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Tuesday
Nov022010

The Overwhelming Binding Force

At the most fundamental level, the bulk of the mass of the stuff that we are all made of is in the nuclear force. Physicists call it the Strong force; and it is the glue that binds the tiniest constituents of matter together. An atom is comprised of a cloud of electrons with a dense nucleus of protons and neutrons. Most of the mass of the atom is in this nucleus. The protons and neutrons have substructure too: they are made of quarks. The quarks are bound together with a peculiar force known as the Strong (or nuclear) force; and it is the residual force from this setup that binds the neutrons and protons together into the nucleus. The energy stored in this glue accounts for most of the mass of the atom! when you break apart a nucleus, you release the energy and you get an nuclear explosion - or you power up the Sun. 

The Strong force is an unusual force law. All other forces in Nature share a common intuitive attribute: when you separate two objects bound by a force, the strength of the interaction gets weaker with larger distances. For example, gravity gets weaker as you go up in altitude away from the earth. Far enough away from any planets and stars, you basically are free from any appreciable gravitational pulls. The Strong force behaves in the opposite manner! Quarks - held together by the Strong force - become more tightly bound when you separate them… it is as if there is a spring joining the quarks that gets stiffer with larger quark separation. This is called confinement - quarks are confined into the protons and neutrons. What if you try to really push the limit and yank a quark away? As you try to do this, Nature kicks in with a vengeance and creates new quarks from the energy stored in the nuclear binding; the new quarks get dragged with the quark you are trying to yank away - just to make sure you cannot separate the pulled quark! Quarks hence always come in the company of other quarks - with nuclear glue holding things together. You just can't yank one away and stare at it on its own…

Due to this unusual attribute of the Strong force, it is very very difficult to do computations with it. In most of physics, one gets a computational handle on complex physical systems using a basic and efficient principle: start with a simpler setting which you can tackle without loosing your hair; then, assuming that the complexity is a small correction to the simpler base, apply a systematic scheme of approximating the problem. Depending on how much precision you need, you can compute additional small corrections to the simpler setting progressively and algorithmically. This is a rather very successful strategy and allows one to handle very complex systems systematically. When you try this with a system of quarks interacting with the Strong force, the whole process blows up in your face: the Strong force is rather strong… the strong binding force between quarks that you are trying to separate cannot be approximated as a simple system plus small corrections. You need to solve the whole damn problem - which is mathematically intractable. This theory describing the Strong force is known as Quantum ChromoDynamics, or QCD. The best one can do is to use a computer to do numerical simulations of the problem - this is known as Lattice QCD. Lattice QCD does work very well, but is certainly less gratifying than understanding things through the good old technologies of the paper and the pen - in the company of a lonely theoretical physicist.

The accompanying first video gives a quick overview of the atom and its nucleus - and a bit beyond. The Strong force is sensitive to an attribute of the quarks known as "color"; basically a cute term to account for the fact that this attribute comes in a triple: red, green, and blue. The Strong force assures that quarks are always held together in "colorless" combinations: three quarks with colors red, green, and blue; or two quarks with a color and an anti-color, i.e. red and anti-red. Yes, Strong colors come in pairs, the main color and its evil twin, the anti-color. Protons and neutrons are colorless combinations of three quarks. In total, we know of six types of quarks, mystically labeled: up, down, charm, strange, bottom, and top… Most of common matter involves only the up and down quarks. The top quark was discovered recently, about only a decade ago. And the glue that holds quarks together is made of a particle known as the gluon… there is a whole industry of particle physics for naming particles, usually involving physicists with a little too much imagination. For example, if Nature has a much longed for symmetry called supersymmetry (see previous post for more), we also have things called squarks… and  sgluons… 

The second video illustrates how we have learned all this stuff: by throwing particles at each other at high speed and watching what comes out (see post on the LHC).

Monday
Nov012010

When Galaxies Collide

We now know that our universe is filled with billions and billions of galaxies; each with billions and billions of stars in it - and often a supermassive black hole at its center devouring its stars... And when you have billions of galaxies, some will occasionally collide! As we image the universe, we see around us colliding galaxies at various stages of their collisions; we hence can reconstruct these majestic events - like a crime investigator reconstructing a crime scene. Through computer simulations, we can then model colliding galaxies and compare with observation. The first video shows a montage of a simulation superimposed with actual images from telescopes of colliding galaxies. The shear power and beauty of these cosmic dances should bring you to tears... 

