Special Relativity I: An Overview

Hello, and welcome back to MPC! Last week, we began to discuss fundamental properties of the speed of light and we got our first taste of special relativity. Today, we will be discussing the history of special relativity so that we can be ready to begin an in-depth study of it next week.

Recall that in one of the very first posts on MPC (“Classical vs. Modern Physics: Modern Physics”) we discussed a bold claim made by Lord Kelvin that only two more problems existed in all of physics, one of which was “issues surounding the speed of light.” Over the past few weeks, we have been discussing the dilemnas that scientists were running into with the speed of light. Most importantly, we discussed the Michelson-Morley experiment and the fact that it’s outcome suggested that, unlike most waves, light does not travel in a medium (a “luminiferous ether”). We also discussed the seemingly unintuitive fact that the speed of light is a constant. There is no doubt that physicsts found these observations very strange, and it seemed as if no one could explain these phenomena. Eventually, an explanation for these strange facts was discovered, but it would take an Einstein to find it.

Albert Einstein was born in Germany in 1879. From a young age, Einstein enjoyed imagining crazy scenarios. For example, he would imagine what it would look like to ride on a ray of light. As a student, Einstein was fascinated by science and math. However, he was not the best student — while attending college, he would occasionally skip class! After graduating from college, Einstein had trouble finding a job, but, eventually, he was able to secure a position as a clerk for the Swiss patent office. While working in the patent office, Einstein had a lot of time to himself. As a result, Einstein’s imagination began to run wild again. His imagination completely changed his life, and the world, in 1905.

1905 is commonly referred to as Einstein’s “miracle year.” Why? Well, it was in this year that all of the time Einstein had spent thinking to himself in the patent office paid off, for he published four groundbreaking papers. One of his papers was on something known as the “photoelectric effect” (which we will cover when we get into quantum mechanics). Another one of his papers was on a concept known as “Brownian motion,” which would help prove the existence of atoms. He also wrote a paper in which he would introduce his most famous equation: E = mc^2 (which we will be talking about in the near future). Most importantly, at least for us today, Einstein wrote a paper titled “On the Electrodynamics of Moving Bodies,” in which he introduced his special theory of relativity.

The special theory of relativity was a radical idea that Einstein propsed to explain discrepencies between classical physics (the Galilean transformation) and the strange phenomena surrounding the speed of light. Believe it or not, Einstein was able to solve the whole enigma with two statements:

  • The laws of physics are the same in all inertial frames of reference.
  • The speed of light is constant in all inertial frames of reference.

Let’s break down the first statement. Laws of physics refers to the equations/ideas that explain the world around us. Perhaps the most well-known law of physics is Newton’s second law of motion, F = ma (force is the product of mass times acceleration). Now, what is an inertial frame of reference? A frame of reference on its own can be thought of as the location from which a phenomenon is being observed. For example, if you were watching a football game in a football stadium, you would be observing the game from your seat in the stands. Therefore, the frame of reference that you would be “in” is some seat in the stands. The word inertial is where it gets a little bit tricky. Basically, an intertial frame of reference is one that is not accelerating. So, in the previous example, when you were watching the game from the stands, you were in an inertial frame of reference (you weren’t accelerating, you were stationary). Likewise, if you were sitting in a car driving on a highway at a constant speed, you would be in an inertial frame of reference (yes, you would be moving, but at a constant speed, meaning that you would not be accelerating). On the other hand, if you were sitting in a car as it was first starting up, you would not be in an inertial frame of reference (the car must accelerate to reach the speed it will eventually travel at).

So, now that we understand what a law of physics and an intertial frame of reference are, does the first statement make sense? Yes, it does! Let’s think of an example, using Newton’s second law of motion. Let’s return to the inertial frame of reference with you sitting in your car that is traveling at a constant speed on the highway. Imagine that you are going at 100 m/s when you pass a mile marker sign. From your perspective, the mile marker sign is passing you at 100 m/s. Let’s also imagine someone else, standing right next to the mile marker, who we will call Al (note that Al is also in an inertial frame of reference, because he is not accelerating). Does Newton’s second law of motion work for both you and Al? According to Al, the sign is not moving, it’s accleration is 0, and the force on it is its mass times zero, or just zero newtons. To you, the sign is moving at 100 m/s, but this speed is not changing. Therefore, you see the acceleration of the sign as 0, and you will calculate the force acting on the sign to be its mass times zero, or zero newtons. Newton’s second law of motion seems to be exactly the same for both you and Al, who are both in an intertial frame of reference. Please note that this is just one simple example: Einstein’s special theory of relativity claims that this concept applies to all of the laws of physics.

**As an exercise, imagine if the car you were in was accelerating (you were in a non-inertial frame of reference). Would Newton’s second law of motion work for both you and Al? Also, try imagining what would happen if, instead of measuring the force on a mile marker, you and Al were measuring the force on object that was actually being pushed, like a crate. Would Newton’s second law of motion work in this case as well? Post what you discover in the comments!**

You may be wondering about that second statement now. We alluded to the fact that the speed of light is constant in previous blog posts, but Einstein was really the first to formally state it. How did Einstein know that the speed of light was constant? Amazingly enough, he derived this from his first statement! There exists a few important equations in physics that are collectively known as the Maxwell equations. We will not cover these equations here, but you should know that, from these equation, the speed of light can be derived. Why is that important? Well, we have stated that all of the laws of physics are the same in all inertial frames of reference, meaning that Maxwell’s equations are the same in all intertial frames of reference, meaning that the speed of light can be derived to be the same in all intertial frames of reference, which is truly amazing!

That’s all for today. Last week, we had started talking about how the speed of light can dictate space and time. Now that we have a better understanding of why the speed of light is constant, we are ready to dive more formally into the concept of time dilation (and eventually length contraction), which we will do next week. See you then!



(featured image: http://schoollyd.com/p/2016/11/writing-a-book-e9sa7s1f.jpg)


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