![\"i-cf62d220b910cb1e754b140a5b2fadd2-sm_office_bone.jpg\"](\"http:\/\/scienceblogs.com\/principles\/wp-content\/blogs.dir\/467\/files\/2012\/04\/i-cf62d220b910cb1e754b140a5b2fadd2-sm_office_bone.jpg\")
“What are you confused about?”<\/p>\nThe dog marches up to my computer as I’m checking my morning email. “What the heck is the deal with relativity?!?”<\/p>\n
“Well, good morning to you, too. How are you this fine morning?”<\/p>\n
“I’m fine, but I’m confused about relativity.” Sarcasm is totally lost on her.<\/p>\n
“What are you confused about?”<\/p>\n
“Well, you’ve got Special Relativity, right, and also General Relativity. Special Relativity is all about clocks that run slow when you’re moving, and bunnies that get smaller when you chase them, and General Relativity is all about bowling balls on rubber sheets.”<\/p>\n
“Actually, that’s just an analogy for the way that mass distorts space-time in General Relativity. There are no real rubber sheets.”<\/p>\n
“Fine, it’s about bending space and bending light and black holes and giant space worms tunneling between planets and stuff. The point is, it’s nothing at all like Special Relativity. How can you possibly call these two things part of the same theory?”<\/p>\n
“Well, I admit, they do look pretty different–“<\/p>\n
“That’s what I just said!”<\/p>\n
“– but at some level, they’re both related to the movement of objects. The usual example people use to explain the similarities is an elevator.”<\/p>\n
“An elevator?” She looks puzzled.<\/p>\n
“You know, like when we go over to campus? We take the elevator up to my office.”<\/p>\n
Recognition dawns. “Oh! The Magic Closet!”<\/p>\n
Now I’m the confused one. “Magic Closet?”<\/p>\n
“You know. It’s a tiny little room, and when you go inside and close the door, when the door opens again, you’re in a different place.”<\/p>\n
“Ah. Yes, well, the point is, an elevator is basically a sealed box that you get in, and it may or may not be moving. Relativity is all about what you can and can’t learn about the motion of the box from inside it.”<\/p>\n
<\/p>\n
“OK, that doesn’t help at all.”<\/p>\n
“Well, as I explained before<\/a>, Special Relativity tells us that there is no absolute frame of reference, and only the relative motion between frames matters. All of the laws of physics behave exactly the same way in an elevator that is moving at constant velocity as they do in an elevator that’s standing still. There’s no experiment you can do from inside the elevator to know whether you’re moving, or standing still.”<\/p>\n “Like that time when we got in the elevator, and you forgot to push any button at all, so we just sat there like idiots?” She wags her tail with exaggerated innocence.<\/p>\n “Yeah. Like that.” We’ll see how many treats she gets tonight. “Anyway, General Relativity extends that to accelerating frames and gravity.”<\/p>\n “But I thought you said that you could<\/strong> detect accelerating motion. Are you changing the story on me?”<\/p>\n “You can distinguish between accelerating motion and motion at constant speed, that’s still true. What General Relativity adds is that you can’t distinguish between accelerating motion and gravity. There’s no detectable difference between being in a stationary elevator in a gravitational field and being in an accelerating elevator in the absence of gravity.”<\/p>\n “So, wait, gravity doesn’t work in the Magic Closet?”<\/p>\n “No, no– gravity still works, it’s just that the sensation of an elevator accelerating<\/a> is identical to a gravitational force. You know how when the elevator first starts up, you feel heavy for a second?”<\/p>\n “Yeah, I think.”<\/p>\n “When it first starts moving, you feel a little extra weight. That’s the effect of acceleration, and what you feel is just like gravity got stronger for a second.”<\/p>\n “It’s not much of an effect.”<\/p>\n “That’s because our building is old, and the elevators need work. If the elevator accelerated faster, it would be a bigger effect. If you had a fast enough elevator, the effect could be just as big as the gravitational attraction of the Earth, making it seem like your weight doubled. If you had an elevator that could accelerate that fast, and you put it out in space, there would be no way to tell whether you were in space accelerating, or sitting near the surface of the Earth standing still.”<\/p>\n “That would be a mean trick. Don’t do that.” She looks concerned.<\/p>\n “It’s just a thought experiment, to illustrate the idea of the equivalence between acceleration and gravitation.”<\/p>\n “Well, ok. But it’s still a mean gedankenexperiment<\/i>.” She’s part German Shepherd, and likes to show off. “And anyway, I don’t see how this gets us to bending light.”<\/p>\n “Well, let’s think about what happens to a beam of light shining across the elevator. If the elevator is standing still, or moving at constant speed, the light will pass straight across the elevator.”<\/p>\n “Right. Light always moves in straight lines.”<\/p>\n “Not quite. If the elevator is accelerating, the light will appear to bend, as the floor catches up to it. The elevator would need to be accelerating very rapidly for it to be noticeable, but if it were, you would see that after one tick of a very fast clock, the floor moved up by one unit of distance, and after two ticks, it moved four units, and nine units after three ticks, and so on, catching up to the vertical position of the light. To a person inside the elevator, it would seem like the light was following a bent path, like an object accelerating down.”