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The Trouble With Small Things

One of the most enigmatic particles of the subatomic world is the so-called neutrino. The neutrino comes in three flavors and plays a central role in the physics of one of the four fundamental forces of Nature - the Weak force. It is prevalent in many radioactive processes and exists copiously all around us. For example, our Sun spits large amounts of neutrinos at us. As you are reading this, neutrinos are passing through your flesh and bones like knife through butter… if you feel a tingling, it's either neutrinos or the broccoli you ate yesterday. 

Two interesting things about neutrinos set them apart from the other particles of the subatomic world. First, they are extremely light. In fact, they were thought to be massless for a long time. Only recently was it discovered that they have tiny masses. Tiny numbers in physics are psychologically troubling. Usually, when something is extremely different from everything else around it - like very very light neutrinos compared to protons and electrons - you would worry that something deep is at work, something that you need to understand better. The extreme lightness of neutrinos is such a philosophical puzzle: it doesn't point to an actual problem in our description of the physics, but it suggests that our description may be incomplete or missing a deep principle at work. 

The second unusual attribute of neutrinos has to do with the weakness of their interaction with the rest of the matter in the universe. Neutrinos travel near the speed of light and just go through virtually everything in the universe. To neutrinos, we and the Earth are mostly transparent. It is hence very difficult to detect neutrinos. Physicists have to build large underground tanks filled with water and live like hermits in caves hundreds of meters below the surface to detect neutrinos… at least that is the official excuse for this lifestyle. 

Neutrinos also play an important role in understanding the cosmological history of the universe. They may for example be the source of the mysterious dark matter that pervades galaxies. And they are crucial for understanding how our Sun powers itself. The first video accompanying this post is a short one and talks about the basics of neutrinos - particularly the ones coming from the Sun. The second video is rather lengthy but very well done; and it goes into the physics of radioactivity and neutrinos in great detail - for those of you trying to understand that tingling you feel now and then...


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).


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.



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.


Grand Unification


Grand Unification has been the holy grail of physics for about a century. It is the belief that all forces of Nature are in reality different manifestations of the same force; that there is a deep unifying simplicity underlying the natural laws that we would be able to see if we could only unlock the key principles at work. There is good reason to believe that this belief is not an unrealistic one. 

By the mid 1800's, physicists had achieved a decent understanding of three forces prevalent in the world around them: gravity, electricity, and magnetism. Gravity was the earliest to be discovered and the most familiar one. Magnets had also been studied extensively by that time and were known to be sources of some mysterious non-gravitational force. And electricity had just been discovered through a series of experiments. Static electricity - responsible for the shock you get when you grab a door knob after petting a particular fluffy cat - had been identified even centuries before. 

In the late 1800's, a dramatic development occurred in theoretical physics: a physicist by the name of James Maxwell demonstrated on paper that the electric and magnetic forces are really the same force, the "electromagnetic force". They can simply be related by changing your perspective: if you just move around with respect to an electric force, you will see a magnetic force as well… The significance of this development was two-fold: it was the first time that we realized that Nature can fool us by appearing more complex than it actually is; and it was the first time that an entirely theoretical and conceptual process lead us to new physics. These two novelties were to become permanent themes in physics from then on.

In the early 1900's, two more forces of Nature were to be discovered: the "weak force" and the "strong force". Both ruled the world at very small distances - where quantum mechanics takes over. Their discovery had to be preceded with some understanding of the crazy quantum world first. The weak force is associated with radioactivity, while the strong force is responsible for nuclear power. And by the mid-1900's, theoretical physicists realized that all four of the known forces - gravity, electromagnetism, the weak force, and the strong force - are related to a series of profound symmetries within the natural laws, the so-called gauge symmetries (see previous post for more). But the four forces still looked very different. Can the success of uniting the electric and magnetic forces of the mid-1800's be replicated once again?

In the 1970's, another dramatic development demonstrated that this was indeed the case. A couple of theoretical physicists managed to show that the electromagnetic and weak forces are actually the same force law in disguise, the "electroweak force": one down, three to go. Their proposal involved the prediction of a new particle, the Higgs particle (see post on the God particle). This particle is yet to be discovered (however see post on the LHC), but the circumstantial evidence for the correctness of the electroweak theory has been so overwhelming that the authors of the work were quickly awarded the Nobel prize. 

So, we're down to three forces: gravity, the electroweak force, and the strong force. In recent years, we have learned that it is indeed very possible to unite the electroweak and strong forces as well - we call these frameworks GUTs (Grand Unified Theories). However, this program has many directions, as well as its share of problems. Only with more experimental data can it get pinned down definitively. But conceptually, there should not be any serious obstacles preventing us from uniting the electroweak and strong forces; unlike the case of their sister force…gravity.

