Albert Einstein’s famous equation may be one of the most famous formulas of all time, but its importance is often misunderstood. It’s not just a cool mathematical trick, but also a critical insight into how the universe works. Dedicated to his future wife, Mileva, who assisted him in his research and the first draft of this paper on special relativity.

**Table of contents**

## What does E=mc^2 mean?

We can think of the speed of light as being a constant, like a car driving at 65 miles per hour on a highway. No matter how hard you push on the gas pedal, that car won’t go any faster. You can’t change the speed of light by pushing on something with more force or by changing the car’s location. The speed of light is, for all intents and purposes, constant. Einstein’s famous equation says that mass is equivalent to energy. It’s just a different way of saying the same thing. The equation says that if you have a car or anything with mass and you want to change its speed, you need to put energy into it.

## Relativity

The most famous equation in physics, E=mc^2, was first published by Einstein in 1905 in a paper titled “On the Electrodynamics of Moving Bodies.” It was later titled “Theory of Special Relativity” when it was published in a book containing several papers by Einstein. This was the paper in which Einstein first presented his theory of special relativity, in which he made several radical claims, such as that the speed of light is the same for all observers, regardless of their relative motion, and that no electromagnetic particle can be accelerated to the speed of light. The most famous equation in the paper is E=mc^2, the energy-mass conversion. The equation itself is puzzling. What does the energy of an object have to do with its mass? Einstein was not the first person to notice the relationship between mass and energy.

## The mass-energy equivalence

The idea that energy can be converted into mass and vice versa was already well-known to physicists. However, Einstein’s contribution was to notice that, from a purely mathematical point of view, the two processes are equivalent, and that this equivalence is inherent in the laws of physics. Einstein’s insight can be expressed as follows: If we have a certain amount of energy, we can calculate the mass of that energy using E=mc^2. If we have a certain amount of mass, we can calculate the energy of that mass using the same equation. Since these are the same calculation in two different contexts, we can conclude that there is a deep underlying relationship between the two concepts.

## E=mc^2 and its consequence: Light is bent by gravity

Einstein’s theory of special relativity holds that nothing can travel faster than the speed of light. The reason is that, as an object approaches the speed of light, its mass increases, and the amount of energy needed to increase its speed further increases. Eventually, the amount of energy needed to accelerate the object to the speed of light is infinite. Thus, no object in the universe can travel faster than the speed of light. Einstein’s theory also predicts that massive objects, such as the sun, warp the fabric of spacetime. Light is also affected by this curvature in spacetime, which means that a beam of light traveling near the sun would be deflected by its gravitational field. Astronomers have confirmed this prediction, observing that light from distant stars passing near the sun is slightly bent.

## Other implications of relativity

Many of Einstein’s predictions are now well-established facts. For example, his theory states that black holes exist, and they do. Special relativity also predicts that the flow of time is not uniform but changes with the velocity of the observer, a phenomenon known as time dilation. Time dilation has been verified in particle accelerators, where a researcher’s watch would tick more slowly as she accelerates towards the speed of light. In general, Einstein’s theory has been enormously successful. It has not only been verified in numerous experiments, but also it has led to new technologies, such as MRIs. However, there are many aspects of relativity that remain unexplained or unproven.

## Summary

Einstein’s famous equation says that mass is equivalent to energy. It is just a different way of saying the same thing. If we have a certain amount of energy, we can calculate its mass using E=mc^2. Likewise, if we have a certain amount of mass, we can calculate the energy of that mass using the same equation. Since these are the same calculation in two different contexts, we can conclude that there is a deep underlying relationship between the two concepts. The most famous equation in this paper is E=mc^2, the energy-mass conversion. The equation itself is puzzling. What does the energy of an object have to do with its mass? Einstein’s insight was that there is a deep underlying relationship between the two concepts and that this relationship is inherent in the laws of physics.