Crazy idea to change scientific education

Well, before you read this, I'm going to voice out a disclaimer that the content in this blog is purely based on personal opinions and reading this blog do not require any advance physics knowledge.

I know the title might sound revolutionary, but if the idea can really be implemented, we will see next generations full with great scientists around. Of course, the idea needs many manpower and strength to even start to see it happen in effect. To be frank, it is one of my aspirations to build a new technology school that can beat even MIT or Caltech in decades or centuries to come, but let's just be realistic to myself about my goals. The first goal of this idea, is therefore, to elicit a CHANGE in MALAYSIA, and particularly, scientific education in Malaysia. I believe that if the foundation of Malaysia scientific education is changed, many areas will subsequently become better. We will witness the rise of economic status in Malaysia, first or more bullet trains in Malaysia, and even Malaysia first Field Medalist or Nobel Laureate. In this blog I will address the problem up to high school students as I am still a high school student myself at the time I write this post.

Caltech, one of the world greatest institute for pure science

MIT, famed as one of the world best for its application of science in engineering and hacking

Okay, without beating around the bush, I will voice out my idea - CHANGE THE TRUE OBJECTIVE OF MALAYSIA EDUCATION, thoroughly. Yes, change is scary, but some changes can be rewarding in the end. A well known fact about Malaysia scientific education is that it is geared towards grades. But beyond grades, what else? Can the students appreciate the beauty of Archimedes's principle, for instance? Do the students feel excited about learning calculus? Do the students feel the great curiosity to explore more about DNA codes and how it really constitutes to human physical characteristics? In my perspective as a Malaysia student, a sad truth is, none of this is instilled inside students' heart. Science is fun, it is everything around us. Then, how can we be not curious about stuffs that work around us? And let's just face this fact, grades are just a number or statistics, it tells nothing about a student's personal drive, passion and perseverance towards science. It also tells nothing about how resilient a student is if he suddenly fails in his test or in his future career, for instance. I have eye-witnessed myself how some of my most sincere friends, while they are really passionate about mathematics, did not get higher marks than those who study math for exams only. And education in Malaysia regards people with higher scores as having a greater potential to excel. This is misleading. Something is fundamentally wrong. The 'something' is the objectives of scientific education in Malaysia.

The objective of scientific education should be INSPIRING AND INSTILLING THE SENSE OF CURIOSITY AND LOVE FOR SCIENCE in students. I will explain how this can be done in the some practical ways or steps. I wish to see a next generations of Malaysians, coming out to talk about applications, new inventions and new ideas about science instead of some statistics or numbers. And for me to be an agent of change, I need to voice out my opinions. Here you go:

1.) To instill a love for learning and a love for science, childhood scientific education is crucially important. If an educator fail to impress a child about how fantastic science is, the child will grow up thinking that science is boring. Therefore, START YOUNG. Instill the passion in science among children. Children's learning is well suited with colorful diagrams, sense of touch, sense of smell, sense of hearing and sense of taste. Make full use of these 5 senses in children when delivering a scientific fact. For instance, if the lesson is about manufacturing plastic, bring kids to factories and let them see and explore about how plastics are made. If a lesson on biology is about the relationship between taste and pH value of objects, let them touch and taste the objects. Fully utilize their 5 senses, and they will not have hard times swallowing facts. In fact, they will get so curious about the world around them that they come to love science. Focus on imparting interesting concepts that can be applied easily in daily life first. Build up the concepts without the need to include very complicated mathematical equations first. And it is worthwhile to spend these much of efforts to let kids love science, because, after all, kids are future leaders. The investment, though requiring huge effort, is really fruitful.

