Special Relativity In A Coffee Break

Relativity, one of the biggest advances in physics, and the theory that made Albert Einstein famous. This article covers the principles of special relativity, including length contraction and time dilation, some of the most abstract concepts in physics.

Back at the beginning of the 1900s, physicists were getting a grip on just how fast light went. They made several ingenious experiments that were able to measure the speed of light to a pretty accurate level, and this meant that they discovered a particularly interesting fact about it. Light, despite being a particle, doesn't get affected by movement the way other things do. If you ride a bick at 60 km/h and throw an apple at 20 km/h, you expect it to hit its target as if you'd thrown it at 80 km/h while standing still. If you shoot a beam of light from your bicycle, it does exactly the same thing as if you'd shot it from the ground, namely, it goes exactly lightspeed to someone standing still. The only problem is that you measure its speed as the speed of light too. That means that you and a ground observer now disagree as to how long the light took to hit its target!

Einstein, being a rather intelligent fellow, realized that these experiments suggested one 'axiom', or key fact, about physics. That fact was that light moves at a constant speed relative to everyone, and that because of this, different observers in different frames of reference have different perceptions of the world. These perceptions aren't illusions, because each observer is equally 'right', the simple truth is that for all of these observers, information about the universe is actually different. Now, this isn't as bad as it may seem, because given information about the things one observer sees, we're able to calculate things as seen by a different observer. Before we go any further, I'd like to clarify what we mean by observer and frame of reference. A frame of reference is essentially the set of all things that are not moving relative to eachother. Joe on the sidewalk and Jim on the sidewalk are in the same frame of reference, while Fred on a bicycle moving relative to Joe and Jim is in a different one.

Now, we'll talk about a few interesting consequences of these assumption. The first is the dichotomy between the phenomenon of length contraction and that of time dilation. In order to create these theories, Einstein considered an experiment in his head, or a thought experiment, because it was virtually impossible to get data on lightspeed relative to concrete objects, because objects can’t get anywhere close to the speed of light. The first experiment imagined a train travelling at a constant speed, and a light beam going up and down at the speed of light inside the train. An observer on the train sees the particle going up and down at the speed of light, but one outside the train would see it going at a faster speed, based on the triangle created by the train’s movement and that of the beam. This is a problem, because nothing can go faster than light for any frame of reference. The answer is that the value for time (the only unknown value in this experiment) had to be different for people on the ground and people on the train. Using math, they found a formula for time in a frame of reference based on another frame of reference and the perceived relative velocities of the two.

The next phenomenon is that of length contraction. Since we’ve already established that time seems different for people in different frames of reference, it’s obvious that if Joe, in his sports car, goes 100 km/h for a length of 100 km as measured by a ground observer, Joe perceives a trip that took less than one hour. The problem is that Joe perceived his own speed relative to the ground at 100 km/h as well, so it follows that when he measured the distance he travelled in his trip, it was actually less than 100 km. Likewise, a ground observer viewed his car as being shorter than if it had been measured at rest.

Using this simple (or complicated) rules, we get all sorts of things, we find that two rocketships moving away from eachother at almost lightspeed as viewed by a ground observer actually only see eachother moving away at close to lightspeed while the ground would see the distance between them getting larger at almost twice that. We also see that the time between events is different for everyone, and that some events that may seem simultaneous actually aren’t. The ‘real’ sequence of events is that which would be observed by an observer that saw the events happen in the same place.

Even though relativity disproves Newtonian physics, it’s good to know that all of the principles of relativity only apply when things are within a reasonable fraction of lightspeed. Since that’s 299 792 kilometers per second, we usually don’t get that close to it, and we can go back to the usual way of measuring things. If you enjoyed this article, check out "Quantum Theory in a Coffee Break," a similar explanation of Quantum Mechanics, a much newer branch of physics.

https://knoji.com/quantum-theory-in-a-coffee-break/

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Suba Lakshminarasimhan
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Graham Brown
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