Trumpet Voluntary - the Triple Bond

Ok, it now behests me, after coming full circle with this blog, to demonstrate the power of what can be learned. This post is just about the most difficult to understand of them all.

The story starts thus: Chemistry talks about "bonding" between atoms. That is, for example, when you get wet, you are not spattered with either oxygen or hydrogen, but water, and water is simply H2O - two hydrogen atoms and an oxygen atom, "bonding" together.

What is this bonding, then? It's when atoms come together rather like Jigsaw pieces do, and they can fit perfectly.

How? Well, broadly, it is this....atoms like electrons flowing around them (yes, FLOWING! after all, moving charges are a current, are they not?) and the number they like to have is about 8 or 16, but they are only happy with certain numbers. Once that "shell" is "full" they become uncooperative (they will not do any more chemistry).

Once the atoms discovered this, they became VERY friendly.

A short course in chemistry is in "order" here.

Electrons, as they whizz, or "flow" around the nucleus (my field of research) like to group together but not always in the same way.

The first group has 2, the second eight, the third eight also. And so on.

Hygrogen was lonely. It has only one electron in a group that wanted two. Oxygen was also lonely, it had the full first group (2) but only six of the second group, which wanted eight.

Then Oxygen and Hydrogen met and their problems were solved in one swell floop!. They could "share" electrons!

Two hydrogens could "share" with oxygen to give oxygen the illusion of eight electrons, whilst hydrogen could "pretend" that both of it's atoms had two!

End of lesson. Well done. That is how water works, said the crying nun.

Now to the point of this post. The above is called a chemical bond. A "single" chemical bond. Oxygen-hydrogen - Easy!

BUT ( there is always one of these is physics, even without the goat) it gets worse. Here's what happens.....

The behaviour of the electrons in atoms can be illustrated by "seeing" where they are. This is where the math comes in, because no-one can actually "see" them.

First off, how do I tell you where I am? Well, right now, I am about 1 meter away from the window and 2 meters away from the the TV in a 90 degress direction. Whoops! I am on the 33rd floor, so I am about 130 meters UP.

That's 3 numbers. One for each dimension. Those 3 numbers tell anybody where I am. It's very easy because I live in a rectangular apartment, and am 130 meters directly up from level ground.

To do the same with electrons is not as easy. They live in a circular apartment and are going round it. Round.... circular.......

Why not use different numbers to tell where the electron is? How about "angle from somewhere" and "how far it is from the somewhere"?

My apartment and I are referred to as "rectangular" coordinates (the three numbers). The electron in the atom can be found by using a more convenient way, using "Spherical" coordinates
(also 3 numbers).

It is now time to show how "easier" it is this way.. copy this link.....

http://en.wikipedia.org/wiki/Spherical_harmonics
(This is the math)

and then this one..

http://oak.ucc.nau.edu/jws8/dpgraph/Yellm.html
(these are the pics that come out of the math)

There are two points to note...1. This is the EASIER way....2. I see past the waves of unintelligible letters in link 1 and all I see are the salient points, which in this case, is the shape of the thing when you draw the picture of it in link 2.

That picture is essential to the understanding of the 021, sorry, "triple bond".

This is another thing I failed to understand. I got the single bit, but double and even triple bonds? Try as I might, my teachers were unable to tell me what they were.

Here is why....

In the chemistry of Carbon, this element has 6 electrons, 2 (full shell) plus 4 (half the next shell). It would like four more. It gets this with hydrogen , but whereas oxygen gets 2 hydrogen atoms, carbon gets 4, to give it the eight electrons it "needs" The molecule formed is "methane", the simplest hydrocarbon ( see my previous post on oil). CH4.

But sometimes, there are only 2 hydrogens available, and what we see is the "double bond", that is, the carbon has a "double bond"with itself and with only two hydrogen atoms, double "2" making four. C2H4 - Ethene. What happens when there is only one hydrogen? It does complex chemical gymnastics and does a "triple bond" with itself and the one hydrogen.

It is best to think about this with "hooks and fish". Hydrogen has one hook, carbon has four hooks or fishes.

Carbon wants a full shell, either by losing four or gaining four, electrons, it doesn't care which.

For 2 carbon atoms, it is easy, just "share" the outer four and both can pretend that either have 8 ( a full shell). In this case, carbon is definitely heterosexual. It doesn't happen.

But HOW can we visulise this, after all, pictures often help. This is what none of my teachers were able to do.

