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Little c Posted January 2, 2001 Mostly Mozart is sponsored by Comfort and Joy, a unique children's store. During last week's show I got a phone call from Brad, who wanted to hear about relativity. My first response was, "ooh, that's a tough one." I find that the theory of relativity says some things that are so counterintuitive that they seem impossible. Which is especially strange because it is all derived from some very simple assumptions. Probably the most famous result of the theory of relativity is that time goes slower for things that are moving at high speed. Brad asked me if race car drivers live longer because they spend a lot of time moving at high speeds. The quick answer is yes, they do, or at least they would if race car driving didn't involve so much crashing. But the difference would be measured in microseconds, because in absolute terms, race cars don't move all that fast. So during intermission I'll tell you how to measure speed in absolute terms, which means measuring it against the universe's speed limit, and then I'll try to explain why time has to look different depending on how fast you're moving. And all of this is based on the principle of relativity, which is that the laws of physics work the same way from all perspectives. If this weren't true, then we would have to choose a single standard perspective from which everything should be measured. But the earth is always moving relative to the sun; the sun is always moving relative to the Milky Way; the Milky Way is always moving relative to other galaxies; and so on. So we can't use any of those as reference points. In fact, just by saying that any particular object is "not moving", you are assuming the existence of some other object that you're comparing it to. The principle of relativity just forces you to acknowledge that all motion and distance is measured from some vantage point. In other words, you can't measure an object's speed; you can only measure its speed relative to yourself. On the musical program tonight, we have lots and lots of piano sonatas. Starting with .... ---- Kootenay Co-op Radio would like to thank Comfort and Joy for sponsoring Mostly Mozart. At the beginning of the program, I said I would tell you how to measure speed in absolute terms. And I went on to explain that absolute speed doesn't exist, because how you measure speed depends on how fast you're moving yourself. This would seem to be a contradiction. But it's not, if you just assume that Sir Isaac Newton was wrong about force, mass, and acceleration. Newton's laws say reasonable things like, if you expend twice as much energy then you can move twice as fast. This works pretty well at speeds around 100. km/h, but if you ever get to play with a particle accelerator, then you'll notice that when you get up to 100 million kilometres per hour, you can double your energy and get less than double the speed. In fact, you can add as much energy as you like, and you'll get less and less speed in return, until you notice that you just can't reach 1. billion km/h. 1 billion km/h, or to be precise, 300 million metres per second, is the speed of light in a vacuum. It slows down a bit when it's going through air or water, but while travelling through space, light always moves at 300 million metres per second. In physics the small letter "c" is an abbreviation for 300 million m/s, because not only is it the speed of light in a vacuum, it's also the maximum speed that anything can travel. Even gravity doesn't move faster than light. Of course, if you've seen Star Trek, you've heard them talk about Warp 9 which is 9 times the speed of light; which would be an analogy to Mach 2, which is twice the speed of sound. But Star Trek is not only totally fictional, it's also kinda dumb, so forget about Warp 9. You can try it, and you might succeed in making something go faster than 300 million m/s. But your chances are pretty slim. Even buying lottery tickets is more likely to pay off. And the Nobel Prize only comes with $10,000 anyway. But if you accept that nothing goes faster than light, you can reach some interesting conclusions. First of all, let's assume that you fly directly at the sun at high speed. Now, don't try this at home! Flying directly at the sun is not good for your health. But imagine you did that, and you measured the speed of the light coming toward you from the sun. Well, you wouldn't even have to measure it because you know that light covers 300 million m/s in a vacuum. And according to Newton's laws, you'd have to add your own speed to that, to account for the fact that you're flying toward the source of the light. So the light should appear to be coming toward you at over 300 million m/s. But, much as this would surprise Sir Isaac Newton, it doesn't work that way. Whether or not you're moving toward a light source, the light always comes to you at the same speed. So when it comes to light speed, you can't just add and subtract speeds as things move toward and away from each other, which is what Newton told you to do. But what you can do is compare the speed of a race car to the speed of light, so you can decide whether it makes sense to use Newton's laws. And it turns out that light is about 5 million times as fast as a 200 km/h racing car, which puts driving well within the world of Newton. --- Mostly Mozart is sponsored by Comfort and Joy, a unique children's store. So, race car drivers don't have much to get excited about when it comes to living longer than the rest of us, but what happens to you if you do get close to the speed of light... well, yes, time starts to slow down. I'll set up another light-speed experiment that illustrates relativity in a different light. You're standing in a train station, watching a train drive past. In one of the cars you notice a person pointing a flashlight toward the floor. There's a mirror on the floor, and a sensor next to the flashlight that measures the time it takes for the light to reach the mirror, bounce back, and reach the sensor. Basically this person is pointing a radar gun at the floor. You happen to have your telescope and timer set up in the train station, so you take some measurements of your own. You measure the same thing as the person in the train: how long it takes for the light to leave the flashlight, bounce off the mirror, and reach the sensor. You and the person in the train both agree that light moves at 300 million m/s, but what you don't agree on, is how far the light had to travel between the flashlight and the sensor. Standing inside the train, the person holding the flashlight would measure 1 metre between the light and the floor, and conclude that the light travelled 2 metres. Standing outside the train, you would notice that the light also had to move in the direction of the train, in addition to the 2 metres up and down. So if the measured speed of light is the same in both cases, and and the measured distance is different, then the measured time must also be different. Improbable as this may seem, it does work. If you put an accurate clock in a supersonic jet, fly it around the world a few times, and compare it to a clock that sat on the ground, the one in the jet will be slightly slow. This effect is called time dilation, and it's just the beginning of a series of strange consequences of relativity. There's a similar effect that makes things look smaller when they get close to the speed of light. But before you get too involved in things like the Lorentz transformation, which is the relatively ugly formula that lets you calculate how much time dilation occurs at a given speed, it's good to consider some things about small "c" or 300 million m/s being the universe's maximum speed. For example, information can't move faster than light. That means that cause and effect can't move faster than light. If our sun exploded, we wouldn't know until 8 minutes later. It's impossible to have a reasonable two-way conversation with someone on another planet, because it would take several seconds for the radio signals to make a round trip. So in a sense, time and distance are interchangeable. If light takes 8 minutes to get from the sun to the earth, then everything else takes at least 8 minutes to make the same trip. So you might as well say that the sun is 8 minutes away. The idea of measuring a distance by how long it takes light to travel between two points, is where we get the term "light year." A light year, of course, is the distance that light travels in a year. That happens to be 400 billion kilometres, which unfortunately is not what people usually mean when they tell you that something is "light years ahead". ---- This is CJLY 93.5 fm in Nelson. Kootenay Co-op Radio would like to thank Comfort and Joy for sponsoring Mostly Mozart. That's about it for this week; up next is Unexplained Transmission Repair, or, if you're listening on Friday morning, then up next is the Blues Power Hour. I'll leave you with some more of these piano sonatas. If you're listening to the Tuesday night show, and there's something you want to hear on a future show, whether it's music or physics, then phone me in the studio at 352-3706 and tell me about it. Otherwise, I'll see you next week. |