Relativity Lite

2 | Relativity Lite IT’S ABOUT TIME! You are at the airport trying to catch a plane you are late for. As you run onto Con- course E, the announcer says the jetway door will be closing in 1 minute, and you see the door 300meters (328 yards) away. With your luggage you can only run at 3meters per second (3 m/s is 6 miles/hour), which means that it will take you 100 seconds to get to the plane, but you only have 60 seconds before the door closes. You notice a sliding walkway (slide- walk) ahead with people standing still relative to it, yet moving at the same velocity you are (3 m/s) relative to the hallway. What would you do? If you run onto the slidewalk, past the people standing still relative to the slidewalk, how fast would you be moving relative to the hallway? Would this solve your problem? * You know that these sorts of gadgets are irresistible to children. What is the first thing a child will do on a slidewalk (or on an escalator)? Run in the “wrong” direction at 3 m/s. If she does so, what would her velocity be relative to the hallway? † She is playing with the idea that in our everyday experience, velocities add and subtract. (This is why we must use the term velocity rather than speed whenever we wish to be mindful of directions, since the latter is only the size of the velocity with no indication of direction. If direction is immaterial, speed and velocity are often used interchangeably.) During the late 1800s, physicists were trying to find how fast the Earth was moving through a cosmic substance that they called ether . ‡ They thought that they could deter- mine the Earth’s speed (like the slidewalk’s) by comparing the speed relative to the ether (akin to the hallway) of one beam of light cast one way from the Earth to another beam of light cast sideways from that direction. But every time they tried this, they found no difference for the two cases. This was a big mystery. Albert Einstein sorted it out it in 1905 by asking what the conse- quences would be for our experiences if the speed of light were the same no matter what the state of motion of the object that projects the beam is. § He also said that there is no abso- lute state of motion (or absolute reference frame ) to which we can compare our motion and thus no need to pose the existence of the “ether.” He showed that the major consequence of the speed of light being the same in all frames of reference is that the passage of time depends on the motion of the viewer. To show the general idea, consider one of Einstein’s thought experiments. Suppose you were reading this book while you sat on a train moving at 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? ¶ Does * Your velocity of 3 m/s would add to that of the slidewalk, 3 m/s, to give 6 m/s. At this velocity, you need only 50 seconds to travel 300 m and have 10 extra seconds to casually walk onboard the plane. † It would be 0 m/s; she would make no progress, and that is why it is fun. ‡ This term was a holdover from the Ptolemaic model of the Solar System, where ether was a substance said to fill the celestial spheres. § A. Einstein, Ann. Phys. (Leipzig) 17 , 891 (1905); 20 , 371 (1906). ¶ Twelve o’clock.