Global Warming– A Contrarian View Saturday, Oct 6 2007

This is a copy of a paper that Ratnakar and I wrote a few weeks ago for IIM Bangalore. We liked it. IIM B did not, and did not consider it worthy. Partly because I ran out of interesting topics today, I have uploaded a copy of this paper. If you disagree with it…be my guest!

 

Executive Summary

This paper seeks to challenge the very assumptions upon which the international system for control of climate change operates upon. With the collapse of communism, capitalism has been left as the only viable economic system available. It is in the background of this fact that efforts by every country that seeks to address the issue of climate change have to be viewed. In this paper, we, the authors take a most unfashionable view. We make 2 sweeping statements that challenge this entire viewpoint.

1. Climate Change is far more complicated than mankind burning fossil fuels. While it would be foolish to deny evidence of a warming across the globe, it would be equally foolish to imagine that humanity can predict the consequences of climate change. Our estimates are at best guesses that may be right. At worst, we may be catastrophically wrong!

2. Predictions of doom have been upon us since the dawn of time. At no time have these so called prophets had anything other than the fear of the unknown to make us fear. While the doomsayers of the first millennium promised divine retribution, the post cold-war scientific second millennium portrays climate change as the bogey man that ill destroy us since the spectre of nuclear holocaust failed to materialise.

The authors do not seek to dispute neither the fact that the earth is warming, nor the reasons behind this global warming phenomenon. We accept the overwhelming evidence that it is largely due to human causes. Where we differ is in the consequences as well as our ability to alter the current situation. As long as Humanity progresses, the world is doomed to growing warmer. We base this gloomy prediction on the most basic of laws, The Second Law of Thermodynamics.

At the same time, we also say that the future is still bright. Disaster movies like “Day after Tomorrow” sensationalise the effects of climate change, and make reasoned debate almost impossible. Our stand is that the overwhelming history of humanity is one of progress. To deny that we will continue to progress is to deny our own history. For India, there are specific challenges which we will outline, but there is no doubt that in our mind that we cannot blindly follow emission targets that cripple growth. At the same time, to expect the developed world to fund our growth with their lowered emissions would only be naive.

Case 1: The case for alternative energy – Dwindling oil reserves

Today, crude oil prices are averaging at $75 a barrel, and even by discounting all external risks that affect the price of oil, analysts agree that the price of oil is here to stay above $50 a barrel. At these prices, previously unviable energy production methods become feasible. The production of ethanol from sugarcane is about Rs. 17 a litre, which is cheaper than the equivalent oil price on an energy equivalence scale.

Is Ethanol the answer?

So, is ethanol the answer to our worlds efficiency woes. The answer is unfortunately…no!

Efficiency of Ethanol

The efficiency of photosynthesis is a woeful 2%, which means that the entire arable farmland of the world would have to be devoted to sugarcane in order to meet the future energy needs of the world. In comparison, commercial solar cells have an efficiency of 12%. Therefore, a solar field would be more efficient than a sugarcane field (though far more expensive to set up).

Pollution and Carbon Neutrality

Sugarcane is also an extremely polluting crop in itself. It requires fresh water, which is a limited resource, as well as a 180 day crop cycle as compared to a 90 day cycle for rice or wheat. In addition, the fertilizers used for growing sugarcane are also made from fossil fuels, and while the net energy gain is positive, it is by no means sufficient or non-polluting

Nuclear Fuel: The Holy grail?

Nuclear Fission plants are a controversial solution. Environmentalists love to hate fission plants: firstly for their extremely hazardous waste products, which do not degrade over time (measurably), and secondly for the safety that has to be maintained at all times. Chernobyl is pointed out as an example of what happens when things go wrong.

Limited Fuel: A bigger Problem

Of course, the real problem is that in the long term, fission plants are limited by the amount of Uranium and Plutonium that can be mined. The total quantity is not expected to last longer than 100-150 years, even at current energy consumption levels, and hence would be a short term solution

Nuclear Fusion: The way ahead?

Now we come to the most ambitious and yet promising project so far. ITER (International Thermonuclear Energy Researchers) is an organization formed out of the leading countries of the world, dedicated to solve the technical challenges towards producing nuclear power from fusion reactions.

The Advantages:

The advantages are incredible. Firstly, the fuel would be hydrogen, the most plentiful element in the universe. Secondly, there would be no problem of radioactive by products, and there would also be no danger in case of meltdown, as in the case of a nuclear fission plant. The method would be completely clean.

