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On Grave Matters About Gravity

Gravity is the force law that acts universally on all forms of matter and energy. If something exists, it must gravitate. Furthermore, gravity exerts the same acceleration on objects of different masses and energies! A feather is pulled by the Earth with the same acceleration as is an elephant - even a rather large elephant with weight management issues. This is known as the "equivalence principle": the principle that the amount of stuff within an object - i.e. its inertial mass - is directly related to the amount that gravitates - i.e. its gravitational mass.

These universal aspects of gravity lead Einstein to propose that gravity is really not a force, but the result of distortions in distances in space. Since all objects have to sail through time and space in a universal way, if the fabric of space-time gets deformed, all things moving on it feel it and can get deflected through a common trajectory. This is the framework of General Relativity: gravity is the curvature of space-time itself; things appear to change course under a gravitational "force" simply because the fabric over which they move is distorted by nearby massive objects. The first video shows a cartoon of this idea. 

Very recently, the string theorist Erik Verlinde proposed an intriguing new perspective on gravity - one that further capitalizes on the universal character of this force law. Verlinde proposed that gravity may be a statistical effect, an entropic force - not a fundamental one akin to electromagnetism. He illustrates his proposal through an analogy with other known entropic effects such as osmosis or polymer dynamics.

In the second video, we see the well-known processes of diffusion and osmosis. When two different solutions of salt water of different concentrations are separated by a semipermeable membrane, over time the two sides equilibrate in salt density. The details of any fundamental force laws acting between the molecules of the water and salt are not important. The water from the less dense solution flows towards the higher density side for statistical reasons: the flow would maximize the level of disorder or entropy in the system (see previous post on the arrow of time). Simply put, the configuration of equilibrated uniform solutions is a more likely arrangement of water and salt molecules and hence will be attained eventually due to statistical considerations. We could be misled to think of this process as one driven by some force that pushes water from one side to the other. However, we should know that this "force" is not a fundamental one, but a fictitious one: it is statistically driven, a collective effect, entropic in origin. This was a larger dose of biology than I intended… so, let's quickly move onto the physics of gravity.

Verlinde proposes that gravity is also an entropic effect rather than a fundamental force law. This is motivated from recent results in string theory, but it can in fact be phrased in an independent and self-contained manner. The universal attributes of gravity encourage such a general scheme or interpretation. And recent suggestions from string theory about gravity having a "holographic" nature further bolster it (I'll write more about this in a future post). 

Verlinde's proposal may suggest that there is no reason to worry about developing a theory of quantum gravity - a rather elusive project of theoretical physics for decades that has only recently been realized within string theory. If gravity is a statistical effect, perhaps there is no sense to worry about its quantum realm at small distances - as much as we would want to worry about forces between molecules in a gas in an effort to understand osmosis. Hence also lies the problem with Verlinde's proposal. At the end of the day, this proposal amounts to the following curious observation: that gravity at large distances has all the hallmarks of a statistical effect. This is not inconsistent however with any microscopic formulation of gravity through string theory - nor does it preclude its need for understanding the small scale structure of space-time… The proposal is a statement about long distance gravity only. It is still an intriguing exercise since it attempts to identify a minimal set of independent physical principles that can realize the well-known long distance attributes of gravity from a statistical point of view.

So, the entropic proposal for gravity to me is simply an interesting story - with a great deal of elegance and pedagogical value. However, it is not a framework that can complete or replace a description of space-time at the smallest distances - a description of quantum gravity. Quoting the ghost of Niels Bohr from a century ago, the proposal is crazy - but it is not crazy enough to be correct…


Mixing The Small With The Big

In the context of standard physics - basically all the physics we know so far and all that we have tested - there is a clear hierarchy between physics at small distances and physics at large distances. We expect that, for any physical system, laws valid at smaller distances are more fundamental, and they can be used to derive less fundamental or approximate laws that work well at larger distances (see previous post on renormalization). This even makes intuitive sense. And when things make intuitive sense, expect new physics to disappoint you at worse, or shock you at best… 

String theory is a framework that unifies the description of all the natural laws within a single consistent language. It relies on quantum mechanics and relativity - two of the three pillars of modern physics - but replaces the third, gravity, with new concepts. As a result, string theory successfully formulates a theory of quantum gravity - a task that had eluded physicists for many decades. It is interesting to try to dissect the mechanism responsible for successfully marrying quantum mechanics and gravity within string theory: what are the key ingredients in string theory - the minimum set - needed to achieve this goal? This is important for two reasons: first, string theory can get elaborate and mathematically complicated, yet the basic physics underpinning should be straightforward and useful to identify to understand the grand picture. Second, it is possible that string theory will not survive the test of time in its current form and may need to evolve and adapt to future experiments; it is then important to pick out from string theory the key pieces that one needs to hold on to, throughout any future evolution.

