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Friday
Nov262010

The M(other) Theory, part 1 

 

This post requires reading a previous post titled "Finding The Exit".

Imagine the world of physical systems as an imaginary landscape of lengths, times, and masses - a vast three dimensional expanse where every point corresponds to a particular physical phenomenon, with an associated characteristic length, time, and mass;  an abstract space that visually organizes all natural phenomena we are capable of ever observing. Three fundamental constants of Nature delineate this magical space. They define boundaries that cannot be crossed - three planes that form a pyramid without a base, in-between which the laws of physics confine all our observations of the world… 

One boundary is determined by the speed of light: we may not observe any phenomenon involving speeds faster than that of light… That's the statement of Special Relativity, discovered in 1905.

Another boundary is set by Newton's gravitational constant. If we land on this boundary, we are looking at physical systems that have collapsed under their own weight to form black holes… Beyond the boundary, we are studying physics inside a black hole - a mysterious place disconnected from the rest of the universe, a region where space itself comes to an end. Our understanding of this physical realm started with Newtonian gravity in 1687 and ended with General Relativity in 1915.

The last boundary is defined by Planck's constant of Quantum Mechanics. Beyond it, we are not allowed to peek since even Nature itself does not know what goes on… This is the crazy realm of uncertainties - the world of Quantum Mechanics -formulated by 1927.

The three walls of this pyramid intersect in three lines - one between each pair of planar boundaries. And the three intersection lines intersect at a single point - the tip of the pyramid. The junction between the Quantum and Special Relativity planes is captured by a set of physical laws collectively known as Quantum Field Theories. The small world of particle physics - of electrons, quarks, and the sort - lies in this region of our magical landscape. The junction between the Special Relativity and the Gravitational walls is described by the framework of General Relativity - also known as Einsteinian gravity. It is the realm of astrophysics and cosmology - the large scale structure of space. Quantum Field Theory and General Relativity together form the basis of all the laws of Physics that we can currently write down to describe our entire world; and they do so with much success, perhaps a little too much...

But this still leaves us with one junction - the one between the Quantum and Gravitational planes. Physical phenomenon in this region require the use of the laws Quantum Mechanics and of General Relativity… While this is possible, any attempt at understanding phenomena in this region - such as the physics near the surface of a black hole - quickly leads to puzzles and inconsistent conclusions. Quantum Mechanics and General Relativity do not fit together! It is safe to say that the theoretical framework for understanding this region - formally known as Quantum Gravity - is still work in progress…

How about the apex or tip of the pyramid? Near this region, we have a confluence of all the laws of physics that we know - a region where gravity, quantum mechanics, and special relativity are all simultaneously important… We know with certainty that this is a realm that we simply do not yet understand - a realm that probes the tear in the fabric of space and time at the center of a black hole! 

The field of String Theory purports to capture all the physics inside our pyramid of physical phenomena - even the junction of Quantum Gravity, and all the way up to the enigmatic tip of the pyramid. To do so, String Theory has to render a judgement with respect to the following grand question: if Quantum Mechanics and General Relativity do not fit together, at least one of the two is to blame; if so, which one? String Theory proposes that it is General Relativity that is at fault. It adopts wholeheartedly the frameworks of Quantum Mechanics and Special Relativity - that is the frameworks underlying Planck's constant and the speed of light. But it rejects the framework of General Relativity, proposing instead that General Relativity - along with its gravitational constant - is an approximate theory; a theory that is not fundamental and that needs to be replaced with a more fundamental framework if it is to make sense in conjunction with Quantum Mechanics.

Hence, String Theory starts with the premise that there are three fundamental constants in Nature: the speed of light of Special Relativity, Planck's constant of Quantum Mechanics, and a new third scale in lieu of Newton's gravitational constant. Newton's constant is then proposed to be a derived concept, built up from the new third fundamental constant. We will call this new third fundamental constant, cryptically, "the tension"... 

We just described the first of two postulates that underly the subject of String Theory. The second postulate is a simple one, yet surprisingly powerful and restrictive. It is proposed that all observables in the physical world should be dynamical and computable. That is, we do not allow for any additional scales in Nature beyond the three fundamental constants: the speed of light, Planck's constant, and the "tension". After two decades of hard work by hundreds of lonely and isolated string theorists, these two postulates lead to the proposition that the building blocks of all energy in the world consist of membranes flopping around in a ten dimensional world… And the "tension" constant introduced earlier is simply the stretching tension of these membranes - a measure of their stiffness. We call this theory "Membrane Theory" or "M-theory" for short. In many computationally practical situations however, these membranes appear collapsed as strings - hence arises the alternative historical name of our new theory, "String Theory" - along with a constant known as the "string tension".

We now need to describe two main aspects of this new framework: (1) How does the three dimensional world that we see around us possibly arise from such a (putting things mildly) crazy suggestion?; (2) How does this framework take us beyond what we already know? In particular how does it resolve the original problems and inconsistencies between Quantum Mechanics and General Relativity? Stay tuned for answers to these questions in future posts… In the meantime, have a look at the remaining four parts of video that present a historical narrative of the subject.

Sunday
Nov212010

Finding The Exit

The process of discovery in physics comes in two basic flavors. Imagine you are thrown in a large and totally dark room, and you are asked to map it out - or even to find the exit door to leave it. You can adopt one of two basic strategies. You could start from a nearby object you can touch and feel, and go from there around the room discovering one adjacent bit of the room at a time. Alternatively, you could "shoot in the dark" by walking towards a random direction until you hit something; if nothing interesting is found, just head into another random direction; and repeat until perhaps you would luck out and even find the door. 

