Thursday, April 5, 2007

c, The Universal Speed Limit

What is the highest possible speed that can be attained by any object?

Logically, you would think that there would be no limit. As long as there's something to exert a force on the object to accelerate it, it would keep increasing its speed. That sounds pretty much like common sense. If you still remember Newton's 2nd Law, it would make sense too: as long as there is a net force being exerted on the body, it will continue to accelerate.

But sadly for us, logic sometimes takes a back seat when it comes to physics. In 1905, a relatively unknown Swiss patent clerk by the name of Albert Einstein wrote three revolutionary scientific papers and published them all at the same time and all in the same publication, at the ripe old age of 26. One of the papers dealt with an entirely new physical theory which was necessary for reasons that I'm not going to explain, known today as the special theory of relativity.

Of course, I'm not going to go into the details of this subject (which is seriously interesting in its own right: You can check out Twin's Paradox ) but one of the predictions it made is that the greater the speed at which you are travelling, the more difficult it is for you to increase your speed.

So, if you are travelling very near the speed of light, it would take the equivalent of a nuclear explosion to increase your speed by just a few fractional metres per second. This also means it takes an infinite amount of energy to get your speed up to the speed of light, hence making speed of light travel impossible.

Putting that in the context of space travel makes it all sound almost impossible. The nearest star to the Earth is Alpha Centauri (I think? One of the nearest stars at least), and that star is about 4.3 light years away. Even if humans were to travel at the speed of light, it would take them 8.6 years to make the trip there and back.

Over the course of history many people have tried to measure the speed of light, or at least have tried to guess whether the speed of light is finite or infinite. We know now that it is a finite 3 x 10^8 ms-1, but the ancients couldn't have known. So here are some of their thoughts, and ingenious (sometimes not very ingenious, but only on hindsight) methods to determine this speed.

Early philosophers (remember the earlier article: science and philosophy were not distinct disciplines until relatively recently) did not have a unanimous opinion. Some philosophers believed that light, being something in motion, must have a speed, while others believed that it was a stretch of the imagination to believe that something can move with such great speeds, and so believed light to travel instantaneously.

This was all very unscientific of course. The first scientist to think of a way to measure the speed of light was none other than Galileo. He placed himself and another student on two hills 1 mile apart, and, by uncovering lanterns and asking his student to note the time at which he saw the lantern uncovered, and comparing that with the real time at which the lantern was truly uncovered, tried to detect if it took any time at all for the light to travel a distance of 1 mile. Of course, this experiment was a spectacular failure, and he was unable to conclude much.

The first good method was carried out by an astronomer known as Romer, who was observing the orbit of one of Jupiter's moons, Io. Io revolves around Jupiter much like our moon, and when you point your telescope at Jupiter in the sky, you can see Io (if it's a good telescope) go behind the planet and becomes blocked by Jupiter, and then reappear again. Romer noticed that the time taken for Io to disappear and reappear again got longer and longer as Earth moved further and further away from Jupiter, and reasoned that this was due to the greater amount of time needed for light to travel between Jupiter and the Earth as we got further and further away.

A quick and ingenious calculation gave him a very good answer indeed for his time: 2.3 x 10^8 ms-1, which is just about 20% off. Not bad for an astronomer in 1676.

Something interesting to mention here: Imagine a bug walking in front of a projector like the projector in your class. It casts a shadow on the screen, so you can see the shadow of the bug walking across on the screen. Now, if we put the screen very near, the shadow would appear to be moving at roughly the same speed as the bug. But as we move the screen further away, the bug's shadow appears to move faster and faster (for those of you who fall asleep at night watch shadows cast on your ceiling by cars driving by outside, many times you'll see the shadows whooshing by). Do you think that by moving the screen further and further away we can make the bug's shadow travel at speeds greater than the speed of light?

Think about it.

153 comments:

CoffeeCoke said...

Yup, the shadow will seem to travel faster than the speed of light but actually it is not. Since shandow can be seen as blocked out light, we can say that the light surrounding the shadow is travelling faster than c. However, this is just an illusion because the light rays are actually travelling perpendicular to the motion of the shadow. Therefore, the faster-than-c movement of the shadow is actually a joint image of many blocked out lighted rays, instead of one "thing" that is travelling faster than c.

joshua said...

so the shadow would move faster than the speed of light since its not a 'thing'

Mr. Liu said...

Absolutely right joshua. Technically, the shadow is allowed to move faster than the speed of light because it can never carry information.

Altaris said...

What about special relativity only applying locally, so for example, if i travel through a wormhole from Earth to Alpha Centauri in let's say 1 hour, but light takes 4.3 years, so relatively I am travelling faster than light.
Zhu Chong

CoffeeCoke said...

errr... Firstly, it would be impossible for you to squeeze through a wormhole. Even if you have managed to do it, you are not travelling at a speed faster than c. What you have merely done would be equivalent to taking a shortcut in spacetime. Correct me if i'm wrong.

gonewind said...

But I think when the screen is placed far enough so that the light takes a significant time to travel from the bug's position to the screen, if we place our eyes at the position of the bug, the shadow will travel 2 times slower than the bug ?

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Dani May said...

wait wait, the nearest star to earth is in the Alpha Centauri System. But the star itself is Proxima Centauri :)
Thought Id say..

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