Utilize 5 senses, instill the curiosity in kids

2.) Secondly, CONTINUE THE EFFORTS IN MIDDLE OR HIGH SCHOOLS. After the students get interested in science at young age, they will move into adolescence. So, keeping up their passion and love is important, too. In middle and high schools, planners and educators play important roles. For school authorities, learn to be less curious about those statistics and start to care about student's interest and personal progress in science. For students, learn to be really curious about facts in textbooks and don't shy away from asking questions, even if they are 'stupid'. And teachers, learn to answer those 'stupid' questions, and don't rebuke students for asking 'stupid' questions. The effort is not by one party alone, but it requires a change in attitude. If the students have the curiosity in young age, with some encouragement, they will start to be brave to ask 'stupid' questions. And teachers, learn to spend time to think about how to deliver science in an interesting way. The approach will be slightly different to those intended to kids because youngsters are more prepared with some advance ideas or concepts. Youngsters also can withstand a suitable amount of 'black and white' textbook. But still, make efforts to make science appealing. Offer some demonstrations in classroom. Let the students know about reasons and applications behind a theory. Reveal the beauty of mathematical equations to students, tell them how our world is shaped through these equations. Then, the students will lose their virginity to science, and that is one of the most wonderful experiences a youngster can have in science education. And also, try to encourage and inspire instead of criticizing a student when students flunked in their tests. Imparting the optimism is important, too. And on the high school curriculum, try to focus more on problem solving than just a certain fixed facts.

It is not enough to tell students about equations. Reveal the beauty inside equations. Let them see beyond equations.

3.) Different students learn at different pace. In general, there are 3 paces of learners, slow learners, moderate learners, and fast learners. CLASSIFY STUDENTS ACCORDING TO DIFFERENT PACES AND DEVICE SUITABLE PROGRAM RESPECTIVELY.  The schools should also have a program specially targeted at specially gifted students to let them gone through accelerated learning. For the fast, gifted learners, they will feel boredom under normal school teaching pace. They are capable of absorbing facts and learn problem solving at an accelerated pace. Therefore, don't be afraid to include a university course or two in their learning. Set up few schools to accommodate the 'genius' in science by giving them rigorous science education and moderate humanities education. For moderate science learners, normal schooling pace is suffice. Malaysia schools mostly are targeted at this group of students, so moderate students should learn at this suitable pace. While for the slow learners, spend the extra efforts to develop science program to suit their pace. Most slow learners who are placed at normal schools will feel left out in the learning pace. So set up schools for these groups of people, too. Slow learners, when given appropriate education, can be successful scientist, too. And slow learner's learning need to be more personalized, so one on one is the best strategy.

4.) ENGAGE STUDENTS IN RESEARCH, FIELD TRIPS, AND OTHER SCIENCE STUFFS OUTSIDE CLASSROOM. One of the greatest misconceptions about science is that it is very academic. This, again, is another misleading concept. Science can be a hobby. There are kids who enjoy hacking. There are youths who enjoy deriving calculus in their spare time. Yes, don't mock people who enjoy science as a hobby by calling them nerds and geeks. In fact, the schools, educators and students need to be open minded about taking in science as a hobby. For university professors, start initiating research mentor program with high school students who are really serious about becoming scientists. Encourage and mentor the students throughout the process. Encourage them and push their abilities and passion in science beyond boundaries. For teachers, organize a field trip to bring the students to some of local university laboratories. Let the students see those advance equipment themselves. The schools should organize more science fairs and competitions for students to take part in. Organize innovation competitions, or give training to gifted students in school in science Olympiads competitions to give an eye opener to them about how interesting real science problem solving can be. Send students to local or overseas science summer camp program, and they will have the opportunity to meet peers of similar interest internationally. And high school students, don't be afraid to approach university professors and ask about joining them in science research. Students need to have the drive themselves, too. And students, don't feel afraid to try out crazy innovative ideas at home. By all means, let the students get involved in science outside classroom, and we will really see it ourselves the emerging of great scientists.

Summer Program, an opportunity to meet peers of similar interests around the globe.

In conclusion, change the objectives, implement the steps, and we will see a gradual (not sudden) change in nation's science standard and technology. MAKE SCIENCE INTERESTING. The efforts can reward the nation. If Malaysia implements the steps, we will see a futuristic nation full with great technology around.

And thank you if you read this blog thoroughly. Even if this blog does not change your mindset, I believe instilling a concept can spark changes in the future too.

3 Myths in Physics

The three myth of physics that constantly trigger me...

1. Stephen Hawking had once proposed chronology protection conjecture. This great physicist, having made use of Einstein's General Relativity to made postulates for Black Hole Theory, once said: If time travel is possible, where are the travelers from the future? 

So, it is known that Hawking challenged the physics community to somehow prove it both mathematically and experimentally (in an indirect approach) that laws of physics prevent time travel. But the hypothesized wormhole did not prevent time travel by mathematical calculation. 

