My 5 days experience in IPhO Selection Camp

For readers who don't know what IPhO is, it simply stands for International Physics Olympiad. And the traditional is that each year, every country will try their best to select the cream of the creams among their high school students through a series of rigorous selection, and to select their best 5 to strive for Absolute winner (highest scorer in the world for Olympiad), Gold Medal (top 33 of participants), Silver Medal (not sure how many percent), Bronze Medal (not sure about how many percent of participants, too), and Honorable Mention (Top 67 of participants). Olympiad is one of the most prestigious competitions high school can ever offer and it is the hardest secondary school competition worldwide. The theoretical problems in Physics Olympiad is not your usual high school problems, where you can strive by just understanding your syllabus and textbook, doing enough past year, etc. It requires you to be a problem solver, to be able to see unusual connection between ideas, and a huge dose of efforts and creativity. Many of these country representatives go on becoming top notch engineer and scientist. Without further explanation, I will proceed with my experience, as well as things I learn, in Malaysia IPhO Selection Camp 2 that was held on 22th April to 26th April.

Day 1 (Arrival)

Well, there isn't anything much happening on Day 1, and in fact, I skip the arrival section, and preferring to come on 2nd day when the lectures and experiments start. Basically on day 1, I'm anticipating hard on what's going to happen on the remaining day of this camp.

Day 2 (23th April 2013)

This is when all the excitement starts. I came to the lecture hall in UKM, and I suddenly felt that I was among a bunch of the brightest physics minds in the nation. I went over to greet my friend from SMJK Katholik, PJ who introduced me to the camp. The chief trainer (Dr. Wan Mohd Aimran), was late for the lecture due to several issues. And the first lecture is just an introduction to what Olympiad physics really is, and he wanted to give us a feel of the questions and solutions.

In 2nd Lecture, Mr. Wee from SMK Tinggi Melaka took over the lecture. The lecture was about falling object with air resistance, and on how to solve it with calculus (prerequisite of calculus is A-Level Further Mathematics or STPM level calculus). Luckily I have been spending months to brush up my math on single variable calculus before going to this camp, so at least I didn't feel left out in the extraordinary pace.

Then here comes the lunch time and socializing time. There are approximately 25 participants in total, 5 of which are STPM Physics subject test highest scorer, another 10 are Upper Six students, 4 from Kolej MARA Banting, doing IB, and 5 from PERMATA pintar, National Centre for Gifted Children, and these 5 participants are among the youngest in the participants (Form 5 this year). After getting to know everyone, and had enough lunch and rest from the mind-blowing section we just had, I went for 3rd lecture, and never did I know that the tougher parts are coming.

3rd lecture, it was about gravitation, but note, it was not your planetary circular orbit, it was elliptical orbit! The math, hence, becomes more and more intensive. Many new terms, such as eccentricity, is introduced. But nonetheless, the basic laws of physics can still be applied here. Conservation of angular momentum is very useful in this problem solving case, and Mr. Wee go on attempting past APhO (Asia Physics Olympiad) question on gravitation, and my understanding on how gravity works improved. I was excited that finally, I knew some of the ABC of astrophysics. 4th lecture was about Alternating Circuit Theory, and the concept is very new to a lot of students. It takes me hours to get the concepts into my mind, and start to understand the derivation, and its physical meaning. An abstract concept indeed. An exhausting day, and more and more are coming.

Day 3 (24th April 2013)

Day 3, Madam Chin from SMJK Perempuan China, Penang, took over the first 2 lectures in the morning. She taught us about moment of inertia and rotational motion. Most of the concepts and maths have been covered in one of the Further Mechanics book I have found in my library. Except I find one of the physical concept that is really interesting, that is, a person in a rolling circular cage. I will not go over to the technical part of this rotating cage with a person inside, but it demonstrates the obvious result that we observe everyday. Imagine a person in a circular cage, and the cage is rolling. The person, when he is at the bottom of cage, he needs not to run hard to stay in the bottom of cage (since there is no relative motion between the person and the bottom part of cage). But the person on top of the cage need to run twice as fast as the translational velocity of the rolling cage, just to stay on top of cage and prevent himself from being 'rolled' to bottom part of cage. Reminded me of some 'Tom and Jerry" funny cartoon moments.