Speaking of bringing you to tears, the second video is about our own galaxy's collision course with a neighboring galaxy, the Andromeda galaxy. Make sure you wrap up your life's to-do list as soon as possible...

Sunday
Oct312010

Renormalization

You are about to read about one of the most profound and beautiful principles in all of physics. It is simple, yet fundamentally important. It was formulated in the 1970's by physicist Kenneth Wilson. Wilson later on mentioned that he had thought about the problem for more than 10 years - during this period, he did not publish a single paper… the subject had consumed him. And in one year, he finally released several papers announcing his discovery and was immediately awarded the Nobel prize for the work…

Imagine you are to study a physical system that is rather complex, with many many constituents. For example, a gas in a box with numerous molecules bouncing around. You also happen to have several pairs of ACME magic eyeglasses that can make your vision immensely more powerful - each one progressively more powerful than the previous - allowing you to probe the gas in more detail. You first stare at the box of this uninteresting gas with your own limited vision and perhaps describe it with a handful of measurements: the strength by which the molecules are bouncing off each other, the mass of the molecules, and maybe a few others - all usually determined indirectly by measuring things like temperature, pressure, and density. You then write some equations that describe the system and use this new theory to make predictions. This is presumably a crude description because you could not see much details about the underlying dynamics. But maybe it's good enough?

Now, imagine you put on the progressively more powerful pairs of magic eyeglasses: you now can see more of the detailed interactions of the molecules and make new measurements accordingly. Does your previous theory of the gas change? There are two possibilities: your theory is "renormalizable", or it ain't. If the theory is renormalizable, you can then use your original equations to describe the more detailed physics you are now aware of; the only change you need to do is to tweak the handful of parameters that you originally had in your theory: the strength by which the molecules are bouncing off each other, the mass of the molecules, etcetera. The equations you wrote originally are otherwise unchanged. If you think about this for a moment, that is simply amazing! That means the details of the physical system are all tucked into a handful of parameters only… 

The other possibly is that your original theory is NOT renormalizable. This means that - as you probe more details of the system - you discover you need to modify your equations, perhaps add to them new physical parameters that you didn't need to previously to make good predictions. As you use more powerful eyeglasses, you may find that you always have to add new modifications to your theory ad infinitum - a plethora of new parameters depending on how accurate you want to describe the system. Still, for a desired level of accuracy, you can still write a bunch of equations and do physics. But this theory now is said to be "effective" - good enough to a certain precision but not beyond. This implies that you really do not understand the fundamental physics underlying the physical system; you just approximate things the best that you can. In contrast, a renormalizable theory can in principle be the ultimate most fundamental description of the physics at hand - an exact theory. 

Every physics theory in the world falls in one of these two categories (to be careful, it's actually three categories - with the addition of a possibility called superrenormalizability, but this is mostly inconsequential for our discussion). Interestingly enough, of the four known forces of Nature - electromagnetism, the weak force, the nuclear (strong) force, and gravitation - three happen to be renormalizable! All except the gravitational force… Thus, in reality, the accepted description of gravity - General Relativity - cannot be fundamental… From Wilson's amazing and general ideas, we know with certainty that we really do not fundamentally understand the oldest force law around us! We also know that our description of gravity will surely fail when we come across a pair of eyeglasses that can see down to 10 to the power minus 33 centimeters… And we know that - until then - we should be ok with using General Relativity, unless some other unforeseen mechanism (like extra dimensions… see previous post) kicks in.

The accompanying graph shows how the three parameters that quantify the strengths of the three renormalizable forces - electromagnetism, the weak force, and the nuclear force - change as we probe smaller distances (with more powerful "eyeglasses"). Higher energy on the horizontal axes corresponds to higher detail. Otherwise, the force laws do not change structural form! Adding supersymmetry to the mix (see previous post), one finds that, at some small distance of about 10 to the power minus 29 centimeters- all parameters unite in strength as shown… this is the notion of grand unification (see previous post for more) - that all three forces are different manifestations of the same force law!

 

Friday
Oct292010

Whither Supersymmetry?