Chronology Protection Conjecture, history must be protected!!!

2. The detection of gravitational waves. There had been thousands and thousands of experiments that directly and indirectly proved Einstein's General relativity (also known as Einstein theory of gravitation). Yet, in this theory, it predicts the existence of gravitational waves. To date, scientists had calculated the frequency of gravitational wave and it yielded 10^ -30!!! This is way too small too be detected by the built model of gravitational wave detector.

Two physicists, Russell Hulse and Joe Taylor, in 1993, had once successfully detect this extremely small frequency of wave, which gave confidence to physicists to use formula and theory of general relativity without doubt. The problem is, it is only detected ONCE (and they were offered Nobel Prize in Physics)!!! There is still no machines that can fully eliminate ground noise and other disturbance. So, the physics community are still challenged till today to build a gravitational wave detector that functions all the time.

Gravitational Waves is disturbance in spacetime, and a mean of how gravitational force is transmitted.

3. Quantum gravity. This is highly related to Einstein's childhood dream, that is to simplify the beauty of all laws of nature given by God into a single equation, perhaps not even an inch long. But, Einstein had this Theory of Everything listed as his unfinished work that had taken out his last two or three decades, he died with those papers placed messily on his table in 1955. The attempt to unify quantum mechanics and general relativity (theory of gravitational) had always resulted in failure, though tried by geniuses physicists. The significance is, if this is done, then Einstein's dream of creating Theory of Everything (TOE) that unifies all four types of major forces in universe will be finished.

It is now proposed that five versions string theory (or more) are the leading candidates of TOE. Yet, in all its splendor and beauty, it can only describes up to Tenth dimensions (the mathematics broke down at eleventh dimension). Hence, it is profoundly convincing that our world need another genius, on equal footing or surpass the supremacy of intelligence of Mr. Albert Einstein.

String theory proposes that there are more than three dimensions of space, where other dimensions are internal dimensions.

Family of Thermodynamics - Fundamental yet Impactful

So, why that old aged Mr. Thermodynamics, huh? I have been pondering about laws of thermodynamics for quite some time, at least I want to dive into both superficial and deep implications of laws of thermodynamics. Thermodynamics is all around us, from the obvious applications in car engines and refrigerators, to even the way haze spread around (haha, sorry for taking in haze example, but the widespread of haze is closely related to thermodynamics, and we shall see it later). In this blog, I will generally focus on second law of thermodynamics.

Okay, I will start off by giving a very brief definitions on the basics of thermodynamics, by expressing it in both technical wordings and layman terms. Here you go:

Technical and Formal

1.) Zeroth Law of Thermodynamics -  If two bodies are in thermal equilibrium with a third body then the first two bodies are at thermal equilibrium with each other.
2.) First Law of Thermodynamics - The total energy of an isolated system is constant despite internal changes.
3.) Second Law of Thermodynamics - Mechanical work can be derived from a body only when the body interacts with another at lower temperature; any spontaneous process will result in increase in entropy.
4.) Third Law of Thermodynamics - Entropy of a substance approaches zero as its temperature approaches absolute zero.

resources: http://wordnet.princeton.edu/

Family of Thermodynamics, in mathematical form, written by myself on my whiteboard

Layman and Informal

1.) Mr Zero - We give each other heat in equal amount, if we have equal temperature (All are equal).
2.) The No. 1 guy - Energy is a stubborn kid, prefers to always be constant in his life, although energy can change in different costumes, its attitude never change. (You can't get energy for free).
3.) 2nd Brother - Your stuff will only get messier, never tidier.
4.) 3rd Little Brother - The more you are chilled and calm, the less you want to mess around with people.

resource: myself

Mr Zero

Okay, enough of these whole bunch of definitions, we shall focus on its impact on our surroundings. Start with Mr Zero in the thermodynamics family. Mr Zero is more fundamental and obvious in our daily life experience. Imagine immersing yourself in hot, lukewarm and cold water, you can immediately tell that whether heat flows into your body, no net transfer of heat in and out of your body or heat generally flows out from your body. Its impact has been used almost in all mechanical devices, yes, Mr Zero is fundamental and impactful, and I will not elaborate too much with Mr Zero.