The Pitfalls:

The technical problems in creating fusion power are significant. Even the most optimistic projections says that it would take 20 years to develop a commercial reactor that produces enough power for a modern city.

Our Choice:

In spite of the uncertainty around Nuclear Power, we favour the use of Nuclear Fusion power as the energy source of the future. This will take many years, in which we must fund our appetite for energy from fossil fuels.

Global Warming is Inevitable –Second Law Speaks

The real problem is the impossibility of prevention. The second law of thermodynamics states that for performing any useful work, some heat has to be rejected to the environment. This is an immutable law, and ensures that whatever we do…however efficient we may be, we cannot break the shackles of the second law of thermodynamics. The only way to reduce the heat we reject is to do less work…burn less fossil fuels…and lower our standard of living. While one or two people in a hundred might accept this, a vast majority would never look to go back to the era of hand to mouth existence that was seen before scientific progress.

What we say is this…in the long term, the costs of development will be seen in global warming (assuming all other things remain equal). Humanity has to adapt and change to it, as it has done so in the past.

Handling Global Warming: Cases

There is little doubt that Global warming will cause widespread changes in the way the world works. Let us take a fictional case of a farmer in north India. Let us follow him through the years of global warming.

Case 1:

For generations, monjural asharaful’s family has lived farming near the town of Faridpur, a small town on the banks of the river Padma, where it meets the sea in Bangladesh. But of late the sea has become more of a monster and has already digested much of his arable land… the water levels only seem to be increasing… Upstream on the great river system of Ganges-Brahmaputra-Padma, Musad Dilal, is a small time farmer near the town of Mirzapur on the banks of Ganges in the Indian state of Uttar Pradesh. he is completely dependent on the south west monsoon for his yield. The monsoon system which has visited India for millenia have o late started behaving erratically. Moreover, when the monsoons are good, theganges overflows and his crop is marooned. Further upstream of Ganges, in the Garhwal hills of Uttarakhand, the glaciers which fed the river system that supports almost 1/6th of humanity are fast disappearing.

The above case is not fiction. As we write this, the glacier that feeds the Ganges has receded to record levels. It is estimated that by the turn of the century, the Ganges will be a monsoon river rather than a perennial snow fed river.

Solution: The reality cannot be changed. But what is changed is this…in the fields of Norway and in Europe, the land will become more fertile. As the Ganges dries up, Industries shall rise up. With Nuclear Power, irrigating the north of the country is no longer impossible. Giant turbines generate enough electricity to move enough water that another Ganges can flow. Humanity will progress.

Case 2: The Hunt for Oil:

The northwest passage, the name given to the ocean link between north west atlantic and the pacific has been a holy grail for years as it has always been frozen. It is a jackpot as not only does it provide a short shipping passage from Europe to North America to Asia but more importantly for the black gold hidden under the ice cap.

Consequences:

One consequence will be the extinction of the Polar bears. But at the same time, huge riches will be available for man to use as he chooses. These resources will spur on a new phase of industrialisation of the frozen north.

Carbon Trading and Compulsory Emission Norms:

Carbon trading since its inception has been dogged by controversy. Still in its initial years, it has been seen more as a licence to pollute than as a real method of stopping emissions. While the carbon credits were supposed to be used to remove excess CO₂ from the atmosphere, in reality, this has not occurred due to the extremely generous initial grants given by the governments to business.

Another huge problem is that countries with large natural reserves of forests are not properly credited for their role, which in turn distorts the market.

However, these are unfortunately only peripeheral to our view. We believe that while regulation should be maintained for pollution control and safety, competitive markets should drive the product manufactured. Carbon Credits distort this, and reward inefficiency.

Predictions of Disaster: Reverend Malthus

The key point that has been made is that humanity has begun to eat up its reserves of precious minerals and energy. Eventually, we will reach a critical stage where we can no longer support ourselves and will face extinction. This was first postulated by Reverend Malthus, who pointed out that population grew geometrically, while resources could only grow at an arithmetic rate.

However, over the last century, his predictions have not come true. Most spectacularly, a wager was placed between the leading biologists and economists of the 1970’s on the future prices of commodities. Malthusians believed that the prices would go up continuously due to greater demand, while economists pointed out that the increased prices would lead to innovation, which would lower prices once again.

The Result:

After 20 years, in 1990, the prices were verified against the 1070 prices. The Real prices of each of the commodities given was lower than it was in 1970, thereby debunking the Malthusians.

