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Rangsk · 01-06-2005, 07:40 PM

Think about it this way:

You're sitting in a magic train with no windows so you can't see anything outside. This train is perfectly smooth and is moving at a constant 50 miles per hour (relative to the ground). You are inside the train. Note that the train is moving at a constant speed, so you cannot "feel" any motion whatsoever. Try to think of an experiment, any experiment, that you could do to tell you how fast you are moving.

You can't. Einstein showed us through relativity that nature's laws are constant no matter how fast you are moving, as long as you are moving at a constant velocity. Moving at a constant velocity is the SAME as being at "rest."

Now lets add a window to the train, and have another obsersver, let's call him Bob, standing on the train platform. Right as you shine the light in the train, he measures the speed at which the light is moving. You both measure the same speed, even though if you had, say, thrown a ball, you would have measured different speeds. This sums up the problem you are trying to grasp - how can this be?

Unfortunately, in order to understand why this is, you have to accept some things about the universe that are not observable in everyday life. In fact, the only reason we know about these things is that we can do similar experiments as shining the light in the train and have shown that it is true. From that, Einstein devoloped the thoery of special relativity (and then general relativity to describe a gravity that does not conflict with special relativity). Special relativity states that an object shrinks in its direction of motion. So, if you had a ruler that measured 1 foot lengthwise when it is moving the same speed as you, if you then put that ruler on a train and positioned it so that its two ends are facing the front and back of the train, then it would appear to be shorter than 1 foot (though by such a small amount at "normal" speeds that it's just not observable in everyday life). On top of that, if you have two clocks, one in your hand and the other on the train, the one on the train would tick slower than your clock.

Remember our magic train with no windows, though. We think we are at rest even though to someone on earth, we're moving at 50 miles per hour. Add a window. I could state truthfully that I am at rest when on the train, and everything else is moving at 50 miles per hour in the other direction. So, I am no different from Bob on the platform, so if I look at Bob holding up a ruler, it will look shorter. And if I look at Bob's watch, his watch also appears to be ticking slower than my watch.

So, to sum up: According to Bob, my ruler is shorter and my clock is slower. According to me, Bob's ruler is shorter and Bob's clock is slower. At this point, you're probably more confused than you were when you asked the question. You're probably wondering, "who's right, then? They can't BOTH be right, can they?" Well, the answer is yes, they are both right, as long as they both continue to move at their own constant speeds. However, if they ever want to meet up, one of them has to accelerate (either the train slows down, or Bob gets onto the train). The one who accelerates is admitting that he was the one moving, and thus his watch will appear to have been slow when they meet up.

So to make it more clear. I'm on the train and Bob is on the platform. If I stop the train and go onto the platform, my watch will read slower than Bob's. If Bob jumps into the train as it zooms past the platform, then Bob's watch will read slower than mine. Of course, once we're the same speed, they will both tick at the same pace, but my watch may show 5pm while his watch shows 4:59pm or 5:01pm depending on who met up with whom (I've exagerated the time difference to a great degree for the speeds we're talking about, but you get the idea).

I went off on a tangent there, but it's all interesting stuff that is a direct consquence of light always moving at the same speed, no matter the frame of reference.

Ok, so back to light. How is it always going the same speed, no matter what your speed is? Well, here's another problem to think about. You have two spaceships on Earth. One moves away from Earth at .9 times the speed of light (.9c from now on, c being the speed of light), and the other moves in the exact opposite direction at .9c. According to Newtonian physics, a guy on one spaceship would look at the other spaceship and see it going at 1.8c! But, relativity makes it very clear that you can't move faster than the speed of light. Remember something, though - speed is a measure of distance over a certain amount of time. In order to measure speed, you need to know a predetermined distance and have a clock measure the time it takes to cross that distance. Remember, though that distances shrink and time gets slower for objects moving at different speeds than you, so the speed you measure on one of the spaceships is in fact slower than the speed measured by someone on Earth! Thus, each spaceship sees the other spaceship flying away at a speed faster than .9c, but smaller than c (there are equations to calcualte this, but it's not important). So, what would you have to do to, say, shoot a bullet at the speed of light. Well, you'd have to accelerate it forever, since the faster it gets, the slower time gets for it.

I probably didn't help that much, but maybe I've given you a truer picture of relativity. If you want more reading material, I suggest reading "The Elegant Universe" by Brian Greene. It focuses on string theory, but it spends the first couple chapters explaining both relativity and quantum mechanics very, very well (much better than me). If you think relativity is out there and hard to grasp, you should read up on quantum mechanics.

