Relativity Lite

12 | Relativity Lite and integration of life in many experimental directions, instanced by all the past and present organic forms. * Clearly, if relativity were not working, evolution would have proceeded at a pace that is between 5 and 256 times slower (2 8 ). † The Earth would have had to wait 18 to 900 billion years for intelligent life to form (instead of 3.5 billion years)—much longer than the Sun’s 10-billion-year lifetime! Put another way, the person attempting to write this book today would likely be a mess of green slime had relativity not offered us its gifts. THERE ARE COPS, YOU KNOW! What about people traveling at super high speeds, such as v = 0.9986 c in figure 6? Suppose your twin left Earth when you were 20 years of age, traveled for 10 years at v = 0.9986 c , and then returned to Earth to tell you about her trip. Tough luck; you would have died of old age a century before she returned! You were both 20 when she left. She is 30 years old (20 + 10) when she returns (both her clock and her body agree with this assertion), but you would be 210 years old (20 + 10 × 19) had you lived. As we increase the speed from this point, we will find that we reach a limit in our ability to graph. But this limit expresses a reality of nature. As the velocity v of a rocket approaches that of the speed of light c , the right-hand side of the rectangle really does approach the right side of the 10 cm square in figure 6. The limit as v goes to c is that the rectangle goes to a square. Then we have to move the square not at all to get its lower right-hand corner to touch the right side of the rectangle-which-is-a-square. That is, c τ = 0 cm. A finite coordinate time period in a rocket moving at velocity v = c relative to the Earth corresponds to zero proper time. What does that mean? If we divide 10 cm by 0 cm we get an infinite time-dilation factor. ‡ We actually never run into this infinite limit because it is impossible to exert sufficient force on the rocket to get it moving at the speed c . The reason is that whatever force is exerted on the rocket to increase its velocity is spread out over a longer and longer period of Earth coordinate time as v approaches c . We would have to wait an infinite amount of Earth coordinate time to see the rocket reach the speed of light. * G. Douglas Straton, And God Laughed When the Birds Came Forth from the Dinosaurs: Essays on the Idea and Knowledge of God (1995 ms.), Chap. 5, p. 115. † The maximal value is assuming that the other 100 µsv of cosmic radiation noted in Alan Martin and Samuel A. Harbison’s An Introduction to Radiation Protection (Chapman & Hall, New York, 1979), p. 53, would have a similar reduction in the absence of relativity; the minimal value assumes that there would be no such reduction. ‡ To see this consider the following pattern: On your calculator divide 10 by 10 to get 1; 10/1 = 10; 10/0.1 = 100; 10/0.01 = 1,000; 10/0.001 = 10,000; 10/0.0001 = 100,000; 10/0.00001 = 1,000,000; and so on. As you divide 10 by smaller and smaller numbers, you get a result that is bigger and bigger. Infinity is the limit of this sequence.