In our opinion, this is no chance. Innovation means that new resources are discovered or new materials that improve human progress are made. For every challenge we face, ingenuity has found a solution.

Indian Scenario: What should we do?

In conclusion, the authors would like to put out an optimistic view of the future. While we do not ask India to ignore climate change, the first obligation is to uplift India’s poor and bring lead them out of their current hand to mouth existence. To sacrifice midnights’ children to save some uncertain future would be a cruel slap in the face of our “tryst with destiny”

 

4 Responses »

 

Physics again–THe Coriolis Force Friday, Oct 5 2007

Ms. Potnis was suggesting to me that I write about Hurricanes and cyclones and other such rainy events. Like the obedient chap that I am, I duly set about researching the topic.

Of course, most of my research gets sidetracked into areas that I really was not looking for. Eg: Anime series turned into Meiji Era history. So from Hurricanes and their names to an explanation of Coriolis force is not really that far fetched.

So without much ado, lets explain the reasons why hurricanes rotate, the fine force of Coriolis.

Fictitious Forces: What do they come up with?

My usual strategy with any topic is to wander over to the Wiki and have a look at it. This time, I was sorely disappointed. Sure, the example was there, and discussed in great detail as well…it was just that I could not understand a word. Equations all over the page, and complicated Greek Letters always make me feel mildly ill, and I had to go away and lie down before returning to the the topic.

The basic problem is that the Coriolis force is not really seen if the observer is an independent one. I would think of it like this; If I were sitting on the moon and observing the earth, there would be no need to explain the Coriolis Effect, as existing physics would explain it all. Its only when the observer and the measurements occupy a rotating frame of reference do things seem to get a bit complicated.

Now, its hard for me to do this with words, but let me have a go anyway. Let us say that I am standing at Connaught place in Delhi which is at 50 Celcius. Now hot air is light, and hence the pressure at Cunnought Place is quite low. At the same time, the Kashmir Valley is at about 5 Celcius, which is rather cold. The air over here is therefore at a higher pressure than in CP. Now, Nature does not like pressure differences, so the air starts rocketing towards me from the Kashmir Valley.

So far so good…but what happens next is interesting. You see, while the air is barrelling down in a straight line down, the earth is rotating, which means that Delhi is now a few miles east of where it was. So to me, the air that is coming down from Kashmir has missed me, and is instead heading towards Punjab and Lahore!

At its simplest, this is the Coriolis force. It is the apparent force that causes things to drift off line when they are moving in a different direction than that of rotation. It is fictitious, because when you shift your point of reference, it disappears.

Now for hurricanes. They are formed over seas, where there is low pressure due to the warm air above the oceans. Cold air from the temperate zones rushes down, but as it arrives in a curved path with respect to the rotation of the earth, it starts rotating and swirling about the central point of low pressure.

So there you have an explanation of the Coriolis force. I am too lazy to type too much more, so am off now!

Leave a Response »

 

Idiots Guide to Black Holes – II Friday, Aug 31 2007

Welcome back to the guide to black holes. If you have not read part I, quit peeking and head downwards to it. If you have, read on! Today, we jump straight into the really strange aspects, having been mostly normal in the previous post.

Wormholes and Time travel — All with rotation

Rotating black holes have already been covered in my previous post. I have mentioned in passing that they have an inner event horizon and an outer event horizon. Which horizon you are in depends on which way you are orbiting the black hole. Technically, if you are in the outer event horizon, you are trapped, condemned to drop into the black hole. However, because there is also an inner event horizon, if you are travelling in the opposite direction, you could be saved if you sort of turned around quickly enough.

Of course, reality does not like being made a fool of, so the theorists said that you would probably escape from a black hole, but you would possibly end up in a totally new universe or even stranger, maybe end up somewhere totally different in space time. So they decided that a Black hole is a sort of  shortcut through space time. And hence you can call it a wormhole. Why wormhole…read my notes for that.

Science fiction writers just loved this though. Finally there looked like something that could make space travel look possible after Einstein put his ridiculous speed of light limit. But the bad news is coming up.

Black Hole Menus — You can have anything to eat, as long as its Spaghetti. 

