}

These two statements—the speed of light is constant, and the laws of physics must stay the same everywhere—may seem simple, but expressing them mathematically, and testing them mathematically, became the cornerstone of Einstein’s work. His famous equation is one example of these mathematical consequences, describing the energy of an object as equal to its mass times the speed of light squared.

It boils down the relationship between something’s energy and its mass to this simple equation, connecting them by that constant, the speed of light. The equation works across any frame of reference, satisfying Einstein’s key rules.

Before Einstein, classical mechanics described objects as having either a kinetic energy—energy it has because it’s moving through a system—or a potential energy—the energy stored in an object because of its position in a system. E = mc^{2} described a more fundamental energy, known as the rest energy, and boils down the relationship between something’s energy and its mass to this simple equation, connecting them by that constant, the speed of light. The equation works across any frame of reference, satisfying Einstein’s key rules.

### Common Questions about Albert Einstein’s Special Theory of Relativity

**Q: What did Albert Einstein do while studying science?**Albert Einstein began working at a patent office in Bern while he continued studying science and philosophy and doing theoretical physics research for his PhD.

**Q: What did Albert Einstein’s special theory of relativity grew out of?**Einstein’s special theory of relativity grew out of some apparent contradictions between two of the foundational pillars of physics: Newtonian mechanics and electromagnetism

**Q: What does Albert Einstein’s famous equation**describe?Albert Einstein’s famous equation, E = mc^{2}, describes a more fundamental energy, known as the rest energy.