The afternoon section on this day, is the hardcore section of the whole camp. It was on electromagnetism. Prerequisite of Magnetic Force (Lorentz Force) on moving charged particle is needed, and a deep realization that the force is cross product (a mathematical technique) of qv (charge times velocity) and B (Direction and magnitude of magnetic field) is needed. The case that Mdm Chin is dealing is that it involves both circular motion of charged particle and helical motion of particle, but I was again amazed at how this idea is solved using the most basic concept of physics. It turns out that we just need to resolve the velocity vector into component perpendicular and parallel to magnetic field B, the perpendicular component will move in circular motion while the parallel component moves with constant velocity (makes me link this idea with projectile motion way of problem solving, and wow, all ideas are connected!!!).

After all the lectures, I had a chat with some of the PERMATA students and Upper six students. And I got to know more what PERMATA pintar is, and realize that one of the upper six students are a friend of my classmate!!! Such a coincidence, the world, for sure, is so small. :D

Day 4 (25th April 2013)

This was a light section day (maybe a heavy section, but because I love this section the most, the toughest turns out to be most delightful section). This day was the climax of the camp (for me personally)!!! In the morning, we were greeted with Quantum Mechanics lecture (the part of physics that I'm madly in love with!!!). It started with storytelling style, on how quantum mechanics developed in early twentieth century, how physicists first observed the completely out-of-common-sense phenomena, Max Planck contribution, and on this wave-particle duality, a crazy idea, that if I translate it into reality, it is like a rock behaving like a wave. The whole small world of particle (where Newtonian Mechanics get trolled, and completely useless in this analysis), is where Quantum mechanics works extremely well, and QM makes a startling accurate on how small particles like electrons behave. But this is not yet the best of QM lecture, more are coming.

The lecture reached the climax when we were given Schrodinger Equation. We were only taught to look into one of the simplified case, where we set potential energy of electron to be zero, and electron being trapped in a box of finite length L. AND WOW, AGAIN, IDEAS CONNECTED!!! The Schrodinger equation was actually a form of conservation of energy, and in the particular problem solving case, it turns out that Schrodinger is 2nd order differential equation that resembles the motion of Simple Harmonic Motion. Woohoo, ideas, sure, are connected to each other beautifully, and I enjoyed how the mathematics leads me to explain things happen in physical reality (that electron oscillates in the trapped box), another idea connected was that it bahaves according the probabilistic wave function. Nice quantum mechanics lecture, had a great time here.

Then, I'm feasted with a lecture on oscillation but take note, it is not your simple pendulum case. Oscillation, is actually a phenomena that we always observe in our daily life. A waiter, holding coffee cup in his tray, when walking to serve the coffee, will have the coffee in the cup seiching, again, oscillations observed. And we were given seiching problem to solved (a past IPhO 1970+ question). Even though seiching is common experience in daily life, the maths is not really simple (tough maths here).

Seiching in coffee cup

After all the theoretical sections, we had experimental sections. Initially we were supposed to carry out experiments, make measurements, but because UKM Physics lab is occupied, the lecturer (Dr. Wan) taught us the technical part of experimental physics (error analysis, data analysis, etc.). Experimental section is considered one of the sections where most participants can score well, and hence we just need to master the techniques.

After all the lectures, I chatted with some of the participants, and we wished each other luck for tomorrow selection exam.

Day 5 (Final Day, the showdown)

Okay, final day is exam day, going to sit for 4 hours physics exam, a mental marathon. The exam had lots of question, and I couldn't manage to finish all the question (and of course, the exam is set to be slightly easier than real IPhO problems, after all, IPhO is the hardest one out there), and neither any participants can finish all the question. I consider myself lucky to be able to solve some of the examinations problem, and left blank for only one whole question. Nonetheless, I tried my best, and I leave the selection of representative to God, allow God to take care of the rest.

My Feeling on things learnt

Indeed, IPhO Selection Camp is a breathtaking journey. I learnt lots of things that classroom experience and syllabus could not bring!!! I am truly grateful for an opportunity to experience something different, and I learnt the real fun part of physics. Physics is interesting, it is not just your high school subject and textbook. I see physics in a more glorious form, that physics is inevitable in daily life, and I consider physics to be the exciting hidden physical knowledge (the mystery), and pursuing my passion in physics is like unfolding the puzzles and mysteries of God, discovering the wonders of God through theories, equations, and most importantly, God's wonderful creation shone forth, and I see it very clearly through Physics. IPhO experience, is, nonetheless, unforgettable and fruitful experience. (y)

Time travel, Just a sci-fi dream? A possibility?