The problem with trying to go down a black hole is best explained with a small story. I am a six foot tall chap, and lets say I jumped feet first down a black hole. In the beginning, things would be fine…I would be falling fast, but that is ok. The gruesome part comes later. As I get closer to the black hole, Newton and Einstein gang up to beat on this hapless traveller. We know that gravitational force is dependent on the square of the distance between the two attracting bodies. And the problem is that my head is 6 feet away from my toes. Back on earth, it makes little difference, as the additional attractive force my feet feels is minimal. But near a black hole, with all its super heavy mass, the problem is quite acute. Heck…its not a cute, its just plain gruesome. In simple words, my feet would be accelerating towards the Black hole faster than my head would. And that is basically like being put in a huge rack (the Spanish inquisition kind). I heard that you gain about a foot in height before your bones and tendons give up and snap. OUCH!

So basically, anything that is silly enough to fall into a black hole will end up getting horribly stretched and elongated. A lá spaghetti. Physicists (imaginative lot them) decided to call the process Spaghettification. And the name stuck. So, unless you fancy getting a lot taller (and thinner) than you ever wanted to be, black holes as a means of travel is out!

Freebies– Power from Black Holes and Killjoys 

Well, you cant keep a good physicist down. Sure, you just ruined his funky space travel plans. But he is nothing if not a creative soul. So he came up with a new idea. Now, those of you who carefully read my section on space time and the ergosphere, your just reward is here. I will show you how to get free energy. It goes like this

1. Take a handy rock, and fling it into the Ergosphere. The dashed thing begins to go faster because it is stealing energy from the black holes rotation, and gradually gains a huge amount of energy.

2. Once this energy gained is greater than the gravitational force of the black hole, it gets flung out again.

3. Grab rock and fish out the energy that it has now gained from the black hole, and you have it. Energy gained for free!

Of course, this was too good to last. A chap named Penrose decided to ruin all those Business plans of those budding physicists and brought them right back down to earth. He pointed out that if you do gain energy from the black hole, conservation laws state that the black hole loses energy as well. And if you keep doing this silly thing, like we run out fossil fuels, the black hole will run out of rotational energy and will stop. And pop goes the balloon of free energy.

All the physicists went away, thinking dark thoughts about Penrose and vowing vengeance. They are still searching for a way to get it, but don’t hold your breath for it. You would probably asphyxiate.

Black Holes and Entropy

Entropy! The concept of entropy was probably best enunciated by Mr. Murphy. “Things tend to get worse.” But physicists love complicating things. And entropy was no exception. They had to put in stuff about high efficiency energy, heat, engines, and stuff like that. But we don’t need any of that stuff. For us, entropy is a simple Thing.

We define Entropy as the measure of disorder of the universe. No more…no less. Now Stephen Hawking (generally regarded as the hot stuff of physicist circles) pointed out that even when two black holes swallowed each other up, the event horizon of the combined entity was larger in area than the event horizons of the sum of the two black holes. People noticed that this was very similar to what the second law of thermodynamics said. (Actually the second law that I remember said NOTHING about area…but hey, that is why I am BlahLa, and he is Stephen Hawking) So, the physicists all came together and said, hey boy…lets talk about the entropy of black holes.

There of course is a small problem. Entropy is measured by the energy levels of constituent molecules (or atoms) and in a hairless black hole, all of these energy levels cant be defined because the black hole swallowed it all up. So while a Black hole may have entropy, nobody could figure out how much entropy it did have. But physicists are a hardy bunch, and they said, “Well, we know the event horizon areas. Why don’t we measure entropy in terms of the area of the event horizon?” This was unanimously accepted, as the cabal of physicists neglected to invite anyone with the sense to ask, “How on earth are area and entropy related” and it is now standard theory. So, if you want some free entertainment go to a physicist, and ask him to try to explain how area and entropy are related. Watching him squirm and twist facts into pretzels and doughnuts (with or without wormholes) will certainly make for an engaging afternoon.

Some Like it Hot–But the Big Bad ones are Cold!

Now, if Black holes have entropy, well they have to have a measure of temperature as well. And this was a sticking point in the whole entropy thing with physicists. For how the heck can you measure the temperature of a black hole? For one thing, it would swallow any thermometers without even a by your leave!

But Hawking comes riding to the rescue again (metaphorically of course). But before we explain that, we will have to discuss some rather esoteric ideas. One of them is Vacuum energy.

Vacuum Energy–Something from Nothing?