The No. 1 guy

No. 1 guy, sure, is stubborn. The total energy in our universe is always constant, regardless to its form. In layman words, No. 1 guy promises to change himself, but he only changes his costumes (forms) without actually changing himself (the total energy in a system). In first law of thermodynamics, the change in internal energy is often converted into net heat transfer into or out of the system and the net work done by / on (note the difference) the system. Hence, all energy is conserved. Implication and application? Yes, look at your refrigerators, car engines, air conditioner, etc. All these devices work based on The No. 1 Guy in the Thermodynamics family. In the sense of cosmology, the universe will always have the same amount of mass- energy (due to mass-energy conservation in Einstein's E = m c^2), but the universe, which is always with its constant energy available, is still vulnerable to its fate of 'death'. This 'death' concept of universe will be discussed in our dear nasty 2nd Brother. But still, I'm more interested in the 2nd brother, who is mysterious and new to many high school students or even layman readers.

The 2nd Brother

He is your messy guy, he always mess around with others. In formal words, second law of thermodynamics states that entropy (the measure of disorder) of a system will never decrease (as implied by the image I have uploaded). So, the concept of entropy can be new to many readers. Here is the thing, when you accidentally break your glass, you increase the entropy of the glass (or the glass you look messier, of course). Now, I will refer back to the spreading of haze into the second law of thermodynamics, a link of concept which might not be obvious to layman readers. Imagine gas in a container, before the cap of container is removed, all the gas molecules are kept in container, so the number of ways and free space of in which the gas molecules can move is restricted. Imagine removing the cap, or increase the space for the gas molecules to move in the piston, there will be more space available for gas molecules (and hence, more directions). Hence, the movement becomes more random (with more free space) and with the increase in randomness, the disorder of the system increases (and hence increase in entropy). Same example of observations of spreading of haze and dye is linked to 2nd law of thermodynamics, The 2nd Brother.

For a piston, an increase in space increases the direction in which gas molecules can move, and hence the movement of gas molecules become more random.

Spreading of Dye, an artsy image, it is also a phenomenon associated with concept of entropy

The 2nd Brother has another nickname, the Death God to the universe. Why such mysterious and disturbing name? Well, second law of thermodynamics is a death warranty to our dear universe. The entropy of the universe will always increase and never decrease. Observe our surroundings, apples decay, metals rust, all credit goes to our dear 2nd Brother in Thermodynamics family that only allows things to get messier (increase in entropy). Now, general readers with interest in science do know that our universe is expanding, and hence there will be more space available to the same amount of energy in the universe. This cases energy to be more disperse and spread out and hence the increase in entropy (an explanation offered earlier on how the  entropy increases when space increases). Even in charcoal, when we burn out our charcoal, the charcoal will turn into a less usable form in dust, with less useful energy available. So imagine stars in the universe being the charcoals, when stars get burnt out, its content is less usable and less heat can be obtained from aging stars that is approaching to its death. New stars will form at slower rate than old aging stars die because there will be less usable gas form available in the universe due to increase in disorder (entropy). With the expansion of universe and slower rate of formation of stars, the increase of disorder and entropy in universe sentenced death to out universe in hundreds and trillions years to come. Our universe will eventually become a cold place where the light emitted by stars will be less and less. And, hence a nasty name to 2nd brother in thermodynamics family.

3rd Little Brother

He is the little brother who looks a lot similar to 2nd brother, and 3rd law can actually be derived from 2nd law (will not elaborate the mathematical details here). His impact? This brother forbids absolute zero temperature (together with second brother). Why? Combining 3rd law and 2nd, you shall see that entropy (disorder) can never decrease and hence the temperature can never get down to absolute zero. In absolute zero temperature, all kinetic energy will be abstracted out of a system, and hence you make something in total stillness. This can't happen, it is forbidden by our Mr. Uncertainty (Heisenberg Uncertainty Principle). In formal words, Heisenberg Uncertainty Principle states that you can never know position and momentum of a particle at the same time. There is always uncertainty about the positions of molecules. Hence, by lowering a molecule's temperature to absolute zero, you are making it in total stillness and you can determine with certainty on where the molecules is and its momentum (momentum being zero). This is forbidden in quantum mechanics, a family of laws in physics.  