All particles that physicists have so far discovered - the building blocks of matter and energy in the universe - carry a quantum mechanical property called "spin". The nomenclature is purposefully chosen to suggest that this property is akin to imagining tiny particles spinning around. However, this is not really a genuine picture since particles in quantum mechanics are fuzzes of probability - instead of tiny spinning billiard balls. Yet, this spin property of particles does behave very much like the good old notion of spin that we know and love - except for one important peculiarity: quantum mechanical particle spin is quantized… This means that, when measured, its value comes out as a discrete multiple of a universal number: spin 1, spin 2, spin 3, etcetera times the universal number. But it's more interesting than that. We also find particles with spins that are half-integer multiples of the same universal value: spin 1/2, spin 3/2, spin 5/2, etcetera. And nothing else. So, spin values arrange themselves on discrete levels - like the steps of a ladder - and come in two categories: integer spins and half-integer spins. 

These two classes have very different properties. Integer spin particles - called bosons - can be compressed together without resistance when there are no forces acting between them. Eventually, at high densities, they form an intriguing new form of matter called a Bose condensate. Superconductivity and superfluidity involve cooling things down to a point where such Bose condensates emerge - along with very peculiar macroscopic properties (see posts on superconductivity and superfluidity). Half-integer spin particles - called fermions - resist such compression: no two fermions can occupy the exact same state (this is known as the Pauli exclusion principle). The accompanying video shows a simulation of two fermions in a box. Quantum mechanically, the particles are simply probability lumps: red for high probability, blue for low. As the fermions are pushed together, they repel quantum mechanically; that is, there is no actual force law acting between these two particles! The repulsion is statistical in Nature. Notice in particular the interesting fringing pattern upon collision: remember these are supposed to be particles… that's quantum mechanics craziness for you (see post on visualizing quantum mechanics). 

All visible matter in the universe happens to be fermonic: for example, electrons, proton, and neutrons are all spin 1/2 particles. All forces of Nature are transmitted through the mediation of force particles: and all such force particles are for some reason bosonic. For example, the electromagnetic force is transmitted through a spin 1 particle known as the photon. These two classes of lego pieces of the subatomic world then have very different roles and character. A few decades ago, some theoretical physicists started contemplating the possibility that fermions and bosons may in fact be related; that there is a deep symmetry in the natural laws that connects these what otherwise are very different types of particles. For a lack of a better term, we call it supersymmetry. There is no experimental evidence for this symmetry yet. However, interesting things happen when such a symmetry is hypothetically considered. For one, one realizes that it is possible to talk about all the known forces of Nature as a single force law (see post on Grand Unification)… very elegant and perhaps very true. Another consequence has to do with understanding gravity within the crazy quantum world: string theory, the only theoretical framework that purports to combine gravitational and quantum physics - requires Supersymmetry to be logically self-consistent. While supersymmetry does not require string theory, string theory does need supersymmetry.

An immediate consequence of the existence of supersymmetry in Nature is the necessity of a plethora of additional building block particles of fundamental physics yet to be discovered. These particles are needed so as to be paired with the ones we already know in a manner that makes the catalogue of fundamental particles more symmetric - supersymmetric. The new particle physics accelerator in operation in Switzerland, the Large Hadron Collider, may be able to see some of these additional particles - and hence confirm the existence of Supersymmetry in Nature (see post 1 and post 2 on the LHC). The discovery of Supersymmetry in the next few years would undoubtedly be the greatest scientific discovery of the new century. But then, the century is rather young.

Thursday
Oct282010

A Cure For Insomnia

According to quantum mechanics, everything is possible - no matter how crazy! You can walk through a solid wall... A friend of yours from across the continent can suddenly materialize next to you at a very inappropriate moment... How about jumping from Los Angeles to the moon? Sure, why not.... Everything is allowed - all Nature cares about is probability. This is the real world, not some bad science fiction movie... We know quantum mechanics is correct from an uncountable number of experiments; even from the fact we're around: atoms making us up would collapse instantly without quantum mechanics...

So, how come the last time you slammed your head on a wall, it didn't materialize on the other side? Well, it's all about probabilities. Quantum mechanics tells us that Nature itself - at a fundamental level - is not deterministic: nothing is certain, everything can happen, and the only thing that mother Nature keeps track of is the likelihood of something happening or not happening. When an event is highly unlikely or highly likely, we effectively see it in a deterministic light - like we're used to: it simply doesn't happen or happens in a predictive reproducible manner. In reality however, there is always a chance to get surprised or shocked...