Take the simplest Spherical Harmonic, the ball-shaped "cloud". Hydrogen atoms each have one of these, and when they overlap - cool! we have H2, or chemical hydrogen, two electrons sharing one "orbit", but how can four electrons share one orbit? This is the clever bit. This is the point where the maths take over. Have a look at the oak pictures (second link). Only the first one is like a ball, all the others have different "bits" sticking out of them, like the balloon sculptures that clowns make. Well, the key is understanding what the bits actually "mean".

The reason they are that shape is that the further out the electron gets from the nucleus, the more angular momentum it has, and using Spherical Harmonics is the only way to illustrate this.

For example, carbon looks like the Y(2,1) picture, basically a 4-pointed star. You can't see it, but there is an extra one in the middle, the "ball" shape. Imagine two of these face to face. Red bits opposite the red bits, blue opposite blue. Push them together and they overlap just like hydrogen's "balls". THIS is the triple bond. Red-red, blue-blue and the "ball" shape which is not shown . 1, 2, 3 electrons being "shared" .

The way to really understand this is to think of the shapes as "probability densities" that tell you just how likely it is to find an electron in "that" shape.

If you put 2 carbon atoms together like this, they form a "triple bond", and remembering that Carbon likes to have 4 hooks, with three hooks already taken with the triple bond, stick a hydrogen on and each of those left, you have the molecule H-C-C-H, which is called "Ethyne".

What has just been "explained" here is not chemistry, but "quantum chemistry", and along with powerful math, gives a beautiful explanation of how chemical bonding works. If you didn't understand, don't worry, it took me a good 4 years to work it out.

Self Destruction?

Most of us drive at least one car. Some families have one for each member.

What do they run on? "Gasoline", "Petrol", "Diesel"?

Well, crudely put, they run on hydrocarbons. That's an organic molelcule. Organic here does not mean it is good to eat, but comes from the fact that the fuel is built up from some of the same atoms that make all life: Hydrogen and Carbon, hence the name.

Organic chemistry is varied and very complicated. I loved it! Examples include alcohol (a perennial favorite), pyridine (the smelliest substance on the planet), formaldehyde (to preserve interest), vinegar( for a neat flavor), bleach (a cleaning agent, rather like 007 but with rather less philandering), butter (something spreadable, rather like Annabel Chong's legs), and the most fascinating of all, benzene.

However, these compounds use hydrogen, carbon, oxygen, nitrogen as well as others, but the car fuel uses only hydrogen and carbon.

Going into the chemistry is not necessary here, suffice it to say that the hydrocarbons are only from chains of carbon with links to up to four hydrogen atoms.

There is hexane, heptane, octane, nonane, and decane which have 6, 7, 8, 9, and 10 carbon atoms each. Most vehicles use a combination of octane and heptane. The more octane the higher the "octane". A noun to an adjective. How quaint.

But where does it all come from?

The story is long and dark. Basically it all comes from the black sticky stuff called crude oil.

In a process called "fractional distillation" the 'tanes are sucked off into separate jars. A bit like boiling water to leave all the impurities in the container. How coincidental is this to brewery distaillaries? None. Same process, just different method to distill organic molecules.

So we get the fuel from crude oil via vast Empires called "refineries".

BUT where does the crude oil come from first?

This is where the long, dark story comes in. Crude oil is just the remains of dead sea creatures that have been pressure cooked. It happens in the rocks but only after millions of years. Their dead bodies get squashed with rock above them, and cooked owing to rock temperature millions of years ago. And then there is the pressure. All three combine and the end result is the oil that we love to pollute our beaches with.

The mere fact that these creatures have been extinct for millions of years is a sure pointer to the fact that at some point, their dead remains will also be gone.

All that will be left will be the black puffs of smoke (pure atomised carbon) from the big lorries.

THEN will be the time to worry.

This has been approached here from a pure logical viewpoint. The goverments have waited until they see the physical effects. Where were Greenpeace when the motor car was invented?

The residue of those creatures now pollute the atmosphere (ever seen EDSA in Manila on a calm day?) so maybe this is going full circle and the creatures once extinguished naturally are extinguishing mankind "naturally" . In this sense we are doomed, as nature cannot be stopped.

Maybe whatever efforts mankind are to do, it is too late because someone never even foresaw the fact hydrocarbons are a limited resource.

I am willing to bet that not even any interpretation of Nostradamus' prophecies even remotely predict this potential catastrophe.

Dur Khaima (part 5)

Our hero was totally dumbfounded, as he knew the Rana would go to his funeral pyre before sunup on the morrow.

After the shock had worn off, and knowing that his love would follow her husband into the flames, he set about concocting plan after plan to save her, each one more outlandish than the last, as he lay on his bed after the evening meal.