The Conclusion

In all our families of thermodynamics, we see that these laws affect us in both macroscopic and microscopic scale, ranging from simple daily life observation with spreading of dye to the death of universe. Physics, in all its implications, is beautiful. I have to admit that The Family of Thermodynamics, after all, is really fundamental and impactful. Hope you enjoy reading and have a nice day ahead.

How Observations in Astrophysics are done, and some unexpected discoveries that follow

Hello world, I have been inactive on blogging for a while due to external examinations going on. However, while I was preparing for my exams, I have thought of some astrophysics ideas to be shared on my blog right after exams. Okay, let's start with some 'flashback' of what have been done in astrophysical researches in past century.

One of the most interesting feature in astrophysical observations is that we make a lot of deduction and extract a lot of information, based on one thing, light itself (in more technical term, electromagnetic wave). I will discuss a few aspects and on how so many information can be extracted, purely based on light itself, and on some examples of past historical amazing discoveries that follows.

Before I proceed to astronomical observations and applications of light, I will bring in some intro of bizarre features exhibited by light, an amazing phenomena in many aspects. In 1900s, physicists discovered a very weird property of matters that emits light. When hot matter is heated up to a very high temperature, it glows. The hotter it is, the brighter it glows. But one of the weird features was that, when the object is heated, it gives out a discrete pattern of different colors of light instead of just a spectrum of continuous rainbow lights. It is as if the colors, frequency and wavelength of lights are quantized (can only have certain fixed value, for example, think of Malaysian currency, we can only have 5 cents, 10 cents, 20 cents and so on. We pay in terms of 5 cents as smallest currency instead of 1 cent). And for a matter to emit light, these must be a transition of energy level of electron from higher energy level to lower ones, and only fixed wavelength (and color) of lights emit will imply that electron can be at certain fixed position only.

Quantization, as the diagram implied, is just like a staircase. In our daily life, the concept of quantization is best to be think of as currency note.

Transition of electron from higher energy level to lower ones will emit light, the mystery of emission of light hence is due to electrons 'jumping' to lower level, and since electron can only be at certain level of energy, only certain colors of wavelength is observed.

So why do I explicitly elaborate on property of emission of light on quantum mechanics aspect? Well, discovery of helium comes from this property of physical law. Remember helium,  the element you often see in your high school periodic table (for those who take chemistry)? Helium is extremely rare on earth and only exist in trace amount (can hardly be detected). In 1968, researchers' pursue for discovery of helium is finally accomplished when astrophysicist made an observation of light emitted by sun during solar eclipse. The first discovery of helium, which subsequently lead to the use of helium in balloons, is done through astrophysics! Helium is discovered through emission of light (that certain object will glow and give specific wavelength), though this first discovery has been an indirect observation.

But astrophysical observations through light is not only used to detect undiscovered elements in periodic table alone! There are many more information that we can extract, purely just based on light. I will feature 2 more examples in this post. Another information we can get (other than elements present in certain planets ) is on temperature range of the planet. This is a direct implication from a physical law, Wien's Law, which states that wavelength of light emitted from glowing object is inversely proportional to temperature of glowing object. This means that the greater the wavelength, the lower the temperature, and this actually explains one of the high school students' myth (the fact that redder sun is colder and blue stars are hotter). From the color (and hence the wavelength of light) itself, we can make startlingly accurate prediction of temperature range of a certain stars, and this, is another amazing application of light.

Wien's Law, to show the inversely proportional relationship between wavelength of light and temperature of glowing
object.

The last application of property of light in astrophysics will be on a phenomena called 'gravitational red shift'. This phenomena is based on 2 important laws, 1.) light is electromagnetic wave 2.) Doppler's effect, when there is relative motion between observer and source of wave, there will be apparent change in frequency. I know the definitions of Doppler effect will sound daunting to many tenth graders, so I will offer a simplified explanation of it. Imagine a lorry sounding a horn as it is approaching you and leaving you, when it is approaching you, you will find that the tone of horn will get higher as it is approaching you and tone of horn getting lower as it is leaving you. This is one of the most common Doppler Effect phenomena in daily life (on the apparent change in frequency of wave), and the same property goes to light, an electromagnetic wave. In astronomical observations, there is apparent red shift of light (that the wavelength of observed light emitted from stars), the light gets redder (and hence the increasing wavelength, and the frequency of light gets lower) and as the frequency of emitted light from stars decreases, this implies that the stars observed is leaving and distance itself from mother earth (just like the lorry example). And actually, the expansion of universe is based on gravitational red shift! Again, amazing discoveries that are beautifully linked to each other.