Physicists (the clever buggers) have this great idea about a vacuum. Now, you and I know what a vacuum is. Its basically…Nothing. In fact, you cant get more of a nothing than a vacuum. But physicists say, “No! What a vacuum is is really a sea of particles. But you cant really see them because them because in order to see them, you need a reference. But since the vacuum is our frame of reference, you can never see them!” Talk about circular logic! But strange as it may, its true. Now, my explanation is going to sound a lot like magic…but bear with me.

Imagine that you had an instrument that could recognize particles. But one of the problems is that you can only detect the particles if you had enough time to sense them. And speed of light puts a limit on how fast you can sense particles. Now, if a particle were to form, meet its antiparticle, and be destroyed; and do all this in less time than light could be used to measure it, it would not break the laws of reality…because nobody is there to see the particle break the laws of reality. Its a bit like Zen. “Who can hear a tree fall in the forest.” For all practical purposes, no-one. In the same way, if a particle were to sneak in and out of reality fast enough, you could technically say that its not breaking the laws of physics.

(Fine…I accept. It still sounds like magic. If you want a better explanation, ask Dr. Hawking)

So, at the end of the day, vacuum can be said to contain a heck of a lot of energy. But nobody can use it, because it is the lowest level of energy. (the whole entropy concept again).

Black Holes and Vacuum Energy:

“But what do Black holes have to do with this?”, you are asking. Here comes the answer. At or near the event horizon, if a particle were formed, and its antiparticle were also formed at the same time, one of them could escape into the universe, and the poor pair would get sucked into the black hole. And suddenly, it would seem as if the black hole would have emitted a particle! Nifty, eh?

So, what it would mean is that a black hole would actually be emitting some energy. And once something emits energy, its temperature can be measured. Once again, Stephen Hawking had saved the day.

Now, the smaller a black hole is, the more likely it is to emit this energy. Simply put, lets explain it like this. A small black hole has less gravity, so it cant absorb as much stuff. But it has to emit the same amount of energy. The net difference means that amount of energy emitted is greater than energy absorbed. So, a small black hole looks hot, because its emitting more energy than it absorbs. In the case of a large black hole, of course the situation is opposite. (If you are still unconvinced, go ask Stephen Hawking!). So, small Black holes are hot things, burning themselves out, and dying off. But large black holes are cold…and will continue to be cold as long as the background energy of the universe is high enough. But just you wait. Even the largest Black hole will finally evaporate once the universe gets sufficiently cold. Of course, this process is likely to take about a google years. That is 1 followed by a 100 zeros. Lets put it this way. That is a Looooong time away.

So, there you have it, ladies and gentlemen. A brief outline of Black holes. All that I know, reduced to as few pages as I could get away with! And if you did not understand a huge amount of it…don’t worry. Infinity is rather difficult to comprehend. Don’t believe any physicists who try to con you into thinking that they understand it either! They are fibbing as well!

2 Responses »

 

Black Holes — The idiots guide part I Thursday, Aug 30 2007

I loved physics when I was a kid. Mainly, it was because of this book called “Physics can be Fun” by Y Perelmen, from Mir Publications. I remember, when I was in fifth or sixth standard, he explained the concept of escape velocity.

Back then, I was a bright kid, and my head was full of facts. So I thought to myself…what if you have a body that is so big that that the escape velocity for that is greater than the speed of light! Then you would have something nothing could escape from. I think I even spent some time trying to convince my friends about this cool idea, but I am not sure that they got it! You can imagine my devastation when I learnt that I was not the first chap to think of such a strange thing! And that they were called black holes (way cooler than my name…which was something like big star or something).

So, lets talk about black holes. In order for a good discussion, I will assume that you chaps know about Newtons law of gravitation. That will be a beginning.

Black holes– An initial definition

A Black hole is something that is big enough that the escape velocity of the body is greater than the speed of light. Since nothing escapes from it (including light) you cant see it. Hence the name.

Black Holes — Singularity…what’s in the name?

Well, the description above is good enough, I guess, but lets think about it logically. IF the body had enough mass that even light could not escape it, then the mass of the body would also start getting compressed due to the gravitational forces. And as it gets compressed even more, it experiences a still higher force, and so on, until the whole blooming thing collapses into a point. Thus, you will have a dashed huge amount of mass compressed into nothing (by definition a point has zero volume). Now physicists love to confuse people, so they decided to call the Black Hole a Singularity. Why? Because whenever you have zero in the denominator, you get a whole huge bunch of infinities, which are a pain to calculate with. Physicists are also lazy, and had no desire working with infinity, so the whole thing was abandoned as a bad job, and the Singularity was left alone because nothing could be explained inside it. This brings us neatly into the next section

Black Holes have no Hair!

