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How Einstein Discovered Relativity
People have a tendency to ascribe more credit and more blame to individuals than is usually appropriate. In the arts and sciences the old cliché “on the shoulders of giants” remains a cliché because it’s true.
Laypeople often assume that Einstein composed his theories of relativity out of thin air because heuristic descriptions of relativity give weird predictions: Two twins at a space-port. One gets on a rocket, accelerates into outer space and, when he comes back, is young and spry but his twin is a geezer. Weird. Also difficult to comprehend where such a crazy idea could come from. Let’s clear that up.
The Origin of Relativity
It was the late 1800s and it seemed as though physics was complete
Sure, there were a few details to be worked out, but isn’t that always the case? The heavy lifting was done. All of electromagnetism was encapsulated in an elegant theory distilled down to the four cool looking Maxwell equations. Gravity had been tied up over a hundred years before by Newton. Nice work, guys, let’s leave the details to graduate students.
At the time, gravity and electromagnetism were the only known forces. (We’re now aware of another two, the strong and weak nuclear forces. To be sure, the weak force was united with electromagnetism in the 1980s – we call the three of them, electricity, magnetism, and the weak nuclear force, the “electro-weak” force. Tidy. There is currently no compelling reason to believe in a force beyond those listed here.)
One of the details that needed to be worked out was a simple college physics homework problem
Let me walk you through it – no math, I promise. (If you want the math, drop me a note: ransom at ransomstephens.com and I’ll send you the gory details.)
First, consider two electrons at rest and separated by some fixed distance. They exert repulsive forces on each other. In the classical theory of Maxwell, Faraday, Ampere, Volt, et al., we think of one of the charges as sitting in the electric field of the other. The field of one charge exerts a force on the other charge, pushing it away.
Now, let’s put the two charges in motion. Or better yet, but equivalently, let’s leave them stationary and let’s you and me go zipping past them. In other words, from our point of view, we see the two charges going past us at a constant speed, the same way we might see a street sign go by while we’re sitting in a car.
When we calculate the force between the charges in this reference frame there’s an additional term. Magnetic fields are formed by moving electric charges – this is called Ampere’s Law, by the way. Now, not only does each charge experience the electric field of the other, but they also experience a magnetic field from the other.
The calculation is pretty straightforward and the result contradicts reality.
The classical theory predicts that, as we move faster, the repulsive force between the two charges decreases until it disappears altogether when the charges reach the speed of light.
Let’s think about that for a second. We, the observers, sit still while the two charges go zipping past. This scenario is identical to having the charges sit still while we zip past in the other direction. This is the grist of relativity, both the old-fashioned Galilean relativity and Einstein’s special relativity. If the charges stop repelling each other in one case, the same thing would have to happen in the other case because, well, we’d be able to see it from either reference frame.
It gets weirder
If our speed were to exceed the speed of light (remember, in 1900 no one was aware that the speed of light is nature’s speed limit!) then the force between the charges becomes attractive. No longer would the charges repel each other, they’d start attracting each other. Just because we’re moving by them – it doesn’t make any sense and so, must be wrong.
It’s an easy experiment too, you can use a sooped up TV tube to get a bunch of electrons up to half the speed of light and check whether or not the force of repulsion decreases. It doesn’t.
This is how science usually works
The old theory breaks down. Einstein realized this and figured out what had to change. Once he modified the old theory, he had a mess of crazy new predictions. Other physicists tested as many as they could – they checked out. He also thought his way through and solved, the seeming paradoxes of his new theory. Later, he extended the idea to the analysis of gravity and this is where the general theory of relativity came from.
Enter experimentalists and other skeptics to check it out and, so far, every prediction of relativity has held up.
Notice another thing. Something quite different from how laypeople tend to think of scientific theory. When the classical theory failed, it wasn’t a great big mistake that brought it down. The classical theory is used every day by electrical engineers. No one is designing electrical devices, like your phone, computer, or watch, with the newer theory. Engineers use Maxwell’s equations except in the isolated cases where they don’t work, namely with transistors and diodes. Similarly, mechanical engineers use Newton’s theory of mechanical forces to build bridges and skyscrapers – no one is worrying about relativistic corrections to the old theory.
“It’s just a theory”
The point is that it is extremely rare that an established scientific theory falls apart completely. The scientific method is not a process of building theories, throwing them out and building new ones. It’s a system of discovery and modification.
(The author, Ransom Stephens, contends that when using the theory of relativity, it’s helpful to do the math as fast as possible, because if you start thinking about the result too soon, you’ll get lost. Well, he will, anyway.)
© 2011 Ransom Stephens