If you don't understand Doppler Effect, imagine a lorry sounding horn as it is coming to you.

I'm only able to post 3 beautiful applications of observation of light in astrophysics. There are more, for sure! And I hope you enjoy reading the tidbits of astrophysics.

On Efficiency and Time Management

Recently, when I came across to Cal Newport's blog, I have found an interesting blog. The title is "You can be busy or remarkable --- but never both". I stood in awe at such an unconventional topic, and after reading through this blog, I went through a moment of reflection on my time management. One of the essence of that post includes:

"Terence Tao is one of the world’s best mathematicians. He won a Fields Medal when he was 31. He is, we can agree, remarkable.

He is not, however, busy.

I should be careful about definitions. By “busy,” I mean a schedule packed with non-optional professional responsibilities.

My evidence that Tao is not overwhelmed by such obligations is the time he spends on non-obligatory, non-time sensitive hobbies. In particular, his blog.

Since the new year, he’s written nine long posts, full of mathematical equations and fun titles, like “Matrix identities as derivatives of determinant identities.” His most recent post is 3700 words long! And that’s a normal length."

It is indeed surprising that even the most remarkable mathematician, Terence Tao, is not 'busy'. A further reading of that blog reveals that we have phases of deep work and phases for other activities. So as I finished reading Cal Newport's blog, I've decided to devise my own time, in an efficient way. In the process, I have found a secret key, and the key to greatest efficiency is flexibility.

After a thorough "think-through", I have found that my efficiency works in 3 phases. These 3 phases occur at different times and there seem to be a cycle between these 3. When disciplined people will most probably make a timetable that sounds like "7.00 am school, 5.00 pm sports, 9.00 pm revision, etc.", I have found that rigid timetable will sufficiently reduce efficiency (at least it works for me). And I have found that for me personally, I work in 3 phases. The 3 phases are, Phase of maximum productivity, phase of medium productivity, and phase of low productivity. This post will generally discuss about my way of exercising flexibility in my time, so maybe readers will have different flexibility and preferences. So at least this time management is applicable to me as my current state of being an A Level student. So here you go:

1.) Phase of maximum productivity. These are the times where I can maximize my creativity. Most suitable activities during this phases are creativity-based work. In this phase, I will have my 100% focus and concentration to sit down and conduct deep work. Most probably I will work on creating my own research paper in physics during this phase. I will also use this phase to tackle toughest and deepest Physics Olympiad level problems. During this phase, many creative ideas will be produced and it is best to work on projects, researches, and problem solving situations that require maximum concentration and greatest creativity. I will optimize this phase to produce good physics.

2.) Phase of medium productivity. This phase can be subdivided into 2 phases, upper-medium productivity and lower-medium productivity. For upper medium productivity, it is best for me to work on something that requires an adequate amount of concentration and routine works. Appropriate activity during this phase is revising for SAT (which requires the routine use of test-taking strategies) or A-Level (routine use of classroom knowledge, yet does not require creativity). Upper medium productivity is suitable to be used to prepare for school exams or admission exams (for me personally). For lower medium productivity, I will work on something that does not require much thinking process. Writing my blog is an example of activity that best suite me when I'm in lower medium productivity phase. So by the time I'm writing this blog, I'm in the phase of lower medium productivity.

3.) Phase of low productivity. This phase is the most unproductive phase, unfortunately. And many individuals, including myself, do experience this phase. I tried to produce something creative during this phase, but the plan just does not work out. And that's the problem that rigid timetable poses to me. After more reflection on this phase, I have found that actually I can benefit from this phase. Appropriate activities for this phase include taking a nap or rest, reading other's blog, logging on the Facebook and Hotmail to check for updates, watching a series of Japanese Animation, etc. I have gone through a moment of reflection on how to best benefit from this phase (as I'm getting bored to keep on logging on to Facebook and Hotmail during this phase), and I have come out with an idea of maximizing the benefits of low productivity. I can use this time to learn to play ukulele, an easy-to-learn musical instrument that will soothe my mind and bring the peace of mind to me when I'm in this low productivity phase. I'd prefer learning ukulele (beneficial) than logging on to Facebook, though I'm still working on reducing the number of hours I spent of Facebook each day.