Have you ever heard of the Grandfather Paradox?

Maybe yes, or maybe no.

For those who don't, I would like to make a restatement of Grandfather Paradox, and for those who do, I would like to ask questions on it, out of my curiosity.

Here's the famous Grandfather Paradox:

"Imagine, if I could go backward in time, I want to experiment with a paradox. Let say, I remember my grandpa first met my grandma on XXth day XX Month in XXXX year. Now, I've just invented a time machine and want to go backward in time, to one hour before my grandpa and grandma first met each other. When I met my grandpa, I say to him, 'why not we go for a race instead?' And he agrees, so the first meeting with grandma was avoided. 

Now, here's a big problem. If my grandpa didn't meet my grandma, so why do my father exist, if at all? And if I'm not here, how would I invent time machine and go back in time, and prevent my grandpa to meet my grandma?"

Well, surely this paradox poses headache to all sci-fi fans, physicists, mathematicians, and all humans who wish to change their past. So here comes the questions, explanations I've gained from numerous resources:

1.) Time travel to the past is forbidden in physical reality. In Stephen Hawking's chronology protection conjecture, he challenges mathematicians and scientists to disprove time travel to past. But so far no one can disprove the arrow of time, and even Einstein has proved that time is more dynamic than it is. So, if mathematics support strongly a theory (or never seem to be able to disprove it), why is our daily life experience seem to defy time travel, based on our intuition? 

2.) Another physical law seems to defy time travel. For those who know Entropy concept, you can skip this first few sentences. But as for general readers, I will make a lucid elaboration here, using daily life situation. Imagine you scramble your egg, and cook in in your frying pan. So, based on your daily life experience, can you reverse the process of cooking the egg, unscramble the egg, and put all the egg shells together? A big no, unfortunately. So, after giving this prominent instance, I will give a more general statement. According to second law of thermodynamics, the entropy (the measure of disorder) of universe will tend to increase (i.e., things tend to disorder), and never decrease. Even if you spend energy to make things back to order, the energy spent will be converted to heat energy, and increase the disorder of surrounding. So, if that is the case, time travel seem to work only in one direction, but in contrary to our daily life experience, the arrow in this law can be pointing towards either past, future, but not both. The question for this second is, if entropy works in one direction, why can't the law proves (by providing concrete mathematics) that it only points to future, and not to the pass?

3.) After providing counterexample of time travel, I will provide an instance that vindicate time travel. Recently, one of the most bizarre theory, string theory, has evolved into a super theory, the M-theory. In M-Theory, there's a possibility of creating something called wormhole, by breaking the Planck Energy Barrier (though current technology, even the particle accelerator at CERN, Geneva, could not break this barrier). If our technology could advance to a level, so advanced that The breakdown of Planck Energy Barrier has become a commonplace, so why can't we open up a wormhole? Well, the entering wormhole itself kills you, tearing you apart, and you'll probably get distorted. So, if one day wormhole is made possible and accessible, then the paradox will arise. Let say this time you try to kill your grandpa instead, a few weird possibility rises. One is that you will feel a mysterious force to prevent you to do so (though this statement has no justification, purely based on my imagination). Another is that the moment you do time travel, the past you know will part away into a parallel world where in the parallel world in that parallel universe, you don't exist. So in any of these 2 (or maybe more) outcomes, here comes my question, if let say the past parted and parallel world do exist, why can't we see them?

4.) Here's a final question, I will keep this short and simple, if people from future can travel through time, why can't we see them? (Or maybe they are forbidden by future law to reveal their identity, but rules are made to be broken, so some of them must've reveal their identity if time travel is possible.)

For those who made your way here by reading through this post, I would like to thank you for your time and effort. But most importantly, I need feedback, comment, speculations, criticisms and constructive comments on this Paradox and Time travel. Is there anyone out there to demystify my curiosity, then?

A simple explanation through equation on time dilation. 2 persons having contradicting views  on how 'fast' time has passed. Einstein Special Relativity for Time Dilation

Theory of Relativity by Einstein

Here is a brief and non-technical explanation on a very popular physics theory. The credit of this article goes to a friend of mine from UCLA. Copy-and-pasted for enjoyment. :)

"To understand general relativity, here’s a brief run-through of what Einstein accomplished with special relativity and how he intended to counter its deficits with his ideas of a general theory.