Yes ladies and gentlemen. Its true. Apparently there are no hairy black holes! (I was so concerned about that). But more seriously, there is this theory called the No Hair Theory, which seeks to explain that Black holes can be completely described by only 3 properties. These are

1. Mass

2. Electric Charge

3. Angular Momentum

Anything else is completely irrelevant because the black hole pretty much swallows all the information available. So for example, a black hole made of matter is absolutely identical to one made of antimatter, so you will be in trouble in either case if you get swallowed. The theory used to say that information is completely destroyed once it enters a black hole. Updates are still happening here, so keep your eyes peeled for any hairy black holes!

Types of Black Holes

When I was a kid, I was pretty proud of myself for thinking of the concept of black holes. But of course, physicists are a real bunch of smart Alec’s, so they had to say, “Hah! There are 4 different types of black holes!” Basically, these four types are split into a combination of charged or uncharged, and rotating or stationary black holes!

Now, I am not sure that the Charged Black holes can be strongly charged, because as everyone knows, the charge force between particles is way stronger than gravity, so it seems hard that a black hole could be formed if its electric charge was too high. The damn thing would blow itself apart before it could attract enough mass. In the same way, non rotating black holes seem a bit tougher to imagine. All stars rotate…(as far as I know), and rotation does not stop if you compress all the mass. Its a bit like an ice skater doing a pirouette. It starts with her extending her arms at full stretch. As she brings her arms closer, she begins to rotate faster. In the same way, the black hole should also rotate faster as its mass gets compressed. So charged and stationary black holes are out! (but I could be wrong).

More about the Singularity

For an uncharged and stationary black hole (Which is easier to explain), its pretty easy. All the mass is concentrated on a single point. At the point of the black hole, the whole general theory of relativity collapses, and we are left with no explanations, and all the physicists shuffle their legs, staring at the floor and sidle away hoping not to be noticed.

Of course, all the quantum theorists still stand around saying, “But you cant have zero length…there is a quantum unit of length after all.” But to heck with them….they haven’t got any good explanations either, so they can all go into a big black hole if they like.

So, to summarise, for a black hole which is uncharged and stationary, there is one point at which the laws of physics give up and go away.

Event Horizon and Rotating Black Holes

First, we say what an event horizon is. Basically, it is the closest anything can get to a black hole without getting sucked in. Every black hole has an even horizon. But for rotating black holes, the situation is slightly more complicated. Now general theory of relativity says that matter distorts space and time around it. Now, it gets a bit more complicated when the matter is going to also be rotating at the same time. General theory goes on to state that rotating masses have rotational inertia, which drags space-time along with them. Sounds logical? Wait a bit longer.

The figure above shows that the event horizon for the black hole is now split into two. The inner event horizon is valid for a body that is orbiting the black hole in the direction of rotation. The outer ellipse is the orbit that a photon would take if it were orbiting the black hole opposite to its direction of rotation. Now here is the funny bit. According to theory, the space-time that is being dragged around by the black hole has to travel faster than the speed of light. Of course, no physical thing can travel faster than light, but there is nothing in the laws that prevent area from moving faster than light! As a result, no stationary object is allowed to exist within the outer event horizon (called the ergosphere), because it would look as if it were moving backward faster than light which is impossible. It can only orbit around the black hole, because then it would look like it were moving slower than light. And here is the funny bit. Its actually stealing a bit of energy from the rotation of the black hole, so theoretically, if it gets enough energy, it should be flung out of the black hole like a stone being twirled around too fast breaking its string.

Falling into a Black Hole— the View from the Outside

From the outside, seeing a body falling into a black hole is extremely weird. It will look as if the object falling into the black hole begins to fall slower and slower, until it looks stationary at the event horizon. Of course, for the poor falling object things are a bit different. It continues to fall beyond the event horizon too, right into the black hole. But the information cannot be relayed, because the light that transmits the information is also trapped.

So there, part I is completed. Part II will have other funky details. Such as black holes escaping to other universes, spaghetti and how its not just an Italian dish. We also discuss entropy and other such interesting details later. So till then, same bat-blog, same bat-link.