<\/p>\n “But wouldn’t that allow you to tell that you were moving? Doesn’t that violate relativity?”<\/p>\n “It lets you know that you’re not either standing still or moving with constant velocity, all right, but that’s Special<\/strong> Relativity. What you can’t do in General Relativity is tell the difference between accelerating motion and the effect of gravity.”<\/p>\n “But… doesn’t that mean that light needs to bend due to gravity?”<\/p>\n “Exactly. For relativity to work, light needs to bend in a gravitational field by exactly the amount that it would appear to bend if we were accelerating upward at the acceleration of gravity.”<\/p>\n “So why don’t I notice light bending toward the ground?”<\/p>\n “The effect is really small near the surface of the Earth, because the Earth just doesn’t have that much mass. If we look at really heavy objects, though, we can see the effect of light bending due to gravity. One of the great proofs of General Relativity was the observation that starlight passing close to the Sun bends very slightly. People have also seen ‘gravitational lensing’ where light bends around colossally huge objects like galaxies. The bending of light in a gravitational field is a consequence of General Relativity applied to accelerating motion, in the same way that the slowing of clocks is a consequence of Special Relativity applied to motion at constant velocity. So, you see, the two theories really are similar.”<\/p>\n “I guess so…” she says. She looks thoughtful for a minute, then picks her head up sharply. “Wait a minute. You didn’t mention rubber sheets at all. What happened to bending space?”<\/p>\n “Ah. Well, you remember how you said that light always travels in straight lines a while back?”<\/p>\n “Yeah, but you said I was wrong.”<\/p>\n “It’s not exactly correct, but it’s close. The correct statement is that light always travels along the shortest path between two points.”<\/p>\n She looks really confused. “What’s the difference? I mean, a straight line is always the shortest distance between two points, right?”<\/p>\n “Not necessarily.” I look around the office, and pick up a basketball. “Look, imagine this ball is a globe. We’re here, in Schenectady, on the ‘S’ in ‘Spalding,’ and Paris is here, a bit above the ‘g.’ What’s the shortest path between those two points?”<\/p>\n “A straight line.”<\/p>\n “You might think that, but the shortest path between those two points is actually what’s called a ‘Great Circle’ route, which looks like a curved path<\/a> on an East-West\/ North-South grid of latitude and longitude. If you want to get from here to Paris, the shortest path is actually curved.”<\/p>\n “No it isn’t. The shortest path is a straight line, through the ball.”<\/p>\n “Well, yeah, ok, if you include all three dimensions. In reality, though, we’re confined to moving on or near the surface of the Earth.”<\/p>\n “Maybe you are. I’m a good digger. I can make a tunnel.”<\/p>\n “Not to Paris, you can’t. Anyway, we’ve been over this– only bad dogs dig tunnels.”<\/p>\n “Oh. Yeah.” She looks sad. “I’m a good dog, though, right?”<\/p>\n “You are an excellent<\/strong> dog.” She wags her tail happily. “The point is, the shortest path between two lines is only a straight line if you’re talking about objects on a flat surface. If you’re looking at motion in a curved space, the shortest path between two points can be a curve, not a line.”<\/p>\n “So… since light always takes the shortest path, and light bends in gravity, that means that gravity bends space-time?”<\/p>\n “You got it. It’s probably better to say it the other way around– that is, gravity bends space, and light takes the shortest path, so light bends in a gravitational field– but whichever way you say it, that’s how the world works. Because gravity and acceleration are indistinguishable, if you want to describe the effects of gravity mathematically, you end up describing space as curved due to the presence of mass.”<\/p>\n “Hence the rubber sheets.”<\/p>\n “Exactly.”<\/p>\n “The rubber sheets are a stupid example, anyway. Who has rubber sheets?”<\/p>\n “Well, there are plastic sheets in the baby’s crib. That’s sort of similar.”<\/p>\n “Maybe.” She looks skeptical.<\/p>\n “Anyway, are you satisfied that General and Special Relativity are related, now?”<\/p>\n “Yeah, I guess.” She thinks for a minute, then, “Hey, can I dig a tunnel to Paris?”<\/p>\n “I already said no. Anyway, it’s impossible. And why would you want to do that, anyway?”<\/p>\n “I don’t know. I’ve just got this weird desire to invade France.”<\/p>\n I sigh. “I guess I walked into that, didn’t I?”<\/p>\n “Pretty much.”<\/p>\n","protected":false},"excerpt":{"rendered":" The dog marches up to my computer as I’m checking my morning email. “What the heck is the deal with relativity?!?” “Well, good morning to you, too. How are you this fine morning?” “I’m fine, but I’m confused about relativity.” Sarcasm is totally lost on her. “What are you confused about?” “Well, you’ve got Special… Continue reading Everything is Relative in the Magic Closet<\/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-2969","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\/2969","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=2969"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/2969\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=2969"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=2969"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=2969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}