Einstein's General Theory of Relativity: Four Steps Taken by a Genius

The revolutionary physicist used his imaginationnot complicated math to come up with your most famous and elegant equation. Einstein's general theory of relativity is known for predicting strange but true phenomena, such as a slowdown in the aging of astronauts in space compared to people on Earth and changes in the shapes of solid objects at high speeds.

But the interesting thing is, if you take a copyEinstein’s original article on the relativity of 1905, it will be quite simple to parse. The text is simple and understandable, and the equations are mostly algebraic - any high school student will be able to parse them.

All because complex math neverwas Einstein’s skate. He loved to think figuratively, conduct experiments in his imagination and conceptualize them until physical ideas and principles became crystal clear.

This is where Einstein’s mental experiments began when he was only 16 years old, and how they eventually led him to the most revolutionary equation in modern physics.


  • 1 1895: running next to a ray of light
  • 2 1904: measuring light from a moving train
  • May 3, 1905: lightning strikes a moving train
  • September 4, 1905: mass and energy

1895: running next to a ray of light

At this point in Einstein’s life, his badthe latent contempt for German roots, authoritarian teaching methods in Germany had already played a role, and he was kicked out of high school, so he moved to Zurich hoping to enter the Swiss Federal Institute of Technology (ETH).

But first, Einstein decided to spend a year of training at a school in the neighboring city of Aarau. At this point, he soon discovered that he was interested in what it was like to run next to a ray of light.

Einstein has already learned in the physical class what isray of light: many oscillating electric and magnetic fields moving at a speed of 300,000 kilometers per second, the measured speed of light. If he would run near the same speed, Einstein realized, he could see many oscillating electric and magnetic fields next to him, as if frozen in space.

But that was not possible. First, stationary fields would violate Maxwell's equations, mathematical laws that laid down everything physicists knew about electricity, magnetism and light. These laws were (and remain) quite strict: any waves in these fields must move at the speed of light and cannot stand still, without exception.

Worse, stationary fields did not fit withthe principle of relativity, which was known to physicists from the time of Galileo and Newton in the 17th century. In fact, the principle of relativity says that the laws of physics cannot depend on how fast you move: you can only measure the speed of one object relative to another.

But when Einstein applied this principle to hisa contradiction arose in a thought experiment: relativity dictated that everything he could see moving near a ray of light, including stationary fields, must be something down-to-earth that physicists could create in the laboratory. But no one has ever seen this.

This problem will worry Einstein 10 moreyears, throughout his path of study and work in ETH and movement to the Swiss capital Bern, where he will become an examiner at the Swiss Patent Office. It is there that he will solve the paradox once and for all.

1904: measuring light from a moving train

It was not easy. Einstein tried any solution that occurred to him, but nothing worked. Almost desperate, he began to ponder, but with a simple, but radical decision. Perhaps Maxwell's equations work for everything, he thought, but the speed of light has always been constant.

In other words, when you see a flyinga beam of light does not matter whether its source will move toward you, away from you, to the side or elsewhere, and it does not matter how fast its source moves. The speed of light that you measure will always be 300,000 kilometers per second. Among other things, this meant that Einstein would never see stationary oscillating fields, since he could never catch a ray of light.

It was the only way that I sawEinstein to reconcile Maxwell's equations with the principle of relativity. At first glance, however, this decision had its own fatal flaw. He later explained it with another thought experiment: imagine a beam that starts along a railway embankment while a train passes by in the same direction at a speed of, say, 3000 kilometers per second.

Someone standing near the embankment will have to measurethe speed of the light beam and get a standard number of 300,000 kilometers per second. But someone on the train will see light moving at a speed of 297,000 kilometers per second. If the speed of light is not constant, Maxwell's equation inside the car should look different, Einstein concluded, and then the principle of relativity will be violated.

This apparent contradiction made Einsteinthink for almost a year. But then, one fine morning in May 1905, he went to work with his best friend Michel Besso, an engineer whom he had known since his student days in Zurich. Two men spoke of Einstein's dilemma, as always. And suddenly Einstein saw the solution. He worked on it all night, and when they met the next morning, Einstein told Besso: “Thank you. I completely solved the problem. "

May 1905: lightning strikes a moving train

Einstein’s revelation was thatobservers in relative motion perceive time differently: it is possible that two events will occur simultaneously from the point of view of one observer, but at different times from the point of view of the other. And both observers will be right.

Einstein later illustrated his pointview with another thought experiment. Imagine that an observer is again standing next to the railway and a train is flying past him. At the moment when the central point of the train passes by the observer, lightning strikes at each end of the train. Because lightning strikes at the same distance from the observer, their light enters his eyes at the same time. It is fair to say that lightning strikes at the same time.

Meanwhile, exactly in the center of the train sits anotherobserver. From his point of view, light from two lightning strikes travels the same distance and the speed of light will be the same in any direction. But since the train is moving, the light coming from the back lightning must travel a greater distance, so it gets to the observer a few moments later than the light from the beginning. Since light pulses arrive at different times, it can be concluded that lightning strikes are not simultaneous - one is faster.

Einstein realized that just this simultaneity is relative. And as soon as you acknowledge this, the strange effects that we now associate with relativity are resolved using simple algebra.

Einstein feverishly wrote down his thoughts andSubmitted your work for publication. The title was “On the Electrodynamics of Moving Bodies,” and it reflected Einstein’s attempt to link Maxwell’s equations with the principle of relativity. Besso received a special thanks.

September 1905: Mass and Energy

This first work, however, was not the last. Einstein was obsessed with relativity until the summer of 1905, and in September sent a second article for publication, already after him, in hindsight.

It was based on yet another mentalexperiment. Imagine a subject at rest, he said. Now imagine that he is simultaneously emitting two identical pulses of light in opposite directions. The object will remain in place, but since each impulse carries away a certain amount of energy, the energy contained in the object will decrease.

Now, Einstein wrote how this one would lookprocess for a moving observer? From his point of view, the object will simply continue to move in a straight line, while two pulses will fly away. But even if the speed of two pulses remains the same - the speed of light - their energies will be different. An impulse that moves forward in the direction of travel will have a higher energy than one that moves in the opposite direction.

By adding some algebra, Einstein showed thatin order for all this to be consistent, the object must not only lose energy when sending light pulses, but also mass. Or mass and energy must be interchangeable. Einstein wrote the equation that connects them. And it became the most famous equation in the history of science: E = mc2.