01-06-2005, 07:40 PM	#9 (permalink)
Rangsk Crazy Location: San Diego, CA	Think about it this way: You're sitting in a magic train with no windows so you can't see anything outside. This train is perfectly smooth and is moving at a constant 50 miles per hour (relative to the ground). You are inside the train. Note that the train is moving at a constant speed, so you cannot "feel" any motion whatsoever. Try to think of an experiment, any experiment, that you could do to tell you how fast you are moving. You can't. Einstein showed us through relativity that nature's laws are constant no matter how fast you are moving, as long as you are moving at a constant velocity. Moving at a constant velocity is the SAME as being at "rest." Now lets add a window to the train, and have another obsersver, let's call him Bob, standing on the train platform. Right as you shine the light in the train, he measures the speed at which the light is moving. You both measure the same speed, even though if you had, say, thrown a ball, you would have measured different speeds. This sums up the problem you are trying to grasp - how can this be? Unfortunately, in order to understand why this is, you have to accept some things about the universe that are not observable in everyday life. In fact, the only reason we know about these things is that we can do similar experiments as shining the light in the train and have shown that it is true. From that, Einstein devoloped the thoery of special relativity (and then general relativity to describe a gravity that does not conflict with special relativity). Special relativity states that an object shrinks in its direction of motion. So, if you had a ruler that measured 1 foot lengthwise when it is moving the same speed as you, if you then put that ruler on a train and positioned it so that its two ends are facing the front and back of the train, then it would appear to be shorter than 1 foot (though by such a small amount at "normal" speeds that it's just not observable in everyday life). On top of that, if you have two clocks, one in your hand and the other on the train, the one on the train would tick slower than your clock. Remember our magic train with no windows, though. We think we are at rest even though to someone on earth, we're moving at 50 miles per hour. Add a window. I could state truthfully that I am at rest when on the train, and everything else is moving at 50 miles per hour in the other direction. So, I am no different from Bob on the platform, so if I look at Bob holding up a ruler, it will look shorter. And if I look at Bob's watch, his watch also appears to be ticking slower than my watch. So, to sum up: According to Bob, my ruler is shorter and my clock is slower. According to me, Bob's ruler is shorter and Bob's clock is slower. At this point, you're probably more confused than you were when you asked the question. You're probably wondering, "who's right, then? They can't BOTH be right, can they?" Well, the answer is yes, they are both right, as long as they both continue to move at their own constant speeds. However, if they ever want to meet up, one of them has to accelerate (either the train slows down, or Bob gets onto the train). The one who accelerates is admitting that he was the one moving, and thus his watch will appear to have been slow when they meet up. So to make it more clear. I'm on the train and Bob is on the platform. If I stop the train and go onto the platform, my watch will read slower than Bob's. If Bob jumps into the train as it zooms past the platform, then Bob's watch will read slower than mine. Of course, once we're the same speed, they will both tick at the same pace, but my watch may show 5pm while his watch shows 4:59pm or 5:01pm depending on who met up with whom (I've exagerated the time difference to a great degree for the speeds we're talking about, but you get the idea). I went off on a tangent there, but it's all interesting stuff that is a direct consquence of light always moving at the same speed, no matter the frame of reference. Ok, so back to light. How is it always going the same speed, no matter what your speed is? Well, here's another problem to think about. You have two spaceships on Earth. One moves away from Earth at .9 times the speed of light (.9c from now on, c being the speed of light), and the other moves in the exact opposite direction at .9c. According to Newtonian physics, a guy on one spaceship would look at the other spaceship and see it going at 1.8c! But, relativity makes it very clear that you can't move faster than the speed of light. Remember something, though - speed is a measure of distance over a certain amount of time. In order to measure speed, you need to know a predetermined distance and have a clock measure the time it takes to cross that distance. Remember, though that distances shrink and time gets slower for objects moving at different speeds than you, so the speed you measure on one of the spaceships is in fact slower than the speed measured by someone on Earth! Thus, each spaceship sees the other spaceship flying away at a speed faster than .9c, but smaller than c (there are equations to calcualte this, but it's not important). So, what would you have to do to, say, shoot a bullet at the speed of light. Well, you'd have to accelerate it forever, since the faster it gets, the slower time gets for it. I probably didn't help that much, but maybe I've given you a truer picture of relativity. If you want more reading material, I suggest reading "The Elegant Universe" by Brian Greene. It focuses on string theory, but it spends the first couple chapters explaining both relativity and quantum mechanics very, very well (much better than me). If you think relativity is out there and hard to grasp, you should read up on quantum mechanics. __________________ "Don't believe everything you read on the internet. Except this. Well, including this, I suppose." -- Douglas Adams