So, how can you estimate the probability of an event from quantum mechanics? Here's a crude but correct method that you can use to impress people in a bar. First, identify the relevant mass, length, and time for the hypothetical event. Multiply the mass with the length times length; divide by the time. Take this resulting number and divide by ten to the power minus 34 (that's roughly Planck's constant): make sure you use kilograms for mass, meter for length, and seconds for time! You can easily convert units using google: for example, you could type "convert feet to meter". Now, take the number you got, multiply it by minus one, and raise 2.7 (that's "e" for the geeks amongst us) to the power of this number: this is an estimate of the probability of the event! That's it, you now know some quantum mechanics! 

Let's give it a try. Say I am considering slamming my head on a granite wall; it has been a particularly long morning, didn't get much sleep last night, and need to wake up somehow. I would like to know the probability that my head will go through the wall. That would certainly make the day more interesting.  So, I need a mass, a length, and a time. My head is rather substantial in weight: maybe 20 kilograms? The wall is about 1/3 of a meter in thickness. With the speed I am planning to slam my head on the wall, the time will be around one second. So, let's put things together with a calculator. 20 times 1/3 times 1/3 divided by 1 second. That's about 2. Divide by Planck's constant, that's 1E-34 on a good calculator. We get roughly 2E+34. Multiply by minus one. That's -2E+34. Final step: raise 2.7 to the power of -2E+34. That's tiny tiny tiny; your calculator will probably just say zero or just blow up... This means I would need to hit my head on the wall many many (many) times to expect to have it go through the wall once... I better start right away.

How about the probability for an electron to just appear out of thin air? Crazy, but how likely is that? You can look up the mass of an electron on google: type "mass of electron": you get 1E-30 kilograms. Say the freaky electron moves a distance of an atom's diameter - a reasonable thing to expect in the world of an electron? that's 1E-10 meters. Say it moves around a percent of the speed of light: electrons can move fast. The speed of light is around 1E+8 meters per second. A percent of that is 1E+6 meters per second. So, the time it needs to travel a distance of 1E-10 meters is 1E-10 divided by 1E+6; that's 1E-16 seconds. So, put these numbers together on a calculator: you'll get a probability of 2.7 to the power of minus one: or 0.37, that's 37% chance for an electron to appear out of thin air! Not bad at all. You now see why the microscopic world is so crazy, and our macroscopic world is so much more predictable...

And here's a simple calculator you can use to play around with this idea:

Length in meters Time in seconds Mass in kilograms Calculated probability
percent
Wednesday
Oct272010

When Stars Explode

When a star exhausts its Hydrogen fuel by burning it into Helium, it collapses under its own weight. For small stars like our Sun, the star eventually fades away into a rather unremarkable object known as a White Dwarf - neatly placed at the center of a spectacularly colorful cosmic painting made of remnant star dust (see post on planetary nebulae). 

If the original mass of the star is large enough however, this collapse ignites the Helium - through nuclear fusion - and burns it into heavier elements such as carbon and oxygen. This process continues until the core of the star transforms into a ball of iron - with lighter elements surrounding it in layers like the layers of an onion. No nuclear fusion can burn the iron core. At that point, gravitational collapse takes on a catastrophic character and a violent (and I really mean violent) explosion tears the star apart - along with its neighborhood… The explosion can be dramatically witnessed from Earth as intense light and copious X-ray emissions. This is called a Type II Supernova and typically involves the release of an amount of energy equivalent to the detonation of 100…twenty five more zeros nuclear warheads… Another type of equally dramatic explosion that we regularly witness in the deep cosmos is known as Type Ia Supernova; this involves two orbiting stars in a dangerous gravitational dance - think of it as salsa gone wrong… in both cases, the space around the star ends up covered with star debris - evidence of a violent event in its past.