Could somehow the Hakim save the Rana? Could their advisors be reasoned with? How about storming the Palace from the inside, disguised as the Hakim's helper? How about bluffing with threats from the English Authorities? This last was the silliest as he forgot he was basically a spy.

The Hakim left the house to go tend the Rana possibly for the last time, and our hero reuctantly decided to discuss with his friends what to do. However, one thing was missing, and this was that they only thought he was fighting injustice, and if the real story had been told, it would have alienated them.

As it was, they were up very late when the Hakim finally came back, after having talked through everything. As the hero came out of his room, the Hakim noticed something profoundly different about him. He was laughing, joking, and ate a fine meal. He seemed not to be the brooding, troubled man he had left there, but once more his carefree self, a self the doctor hadn't seen in months. He commented to his friends about it. Our hero overheard, and patted him on the shoulder with a smile

"Sir, I know what you are thinking. Have I gone mad? The truth is Sir, " and he flourished another smile, " I have given up. They say drowning is quite pleasant once you have accepted it".

The Hakim felt like a great weight had been lifted off his shoulders. He had envisioned all kinds of things involving flashing Tulwars, pistol shots, and maybe hostages.

There was a legend in the city that when the bell tolled for the death of a Rana, his spirit, mounted on a beautiful golden horse, galloped through the open city gate, eager to be reborn a warrior.

But that was just a rumor. However, the Hakim's news was bad. The Rana had but hours to live.
The Hakim also told him that during his time in the city, he had time to make five sets of clothing, from material available in the markets, in the colors of the palace servants, orange and yellow. He had had a feeling they would be needed come the time, but now there was no plan, thankfully, they would not. However, he kept them handy just in case.

In all this excitement, they had forgot the time, and almost without warning, the palace bell began tolling. They looked at each other, and our hero stood up.

"Well," he said, " this is it".

They asked him what.

"I have my revolver, and I intend to beat those crowds to the Chattris (out-buildings) and the pyre. I will not let the princess die a horrible death. I at least can spare her from the flames. I intend to shoot her. "

And without another word, he left.

He mounted his horse, and urged him to the now open city gate with all haste, and maybe it was the golden sparks of a coming sunrise, that some of the city, for years hence, swore they had seen the Rana'a spirit hurtle past them that fateful night.

The horse knew his master was excited and somehow that spurned him on. It was so exhilarating that our hero couldn't resist singing the well-known hymn;

"The golden evening brightens in the west;
Soon, soon to faithful warriors comes their rest;
Sweet is the calm of paradise the blessed.
Alleluia, Alleluia!"

and suddenly he fell silent, for on the back of his singing he could hear his echo from the other side of the valley in that quiet morning light.

Presently he arrived at the appointed place. He hushed the horse, secured him and wondered where and when he should fire that loving shot.

He climbed onto a ledge overlooking the pyre, but which had a good view. In his waiting he wondered how history would remember him. The Great Rana being bore by his advisors, followed by his two brides, the young one, and then the elder one, barefoot and unveiled. It isn't every day that common people get a look at a high-born woman, and it was told that the younger bride was one of exceptional beauty, and, of how an unknown madman......

He steeled himself. This was going to be a great tamarsha (show). About an hour later he heard a humming noise. It was the beginnings of the crowds come to look. Soon the place was overwhelmed with a seething mass of city dwellers, all eager to feast their eyes on the younger bride's beauty. Then it went quiet, and the hero was almost boxed in by the crush.

And then they heard it. The procession was on it's way.

It was quite some time before there was a real noise, the sun was now up, and it was going to a hot day. A great cheer went out from the awaiting people around, making it easy so as the shot was not to be heard. However, he was wedged tight on the parapet and his companions would be sure to see him take aim.

Then they saw the bier, and an even louder shout was heard. It was flanked by two elephants, obviously obscuring what was coming behind. The elephants passed and there she was, her little head held regally high, open and unveiled. At only 16 she was taking it rather well, thought our hero, as everybody greedily looked at her classically Indian beautiful features, her slender body, covered only by a Sari, but wearing some of the most magnificent jewelry ever seen. But where was the other Princess?

His thought was distracted by somone pulling on his arm, and turning around saw the uniform of a palace servant. He had been discovered! However the voice he recognised. It was the Hakim dressed in the robes he had made, pressing him to follow. This he did, down a staircase cut from rock, and into a large room. There he found his guide and the horse master, but he saw only one. She was standing by the chik (bamboo curtain) and he very nearly lost control and took her in his arms, but just in time remembered that none of his group actually knew the truth.

