Friday, May 25, 2007

The Last Days

There are times when you wake up and feel that you can do nothing right, and you just want to return to your sleep and dream away the rest of the day, without having to think and make the right decisions all the time, just the way we like it. There are days when you wake up and you ask yourself what's the point of getting up and subjecting yourself to the same old things again and again.

But for the past 6 months, despite the incredibly early get up timing of 5.45 am (Okay. I know what you are going to say. You do that everyday, and you've been doing that for the past (insert double digit) years. But no other job I could have picked requires this!) after shaking off the initial lethargy, there's a sense of purpose to the day, and more than that, a sense of meaning in life that is very hard to come by.

I try my best every lesson to interest, inspire and at the very least help you learn the bare essentials in a subject that you may not enjoy thoroughly, but still have to take anyway. I tried, and many times I think I failed. I looked at other physics teachers and felt pressure looming over my head, as I watched them plan flawless lessons and whip out incredible applets and other resources for use in the classroom, and sometimes you feel so emotionally drained: because you try your best, and you don't know whether that is enough. You feel for the subject, you know exactly what the concepts you are trying to get across are, but you can't convey it in that particular way that everyone instantly gets.

This has got to be the most frustrating and life-consuming job ever: there was never a lesson that I walked out of without feeling drained and tired. There were a few days when I would be in the physics lab teaching pin-sighting method, and then I'll trot down to the chemistry lab to teach how to test gases, and then back to the physics lab again.

But at the end of everything, what keeps a teacher going is the students. And strangely, despite all the rather frustrating times, and scolding (though I'm sure most of it bounced of you, though I mean it all the time) and marking scripts with god-awful mistakes that make you feel like quitting the job because obviously you have got absolutely nothing across, I enjoyed myself in all the classes, each with their own weird concoction of terrors. Ha. Just kidding. It was fun, and, for lack of a better way of putting it, you guys were entertaining, and in many cases surprising both on an intellectual level and maturity.

In some ways, we are tied together. There is something inexplicably strong about the bonds formed in the process of learning. I hope you'll remember something in this 6 months, and hopefully it's something fundamental, although I'm being sickeningly self-righteous here, believing what I try to teach is the right thing to learn. But every teacher inherently thinks he's correct. So indulge me.

Good luck to all of you guys, avid (ha, avid) readers of this blog. I wish you the best of luck with your time here in RI, because I swear this place is the place that will define who you are in the future. Don't give your new physics teacher a torrid time! Though I trust that he will do a better job than me. I seriously think you all are getting short-changed in some aspects. Other teachers seriously have some cool stuff up their sleeves.

Don't worry, I'll keep updating this place to follow your syllabus and all: I can roughly remember what the next few chapters are. As my English teacher (Mrs. Selvan) emailed me when I sent her my farewell email to the RI staff:

"This is not a farewell. It's a till then.
So till then!
(I don't care, our paths must cross again!)"

Till then!

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.

Friday, May 11, 2007

Doppler

The Doppler effect is an effect that we encounter in our lives rather often: When an ambulance or any vehicle with a siren approaches us, we can hear the pitch of the sound (i.e. the frequency of the sound) increase as the vehicle approaches, reaching a peak frequency when it is directly beside us, and then taking a swift plunge to a lower frequency when it recedes from us.

Let's have a look at what's going on. So far in class we have only been looking at stationary sources, like in a ripple tank. The source of the wave, i.e. the dropper or the damper in the ripple tank does not move with respect to the wave. It just taps the water surface, that's all.

The Doppler effect comes into play when the source begins to move. Here's a diagram to give a quick illustration:


You can see very clearly the bright spot is the where the source of the wave is, and the source is moving towards the left. As the source moves, you can see how each wave produced is centred slightly to the left, and so the wavelength of the waves on the left hand side is comparatively smaller to the wavelength of the waves on the right.

If you happen to be standing somewhere on the left, you would hear (if the waves were sound waves) a shorter wavelength sound, i.e. higher frequency sound, since the speed of sound is rather fixed in air. As the source passes you, and you suddenly end up to the right of the source, the frequency takes a plunge. This explains the ambulance approaching and receding you perfectly.

Now what is so splendid about this? A quick flick of the mathematics wand will give you some rather involved equations that in principle are quite simple, but in reality some pretty tedious stuff. Anyway, the cool thing about this effect is that it leads to some wonderful applications, such as in the radar.

As you probably can remember (or should remember), radar works by shining radio waves in all directions, and waiting for the reflected radio waves to come back to produce a blip on the screen. As the radio waves arrive at the airplane, they reflect off the surface of the moving airplane, which gives the effect of a moving source. The Doppler effect in this case will actually increase the frequency of the approaching aircraft, and a quick calculation (done preferably by the computer) gives us the speed of the airplane. This procedure is also used by the traffic police to determine the speeds of vehicles.

