Relativity Lite

To c or Not to c  | 1 CHAPTER 1 To c or Not to c Einstein’s famous special theory of relativity has gained unquestioned acceptance in the sci- entific world. It has been proved in countless ways and is the foundation upon which grav- itation and high-energy quantum physics are based. Is it something that a “normal” person can understand? Relativity forces us to abandon our ideas about time, which is a hard thing to do, but the basic mathematics of it are relatively simple—just a picture away. The picture depends on extending something you know about on an intuitive level. Sup- pose I tell you that you have an hour to drive and that you must go south at 50 miles/hour. Can you tell me where you will end up? * Suppose I tell you to go south at 100 miles/ hour: Where will you find yourself after one hour? † Suppose I tell you to go south for two hours at 50 miles/hour, where do you end up? ‡ So you see, you know the distance trav- eled if you know how fast you are going and how much time is allowed. That is, distance traveled is velocity × time. Let’s check this against our intuition for the last case: 100 miles = 50 miles/hour × 2 hours. § But I’m a slow typist so I want to abbreviate this understanding by using the first letter of each word: d = v t . Any heart attacks yet? Well that one relation, which you already understand enough to do the calculation in your head , is all the math you need to do much of relativity! * Fifty miles south of your start. In my case, Salem, Oregon. † On the way to jail. ‡ One hundred miles south of your start. In my case, Eugene, Oregon. § Of course, the 50 × 2 on the right-hand side gives 100, the numerical part of the result on the left-hand side, but also notice that the hour in “2 hours” cancels the hour in “miles/hour” (or “miles per hour”) leaving just “miles” as the unit of the result—correctly a unit of distance. Another way to say this is “hour/hour = 1,” and 1 times anything just gives that thing back.