So these are the 3 phases that describe my productivity. The key to be remarkable, as I have found, is the ability to optimize the benefits of each phase. Each phase exists for a purpose, and I believe that failure to make full advantage of each phase will only mean one thing--- poor time management. So I will strive to make myself more flexible instead of planning a nice looking timetable, and to gain maximum benefits from each phase. 

If we are looking for next successful physicist/ mathematician, we can ignore the guy who rush back home to check for his email, while rushing to prepare for next meeting. Instead, look for the quite fellow who stares at the cloud, thinking about what works can be done in this afternoon.------Paraphrase from Cal Newport blog.

Why Physics?

Many people asked me this simple yet profound question before. Why Physics? What makes physics so interesting to you? What is the significant of physics to you? It took me awhile to figure out why, I mean ---exactly--- why I like physics. And here are my own explanation on why I enjoy physics.

A common cliche answer might say that we study physics because of its practical purposes. While that is the reason why many people get into physics, that is not the primary reason I got into physics. In contrast, I personally see that going into physics with practical purposes is some sort of 'dull' reason. I hold a different reason for me to enter physics.

To highlight the essence of my reason, I will offer this quote from Richard Feynman:

Physics is like sex: sure, it may give some practical 

results, but that's not why we do it. - Richard 

Feynman

This quote essentially caught my reason to study physics, to pursue physics. Yes, physics may produce some practical results, but for me, the most interesting reason as to why one study physics should originate from the motive that one study physics simply for the pleasure of doing it. In my opinion, one should just focus on producing good physics (just for the pleasure of producing good physics), rather than producing good physics for some practical purposes like getting a Nobel Prize in Physics. I think this is important to have the right motive to study physics because the right motive gives the right drive, the right energy to keep on doing physics. One will not get disappointed simply because no recognition is given to oneself who produces good physics. This can be quoted from Terence Tao, one of the youngest Field Medalist mathematician, from his "10 essential career lessons":

2. Focus on contribution

One should never make prizes or recognition a primary reason for pursuing mathematics; it is a better strategy in the long-term to just produce good mathematics and contribute to your field, and the prizes and recognition will take care of themselves. -Terence Tao

Yes, one should focus on contribution, enjoy the pleasure of pursuing and striving to just produce good mathematics (this applies to physics, too). Many of young aspiring academicians make Nobel Prize their primary reason to do physics (or mathematics, chemistry, biology, etc), in which I think is a 'bad' reason to focus on achievements. Focusing too much on achievements can drain one's brain energy and focus when one fails to get recognition desired for a long term. I think it is essential to focus on contribution, but one should note that one should enjoy the pleasure of making contribution, just like Richard Feynman. One of the most remarkable thing I love about Richard Feynman is that he loves doing physics just for the fun of doing it. He never takes in practical purposes as primary focus, instead, he just loves the process of producing physics. He emphasizes the fun of producing physics, and the fun of producing good physics is like going to an adventure. One should not care too much about what comes out at the end of adventure, but one should just enjoy the adventure itself. For me, the same thing applies to physics. I see physics as an exciting adventure. It's like climbing a rugged, rocky mountain without knowing what lies at the peak. Even though one may not be able to reach the peak, the moments and memories during the climb is splendid, and one should not focus too much on the end results. I cherish my journey and experience with physics, and that makes physics interesting to me.

