![\"i-6645388eba06e7ccb01b7fa64289f1e3-walking_what.jpg\"](\"http:\/\/scienceblogs.com\/principles\/wp-content\/blogs.dir\/467\/files\/2012\/04\/i-6645388eba06e7ccb01b7fa64289f1e3-walking_what.jpg\")
<\/p>\n<\/p>\n
We’re just starting out on a walk, and no sooner do I open the gate from the back yard than the dog takes off at a run, hitting the end of the leash and nearly pulling my arm out of the socket.<\/p>\n
“Whoa, there,” I say. “Take it easy.”<\/p>\n
“Come on<\/strong>,” she says, “We need to go fast! Let’s go, let’s go, letsgo!”<\/p>\n “What’s the hurry? It’s a nice day, there’s no rush.”<\/p>\n “We need to go fast. If we go fast, I’ll be younger than that annoying dog out back.”<\/p>\n “You know, I’m all in favor of exercise, but I think you’re overstating the benefits.”<\/p>\n “No, silly, it’s not about exercise. It’s physics. When I go fast, time slows down. It’s Simple Relativity.”<\/p>\n “The name is Special Relativity, actually.”<\/p>\n “Whatever. The point is, light bounces around in triangles, so time slows down, and I get younger. So let’s gooooo!!!”<\/p>\n <\/p>\n “OK, you’re garbling the explanation a little. The reason time slows down is that the laws of physics are invariant under the Lorentz transformation between moving frames. The business with light clocks is just an illustration of the basic effect, a gedankenexperiment<\/i> that Einstein used to explain things.”<\/p>\n “You just love busting out the big German words, don’t you?”<\/p>\n “You have to like a language where you can just keep gluing words together. Germans must play Scrabble on a board the size of a parking lot.” We’ve reached the corner of the street, and I stop to let a car pass. When we start going again, she races right to the end of the leash, and resumes pulling. “Anyway, the point is, it’s a particular thought experiment that demonstrates the general principle.”<\/p>\n “Right. Light, triangles, slow time. Let’s go. If you insist on explaining this, do it while we walk.”<\/p>\n “You’ve got to admit, it’s an ingenious idea. You can imagine making a ‘clock’ by bouncing a pulse of light back and forth between two mirrors, and recording a ‘tick’ every time it hit one of the two.”<\/p>\n “That’d be one fast clock.”<\/p>\n “Sure. If you put the two mirrors one meter apart, it’d tick roughly once every six nanoseconds, which is pretty fast. It would keep very regular time, though. And, anyway, any kind of clock you care to use would have to give you the same results.”<\/p>\n “Why is that?”<\/p>\n “Well, otherwise, you would be able to tell the difference between moving and standing still<\/a> by comparing two different types of clocks, and that’s not allowed.”<\/p>\n “Oh, right. So what’s the deal with the triangles again?”<\/p>\n “Well, the point of the gedankenexperiment<\/i> is that an observer at rest with respect to the clock will see the light bouncing straight up and down, say, covering a distance of twice the mirror separation between ‘ticks.’ A moving observer, though, will see the light taking a sort of zig-zag path.”<\/p>\n “Like that kid over there with the ball?” I look up ahead, and there’s a kid standing in a driveway bouncing a basketball. “He sees it going straight up and down, but if we go by really fast, it looks like it’s going sideways, too.” She redoubles her pulling on the leash, and almost yanks me off balance.<\/p>\n “Slow down<\/strong>, will you?” I haul on the leash, and she lets up a little. “Anyway, yes, that’s the basic idea. The ball looks like a series of parabolic arcs, where light would travel in straight lines, but in either case, the path seen by a moving observer is different. And that makes it take longer.”<\/p>\n “This is the bit with the triangles?”<\/p>\n “That’s right. In the light clock experiment, the moving observer sees the light moving along the hypotenuse of a right triangle, with one of the other two sides being the separation between the mirrors, and the third side being half the distance moved by the mirror between ticks. The path taken by the light is longer than it is according to the observer standing next to the clock. Which means the time between ticks is longer.”<\/p>\n “OK,” she says, “That’s the part I don’t quite get. Why does it take longer?”<\/p>\n “Well, the path is longer, but the speed of light is the same. The speed of light is determined by the laws of physics, and the laws of physics are the same for any observer. Otherwise, you’d be able to tell the difference between moving and standing still.”<\/p>\n “It always comes back to that, doesn’t it?”<\/p>\n “That’s why they call it relativity.”<\/p>\n But can’t you tell that you’re moving when you see the zig-zag path?”<\/p>\n “You know that you and the clock are moving relative to one another, but not which of you is moving in an absolute sense. You could be moving while they stand still, or you could be standing still while they move. It looks the same, either way.”<\/p>\n “Oh. That’s pretty weird.”<\/p>\n “You get used to it. Anyway, the point is, as you said, that moving clocks run slower than stationary ones. The faster the motion, the bigger the difference.”<\/p>\n “Right, so we need to go fast<\/strong>!”<\/p>\n “The thing is, ‘fast’ in this context means ‘at a speed comparable to the speed of light.’ Even at our current exceedingly brisk walking pace, we’re not going more than a few meters per second. Which means you would need to walk for a billion years to gain one second on that annoying dog out back.”<\/p>\n She stops dead. “A billion years?”<\/p>\n “A billion years.”<\/p>\n “That’s a long time.” She thinks for a minute. “I don’t think I can walk that long.”<\/p>\n “No, you can’t. So we might as well walk at a slower pace, all right?”<\/p>\n “I guess.” We start off down the street again, at a much more comfortable walking pace. “Of course, there’s another way we could do this, you know.”<\/p>\n “Really? What’s that?”<\/p>\n “I could go a lot faster if you would let me off this leash…”<\/p>\n","protected":false},"excerpt":{"rendered":" We’re just starting out on a walk, and no sooner do I open the gate from the back yard than the dog takes off at a run, hitting the end of the leash and nearly pulling my arm out of the socket. “Whoa, there,” I say. “Take it easy.” “Come on,” she says, “We need… Continue reading Time Dilates When You’re Chasing Bunnies<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[61],"tags":[],"class_list":["post-2620","post","type-post","status-publish","format-standard","hentry","category-physics_with_emmy","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/2620","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=2620"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/2620\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=2620"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=2620"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=2620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}