She turned to look at him and her face was one of stone. He was rooted to the spot. Could this really be her? Her features were still the same but she looked so...so thin and alien . She resumed her gaze onto the scene below them. The Hakim's explanation of the situation was simple. They had learned that the elder princess was NOT to be burned on her husband's prye, but made to watch her sister, and then her eyes were to be put out. He hadn't noticed before but in the corner there were four more people, one of them dead, plus a hot brazier with a poker in it. His face went red with fury. The Hakim stopped him. They had learned where this was to be done as the younger princess had told the Hakim in a moment of grief.

They had put the uniforms on, actually arrived with the cortege, and came upon the place exactly as told. The Hakim, being a doctor, disposed of the guard silently the only way he knew how. He had put a dagger through his eye. From then it had been easy, but they had to find the Sahib.

What a relief, he thought, so our hero called to everyone to escape quickly before the alarm was raised, but the Princess didn't move. He went over to her.

"Don't you know me, Larla?"

She turned to him. It was her sister, the younger bride. She had always been terrified of fire. He replied she didn't look it.

"It is just a show for her. Once she sees those flames, she will be absolutely mortified with terror"

" What shall I do?"

" Do for her what you would have done for me. "

He looked out. He was now lower, but further away.

"'Tis all of forty paces. " he thought.

She must have read his mind.

"Do it, please, if not for her, then for me."

He looked around.

"She is the Rani, Sahib" the guide said.

He sighed, took his hunting knife, and cut a gap in the chik large enough for a revolver, but small enough not to be noticed. He peered out. The cortege had stopped, and all was quiet . His fears returned about the sound of the shot.

The Rana was placed on the pyre, and the Rani followed. The Palace advisors now began to remove the jewelry from the little girl, after all, THAT must not be burned. That finished, she lay by her husband, and cradled his head on her tiny thigh.

"NOW!" the elder princess urged. " Once she sees the fire all the show will be over"

He waited. The young heir, as chosen by the advisors of course, was given a flaming torch. Being only five, he nearly dropped it.

Only when the pyre had been touched with the torch, and the tinder-dry wood laced with spices was ignited, did something happen.

The crowd roared, and the little girl on the pyre looked up and saw that it had begun. Her face a mask of horror, she stood up, and looked in panic all around her as the fire was already singeing her beautiful long hair.

He took aim and fired.

It sounded deafening in the room, and the little girl on the pyre threw up her arms in apparent grief and collapsed onto her husband. The crowd roared approval.

With that, the party, four men and a girl, raced from the room. The guide suggested killing the three other palace guards, but the Hakim would not allow it. They ran outside to the awaiting four horses, mounted and took off in the middle of the tamarsha, heading for the secret gap in the uncrossable foothills.

They hadn't got 100 yards when a shot, a rifle shot, was fired from behind them . At once the Hakim regretted not having killed the three guards.

They raced on, hero and heroine on one horse, the other three with one each. But the ground was stony, their horses not used to it, whereas the Rana's horses had been trained to run in such country. The chase was on. They were 200 yards from the passage when the horseman realised they wouldn't make it, so he turned full circle and ran head-on into the pursuers, bringing them down with himself, and the passage, guarded by a huge rock, was upon them. They took refuge behind it. With four muskets between them, it was decided the princess's safety was most important, so the Hakim would remain behind, even though he was not used to guns, the rock providing much cover.

This done, the guide and our two lovers, went through that same narrow passge that had been traversed only the day before, it seeming a lifetime ago. Slowly the sound of the gunshots receded. They travelled until the guide thought them safe enough to stop, and decided to go back, leaving our two alone.

During this time, she told of how her sister had mistreated her badly and did not want her sharing the Rana's bed, being a half-caste. Her sister had become jealous and had her locked away with little food. When the Rana became ill, it was decided that the elder sister would not be allowed to "contaminate" the pyre, and, as a punishment for being half-Russian, the death of the younger bride was to have been the last thing she saw.

Again, there was rage in him, but his rage turned to concern when there was no sign of the guide, and there was the smoke from a camp fire on the horizon. His concern grew as the guide was just that, being the only person who could lead them over the hills

They fell asleep waiting.

When they awoke, the guide was cooking chuppatis.

He told them he had spotted the Rana's men early and had returned to the passage by another route.

The Hakim had died defending them.

Knowing the country better it was soon a matter of time only before the guide overtook the enemy, who were ignorant of all the paths, to get back to the sleeping couple. But they still had to hurry.

Six days later, they found themselves in familiar country, and their guide left them with heartfelt thanks. But how to explain the Princess? She could never be a Princess again, and she was a widow. They could not openly marry, as it would arouse both distaste and suspicion and may lead to them to certain death would the Rana's spies find out, and they would.