The adventure in physics can also be interesting because I think of it as a sense of discovery. There is always something new in physics, many new discoveries are found day by day. Yes,the discoveries might or might not make significant contribution to society, but I just love the thrill of having discover something new. I'm not a talented inventor myself - never feel interested to create some new gigantic machine or mind blowing technology. I have a heavy declination to build theory - theorem builder. I love to just produce good theories and have them experimented rigorously in great laboratories like NASA (making astrophysical observation), CERN (particle physics experiment), Lawrence Berkeley National Lab, etc. That's why I am never suitable to be an engineer and work in the corporate ladder where one always focuses on practical usage of certain invention. I'd love to work in great laboratories in the world, and I am undecided whether to be a theoretical physicist (Richard Feynman, Albert Einstein, James Clerk Maxwell are famous example of theoretical physicists) or an experimental physicist (Michael Faraday is a widely known example in experimental physicist). I don't know yet which part of physics interests me the most --- it can be quantum physics, it can be astrophysics, it can be cosmology, it can be particle physics or nuclear physics --- I don't know, but I will explore all areas of physics and find one field that interests me badly, and specialize in that field when I further my education pathway to graduate level and postgraduate level.

So this post has captured all the essence on the "why physics" for me. Hope you enjoy. If any one of the readers get interested into physics after reading my post, then congratulation, a physicist is born!

My favorite physicist, Richard Feynman. 

Terence Tao, one of the most profound mathematicians that  I admire

Michael Faraday, whose experimental discovery of electromagnetism contributed heavily to today's technology of electricity, and much more!

James Clerk Maxwell, regarded as one of the top ten physicists who impacted the world heavily with his Maxwell equations

4 Maxwell's equations, It unifies everything we need to know about classical electromagnetism. Heavily contributed to society along with Faraday's discoveries

Albert Einstein, my 2nd favorite physicist

Kaprekar's constant, a math magic trick

When I browse through Recreational Mathematics in CHS Maths Class, I came across with a comment, mentioning the number 6174 has its special feature and properties. So, driven by curiosity, I googled the number 6174 and eventually found out how 6174 works as Karprekar constant (the detail about karprekar constant will be discussed below). It turns out that Kaprekar constant is a mathematical magic trick which is quite interesting, and I will teach you about rules of this game of Kaprekar below.

6174 is a Karprekar constant named after Indian Mathematician D R Karprekar. These are 4 steps in this Kaprekar game which make the number 6174 distinctive from other numbers. Here they go:

1.Take any four-digit number, at least two different digits (leading zero is allowed). (e.g., 0110, 2378, 1220,   0022, 0997 etc)

2.Arrange the digits in ascending order then in descending order to get two different four-digit numbers (adding leading zero if necessary). 

3.Now, (Bigger four-digit number) - (Smaller four-digit number) Subtraction of smaller number from the greater number obtained.

4.Repeat steps 2 and 3 from the final answer obtained in the previous step three.

This is where the miracle of mathematics happens!!! The above process, known as Karprekar's routine, will eventually lead you to the number 6174, in at most 7 times iterations (repetitions). This is the magic of maths!!! The miracle, the wonder, and the beauty of maths.

However, the only condition of four-digit number which does not lead to 6174 is repdigit (ie, 1111, 2222, 3333, 4444, ...). These repdigits will eventually lead to zero at the first step 3 process itself. So, here are some examples and workings for proof of Karprekar's constant:

Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 3524:

5432 – 2345 = 3087    8730 – 0378 = 8352    8532 – 2358 = 6174 (3 iterations)

All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4:

2111 – 1112 = 0999                      9990 – 0999 = 8991 (rather than 999 – 999 = 0)   (leading zero is aloowed)                 9981 – 1899 = 8082                      8820 – 0288 = 8532                8532 – 2358 = 6174  (5 iterations)

9831 reaches 6174 after 7 iterations:

9831 – 1389 = 8442                      8442 – 2448 = 5994            9954 – 4599 = 5355                     5553 – 3555 = 1998 9981 – 1899 = 8082       8820 – 0288 = 8532 (rather than 882 – 288 = 594)         8532 – 2358 = 6174 (7 iterations)

8774, 8477, 8747, 7748, 7487, 7847, 7784, 4877, 4787, and 4778 reach 6174 after 4 iterations:

8774 – 4778 = 3996         9963 – 3699 = 6264        6642 – 2466 = 4176       7641 – 1467 = 6174  (4 iterations) 

http://mathworld.wolfram.com/KaprekarRoutine.html  for a more technical view of this Kaprekar's Constant.

Resource: donsteward.blogspot.com

A complete route to Kaprekar's Constant, from Wikipedia

Hope you enjoyed!!!

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!"