Special relativity is rooted, essentially, in one of the principles of Galilean relativity: to whit, the idea that it is impossible to say whether or not you are moving. For instance, if you were running with respect to a stationary bus, you could just as easily say that you’re standing at rest and that the bus was moving away from you. Similarly, if you were standing at rest and a train whooshes by, you could just as easily say that you’re in motion and it’s actually the train that’s stationary with respect to you: there is no way to determine which one of you is really in motion. That is the principle of Galilean relativity states: there is no test with which you can determine whether or not you are in motion. There is only relative motion; determining absolute motion is impossible.

Einstein decided that this principle was a fundamental physical law, and tried to hypothesize what would happen if you always measured the speed of light to be constant. After all, it’s a clear violation of absolute motion: light is always moving, and you can’t allowed to say that there’s any relative motion going on between you and a photon. Furthermore, if you didn’t measure it to be moving at the same speed always, you could use it as a test to determine if you’re moving: an observer at rest while you’re in motion calls out a different speed than the one you measure, and suddenly you know you’re in motion, simply by working out the math. Fair enough. So Einstein rolled up his sleeves, and came up with thought experiment after thought experiment to see what would happen. The results? Time dilation and Lorentz contraction (the relevant thought experiments that showed this I won’t go into, as you’re already familiar with them). In your own frame of reference, moving at a particular, invariant speed, you would observe fundamental quantities to be quite different from another observer moving at another speed. If you tried to see whether or not you were moving with respect to a photon, time and space would change for you so that you would always measure the speed of light to be the same, regardless of how fast you moved. Galilean relativity, with one major modification, has been preserved: light is permitted to be in a state of absolute motion, and your measurement of time and space would change so that you could no longer really tell if you were moving with respect to the photon – you would measure the speed of light to be the same in all reference frames, making it impossible to use as a test for absolute motion. It was thus still impossible to determine a state of absolute motion, except unless you excluded light from consideration.

That, then, was the edifice on which special relativity is based on: preserving the idea that absolute motion is a no-no. Yet special relativity is called special for a reason: it only holds if you’re constantly moving at the same velocity. Indeed, all the laws of special relativity held for the special case of when you weren’t accelerating at all. That was Einstein’s problem: how do you preserve the Galilean principle if you’re accelerating?

You see the problem. Acceleration means taking inertia into account: you ‘feel’ a certain force operate on you whenever the car you’re in accelerates or brakes, and you can instantly tell that you’re in motion. True, Newton’s third law states that an equal and opposite force operates on the car; but what if you were accelerating with respect to a house twenty metres away? You couldn’t honestly say that the house felt a similar force: its twenty freaking metres away, for goodness’ sake, you’re nowhere near in contact with it. How do you accommodate the force?

This occupied Einstein’s mind for years. And one day, he got it.

Imagine, for a moment, you’re in an elevator that’s initially moving at a particular speed, say, down. Suddenly, it accelerates: you feel a rushing force as this happens, and must conclude that you are, sighing as you do so, in motion. But wait! Little did you know that, in actual fact, the elevator hasn’t accelerated at all: it’s merely that the mass of the Earth has spontaneously changed (yeah, I know it sounds ridiculous, but bear with me for a moment). Thus, the force of gravity changed – so what you’re actually feeling is simply the force of gravity.If you think I’m going barmy saying all this, here’s another way to think of it. Would you, as an observer in that elevator, be able to distinguish between the two situations? You could say, on one hand, that you were at rest with respect to the elevator (you’d be moving at the same speed as it is, remember) and that the elevator accelerated. Or you could also say that the elevator was perfectly stationary (at rest with respect to you) and that its (or the Earth’s) mass changed spontaneously, so you felt a force that made you feel as if you were in motion. There is no test to determine which of these situations is correct. 

This was the germ of general relativity: a theory of relativity that could take into account accelerating frames of reference and not just those at a constant velocity. Einstein’s great insight was to realize that a body in acceleration with respect to a stationary observer is virtually indistinguishable (to the observer) from a body that is at rest in a changing gravitational field with an observer that is in motion. Einstein could account for the force now: he linked it to a changing gravitational field. Accelerating and being stationary in a changing gravitational field are indistinguishable. And thus the Galilean principle was saved once more.

Now here’s a thought experiment from special relativity. It’s important to GR, so I’m going to explain it to you.

