Saturday, May 19, 2007

Relativity! Galilean Relativity, that is.

I'm sure you are getting a hang of how important a physicist Galileo is. Recently we had a very splendid argument in 3F about whether a ball that is dropped by a person that is walking will fall in front of, behind or at exactly the same spot at which the ball would have dropped if the person were completely stationary with respect to the person.

Actually the answer should be immediately apparent to everyone if you just imagine yourself playing basketball: how would it be possible to dribble if everytime you let go of the ball the ball falls somewhat in front of you, or somewhat behind you? Another thing to try: place a wastepaper basket in front of you and try to drop a paper ball into it as you walk by the basket. You will find that you have to let go of the paper ball somewhat before you arrive next to the basket for the ball to go in. This is because you must time the paper ball to arrive at the paper basket at the same time as when your feet arrive at the basket.

Returning to the dropping ball experiment described earlier: note that whether the person is stationary or moving with some constant velocity (this is important: I will come to it later) the ball still drops next to the person's feet. Nothing impressive here, but as usual, there's a physics twist to it.

Imagine now that you are in a very very very dark room that is extremely quiet, but the ball is glow in the dark. You drop the ball. Where will it land? Now the answer is, obviously, that it will land at your feet. But notice something: I've given you absolutely no details as to what speed you are moving inside the room, because it doesn't matter at all!

So when you are within the room, say you were drugged and placed in the room by a sinister physicist, and then ordered to bounce the ball, you would have no way of telling whether you are stationary within the room, or riding on one gigantic travelator travelling at constant velocity.

Why am I so insistent on constant speed? Because even if you were severely drugged, you would immediately know if you were not travelling at constant velocity. You would feel your stomach lurch if you were suddenly heading downwards, or your feet suddenly feeling heavier if you were to rush upwards, just like in an elevator. You would be thrown to your left if you were suddenly turned to the right, just like in a car. So you can be sure that you are moving if you were not travelling at constant velocity. But if you just happened to be travelling at constant velocity, no matter how you bounced the ball, you would never be able to tell whether you were moving or were truly stationary.

If you can remember your last trip on a plane, imagine that few hours after take off and before the landing preparation while you were getting from one place to another: was there any real way to tell that you were moving? For all you know, the plane could have been stationary! You can walk with the usual ease of walking on solid ground, the stewardesses can serve their food and drinks without worrying about spillages and trolleys rolling away.

Another thing to think about: do you feel like you are moving now? Well you are! Because the Earth is moving at a constant speed of 30 km per second around the Sun!

So why don't we feel this motion of the Earth, on the plane, or when we're dropping glow-in-the-dark balls on a travelator that may or may not exist in a dark room because some weird-ass physicist told us to? The answer is in a property of all motion: Galilean Relativity.

Galilean Relativity is not hard to understand, unlike its more famous counterpart, Einstein's Theory of Relativity. Basically, it states there is something somewhere in this universe that is truly stationary: whatever it is, wherever it is, we aren't interested, but all of the laws of physics that we know, like Newton's Laws of Motion, would apply at that place. Galilean Relativity then goes on to state that if a physicist were to watch any object, say a car travelling at constant velocity from that truly stationary place, then the laws of physics would apply in the car as well. To phrase it in another way, we will never be able to tell the difference between constant velocity travel and stationary states.

Of course, the immediate question is, doesn't the laws of physics apply in ALL situations? Sadly, for the basic laws that we have encountered and will encounter in secondary school physics, they don't. Think about it: you are in a car that suddenly comes to a stop. What happens? well, of course, you are thrown forward, but a good follow-up question to ask is why? Normally physics teachers would explain it away as a phenomenon known as inertia: something that is moving will continue moving unless a force acts on it.

But imagine for a second you are back in that dark dark room standing on a travelator that you didn't know was there, and suddenly, the travelator stops, and you fall down. You would be totally caught by surprise, and the immediate thought that would come into the mind of any self-respecting physicist or science student doing the test would be that a force made him fall down. That is what Newton's first law dictates: any kind of change in motion must have been caused by a force.

However, only the sadistic physicist planning the experiment would know the truth: it was the travelator that came to a halt. So the truth was there was no force! You can see from here that an observer in the dark dark room who can't see what's going on would make a wrong prediction, because the laws of physics does not hold when the travelator doesn't move with constant velocity.

So this is why you can walk around with ease on an airplane, and you won't feel yourself moving with the Earth, because both the airplane and the Earth are travelling with constant velocity, which immediate ensures that the laws of physics will apply perfectly to us, and we will not be able to tell the difference between constant velocity travel and stationary states.

Of course, there is a crucial problem at work here: note that Galilean relativity requires that there be some truly special place in the universe which is truly and exactly stationary. Traditionally in solving physics problems we usually take the Earth as truly and exactly stationary, which of course is not true. Perhaps the Sun then? Unfortunately it is also performing an orbit around the Milky Way, which in itself is performing an orbit around our local galaxy cluster etc. etc. ...

Philosophically, before and during Galileo's time, it was commonly assumed that the Earth was that special place, being a place of God's creation, but since that time, physicists generally believe that there is no special place where the laws of physics truly hold, about which everything moves and revolves at their true speeds. But Galilean relativity requires just such a point.

Today we know that Galilean relativity is merely a rough approximation fo the theory of relativity proposed by Albert Einstein early last century, but the full argument is rather involved, but generally boils down to a belief by scientists that there is no special point at which the laws of physics will hold. Today, Einstein's relativity believes that the laws of physics holds no matter how we move: a conclusion that has far reaching consequences that have been briefly expounded. Please, do find out more for yourselves.

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