Welcome to week 12 of Science Friday! For the last two weeks, we have covered the basics of classical gravity. This week, I am going to shift gears to modern physics—more specifically the special theory of relativity as proposed by one of the greatest minds in the history of the human race, Albert Einstein. Before we cover [i]special[/i] relativity, we need to understand what classical relativity is. After the establishment of classical physics by Newton and Galileo in the seventeenth century, it was understood that motion is relative. That is, there is no one correct way to state how an object is moving. The description of motion is entirely dependent on what is called a [i]frame of reference[/i]. To understand this better, let’s consider a concrete example. Suppose you are driving a car down a road at 70 mph. The coffee cup in the cup holder next to you is not moving from your frame of reference. However, from the frame of reference of a bystander on the side of the road, the coffee cup is in fact moving at 70 mph. So who is right? The answer is both of you are. In Newton’s classical physics, while motion was not absolute, time was. Even though you and the bystander would disagree on the speed of the coffee cup, there would be no disagreement regarding the time it takes to cover 70 miles. With the advent of electromagnetic theory in the nineteenth century, it was discovered that light (electromagnetic radiation) travelled at a constant speed—the speed of light. Since this speed is ingrained into Maxwell’s equations, its relativity was under question. In 1905, Einstein published his special theory of relativity. It consisted of two postulates. The laws of physics are the same for all inertial (non-accelerating) frames of reference. The speed of light, [i]c[/i], is the same for all inertial frames of reference The second postulate of special relativity is somewhat tricky to understand at first glance. Let’s say there are two people, A and B. Person A is at rest (relative to a third stationary object for our reference) and Person B is moving at 95% the speed of light away from Person A. Let’s say both Persons A and B turn on a flashlight in the direction they are facing. Under Newtonian physics, we would assume that the speed of the light beam would appear slower to Person B than to Person A. This is not the case. Both Person A and B observe the light beam to be moving at the exact same speed—186,000 miles per second in free space. If this is true (which it is from empirical evidence and mathematics), then it means that time and distance can no longer be absolute. In fact, for moving objects, time slows down and the length in the direction of motion shortens to keep the speed of light constant. These phenomena, known as time dilation and length contraction respectively, are readily calculable using algebra. The equations for time dilation and length contraction are below: T = A(To) X = (Xo)/A where T is the relativistic time, A is the Lorentz factor, To is proper time, X is relativistic length, and Xo is proper length. “Proper” time/length refers to the time taken or length measured in the system where there is no relative motion. The Lorentz factor is an expression that changes depending on the closeness to the speed of light. The closer to the speed of light, the greater the Lorentz factor. Let’s consider an example. Bill and Jane are at a 100 mile long straight track (viewed when they are not moving with respect to the track). Jane decides to take off down the track at 99% the speed of light while Bill “observes.” A few questions: How long is the track from Jane’s reference frame? How long is the track from Bill’s reference frame? How long did the run take for Jane? How long did Jane’s run take from Bill’s perspective? The answer to question 2 is easy. Bill perceives the track to be 100 miles long. Jane, however, views the track as shorter. The Lorentz factor at 99% the speed of light is approximately 7.0. Note that the Jane’s proper length for the track is Bill’s relativistic length of the track. X = Xo / A X = 100 / 7 miles Jane perceives the track to be only around 14.3 miles long! Using this relativistic length (from Bill’s perspective), we can calculate the time she perceives it took her to complete the run. t = d / v = 14.3 / (.99 x 186000) = 0.000078 seconds Bill calculates the time it took Jane to cover the track’s distance as t = d / v = 100 / (.99 x 186000) = 0.00054 seconds As we can see, Jane perceived to finish the run 7 times quicker than what Bill measured since Jane measured a track that was 7 times shorter. Both Bill and Jane’s measurements are equally correct for the frames of reference they are in. An extension of time dilation is the twin paradox, which is not something I have time to cover in this week’s SciFri. Instead, I will discuss how mass changes with speed. In ordinary settings, we consider mass to be a property that is unchanging. However, just as time slows down and length decreases with speed, so does mass increase. In fact, the reason why no object with mass can ever attain the speed of light is because the mass of the object would approach infinity as the object approached the speed of light, meaning that an infinite amount of kinetic energy would be required to attain light speed. This, obviously, is not possible. I hope you enjoyed this week of Science Friday! If you found any confusing or erroneous parts of my post, please post a comment! Otherwise, I am interested in reading your general responses and questions. To check out my previous postings of SciFri, click the #sciencefriday tag and click “All Time” next to “Created” to view all threads. Tune in next week for more science!