Imagine you’re in a circular chamber that’s spinning round and round at a constant angular velocity. For some reason you want to measure the value of pi: this is weird, but you’re a mathematician who wants to be a theoretical physicist, so that’s okay. Now what’s pi? The ratio of the circumference to the diameter of this oh-so-wonderful circular chamber you’re in. Ergo, you have to measure both the diameter as well as the circumference to arrive at a value of pi. So you steady up your nerves, ignore your dizziness and set to work.

First, you measure the diameter. So far so good. Because you’re measuring something perpendicular to the direction of the chamber’s motion, Lorentz contraction doesn’t happen: your rod stays exactly the same length, and you manage to arrive at a reading that is exactly what you’d find if the chamber was at rest. Hopes high, you begin to measure the circumference of the chamber. But now you’re in the direction of motion: Lorentz contraction makes your ruler shrink, except you don’t realize this because you’re also moving at the same speed. Naturally, when you finally check your readings, you’re surprised to see that the circumference is actually longer than what you measured it to be at rest. And when you put those two numbers together – a longer circumference divided by the same diameter – you get a value for pi that is no longer 3.14159etc.

The value of pi – your measurement of it - has changed while you were moving at a constant velocity. You can be tempted to ignore it, but this will always be true. What can you conclude from this?

If you are as well-versed in mathematics as I suspect you are, then you probably already know where this is going. Different values of pi are characteristic of regions that are not Euclidean: that are not perfectly flat, so to say, that are curved in one way or another. One example is the curved surface of a (soccer) football, where it is perfectly possible to draw a triangle with three right angles, and other weird things. Thus one is forced to conclude that an observer moving at a constant velocity measures events to no longer conform to a Euclidean background: that the events a speeding observer notices is virtually indistinguishable from those that occur on a curved surface. Space and time distort from him in a way that make sense only and only on a curved surface: thus, even in special relativity, one finds evidence that space and time are curved for the observer, and that the observer will accordingly behave as if he’s on a curved surface.

A word of caution here. When I say space and time curve for the observer, I don’t mean they literally curve. Time and space are not, as a friend once told me, ‘fly rods that can be bent over physically’. It is merely that your measurements of time and space are such that they are typical of a curved surface: distances become longer or shorter, the time taken to cover them vary, and so on. Time and space do not ‘curve’: only your measurements of them – distance, length, time – do, so that you could very well conclude you’re moving on a curved surface.

And all this happens when you’re moving at a constant speed: within even the bounds of special relativity. When you’re accelerating – switching from velocity to velocity – your measurements of space and time are going to ‘curve’ more and more: you will measure successively changing values of pi, longer distances, longer times to travel. And since acceleration is indistinguishable from a changing gravitational field, this means that objects that are really in a gravitational field will measure the same things: they will begin to behave exactly as if their measurements of space and time were similarly twisted, so that they too were on curved surfaces that gained more and more curvature as the force of gravity increased. 

Thus, an object in a gravitational field will begin to behave as if it is on a curved surface that is steadily growing curvier (I’m sorry, that word evokes images of bikini babes. Nevertheless, it is all I have). This, I think, is Einstein’s most profoundly insightful idea. Gravity isn’t a force that changes the trajectory of objects around it; what actually happens is that objects within a gravitational force are merely trying to obey Newton’s first law (continue unimpeded with the same velocity in the absence of a force) while on a curved background. Geodesics are straight lines on their surfaces too, remember? There is no ‘force’ involved: merely an object trying to follow Newton’s Euclidean laws in a non-Euclidean world. I always find this magical.

And that’s it, really. To summarise: 

Being at rest in a changing gravitational field is indistinguishable from accelerating. When you’re moving at a constant velocity, you are forced to make observations that only make sense if you accept that your space and time are those that are appropriate to a curved surface. Thus, when you’re accelerating, your observations correspond to steadily changing curved surfaces, and you will behave exactly like you were on a curved metric. Since accelerating is indistinguishable from being in a gravitational field, objects that are in a gravitational field behave as if they are on steadily changing curved backgrounds too. They carve out geodesics instead of straight lines because, on a curved surface, geodesics are the only ‘straight’ lines possible. Hence, planets form ellipses around the sun: space and time are so warped for them that their closest conception to a straight line is an ellipse.

That’s all there is to general relativity. It’s probably not the best kind of explanation I could give – I was trying to convey the main ideas the quickest way I could – so do tell me if there’s anything I didn’t clarify enough. Hope you like it. Thanks!"