3 Responses »

 

What are vectors, and why should I know about them Friday, Jul 6 2007

Before we dive any further into Newton, forces and other things, lets go a bit into the fantastic world of vectors.
first, a definition. Vectors are defined as things that possess a magnitude as well as direction, in contrast to lowly scalars, which only get magnitude.
“So what is the big deal?”, I am sure you ask. Well, it does not seem like much, but let me try to explain it like this.
If you wanted to lift a rock, pushing down on it would not lift it. Instead , you would have to probably pull the rock up, and there you go, one rock lifted. Here, the direction of the force is just as important as the magnitude. So, we can then say that force is a vector. Now how about travelling. Let us say that I have taken my car, driven down from Bangalore all the way to Chennai, and back again. So I have covered 600 (or so) kilometres doing this. My tyres and my petrol tank make that clear. But the fact of the matter is that I have not really moved 600 kilometres from my home…I am back there, lounging. So while the distance travelled might have been 600km, my displacement from my initial condition was zero.
So for now, just remember that a vector is rather more complicated than a scalar, and although the vector may be very strong (has high magnitude), it may not do much to you (beacuase the direction of th high magnitude is low.
We wont even go into tensors, and where they fit into the situation. We can worry about tensors we we come face to face with one!

Leave a Response »

 

Zeno’s Paradox Friday, Jul 6 2007

I must say, I did intend to complete a discussion of Accelaration and Newtons laws today, but in trying to figure out the principle of differentiation, I came across this pretty interesting one which is a sort of introduction to limits and infinity (and beyond too!).
I promise that this will help while we discuss differentiation.

This one is about the greeks. There was this philosopher named Zeno, who was generally regarded as hot stuff in the philosophical circles of Greece. What did he come up with? Well, mainly he was of the school of thought that said that all motion is impossible, or some such thing. In order to prove it, he came up with these paradoxes, which at first sight seem terribly convincing. For example, there is his famous one about Achilles and the tortoise. (For those who came in late, Achilles was a mighty greek hero. He was a great runner. And showed a clean pair of heels to all his competitors. And was shot in the heel, causing his death. For the unabridged version, read the Illiad, by Homer). Below is a quote from the Wiki (always useful).

In the paradox of Achilles and the tortoise, we imagine the Greek hero Achilles in a footrace with the plodding reptile. Because he is so fast a runner, Achilles graciously allows the tortoise a head start of a hundred feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run a hundred feet, bringing him to the tortoise’s starting point; during this time, the tortoise has “run” a (much shorter) distance, say one foot. It will then take Achilles some further period of time to run that distance, during which the tortoise will advance farther; and then another period of time to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, Zeno says, swift Achilles can never overtake the tortoise. Thus, while common sense and common experience would hold that one runner can catch another, according to the above argument, he cannot; this is the paradox.

Now, try to spot the hole in that logic. Its actually quite tough. But I shall spare you, the reader from thinking this through. The problem with Zeno’s logic is this. He assumes that for there are an infinite number of steps for Achilles to take to overtake the tortoise (Infinitely small steps). And since it takes a finite time to complete each step, it will take infinite time to complete infinite steps. In functions, this is called a one-to-one correspondence. But this is not necessarily true. Let us quantify the tortoise and Achilles problem like this.

In the case of Achilles and the tortoise, suppose that the tortoise runs at a constant speed of v metres per second (ms-1) and gets a head start of distance d metres (m), and that Achilles runs at constant speed xv ms-1 with x > 1. It takes Achilles time d/xv seconds (s) to reach the point where the tortoise started, at which time the tortoise has travelled d/x m. After further time d/x2v s, Achilles has another d/x m, and so on. Thus, the time taken for Achilles to catch up is


The above value is a finite number, which means that Achilles will eventually catch up with the tortoise. Notice, that without a definition that implies that distance and time can be related, this problem cannot be solved at all.

p.s: Almost all the material is lifted from the Wiki. The link is given below for those who wish to have a full explanation (and to get thoroughly confused…I was).
here

Leave a Response »

 

