Chapters 21 and 22 of 'Einstein' - all chapters at www.bryantwieneke/blog
21. Einstein knew immediately how to start his proof. He had been waiting for a long time to have a conceptual framework to guide his work on this problem. Now he had one.
His Patent Office experience was a good reference in situations like this because he had to focus on one thought at a time, connecting the logical points leading toward a conclusion. And he knew he had to spend at least as much time explaining the logic as on the mathematical underpinnings of his argument. He began by briefly summarizing his point of departure as follows: "We have to bear in mind that all our propositions involving time are always propositions about simultaneous events." This point was not only his point of departure, it was fundamental to the logic he planned to use in developing his argument. Next, he described imaginary clocks he planned to use to give physical meaning to the concept of time and tie it to the concept of simultaneous events. The timing of external events needed to be measured in more than one place, by more than one clock, and these clocks needed to be synchronized
With these preliminaries out of the way, he described a situation where a rigid rod with a clock at each end was set in motion, and a beam of light moved between the two ends of the rod. Einstein stated the obvious, that a stationary observer, one not traveling with the rod would say that the beam of light hits both clocks at the same time. This was to be expected. It was what classical mechanics had been saying for centuries. The unexpected part, and the part no one had ever thought to ask about before, was what the observer who was traveling with the moving rod would say. Because it took a tiny fraction of a millisecond for light to travel the distance between one end of the rod to the other, the beam of light traveling between the two ends of the rod could not hit both clocks at the same time. In other words, the clock on one end of the rod would show that the beam of light hit it slightly later than it hit the other end, due to the travel time between the two ends.
Einstein represented these situations with mathematics that came naturally to him and manipulated the equations deftly. Concentrating fiercely, he manipulated the equations, and came out with an inequality that showed beyond doubt that an observer on the platform and an observer on the moving train experienced the same event at different times. Albert was pleased because it was not only what he expected; it was an absolutely essential point. There were no problems with the mathematics. In fact, the proof of this part had been even faster and simpler than even he could have predicted. Beneath the series of equations, he wrote his inescapable conclusion: there was no absolute meaning to the concept of simultaneous events. Albert Einstein took a deep breath and sat back in his chair. He glanced at the clock on the wall of his study, which showed that it was 12:30 a.m. Not bad, he thought. He could flesh it out later with all the explanations and definitions, but the important part to him was that the math came out right. And it did. The concept of simultaneous events had been destroyed in little more than an hour. 22. Rising from his desk, Albert yawned and walked into the living room, which was still lit only through the open doorway by the lamp in his study. He was carrying his cup. When he reached the kitchen, he turned up a lamp. He picked up the kettle and tested it. Convinced there was enough water for at least one cup of tea, he lit a match and started a fire in the stove. He emptied his cup and waited while the water heated. The next step was going to be more difficult. Disproving the concept of simultaneous events was not an end in itself; rather, it was the first domino that had to fall to discredit the notion of absolute time. Inasmuch as absolute time was essential to almost every aspect of classical mechanics, physicists would need to change the way they looked at the world without it. In short, they would need to view the world and its component parts as relative phenomena, not absolute. While the death of the notion of simultaneous events convinced Albert this was the correct view, he still had to prove it.
He would need to lay his cards on the table and show the effrontery of his argument. He needed to take the last, lonely absolute – the constancy of the speed of light – and show that it was inconsistent with the classical notion of absolute time and space. Then he would need to take the same argument, turn it on its head, and show that the constancy of the speed of light was consistent with a “relative” view of the world. Once he had proven this point and established logically and mathematically that only a relative view of the universe was consistent with the only remaining absolute, he would have a strong foundation for his proof. Scientists might argue with his methods or his ideas, but they could not argue with the constancy of the speed of light and calculus. At least, the reasonable ones could not. When the kettle began to whistle, he pulled it off the stove and filled his cup, with the scalding hot water making tea instantly as it filtered through the strainer. It was hot and strong, just the way he liked it. He turned down the lamp and moved toward the door. He looked up just in time to find himself face to face with Mileva. He jumped slightly. Some of the hot water spilled onto the saucer, but not fortunately onto his hand or Mileva. “You startled me,” he said, stating the obvious. “Did you spill the tea?” “No, I don’t think so.” Mileva did not respond, facing Albert in the half light, as he wondered what she was doing there. “Do you want something? She shook her head. “No, I don’t,” she replied. Her voice was still tight, with a hint of the testiness she had been carrying with her lately. “It’s very late, Albert,” she pointed out. “I know,” he said. “But tomorrow is the Sabbath, and I don’t work.” “You still need your sleep.” He did not want to argue with her. On the other hand, he did not want to go to bed, especially when things were finally coming together after years of working, off and on, on the problems with mechanics. His next step was to show that the death of the concept of simultaneous events also signaled, by extension, the death of time as an absolute.