In despair, they took a small merchant ship, the captain of whom was known, just to lay low. During the voyage they were married by the captain, as they made their way north to Peshawar. However, it was totally unthinkable to present himself there as the husband to a widowed Hindu Princess.

He has once been told he was "two people in one skin", with loyalties neither with England or India, to the effect that he would always have to take sides.

They realised that he had now become a third person, himself, with his love becoming the other half. Having been put down near the borders of Afghanistan, it came to pass that to find that "Third" country, the one that would be theirs and theirs alone, would make everyone happy. So on they trekked on horseback, through the desolate but lonely passes, to look for it.....

....and rumour has it, they found it.

Just what is a Quark anyway?

Apart from being a character in Deep Space Nine, a "quark" is a very fundamental building block of nature. The best way to explain what they are is to tell how they came about.

It was the 1960's, and the people at SLINAC (Stanford Linear Accelerator) and CERN (Centre pour European Recherche Nuclaire) thought they had finally got the big picture of atoms, nuclei and stuff. But the machines doing this smashing suddenly produced some particles never before seen. They behaved differently from the others and were labelled "strange". They disappeared very quickly into energy according to E = mc**2. None were present in nature.

Where did they fit in? The whole kaboodle could be explained by a whole new way of thinking: that protons and neutrons themselves were made up of something even smaller. Indeed, scattering experiments (firing the particles at themselves) seemed to indicate, by the pattern alone, that there was something else inside. Electrons had nothing inside them. Scattering experiments with them told us they acted like true "point" particles.

But just what was inside the protons and neutrons? They settled on the name "quark" and the proton and neutron had three each. One had two "up" quarks and a "down" quark, and the other, two "down" and an "up". "Up" and "down" being arbitrary names having nothing to do with the normal meaning, they might as well have called them "Laurel and Hardy", or even worse,"Bill and Ted".

But what were the strange particles? They reasoned that these must have another "flavor" of quark inside (nothing to do with taste!), which they called "strange". They predicted other particles to turn up with other combinations of up, down and strange, and sure enough, as energies (accelerator energies) went up, these predicted particles turned up. Then they reasoned, "Why stop at three quarks?" - there could be more. They tentatively predicted a fourth, and they called it "charm" (!), and this would produce around 33% more new particles. The lowest energy of these was called the "Charmonium", and yes, it was found, along with all the debris. It was essentially a quark-antiquark pair, or "bare" charm.

How many more were there, and where would it stop? For reasons not appropriate to be given here, they figured out there were no more than 6 in total, and they called the last two "top" and "bottom".

These quarks were getting heavier and heavier and were very hard to produce, but the last one to be detected was bare bottom, in the mid-80's.

It has to be borne in mind that it was never the quarks they saw, just big particles with quarks inside. The question arose - why can't we get a quark on it's own. It would be pretty easy to detect, as each had either 1/3 or 2/3 of the charge on the electron. However, not one had been seen,

The reason they gave was astonishing. Up till then the forces of nature were gravity, electromagnetism, the weak force (only affects electrons and neutrinos), and the "strong" force, which keeps a nucleus together against the static electromagnetic repulsion of the protons.

They reasoned that inside the protons, the strong force was the real strong force, much stronger than had previously been thought, and it was this that was "holding" in the quarks, as if they were tied to it with elastic bands. ( see previous posts for more info). Try to pull a quark out, and the elastic gets more stretched, as it gathers energy from the "pulling", until SNAP it breaks in the middle, not with a loud noise, but a new quark-antiquark pair, matter from energy (E = mc**2). The quark goes back into the old particle, and the new antiquark makes another new particle with the quark just pulled out!

There was another problem with this scenario. It goes back to an old rule developed by Wolfgang Pauli - no two particles can have the same description and be at the same place.

But in the proton there were two "up" quarks!! They figured. that the strong force, like electricity, had the equivalent of "charge", but whereas electricity has two, plus or minus, the strong force had three, and they called these three "color" charges (nothing to do with rainbows). So, in a proton, an "up " must have a different color charge to the other "up".

Because of this "color field" they named the theory Quantum ChromoDynamics.

Believe it or not, that was an introduction. I have left much out.

There IS truth out there!

The Angry Bits

This blog has now come Full Circle (as M Palin would put it) as I am now at a similar position as I was when I started this thing. I now work at CERN again. My permanent post is at Incheon University, but I am the (silent) manager of a project at CERN called the SSA.

The SSA has nothing to do with what CERN is about however.