So, that leaves the oldest force law, the gravitational force, the orphan of the story. Unfortunately, this last step of unifying all the forces of Nature is a major one: it involves resolving serious inconsistencies between gravity and quantum mechanics. To date, the best known candidate theory we have to address this issue comes in the form of String Theory (see previous post for a bit about this subject; more to come in due time…). It is however the case that testing this benchmark experimentally may come either centuries into our future or tomorrow… It feels like we are in striking distance of Grand Unification, yet the last hurdle is indeed a humongous one.

Accompanying this post are two video excerpts, parts of a longer documentary that explores this narrative. It's a total of 25 minutes of video for both, but the presentation content is well done and includes interviews with some of the most interesting theoretical physicists of our time - including Steven Weinberg, a co-author of the electroweak unification work.


Mirror Mirror On The Wall

Nature employs a handful of tricks over and over again to achieve complexity across many physically disparate systems. It is almost as if It runs out of ideas. On the other hand, these few principles are simply astounding - both in their frugality and their conceptual depth. In these posts, I will occasionally focus on these profound and general tricks of the natural laws to underscore the unity and elegance of physics. In the process, this will also give the reader a flavor of how theoretical physicists think: an abstraction from a concrete physical situation, a subsequent chain of logical steps guided by a "thought experiment", and the dramatic conclusion one is finally driven to by consistency. This post's topic is about Gauge Symmetry. Prepare yourself for possibly being a bit perplexed at first, then brought to tears (of enjoyment or pain) once you realize the punchline. When I learned this subject many (many) years ago for the first time, I realized immediately that - if physics can be so deep and cool - I really needed to become a physicist professionally.

In 1932, physicists experimentally discovered than the particle known as an electron has an evil twin: we call it the positron. It has identical properties to the electron in every respect except one: when an electron is thrown in front of a magnet, it spirals in a certain direction; its evil twin, the positron, spirals in the opposite direction (see attached image of actual data! the spiral red and green tracks on the left are those of an electron and a positron). We say that the electron and positron feel a "magnetic force"; and that the electron has some attribute called electric charge, say of value 1, while the positron has a value of -1 for its charge. And by writing some equations, this difference in charge is used to account for - by construction - the different spiraling directions. But what is this seemingly arbitrary thing called "charge"? And what is this mysterious magnetic force that seems to be acting through thin air around a magnet?

The electron and positron are basically the same animal except for this contrived "charge" attribute… So, perhaps they are two faces of the same thing? Let's abstract away a bit. What if we can come up with some notion through which we can talk about both particles within the same language. Let's sip a bit of good italian red wine, and imagine the following. Say the electron and positron animals belong to the same species. Imagine each comes with a birthmark that distinguishes it - in the shape of a tiny imaginary circle with a hand on it…like an analogue pressure gauge. Think of it as a tag. When the gauge's only hand points to 12 o' clock, the animal is the electron; when it points to 6 o'clock, we have the positron. But we have a whole circle worth of a gauge; why can't the hand point in any direction, not just noon or 6 o' clock? A bit more wine. So, let's allow that. This is a common conceptual step often used in physics: embed a concept in an abstract context and then generalize. Often, this leads to nowhere; sometimes it leads to a revolution… Now that the hand on the gauge can point in any direction, how should we think of the other time spots on the gauge? So, let's revise our thought experiment. If the hand on the gauge points in any direction, we say we're tagging an electron; when we mirror the hand vertically about the horizontal 9 to 3 o'clock line, it'll be the positron. For example, if we choose 1 o'clock to tag the electron, then the horizontally mirrored position - that is 5 o'clock - would correspond to the positron; 7 o' clock for the electron would give 11 for the positron. And any initial direction of the gauge's hand can be chosen to correspond to an electron.

Let's summarize: we wanted to combine an electron and a positron into a single species - to understand this electric charge thing that is the only thing distinguishing them. So, we came up with an abstract representation in our imagination: a particle tagged with a gauge. Any direction of the hand on the gauge is equivalent to any other. Pick one direction and call it an electron; flip the hand about the 9-3 o' clock line, and you are now talking about a positron. More wine?

Imagine two electrons a large distance apart. Both have the hands on their gauges point say to 1 o'clock by choice. Now, let's say someone sneaks in and rotates the hand on one of the electrons a tiny bit. The fact that the rotation is a tiny bit - as tiny as we want - implies that we should not change the interpretation of the animal as an electron: only a mirror flip of the hand would do that, and a flip ain't a tiny rotation. The other electron doesn't know about what just happened; at least not yet, because it takes some time for information to travel large distances. This means we should be able to choose to associate any orientation of the hand on the gauge with an electron at different points in space simultaneously… We say "the laws of Physics should be local"; what happens near a star far away cannot instantly affect what happens in Los Angeles. But this then means that we need a mechanism for rotating the hand of the gauge as we move an electron across a path in space! How else can an electron be considered to remain an electron as it is dragged across a path where the gauge hand orientation for an electron is different… Could this mechanism be some mysterious force pervading space? If we were to look at the details of this force that is needed to make sense of this logic, it comes out precisely as what we see around us as the electric and magnetic forces! We just discovered the electromagnetic force…

Let's summarize once more: we lumped the electron and positron together and added an abstract tag in the form of an imaginary gauge. We generalized a bit and allowed for arbitrary rotations of the hand of the gauge at different points in space - because information cannot travel instantly across space. This is called a Gauge Symmetry. We realized that this necessitates a mechanism to rotate the hand of a gauge dynamically. This implied the existence of a force, the electromagnetic force.

