The revolutionary physicist used his imagination, rather than complex mathematics, to come up with his most famous and elegant equation. Einstein’s general theory of relativity is known to predict strange but true phenomena, such as astronauts slowing down aging in space compared to people on Earth and changing the shapes of solid objects at high speeds.

But the interesting thing is that if you take a copy of Einstein’s original article on relativity in 1905, it will be quite easy to disassemble it. The text is simple and straightforward, and the equations are mostly algebraic — any high school student will be able to disassemble them.

All because complex mathematics has never been Einstein’s fad. He liked to think figuratively, to conduct experiments in his imagination and to conceptualize them until the physical ideas and principles become crystal clear.

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

On 1895, running alongside a ray of light

By this point in Einstein’s life, his poorly concealed 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 in the hope of entering the Swiss Federal Institute of Technology (ETH).

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

Einstein had already learned in the physical class what a beam of light is: a set of oscillating electric and magnetic fields moving at a speed of 300,000 kilometers per second, the measured speed of light. If he were running close to the same speed, Einstein realized, he could see a lot of oscillating electric and magnetic fields next to him, as if frozen in space.

But it was impossible. First, stationary fields would violate Maxwell’s equations, the mathematical laws, in which everything that physicists knew about electricity, magnetism and light was laid. These laws were (and remain) fairly strict: any waves in these fields must move at the speed of light and cannot stand still, without exceptions.

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

But when Einstein applied this principle to his mental experiment, a contradiction arose: relativity dictated that everything that he could see moving alongside a ray of light, including stationary fields, should be something mundane that physicists could create in a laboratory. But no one ever watched.

This problem will worry Einstein for another 10 years, throughout his entire way of studying and working at ETH and going to Bern, the capital of Switzerland, where he will become an examiner at the Swiss Patent Office. It is there that he will resolve the theory once and for all.

On 1904, measurement of light from a moving train

It was not easy. Einstein tried any solution that occurred to him, but nothing worked. Almost in despair, he began to think, but a simple, but radical solution. Perhaps Maxwell’s equations work for everything, he thought, but the speed of light was always constant.

In other words, when you see a passing beam of light, it does not matter whether its source will move to you, away from you, to the side or anywhere else, 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 Einstein saw to reconcile Maxwell’s equations with the principle of relativity. At first glance, however, this decision had its own fatal flaw. Later he explained it with another thought experiment: imagine a beam that runs along a railway embankment while the train passes by in the same direction at a speed of, say, 3000 kilometers per second.

Someone standing near the embankment will have to measure the 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 Einstein think 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 years in Zurich. The two men talked about Einstein’s dilemma, as always. And suddenly Einstein saw the solution. He worked on him all night, and when they met the next morning, Einstein said to Besso:

Thank you. I completely solved the problem.

May 1905, lightning strikes a moving train

Einstein’s revelation was that observers 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 another. And both observers will be right.

Later, Einstein illustrated his point of view with another thought experiment. Imagine that an observer is standing next to the railway again and a train rushes past him. At that moment, when the central point of the train passes by an observer, lightning strikes at each end of the train. As the 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 simultaneously.

Meanwhile, exactly in the center of the train sits another observer. From his point of view, the light from two lightning strikes travels the same distance and the speed of light will be the same in any direction. But as the train moves, the light coming from the back of the zipper must travel a longer distance, so it hits the observer a few moments later than the light from the beginning. Since light pulses come at different times, it can be concluded that lightning strikes are not simultaneous — one happens faster.

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

Einstein frantically recorded his thoughts and sent his work for publication. The name was “On the electrodynamics of moving bodies”, and it reflected Einstein’s attempt to link the Maxwell equations with the principle of relativity. Besso was given 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 he sent the second article for publication, already in pursuit, in hindsight.

It was based on another thought experiment. Imagine an object at rest, he said. Now imagine that it simultaneously emits two identical pulses of light in opposite directions. The object will remain in place, but since each pulse carries a certain amount of energy, the energy contained in the object will decrease.

Now, Einstein wrote, what will this process look like for a moving observer? From his point of view, the object will simply continue to move in a straight line, while the two impulses will fly away. But even if the speed of two pulses will remain the same – the speed of light – their energies will be different. A pulse that moves forward in the direction of motion will have a higher energy than that which moves in the opposite direction.

By adding a little algebra, Einstein showed that in 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 should be interchangeable. Einstein wrote down the equation that binds them. And it became the most famous equation in the history of science: E = mc2.

Einstein's General Theory of Relativity. Steps to a genius solution.
Click To Tweet

The post Einstein’s General Theory of Relativity. Steps to a genius solution. appeared first on Upcosmos.com.