CERN has been operational since the 1960's, the World's biggest scientific collaboration. It is perhaps the largest telescope in the world. We use bigger and bigger telescopes to see into space, which by virtue of being far away, details are small. Similarly, CERN represents a telescope devoted to "seeing" the very small, by virtue of them actually being small. We call the largest one the Large Hadron Collider, the LHC.

It bashes bits together and has already been under scrutiny in this blog (Three jets are better than two). It makes Hadrons.

A "Hadron" ( pronounced " Hey! - dron!") is a particle bigger than a proton or neutron. It is important to remember that everything we see around us is made up of only protons, neutrons and electrons. "Hadrons" are created by smashing protons together to get "angry" bits - bits that don't belong in the real world. We called them "strange particles" at first, because we didn't know what they were.

Now we know that all the evidence fits like a jigsaw puzzle into thinking that all hadrons (protons, neutrons, plus angry bits) are made up of three new particles called "quarks" (from the book "Finnegan's Wake"). These quarks build up all the particles, except the electrons which seem to act like they have nothing inside at all.

All these particles are very small and behave unlike normal particles, ie billiard balls. It was first realised they were different by Neils Bohr. This was then made into a formula by Prince Louis De Broglie, and then finally made rigorous by Schrodinger et al. as Quantum Mechanics.

The basic concepts behind quantum mechanics are thus: 1. All particles also behave like waves of something ( they give answers that can only be explained by considering them as a stream of waves. "Waves of what?" I hear you say - the answer to that only comes when you understand the math behind statistics and wave mechanics - trust me) 2. You cannot know with infinite accuracy all things at the same time. 3. A new thing called 'spin" has to be called for to explain some of the things we have seen (It is NOT real "spin" as in going round and round, but just another number (we ran out of names to call these things early on)) 4. Some of the effects we have seen can be explained by a particle description AND a wave description , depending on the way we look at it. 5. These things only happen when the particles in question are very small.

So what does CERN do? Simple, we bash the bits together to get new ones, well, we used to. We have just about gotten sick of all the new bits we get out of our collisions, and now we refine the bashing to get the bits back in more useful ways. It's a bit like a car crash, we now know what bits to expect out of the car crash, but now, we bash them together at different "angles" to see which parts survive best at those angles.

The upshot of which is that we are continuing to refine the theory (Quantum ChromoDynamics or QCD) so as to predict next which bit of the engine will come out of our crash and which way it will go.

If it comes out the right way, we predict stuff about the wing mirrors, etc, if not, and we get more angry bits, we go back and try again with a different version of the theory to explain what happened before the prediction went wrong.

As for the SSA, it is just a tool to make the data collection easier, nothing fancy.

The final upshot is that there are no more angry bits any more.

Are you Still Uncertain?

This post is aimed at someone on the Chess site www.chess.com who told me I don't know the Uncertainty Principle.

In short it is this:

Dp.Dx >= h/(2*pi)

where

Dx is the uncertainty in the position of a particle

Dp is the uncertainty in the momentum of it

h is Planck's constant which is:

6.626068 × 10^-34 m² kg / s

pi = 3.1415926.......

and ">=" means "greater than or equal to"

The Uncertainty here is best explained with reference to my car example in the Calculus post. If the car is travelling at 30 kph, it is not travelling at EXACTLY 30 kph because of bumps in the road, uneven tire pressures, wind, etc. A more accurate statement would be "approximately 30kph", or better still, "somewhere between" 29kph and 31 kph. The speed would then be 30kph "give or take" 1 kph. The "1kph" is called the "uncertainty".

Thus Heisenberg's Uncertainty Principle says that the uncertainty in position, multiplied by the corresponding uncertainty in momentum, can be no less, even in principle, than a certain number (h/(2*pi).

The astounding thing to come out of this is that there is even a number.

Ok, so the number is very small, and has often been quoted as the "measurement" of how small quantum mechanics has to be in order to effective.

This is deeply related to the double slit video posted earlier. If you see the electron then the photon's momentum in order to see it, and it's uncertainty, is enough to raise the uncertainty in the position of the electron so as to destroy the diffraction pattern .

The uncertainty relation has its roots in wave theory, where a wave "packet", caused by many waves of similar wavelengths superimposed, results in a bunch of waves, travelling at a particle's speed (the group velocity), but the waves themselves (the phase velocity) travel at a speed much greater than that of light. It's dealt with here:

http://gnabgib.blogspot.com/2005/06/groupie-or-just-phase.html

The uncertainty in the wavelength is equivalent to the uncertainty in momentum, according to the De Broglie formula (wavelength of "particle" equals "h" divided by momentum), and the uncertainty in the position is equivalent to how "big" the "bunch of waves" is.