He felt an eagerness to get back to his desk, but suddenly realized he might have an opportunity to close the gap between them by telling her what he had discovered. She is a physicist, he thought. She might appreciate the importance of this insight about simultaneous events. “Do you want to hear what I’ve been working on tonight?” he asked. She grimaced. “Not now, Albert. It’s the middle of the night.” “It won’t take long,” he persisted. “It’s a very interesting development.” She sighed and stared at him with skepticism. “I’m not sure anything is going to be interesting at this hour.” She did not agree to listen, but she stopped complaining about the hour and did not walk away. He took these as positive signs, despite her sagging posture, which suggested a certain impatience. She also had a continued look of skepticism on her face, or at least on what he could see of her face in the dimly lit doorway between the kitchen and sitting room. “Something came together just a little while ago,” he began. “It struck me when I was thinking about what would happen if two trolleys were traveling near the speed of light, where the rate of passage of time might change.” She yawned as he spoke. It occurred to him in passing that she never used to yawn when he described his thought experiments. “Anyway,” he continued. “I played with the idea of what would happen if there was an observer on each of the two trolleys traveling at that speed, and then some external event occurred, like the explosion of an asteroid or something.” Mileva still looked skeptical, but she was standing up a little straighter. She seemed to be listening. “If the two trolleys were traveling at different speeds, the two observers on the trolleys would see the asteroid explode at different moments. They would not see it explode at exactly the same instant.” Mileva was clearly interested in his comments now.
“Why would they see it at different times?” she asked. “What happens at the speed of light that would affect how they see it.” “I think time passes more slowly as one approaches the speed of light,” he replied. “And the faster you go, the more it slows.” “You’re saying time would not pass at the same rate on trolleys moving at different speeds?” “That’s right.” She assumed a quizzical look. “That’s crazy, Albert. Ninety-nine out of a hundred scientists would say that’s crazy. Maybe a hundred out of a hundred.” Albert smiled. “I know. But the beauty of this idea is that it doesn’t matter how fast you’re moving, because the principle applies at any speed. Mathematically, when I lay out the equations that correspond to this situation, I don’t assume that the observers are moving near the speed of light. The same phenomenon occurs to someone on a train passing through Bern.” With the quizzical look remaining on her face, she began to shake her head. “That’s not possible,” Mileva said. But he could tell her interest had been piqued. There was no longer any malice in her voice, no edge to it. She was clearly interested in Albert’s exposition of his idea and seemed to be challenging him not because she doubted him, but because she wanted to know more. “The key is the constant speed of light,” he explained. “A person who is moving experiences an external event at a different time than a stationary person, and two people traveling at different speeds also experience an external event at different times. This occurs near the speed of light or at the speed of a Bern train. The only difference is in magnitude. Differences are greater as one approaches the speed of light.” “That doesn’t make sense,” she repeated. “It only doesn’t make sense because we view the world a certain way. Especially as scientists because all the laws of mechanics are based on absolutes.” “But they work. They work perfectly in all applications.”
“They work, but they do not work perfectly,” he corrected her. “They seem to work perfectly because we are not able to measure the subtle differences. The differences are so small that it’s only recently, when we’ve been able to measure phenomena more accurately, that we can tell there are differences. But you know that more and more experiments are showing that absolute measurements don’t tell the whole story. “I know,” she admitted. “But it still doesn’t make sense.” “Mileva, let me explain a simple situation that doesn’t make sense. Let’s say you are on a train pulling out of the Bern station. There is a light beam in front of the train and behind the train. Both these light beams are activated at the same instant, according to an observer standing on the platform at the station. Now, if light travels at a constant speed, very fast but still finite, wouldn’t you see the light beam coming from in front of the train before you see the one coming from behind? The one in front has less distance to travel – it has to hit you first.” She stared at him, apparently without an argument to make. “Now, under those circumstances, the only thing that doesn’t make sense would be to argue that an external event like the activation of a light beam occurs at exactly the same instant for everyone, no matter where they are, or whether they’re moving or standing still.” Mileva stood in the doorway with a blank look on her face. “You can prove that there is not one definite point in time at which events occur?” she asked, still slightly dumbfounded. He nodded, the faintest hint of a smile at the corner of his lips. He could tell that he had convinced her that he was on to something, maybe even something important. “Then what?” “Then I use that information to prove absolute time does not exist. And then the most difficult part, which is finding something to replace it with.” She stared at him, as if almost afraid to ask the next logical question. Finally, after several moments of silence, she took the plunge. “What would you replace it with?” “Relativity, of course,” he replied blithely. “What else is there?”