One of these new key ingredients in the string theory soup is the concept of mixing the big and small. In string theory, when one tries to probe smaller and smaller distances - say by throwing things at each other at high speeds - one finds that, after a certain minimal distance, one cannot probe any smaller distances! Trying to do so leads you to a physical process that instead probes larger and larger distances… the big and small gets mixed and confused! There is an easy way to understand this very strange behavior. In string theory, everything is made of, well, strings… the building blocks of Nature are tiny strings. If you dump energy into a string, say to accelerate it to high speeds, you will initially find that the size of the string shrinks. This is natural and expected from quantum mechanics. With higher energies, you thus can probe smaller distances since your probe - the string - is smaller. However, when you try to dump too much energy into the string, it instead prefers to stretch! This phenomenon is dictated by the properties of the string and good old thermodynamics. The string finds it more favorable to store the extra energy by extending its length against its tension… Hence, since everything is made of strings, you cannot "see" distances smaller than a certain minimum distance no matter how hard you try: the probe that you would use - which is a string - cannot get smaller than a certain minimum size. This seems to be crucial to combining quantum mechanics and gravity. The trouble with traditional gravity is that, at very small distances, it makes no sense. String theory caps things off by providing a mechanism for forbidding you from reaching arbitrarily small distances - and hence resolves the quantum gravity paradox through a very elegant mechanism.

Nowhere this mixing of big and small is more dramatic within string theory than in the process of understanding a black hole horizon (see post on black holes). A black hole - basically a hole in the fabric of space and time - has typically a spherical surface called the horizon that hides the hole in its center. Traditional physics proposes that the horizon of a large black hole is an imaginary boundary that anyone could cross without any hindrance; of course, once you cross it, you are trapped inside the black hole forever (see post on the information paradox). Recent computations in string theory have been suggesting that this may not be the case. When a string falls towards a black hole and reaches the horizon, its size starts to stretch; it stretches so much that, by the time it crosses the horizon, the string is about the size of the horizon! That means you may never be able to reach the problematic hole or tear in space-time behind the horizon since you cannot get a probe smaller than the horizon to penetrate it… 

The accompanying video is an animation I had prepared for a colloquium some time ago showing one version of this picture that arises from string theory: the ball of stringy goo that is sloshing around is the black hole in this framework (known as the Matrix theory formulation). Notice how the goo tends to fuzz up to the surface, sitting at the would-be black hole horizon. In this picture, the center of the black hole may be hollow, everything that is the black hole sits at its horizon, like on a spherical membrane. If you try to cross the horizon, you will be absorbed, consumed, and thermalized by this membrane of goo… Pre-string theory physics proposes instead that all the black hole mass is concentrated at its center, punching a hole in spacetime.


Type I And Type II Personalities 


Here's part 2 of my post on superconductivity (see previous post for part 1). So, we have a strange material that, when cooled down enough, undergoes a dramatic change: it suddenly starts conducting electricity without loss of energy. That's a superconductor, and we talked a bit about the underlying microscopic mechanism in the previous post. There is however much more to a superconductor in terms of freaky behavior.

During your troubled childhood, you probably have had a chance to play around with magnets. You noticed that magnets can be oriented to repel or attract each other. This is the magnetic force, part of the fundamental electromagnetic force. A magnet projects around it an energy field through empty space. At points nearby the magnets, space literally store a bit of energy due to the proximity of the magnet. This energy field is connected to the repulsion or attraction that you experience when you bring two magnets close to each other. In Nature, energy is money: it is costly to generate energy and Nature would rather not do it unless It really has to… 

Now imagine you bring a magnet close to a block of some material. The magnetic energy field will in general penetrate inside materials as well. However, a material could in principle react to the proximity of a magnet by spontaneously generating a current within itself - by moving around its own electrons. This is because an electric current also generates a magnetic energy field, and it is possible for the magnetic field from the current to cancel the one from the magnet within the body of the material. That is a good thing from Nature perspective: the magnetic energy inside the material costs energy, and if it can be canceled by moving the electrons in the material, life would be improved. The problem is that generating a current in a material is also energetically costly… in general, it does not pay off and the magnet's magnetic field does penetrate readily into the material - sometimes slightly modified by the material's lame attempt to put up a fight to the intruding magnetic field.  