What does it teach us? It teaches us that we cannot measure everything.

This is something that the books don't teach, and is a piece of knowledge only available through complete understanding. That means, you can find it nowhere on the web either, unless you ask Mr Feyman, who would probably say the same, but unfortunately he is rather indisposed at this time.

The fundamental obstacle that faces us all in quantum mechanics is trying to envisage "particles" as "waves". It did in 1924 and still does now.

Little Shimmy

Let's just take a sidestep for a minute.

Science is wonderful because:

1. You get liquids climbing out of their own containers (Liquid Helium does this with no help at all!)

2. You get objects with so much stuff in them, that light cannot escape (Black Holes)

3. There is a law which states that time cannot be reversed (2nd law of Thermodynamics)

4. The faster you go the heavier you get (Relativity)

5. The faster you go the more time slows down for you (Relativity again)

6. There is more energy in a grain of salt than the entire energy output the Earth has ever produced (nuclear fusion)

7. Stuff can be created out of nothing (E = mc2 and the Heisenberg Uncertainty Principle)

8. Light comes from electricity (Maxwells equations)

9. Water in a fission reactor glows blue (Cerenkov radiation from electrons)

10. DNA's sequence is actually a code for copying itself (genetic code)

11. The entire universe is made up of only 12 particles, plus the photon (only quarks and leptons exist - everything else is made up from them (Quantum Chromodynamics and ElectroWeak Theory))

12. "Science is not only more beautiful than we know, it is also more beautiful then we CAN know"

(with apologies to JB Haldane)

Dur Khaima (part four)

Luckily for our hero, he became stationed at Peshawar, a
frontier town on the borders of Afghanistan, where there
was always plenty going on, taking his mind off what had
transpired.

But he never forgot her, and often would idle the time
away disconsolately thinking about what might have been,
and the cruel fate that had been dealt to them both.

His love, in her own way, had expressed that it would be
much worse for her than for him, since she was confined
to a Palace, whereas he was still free, with time to
forget her. "Never" he would say to her, " I will never
forget, and if you ever need me, Larla, I will come. If
I am not dead, I will come. "

However, time passed, and he spent his days, fighting
campaigns, indulging in British India Society Circles,
and as a secret agent (his upbringing, swarthy
complexion, and mastery of the vernacular, allowing him
to be mistaken for an Afridi, one of the border tribes
of nearby Afghanistan).

However, he never could quite fit in with either India
society, nor British Society. Some of his "chaps" said
he was like "two people in one skin".

As a result, he was branded a "dull dog" and often
ostracised by his own, and one day, incurred the wrath
of his closest Indian friend by pretending to worship
Allah by facing Mecca and praying, a habit he had had to
learn when in Muslim disguise.

Then shortly after, he had word through the famous
Indian grapevine, from the Hakim who had once treated
the despot Rana with boils. Apparently, the younger
bride, having no faith in the Rana's doctors, had called
for him from her own country, and the Hakim, knowing the
Sahib (Indian for Englishman) well, had left him word
via his servant.

The Hakim was in a place close to an army Cantonment
only 100km, as the crow flies, from the city where his
love was. He pressed on with all dispatch to get there.

The Rana was ill, desperately ill, he was told, and the
custom of Suttee was still practiced there, but being so
far from British influence, the Laws were largely
ignored there for the same reason the Rana tried to
double-cross them in the first place.

The term "Suttee" literally means "to go within" and as
kings (Ranas) were traditionally burned on a funeral
pyre after death, Suttee decreed that their living wives
would join him there to be burned alive ("to go
within"), hence the prohibition by the "Ruling" British.
Normally widows are "put away" into seclusion as being
bad luck. It is widely held, however, that some Munshis
misinterpreted the "go within" to not mean "go within
the house" but to "go within the flames".

So, the Hakim was on his way the Rana's City, and
naturally, if any news of the elder bride could be
relayed, it would be a great relief.

The Hakim and the Sahib finally devised a method of
communication using pigeons carefully hidden in a secret
compartment below the Hakim's cage that he used to carry
live chickens, as he didn't trust the Rana's food
markets. If there was any news, a pigeon would be sent
with a message tied to its leg.

Thus satisfied, the Hakim was allowed to proceed, and
yet another anxious wait followed for any news.

Weeks passed, and then more weeks, until one day, there
was a flutter of feathers at the verandah.

A pigeon.

With some haste, the Sahib removed the message and to
some relief, his girl was fine, but to his horror he learned
that the Rana was dying.

He was aghast.

