Relativity Lite

To c or Not to c  | 3 that match the 12:10 showing on your wristwatch (or smartphone)? What time would it show three hours later? Not three o’clock, like on your watch? What about three days or three months later? Indeed, since you are moving at the same speed that the light is, it would never overtake you with new information. It would always read twelve o’clock. It turns out that matter like you and the train cannot ever reach the speed of light for reasons we will show a bit later. So we have to modify the thought experiment a bit and say you are reading this book while you sit on a train moving at the 99.86% of the speed of light away from a clock fixed on a tower. If you passed the tower precisely at twelve o’clock, what time would the clock face show 10 minutes later as you look back at the light coming from it? Well, it would be slowing overtaking you and would read something like 12:03, but it would still not match the 12:10 showing on your wristwatch. The picture we develop in the next section will allow us to determine whether the clock shows 12:01 or 12:00.32 or 12:03. We think of light as the colors red through violet in the color spectrum. But consider, why is it that you wear sunglasses that block out ultraviolet radiation? UV is a higher-energy form of light that the dyes in our eyes do not register but that will interact with (burn) our bodies. X-rays, gamma rays, and so on are even higher-energy forms of light. On the other side of the visible spectrum are the lower-energy forms of light starting with infrared, microwave, radio waves, and radar. They all travel at the same speed. The speed of light is always represented by the letter c and has been measured to be c = 186,000 miles/second. Once we know the value of c , we can measure the distance to a spaceship by counting how many seconds pass between when we send it a radio wave and when it returns the wave to us. Likewise, when we bounce a laser beam off the Moon, we notice that there is a 1.28-second delay for each leg of the trip. That means that the distance between Earth and the Moon is d = c t or d = 186,000 miles/second × 1.28 seconds = 238,000 miles. DID YOU EVER WISH YOU HAD MORE TIME? Consider a beam of light bouncing between the mirrors of a spaceship moving, perpendic- ular to the light beam, at speed v relative to the ground, as seen in figure 1. To someone sitting in the ship, the distance the beam must travel is simply the height H of the ship. The distance is the velocity c times the time of travel τ between bounces as measured in the ship or H = c τ .