Showing posts with label Physics. Show all posts
Showing posts with label Physics. Show all posts

April 12, 2011

Faster Than The Speed Of Light?

I'd like to put up this excellent short piece by W. Daniel Hillis, the renowned computer scientist and engineer. It was originally published in How Things Are: A Science Toolkit for the Mind by John & Katinka Brockman (1996), and it outlines the bare basics of why it is impossible to travel faster than the speed of light. This may bring disappointment to sci-fi movie fans with a liking for 'time travel' movies, which often propagate the idea that time travel is possible after travelling faster than light speed. Far from shattering illusions of the possibility of doing so at some point in the future, this article actually serves as a quick crash course into a basic issue of physics. Slightly technical in the beginning but gets easier and easier to understand, eventually resulting in a realisation of learning. Enjoy.

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Special Relativity: Why Can't You Go Faster Than Light?

You've probably heard that nothing can go faster than the speed of light, but have you ever wondered how this rule gets enforced? What happens when you're cruising along in your spaceship and you go faster and faster until you hit the light barrier? Do the dilithium crystals that power your engine suddenly melt down? Do you vanish from the known universe? Do you go backward in time? The correct answer is none of the above. Don't feel bad if you don't know it; no one in the world knew it until Albert Einstein worked it out.

Image courtesy: Fx-1988

The easiest way to understand Einstein's explanation is to understand the simple equation that you've probably seen before: e = mc². In order to understand this equation, let's consider a similar equation, one for converting between square inches and square feet. If i is the number of square inches and f is the number of square feet, then we can write the equation: i = 144f. The 144 comes from squaring the number of inches per foot (12² = 144). Another way of writing the same equation would be i = c²f, where c in this case is equal to 12 inches per foot. Depending on what units we use, this equation can be used to convert any measure of area to any other measure of area; just the constant c will be different. For example, the same equation can be used for converting square yards to square meters, where c² is 0.9144, the number of yards per meter. The c² is just the conversion constant.

The reason why these area equations work is that square feet and square inches are different ways of measuring the same thing, namely area. What Einstein realized, to everyone's surprise, was that energy and mass are also just two different ways of measuring the same thing. It turns out that just a little bit of mass is equal to a whole lot of energy, so in the equation, the conversion constant is very large. For example, if we measure mass in kilograms and energy in joules, the equation can be written like this: e = 90,000,000,000,000,000 m. This means, for example, that a charged-up battery (which contains about one million joules of energy) weighs about 0.0000000001 grams more than a battery that has been discharged.

If we work with different units, the conversion constant will be different. For instance, if we measure mass in tons and energy in BTUs, then c will be 93,856,000,000,000,000. (It happens to work out that the conversion constant in a particular set of units is always the speed of light in those units, but that is another story.) If we measure both energy and mass in what physicists call 'the natural units' (in which c = 1), we would write the equation: e = m, which makes it easier to understand; it just means that energy and mass are the same thing.

It doesn't matter whether the energy is electrical energy, chemical energy, or even atomic energy. It all weighs the same amount per unit of energy. In fact, the equation even works with something physicists call 'kinetic' energy, that is, the energy something has when it is moving. For example, when I throw a baseball, I put energy into the baseball by pushing it with my arm. According to Einstein's equation, the baseball actually gets heavier when I throw it. (A physicist might get picky here and distinguish between something getting heavier and something gaining mass, but I'm not going to try. The point is that the ball becomes harder to throw.) The faster I throw the baseball, the heavier it gets. Using Einstein's equation, e = mc², I calculate that if I could throw a baseball one hundred miles per hour (which I can't, but a good pitcher can), then the baseball actually gets heavier by 0.000000000002 grams - which is not much.

Now, let's go back to your starship. Let's assume that your engines are powered by tapping into some external source, so you don't have to worry about carrying fuel. As you get going faster and faster in your starship, you are putting more and more energy into the ship by speeding it up, so the ship keeps getting heavier. (Again, I should really be saying 'massier' not 'heavier' since there is no gravity in space.) By the time you reach 90 percent of the speed of light, the ship has so much energy in it that it actually has about twice the mass as the ship has at rest. It gets harder and harder to propel with the engines, because it's so heavy. As you get closer to the speed of light, you begin to get diminishing returns - the more energy the ship has, the heavier it gets, so the more energy must be put into it to speed it up just a little bit, the heavier it gets, and so on.

The effect is even worse than you might think because of what is going on inside the ship. After all, everything inside the ship, including you, is speeding up, getting more and more energy, and getting heavier and heavier. In fact, you and all the machines on the ship are getting pretty sluggish. Your watch, for instance, which used to weigh half an ounce, now weighs about forty tons. And the spring inside your watch really hasn't gotten any stronger, so the watch has slowed way down so that it only ticks once an hour. Not only has your watch slowed down, but the biological clock inside your head has also slowed down. You don't notice this because your neurons are getting heavier, and your thoughts are slowed down by exactly the same amount as the watch. As far as you are concerned, your watch is just ticking along at the same rate as before. (Physicists call this 'relativistic time contraction.')

The other thing that is slowed down is all of the machinery that is powering your engines (the dilithium crystals are getting heavier and slower, too). So your ship is getting heavier, your engines are getting sluggish, and the closer you get to the speed of light, the worse it gets. It just gets harder and harder and harder, and no matter how hard you try, you just can't quite get over the light barrier.

And that's why you can't go faster than the speed of light.