An Introduction to Science Friday, Jun 15 2007

Today, I decided to begin a new (and hopefully regular) section. As someone who has always been interested in Physics, I thought that my inimitable qualifications (ie: none at all) enabled me to give some gyan on things that I thought interesting.
Well, that is enough of an introduction. Now on to what I think is the fundamental principle of mechanics. Forces.
The first question to ask is, “What on earth is a force?” This is what my 8th standard Physics Book had to say on the subject.
“A force is anything that changes, or tends to change the state of rest or of uniform motion of a body in a straight line.” Hmm…fairly categorical that. But what does that statement actually say?
By using the Bala (tm) method of analysis (ie: reading the sentence), we can break it down to its bare meaning which every one of us has seen or felt. To move something you have to push!
Now consider the meaning of the statement in more detail. Newton (or whoever) says that for something to change its position, some effort (force) has to be applied. Why is this so? Now we come to the concept of Inertia.
“Inertia is a property of a body which resists its change from a state of rest or of uniform motion in a straight line” (Yes, you guessed it. Its from the same textbook!)
So, coming back to English, we can define Inertia as the tendency of a body to resist a change in its state, whatever it may be. Why should a body resist this? I don’t know. And I doubt too many people do. Anyone who claimed to know why a body resists change has invariably given up in despair or has stormed away after enough “But Why?” thrown in his direction. But the fact of the matter is that for some reason, nobody likes being moved. So there!
Now for a quick recap of what gyan I have given. Force is that which tries (successfully or not) to change a body’s current state (of rest or of motion). What this means in reality is that you need some force in order to start a body moving and you need some force to stop it from moving once you get it going.
This is seen in real life. To move a car, we need to use some force (whether from the petrol engine or from push-starting the dashed thing). And to stop it, we need to press the brakes, which in turn apply a force on the wheels. So that is the first fundamental concept.
Next time, I shall start giving gyan on momentum; after touching upon velocity, vectors, along with polysyllabic words like differentiation and conservation…And all with equations too.

Oh…and welcome to the blog!

Leave a Response »

 

My long due Basic Physics Tutorial! Sunday, Aug 27 2006

Well, my profile details claim an interest in physics and mechanics…and I don’t think I have made even 1 post on that topic. So…here goes.
Be warned…I am not very good at maths…nor drawing. Just try to make pictures in your head. Of course, if you can’t, the fault lies with the poor author!

Topic 1–> Why is it easier to balance a Bicycle when it moves?

This is something that has forever intrigued me…since I learned how to ride a bike…and had my first fall….which was while stopping the dashed thing!

So here goes. Get your imagination hat…put it on…and read further

Imagine a stationary cycle, with “Yours Truly” seated on it. (I weigh more than 80 kilos). Now, if I tilt sideways even the tiniest bit, the centre of mass of the cycle no longer lies between the wheels…and whoops, the result is an unfortunate bala, smeared with dust/mud. After all, the tiny force that is now not aligned with the centre line of the cycle acts to increase the instability of the cycle, leading to a greater force which is not aligned…which increases it even more…and so on and so forth.

So how is a moving cycle different? After all, when you shift even slightly, surely your weight is not on the centre line of the bike, and the results should be similar. But it does not happen. Why?
Here is why. The rotating wheels have a rotary moment of inertia, which when you tilt them means that there are two more forces sitting around other than just your body weight.

Warning: Tech Data coming up. Skip if you do not want
Any motion in a curved path represents accelerated motion, and requires a force directed toward the center of curvature of the path. This force is called the centripetal force which means “center seeking” force. The force has the magnitude as given below.
Now for the meat…how does this centripetal force come into picture for a bicycle? While the bicycle is perfectly straight…well, it does not. But when you tilt the dashed thing, what happens. Your rotating tyre is also tilting, which now means that the centripetal force, which was doing nothing very special, now suddenly is acting at an angle to the vertical.
This angle means that the centripetal force now has two components….one directed in the vertical direction. ie: towards the sky/ground. And the other, horizontal direction.
Now, vertical makes no difference to us. However the interesting thing about the horizontal component of this force is that it tends to push the weight back to the centre line, thereby keeping the cycle stable.

Now, I dont have a scanner, which lets me write out the equations as well as the figures, so I will save that for another day, but suffice to say, the words above are an (somewhat unclear) explanation of this rather nifty real world problem. I especially like it because this is one thing that I figured out for myself rather than learning from a book. The book gives the information faster, but learning it intuitively is sooo much more fun and enjoyable!

k…any other nifty physical problems…well if you have them, I would be more than glad to think of their solution…but remember, it took me three fruitless years before I actually came up with the above explanation for the cycle thing. So questions are welcome…Just do not expect good answers.

p.s: I have to acknowledge the input of http://hyperphysics.phy-astr.gsu.edu/HBASE/cf.html, for the middle portion of my post, as well as that equation. Their page is not half bad either!

Well, till the Zener diode, and how physics is a lot like magic!
Ta Ta.

Leave a Response »