This is also how missiles decide when you to explode when they are in midair. Contrary to popular belief, missiles do not go off when they come into contact with the plane. Instead, they usually have a radar of their own built into the missile. As the missile approaches the plane, the frequency increases, and then suddenly drops when the plane starts to recede. This is one of the signals for the missile to detonate itself.

A common occurrence when jet planes fly past is the sonic boom. This is the Doppler effect at its extreme: the source of the wave is moving at pretty much the same speed or faster than the wave itself:

You can see that the waves are unable to move away from the source, because the source is travelling at the same speed as the waves being produced, and by the time the waves reach the observer, all the waves will simultaneously arrive and be heard, which would probably make for a rather loud sound.

Finally, I've been talking so much about sound, sound and sound, but the Doppler effect actually applies across the board to all forms of waves, including light waves.

One of the most important discoveries made in the 20th century was that galaxies and other distant objects in our universe were actually moving away from the Earth. You have to realise that before the 20th century at the advent of advanced astronomy techniques, many people held a firm belief in the static nature of the universe. Scientists thought that the universe was eternal and never changing, until a few brilliant ideas (see Olber's Paradox) and the Doppler effect observed in light helped us realise that the universe was expanding.

Using spectroscopic techniques, scientists back then were able to deduce what elements were present in gas clouds in space. When the light arriving from these gas clouds were dispersed by a prism (split up into the rainbow colours) astronomers were able to see certain missing colours, which corresponded to certain elements.

They soon realised that many of the lines did not appear where they were supposed to, but rather they all seemed to be squashed towards the red side of the spectrum:

This meant that when the light arrived on Earth, the wavelengths were longer than expected. If you observe the Doppler effect carefully, this would mean that the object that was being studied was moving away from the Earth. Astronomers called this phenomenon the redshift, because the spectral lines were all shifted towards the red side of the spectrum.

What was even more incredible was the fact that this redshift became more pronounced the further away astronomers looked, which suggested that the further away an object was, the faster it was moving away from us! An excellent astronomer named Edwin Hubble (of Hubble Telescope fame) was the discoverer of the law in 1912 (known as Hubble's Law) that the speed v at which something in our universe was receding from the Earth, is directly proportional to the distance d from the Earth:


Where H0 is the Hubble's constant. Let's consider a galaxy that is a distance D from us right now. Here's something amazing: since we believe that everything began with the Big Bang which basically says that everything in our universe started from a single point, the distance D is very roughly the distance travelled by the galaxy since the time when the galaxy and the Earth were still together at the start of the Big Bang. The velocity of the galaxy, v, let's assume to be constant. If we take D divided by v, we should get the time taken for the galaxy to go from the Big Bang to where it is now, i.e. we would roughly get the age of the universe!

So from the equation, t = D/v = 1/(H0). From astronomical observations, we do have a rather good idea of the value of H0, and it turns out that our estimate of the age of the universe from this method is about 15 billion years old.

Incredible? I hope you think so!

Thursday, May 3, 2007

Sonoluminescence and Other Creatures

As I've mentioned a few times in class, physics is an open science. The number of unsolved problems in physics are quite stupendous, and some of them seem to be questions that we really ought to know about.

One really fine example of how limited our knowledge is in physics is the fact that we are currently unable to provide a complete understanding of how fluids flow. Physicists are unable to supply a law that governs the behaviour of turbulence (which we sometimes encounter during airplane trips). The extremely famous physicist, Werner Heisenberg, who pioneered quantum physics and gave us the infamous Heisenberg Uncertainty Principle once quipped, "when I meet God, I am going to ask him two questions: Why relativity? and why turbulence? I really believe he will have an answer for the first."

Many of the open questions in physics are rather esoteric, but some of them can be rather spectacular. You can check out a list of unsolved problems in physics at Wikipedia, and you can scroll down to click a few of the links at the bottom which give more insight into the nature of these problems.

I'd just like to point out something weird and intriguing in that whole list: sonoluminescence. Sonoluminescence arises when a liquid is excited by ultrasound. Bubbles are formed within the liquid in the presence of the ultrasound (remember that sound waves are pressure waves? They create differences in pressure in the medium, which in this case is the liquid. The rarefactions are areas of low pressure, and in special cases a bubble can form at a rarefaction, which will pop when it becomes a compression), and when they burst, somehow or another they release light.

This process is really very strange if you think about it: why would a collapsing bubble give off light? It becomes even weirder when some scientists actually believed that the temperatures within the bubble actually reached as high as one megakelvin, or 1,000,000 K.

Sonoluminescence is still an unsolved problem today, but you can check out some of the mechanisms that have been proposed by physicists in the Wikipedia entry. In the mean time, don't forget that although what you are studying seems to be written in stone, physics as a science is rather lost at the moment. Everything seems to make sense at some level, but each individual piece is difficult to string together to give a definite picture of the universe, which is more or less the ultimate goal of physics. I hope you can click some of the links available in this post here. Most of the open questions are explained in nice and easy terms.

Happy reading!