But a superconductor has a trick up its sleeve: it can conduct electrical current without loss of energy. So, if you get a magnet close to a superconductor, the superconductor can circulate arbitrarily large amounts of electric current within it to make sure the magnetic energy field inside of it is canceled! A superconductor repels magnetic fields! See the first picture attached to this post for a depiction. The end result is that the superconductor acts like a magnet as well in response to the proximity of the external magnet, and superconductor and magnet repel each other: hence, you get magnetic levitation (see videos in previous post). 

But Nature has more elaborate tricks up its sleeve… Imagine you ramp up the strength of the external magnet so that it generates more and more magnetic energy fields around it. A superconductor involves a microscopically delicate balance of forces that binds pairs of electrons together (see previous post for the details). If enough magnetic energy field from an external magnet is present, this delicate balance can be disturbed as the electrons feel an external magnetic force. So, it is possible  to destroy the superconducting state of a superconductor by putting it in the vicinity of a very strong magnet. But things are much much more interesting than this… When one attempts to destroy a superconducting state with a strong magnet, one finds two very different types of behaviors - depending on the detailed properties of the superconducting material involved. We call these two different types of superconductors Type I and Type II.

Imagine a region of strong magnetic energy field penetrating a superconductor. And imagine that this region of magnetic field penetration is in the shape of a rough cylindrical blob: inside, there's magnetic field and the superconductor is no more, outside there is no magnetic field and the superconductor is still putting up a good fight. The interface between these two regions - the boundary of the blob - is a place of tension and can pack energy. There are two possibilities however. Possibility 1 or Type I: the energy in the interface costs additional net energy, and such regions would rather coalesce and merge to reduce the size of the boundary - imagine droplets of water or mercury merging together to form larger and larger blobs of water or mercury. If you are science fiction fan, imagine instead the liquid metal in the Terminator movies, or the Klingon blood in empty space in Star Trek… The end result is that the region where the magnetic energy field penetrates into the superconductor grows in size quickly and overtakes the whole body of the superconductor; or I should say the late superconductor which is now no more.

Something amazing happens however in Type II superconductors. The contribution of the interface to the total energy balance of the situation is negative! The blob of magnetic energy field penetrating the superconductor would rather maximize the size of the interface… As a results, such blobs fragment into smaller ones - instead of combining as in the Type I case. You then generate a dramatic cascade of magnetic energy regions disintegrating into smaller and smaller regions and the superconductor gets threaded with a lattice of cylindrical vortices of magnetic field (see accompanying actual picture of vortices from the 2003 Noble prize announcement for superconductivity). In between these vortices, the material is still superconducting; within the vortex, it's not. But why don't these regions of magnetic energy fields, these vortices, collapse further - perhaps disappear all together? The reason is a delicate one: there is a minimum amount of magnetic energy field in a vortex that you cannot eliminate without having to rearrange the energy distribution in the entire body of the material; and this costs loads of energy and would rather be avoided. There is then a global aspect of these magnetic vortices that is sensitive to the material's entire state; as if things are held together by a larger order beyond the physics of the local neighborhood of a vortex. What is quite amazing about this is that these vortices behave very much like particles: you can scatter them off each other, they can combine and decay, there are forces between them, there are even anti-vortices around… check out the videos accompanying this post for some entertainment value. The first video is about dynamics of vortices - actual video of vortices in action! The second video is a simulation; focus on the top graph only since that depicts magnetic energy. The lattice of magnetic vortices in a Type II superconductor can also "pin" a levitating magnet as seen in the videos of my previous post. It's like you are putting magnetic nails through a floating superconductor - pinning its orientation in mid-air… beautiful, amazing, elegant, and intricate physics across the board… that's superconductors for you in a nutshell - actually in two nutshells.


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...


Synchronized Swimming

Three key conceptual ingredients underly the phenomenon of superconductivity, each one more beautiful than the other. When certain materials are cooled down to very low temperatures, it is found that - at some critical temperature - the material is able to conduct electricity without any loss of energy! Hence the term "super"conductivity. The importance of practical applications of this cannot be overstated. Its conceptual physics underpinnings are however even more dramatic. Here are the three key ideas involved in this remarkable phenomenon.