Let's say we didn't know about the electron and positron. One Saturday afternoon, a bored and socially challenged theoretical physicist just cooked up this crazy idea of particles tagged with gauges. Through the steps we went through, he or she is lead to the concept of Gauge Symmetry, and concludes that there has to be some force in Nature called electromagnetism. From Gauge Symmetry to a force law… the raison d'être of the force law is the symmetry…

Every one of the four forces of Nature we know of - gravity, electromagnetism, the weak force, and the nuclear force - all originate from slight variations of this narrative. Gauge symmetries are the origins of all the forces of Nature. For example, gravity arises from a gauge symmetry in 3D: a sphere of a gauge with its hand pointing in any direction in the full three dimensional span of space. Sometime back in time, someone said: let there be this or that gauge symmetry, and we had forces that bind things together!

Why gauge symmetry at all? That we do not understand yet - but there is a beautiful mathematical context to this that I will avoid talking about right now. We have rephrased the deep philosophical question "why are there forces in Nature?" into a new deeper one "Why are there certain symmetries in Nature?"; that is progress and a triumph of imagination and logic; but the work is certainly not done.

It usually takes me around 20 minutes to write these posts; this one took one full hour… This was the most challenging thing I've written so far… The subject is very difficult to explain because of the level of abstraction required. I needed to come up with a visual picture; in reality, gauge symmetry is described by rather elaborate mathematical equations. Yet it is so simple at its core; beautiful, and so fundamental to the world we live in. The norm is to avoid talking about this subject outside the circle of professional physicists. I do not know how much I succeeded in relaying the power, beauty, and essence of this principle that is all over physics. I hope however that I at least succeeded in giving you a feel of the crazy thought process involved in discovering new great physics from a theoretical and mathematical perspective; and in convincing you that a glass of good wine can sometimes take you a long way in understanding physics.


From Void, Through Inflation, To Now

Check out the picture accompanying this post (courtesy NASA). It is a graphical timeline of the history of our universe. Let's walk through it step by step - from left to right.

Quantum Fluctuations: the universe starts off as a tiny blob of quantum fuzz, perhaps 0.000...thirty more zeroes...1 centimeters in size; basically out of void and nothingness - the uncertainty inherent in the laws of quantum mechanics (see post on the quantum world for more). The physics during this period is not well understood - it lies in the realm of String Theory. The temperature of the quantum fuzz is 1000…plus twenty more zeroes degrees… at these temperatures, all the laws of physics are expected to be highly symmetric and the forces of Nature unified.

Inflation: the random quantum fluctuations get frozen out during a remarkable period known as Cosmological Inflation: a violent expansion of the universe driven by the repulsive force of dark energy (see post on Dark Energy for more). This lasts only 0.000…thirty or so zeroes…1 seconds; but it is so violent that, at the end, the universe is only about 100 times smaller in size than what we see today! The explosive expansion cools down temperatures to a comfortable 1000…fifteen more zeroes degrees.

In the next few seconds, the expansion continues but slows down dramatically (see comments about the graceful exit in another post). The laws of physics loose their symmetric form and the force laws start fragmenting into different branches, as we see them today: electromagnetism, gravity, weak force, and nuclear force. Protons and neutrons form first, then Hydrogen and Helium as the matter condenses out of the vacuum into a cooler universe. By the time we reach a few hundred thousand years since the beginning, atoms abound and the stuff in the universe goes from opaque to transparent: that's the point labeled Afterglow Light Pattern in the timeline. This is the Cosmic Microwave Background (CMB) radiation that we image today (see other post on the CMB for more). The temperature is now a chilling 3000 degrees.

The universe continues to expand and cool down at a slower rate for the next 14 billion years. We first go through the Dark Ages - when witches were burned alive and alchemy was common. Then we have the formation of the first stars about 400 million years since the beginning. Then we get galaxies, and finally here we are living our miserable lives.

This picture of the history of our universe crucially relies on that initial critical and delicate period called Inflation - when the universe underwent a violent expansion that stretched space faster than the speed of light. Without the inflationary epoch, it is effectively impossible to realize a universe that looks like ours today (see other post on the multiverse). The video accompanying this post gives an excellent and brief description of what Inflation is, including a discussion by the father of the inflationary theory, Alan Guth. Enjoy.