Whatever remains of the star after a Supernova further collapses until all the particles making up its atoms get converted to a single type of particle known as a neutron. Neutrons are electrically neutral but resist tight packing due to quantum mechanical effects I will talk about in another post. The end result is known as a Neutron Star - a dense ball of neutrons. This is a very very peculiar object: typically 50-100 kilometers in size, but immensely dense - heavier than our Sun… It can spin at very high rates, emitting a sweeping beam of X-rays and other cosmic radiation from its poles - like a lighthouse beacon. We can see these beams from Earth and measure the spin rate; we call these objects Pulsars.  This is the end game for a star that was originally larger than our Sun but was still lighter than five times the solar mass. For even larger stars, the intense quantum mechanical pressure generated from packing neutrons is not enough to stop the collapse. The result is instead a black hole (see post on black holes). The largest Supernova recorded so far occurred in 2006; the mass of the original star was about 150 times that of our Sun…

The first accompanying video gives a brief overview of supernovae, and talks in particular about the Type Ia kind. The second video talks about neutron stars that arise from Type II supernovae. I also prepared a short slideshow of images of famous supernovae in a third video. The soundtrack is titled "Chinar Es" - roughly translates to "You are glorious" - an ancient Armenian tune composed around year 700 A.D. by Nerses Chnorhali. I titled some of the slides with the year of the star explosion.

 

Tuesday
Oct262010

Visualizing Relativistic Squirrels

Over the years, I've noticed that squirrels living on the campuses of universities and colleges are somewhat "troubled". Imagine you come across a deranged squirrel and you see it suddenly racing towards you at 10 kilometers per hour (based on a true story…). For some reason, you decide to run towards it at 10 kilometers per hour (in reality, I ran faster and in the opposite direction). How fast will you see the squirrel attack you? Well, 10 plus 10, that's 20 kilometers per hour. This is the good old velocity addition rule that we all instinctively relate to. Let's change things a bit. The deranged squirrel now runs towards you at three quarters the speed of light… you run towards it at three quarters the speed of light. How fast will you now see the squirrel attack you? Three quarters plus three quarters, that's 1.5 times the speed of light, right? Wrong! 

The velocity addition rule we are all used to is only approximately correct and works well for speeds much much less than the speed of light (which is 300,000 kilometers per hour). When the speeds involved get more than 10% that of light, the usual velocity addition rule will give you the wrong answer appreciably. The correct answer is obtained using the Special Theory of Relativity. Developed in 1905 by Einstein, Relativity proposes that the speed of light is a law of Nature; and that laws of Nature should appear the same to all observers moving with constants velocities. These are the two postulates of Relativity. They were inspired by the development of Electromagnetism a few decades before - light is after all an electromagnetic disturbance. If the speed of light is to appear the same to different observers that are moving around, you can't then just add velocities… a carefully revised thought process can then tell you that there must be an upper limit on speeds in Nature - a speed limit given by the speed of light. In short, no information can travel faster than the speed of light. 

As a result of the existence of a bound on speed, there is always a time lag in the relay of information. When you are imaging the world with your eyes, light is reaching your eyes from all directions to give you a picture of the world. If you start moving around at speeds comparable to that of light, different objects around you - located at different distances - may start projecting their images in an appreciably asynchronous manner - with a time lag related to how far away they are from you at different points in time. Basically, the light from the objects is playing catch-up with your fast changing position. This creates elaborate distortions of the world as you perceive it. For example, if a squirrel whizzes by you at half the speed of light, you'll see the squirrel 87% thinner… So, how would then the world look like if you were able to travel at speeds near that of light?

The accompanying video was developed as part of a PhD thesis by a graduate student in physics. It is an actual genuine simulation of how things would look like if you were to travel at high speeds. The video has a voice over (a really really bad one), but it would still help if I give a brief guide of what you are about to watch. On the top right corner of the video, you will sometimes see numbers like 0.280 c; this simply means 28% of the speed of light - it's an odometer readout. On the lower left corner, you will see the greek letter gamma (looks like a V) next to a number; this is called the gamma factor and tells you how abnormal things are getting compared to the usual perspective you're familiar with at slow speeds: the closer is gamma to one, the more "normal" are things. For example, the waistline of the squirrel mentioned earlier is given by its original size divided by gamma; for gamma equal to one, there is no distortion. There are three visual effects in Relativity that one needs to consider when trying to picture how things look like at high speeds: geometric aberrations, the doppler effect, and the intensity effect. The video turns these effects on one by one to demonstrate things in a more manageable manner. Geometric aberrations distort the shape of things, like the thinning of the squirrel's waistline. The doppler effect shifts the color of light that you see according to the speed you are moving with. And finally, the intensity effects concentrate the light around you to a point in front of you - along the direction you are heading. Now, time to play the video. Prepare yourself for a real freaky show. Remember, this is absolutely realistic, it is a simulation not just a random animation. I think you'll agree that the first astronaut who will experience these effects will need to change underwear soon afterwards.

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