(1) The quantum world - i.e. the real world - looks very different from the world we are used to (see this and this previous posts for more). In reality, all matter is to be described by waves of probabilities - waves that behave very much like those on the surface of the ocean. What's waving is not water, but the likelihood that a particle of matter is here or there. And these probability profiles propagate, combine, and scatter much like water waves do. When one has a large number of constituents in a system, the wavelets of each particle add up incoherently and the quantum effects are washed away (no pun intended) at large macroscopic distances. Occasionally, one can however arrange to sync the wavelets of matter so that they reinforce each other and form a substantial probability tsunami that brings the freaky quantum world into our own safe and naive realm. This happens typically when you cool down a system of particles to low enough temperatures. However, the effect is most dramatic when the particles are bosons instead of fermions (see post on bosons and fermions). The result is what is known as a Bose condensate: a collection of quantum wavelets in sync and adding up to a macroscopic probability profile. This is for example the case for photons in a laser, electrons in superconductivity, and molecules in superfluidity (see post on superfluidity for a bit more).

(2) A typical metal can be visualized as follows: a lattice of atomic nuclei spread around in a regular pattern - forming the scaffolding of the material; and waves of electrons propagating through the lattice randomly. When a piece of metal is hooked up to a battery, the electrons are forced into motion in a certain direction, like water through a pipe. However, electrons are attracted by the nuclei and repel each other through the electromagnetic force. The result is that the flow of electrons is not a smooth one; it is interrupted by various obstacles - other electrons and nuclei in the material. This is a source of energy loss for electrical energy flow. Hence, current in a metal typically involves "resistance", a mechanism for loss of energy. When certain metals are cooled down to very low temperatures, there is the possibility for the electrons to form a coherent Bose condensate - generating an electrical flow more akin to soldiers walking in step and reinforcing the efficiency of the flow. But the electrons are not bosons, they are fermions… To realize the quantum syncing of electron wavelets as needed, we would want bosonic particles. Nature comes up with an amazing solution to this puzzle: if you bind two electrons together - as in an purely "electron atom" - the result is a boson. From my previous post about bosons and fermions, you may remember that a boson is associated with integer spin, and a fermion with half-integer spin. Electrons have spin 1/2; two bound together necessary generate integer spin, and hence a bosonic entity. So, pairs of bound electrons - known as Cooper pairs - can potentially form a Bose condensate at low enough temperatures, which then can carry electrical energy flow through the material at very high efficiency, all the way to 0% energy loss: a quantum effect involving the syncing of probability waves and manifesting itself through a dramatic macroscopic effect…

(3) But there is a problem with this story: electrons are attracted to the metal nuclei but repel each other electromagnetically… How the heck can you then bind two together? Once again, Nature kicks in with an amazingly intricate solution. At low enough temperatures, in certain materials the lattice of atomic nuclei deforms under the influence of the electrons flowing through it. It does so in a very special way. The accompanying figure shows a cartoon of the setup. The deformed nuclei mediate a pull between the two electrons, hence binding them through a precarious balance of forces! The mechanism is ingenuous, counter-intuitive, and delicate: all ingredients of Nature working at its best.

With all these factors colluding together, certain materials can transfer electrical energy or current with no energy loss - at low enough temperatures. But this is not the end of this amazing story. Superconductors exhibit other dramatic effects having to do with their interactions with magnets. For this, we will need to talk about two types of superconductors - enigmatically called type I and type II. But we'll need another post just to address this subject. Meanwhile, have also a look at the videos in my previous post to see superconductors in action.


The Deserted Island

If I were to be secluded on a deserted island - which actually would not change much my daily routine - and was asked for five physics topics to take with me, one would be superconductivity. Superconductivity is the phenomenon of current flow with zero resistance in certain substances cooled down to low temperatures. Several reasons why the topic would be on my short list on the (hopefully tropical) island: (1) It involves a delicate microscopic mechanism that you would never be able to guess at unless you were both a genius and intoxicated at the same time; (2) The physics involved is one of the most profound techniques Nature uses to achieve a change of state - for example, it is the same one that is also responsible for the Higgs particle (see post on the "god particle") giving mass to all matter; (3) It involves a phase transition - a phenomenon whereby a state of matter undergoes dramatic change that reflects intricate microscopic dynamics; (4) It is one of the few places in Nature where the crazy effects of quantum mechanics - usually tucked into the microscopic world - peak out directly into our macroscopic world.

The first video demonstrate superconductivity, along with the magnetic pinning phenomenon in so-called Type II superconductors. The second video talks about a current practical application of this physics. All this is in preparation to a post coming up tomorrow on the actual detailed physics of superconductivity. In the meantime, enjoy.


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).