This was the worst possible news. It was at that moment
he decided to go back to the City, but not as a Sahib,
but an Afridi. He hired a skilled horseman and a
knowledgeable guide, bought a fiery mare and started off
over the barren hills between them and the Rana's City,
a route never usually travelled by ordinary means.

The journey was not easy, but the guide seemed to find
paths where there appeared to be none.

Five days later, they came upon a seemingly solid wall
of rock. Without hesitation, their guide headed straight
for it. Closer inspection revealed a narrow cleft not
visible from afar, and into it they proceeded. The
passage through the rocks was so narrow, that at one
point one of the horses nearly became wedged. One hour
later, they emerged into a clear evening sky at the top
end of the very valley the bridal camp had been lured
into almost three long years ago.

Immediately they launched into their plan, that of
mingling with the adjoining local farmers, out for the
day grazing cattle and now returning eagerly for the evening
meal. Three new faces amongst many were not questioned.

The evil in the place was still as permeating as ever,
as they made their way, as unobtrusively as possible, to the
Hakim's house, entering separately so as not to arouse
suspicion.

The Hakim was extremely disturbed to see them there, as
if ever discovered it could only mean a swift death from
a convenient "accident", especially for the Sahib who
had entered secretly and not as an officer.

However, this was only part of the Hakim's deep concern.

There was far more terrible news. All four of them knew
that Suttee was still observed there, but the Hakim's
next five words cut like a knife through our hero's
heart.

"The Rana will die tonight".

Dur Khaima (part three)

After many hours of soul-searching about possible avenues for their future, the unfortunate guy reluctantly agreed (secretly, on further rides) with his love that the wedding must go ahead.

During this time, the enormous Bridal Camp was approaching the territory governed by the soon-to-be-wed Rana, and preparations far outweighed him seeing his love even secretly.

Added to this, his problems became far worse when upon their encampment deep within the Rana's influence, they found themselves virtual prisoners in a deep valley heavily guarded by manned Fortresses armed with cannon.

Then came the real blow. The Rana subsequently demanded almost twice the bride price previously agreed as compensation for the expensive ceremonies he would have to take for marrying a half-caste, the Elder Bride, as she was one-quarter Russian.

Many Official meetings ensued, during which he discovered that the Rana did not look the 40 years he was supposed to, but more like 70, owing to his opium addictions and countless other vices. Moreover he was apparently very sick.

This so outraged our gallant British Officer, not only in principle but because they had openly referred to his love by the insulting term 'half-caste', that he did all in his power to try and dissuade the Rana from any action. But the Rana didn't care about threats of being reported to the British Authorities, as his state was so far from the nearest Political Officer that it would be months before any decision, let alone reply could be made.

So the love-lorn guy did the only thing in his power : he called the Rana's bluff. In the dead of night, they all sneaked out of the valley, 500 elephants and all, risking being fired upon by the cannon.

Our guy was banking on the fact that the Rana would never risk firing upon such distinguished company, as if and when the British got to hear of it (and they would), they may leave a garrison in the city, and this was the last thing on his mind.

Even while the Rana and his subjects were debating this, the bridal camp was nearly half way out of the valley, and by morning, they had made a new camp, being politely greeted by the Rana's entourage, as if nothing untoward had happened. In fact the services of the Officer's doctor were required, as the Rana had been overcome with a serious attack of boils. The doctor was despatched and subsequently easily cured the boils, and our hero turned his mind to other things.

Once again, he tried to dissuade his girl not to go through with it, and this time he was so desperate he requested a private meeting right in front of her uncle's eyes. Only by virtue of his heroic deeds was the meeting allowed so close to the wedding. His uncle physically gasped with shock when he witnessed their manner of greeting for the last time.

He tried every argument he could possibly think of, but she would not change his mind. Her reason was simple. It was her sister, the younger bride, the 14-year old, whom would find life hell if she was companionless. This she could not allow, and no amount of pleading or anger or even emotional blackmail could reverse her decision.

He had lost her. To an ugly husband who didn't love her, and a prison in the Zenana quarters in a place full of corruption and vice.

He turned away, looked back with one long, last look, and left the tent.

Being a British Officer, the next day he had to put all this behind him, and watch dispassionately, as the Love of His Life was married to someone else right before his eyes.

However, as he was later to find out, had he known the Rana better, it may have been better for them to take their chances and run away after all.

He wants to leg it but can't

A guy has been banned from the olympics because without legs he is better.

Story here

http://news.bbc.co.uk/sport1/hi/olympics/athletics/7141302.stm

Where is Steve Austin when you need him?

This guy does not need him. I myself would be happy at my victory!

The mere ruling means he is superior to us. Good for him, I say!