This large dark room represents the physical world around us. The first method of exploration corresponds to a process of meticulous experimentation, discovering bit by bit new phenomena - often from a basis of already well established physics. The second method starts with a pen and paper, without any urgent need for explaining new and exotic data from some experiment. It is driven by logical and sometimes esthetic considerations, and lots of imagination. The first method is robust and the norm for all the sciences, including physics. The second method is rarer and leads mostly to disappointments; but, when it works, it leads to a revolution, to a sudden leap of knowledge perhaps worth centuries of traditional work - to finding the room's exit door, to great enlightenment. 

In the history of physics, both methods have played crucial roles in bringing us to our current state of knowledge of the world. The first method is well known and appreciated; the second less so since it often leads to nowhere. However, its impact on physics is immense. The most dramatic example of a revolutionary leap driven by theoretical considerations was the development of the theory of Special Relativity, and soon after that, the theory of General Relativity by Einstein. In both cases, experiments only followed the theories to quickly confirm the counter-intuitive predictions that were implied by the theories. Soon after these developments, quantum mechanics was formulated in a tour force of physical ingenuity through the first method of physics exploration - through meticulous experiments and ideas developed to explain the results. The beginning of the 20th century thus consisted of a two punch discovery extravaganza - first with theory leading experiment, then experiment leading theory.

String theory is  an exercise of "shooting in the dark" akin to General Relativity. It is motivated by strong indications that our current best understanding of the gravitational force - given by the theory of General Relativity - is logically (and ironically) inconsistent with quantum mechanics... Experimentally, we do not currently have the technology to demonstrate and understand this paradoxical inconsistency. However, theoretical considerations rather overwhelmingly force us to accept that General Relativity cannot be a fundamental description of gravity and spacetime; rather, it must be an approximate framework that would fail to describe the real world correctly when one looks at gravity at very small distances - distances of the order of ten to the power minus 33 centimeters...

Historically, string theory was developed with very different motivations. In a series of posts - of which this is the first introductory one - I will try to give an overview of string theory with the benefit of historical hindsight - using a chain of logic instead of a historical thread. Hence, let's put history aside and talk about this very intriguing new framework of theoretical physics with an attitude that we are attempting to take a giant leap, find the exit, and reach enlightenment that brings unity to all pillars of modern physics: gravity, quantum mechanics, and special relativity. Until the next post in this sequence, have a look at the accompanying four part videos about the subject - presented from a historical perspective. 

Thursday
Nov182010

The Spinning Carpet

According to the General Theory of Relativity, the space around a massive planet or star is distorted and curved due to the energy content of the planet or star. The distance between two fixed points in space changes when the two points find themselves in the vicinity of an astrophysical object such as the Earth; and this effect is what is perceived by us as Earth's gravitational pull. Things get much more interesting when an astrophysical object is spinning… The fabric of space is dragged around by the spinning object - pulling with it nearby probes. The effect is known as frame-dragging and is expected to be particularly dramatic near the surface of black holes. Near a spinning black hole - a rather common scenario - the space is spun so violently that a nearby spaceship, planet or star is forced to spin with the black hole, whether it wants to do so or not! This same frame-dragging effect is also present close to our spinning planet. But the Earth's gravitational pull is much weaker and the corresponding frame-dragging effect is rather subtle. Despite this, recently, a group of experimental physicists attempted to measure this phenomenon using a special satellite. 

The first video talks briefly about the general aspects of frame-dragging near a black hole. The video starts with a very interesting and somewhat related recent phenomenon involving a jet from a supermassive black hole blowing through another galaxy… The remaining three videos (they are 3 parts of a 25 minute long documentary) present a detailed discussion of the recent experiment that studied frame-dragging near the Earth's surface - the so-called Gravity Probe B experiment.

Monday
Nov152010

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.

Thursday
Nov112010

How To Light Up A Pickle

Here's a class demo I did with absolutely no instructional or scientific value; in case you are looking for replacements for your lightbulbs... DO NOT DO THIS AT HOME!

Wednesday
Nov102010

The Physics Of Bad 3D Movies

Imagine a beam from a high powered laser coming straight towards your face. As the beam hits your face, you will quickly discover that it - and more generally light - is electric and magnetic in origin. You will realize this because the electrons in the atoms making up your soon to be fried cells will start oscillating violently as the beam passes through them; and electrons are electrically charged and experience electric and magnetic forces. But from the oscillation of the electrons you will also realize that there is more structure to light than you may have thought: as the light passes through an electron in a certain direction, the electron will jump around and move in a plane transverse to the incoming beam; that is if the beam is coming in horizontally, its effect on the electron can be up-down and/or left-right. To be complete, the electron will also be pushed in and out along the beam for somewhat different reasons, but that motion is irrelevant to my argument. This tells you that light carries with it a two dimensional plane's worth of information: you can arrange for a laser to move the electrons only up and down, or only left and right; or a combination of both. We say light has two polarization states, or two degrees of freedom. Your eyes are not setup to see this additional information in a light beam; hence, this may come as a surprise.

However, we now have technology to mold the polarization of a light beam as we desire. This is done by letting the beam pass through certain special materials - called cryptically polarizers: the emerging beam can be made, for example, to oscillate electrons up and down only, or left and right only. If you polarize a beam left and right, then make it to pass through a polarizer oriented up-down, you can kill the beam. This has many uses, the most recent and sexy one being the emergence of 3d movies and 3d televisions.

You perceive distance and perspective in life because you have two eyes. Each eye sees a slightly different perspective of the world, and your brain puts things together for you for free and hence you perceive distance.  When you want to replicate that in a bad movie, you use a camera with two eyes - or just two cameras mimicking two eyes. You then project the video from each "eye" onto the same screen in such a way that light from one video passes through a polarizer that orients the polarization of the light say up-down; the other, left-right. Actually, one does a slightly more practical setup using so-called circular polarization, but that detail is irrelevant to the physics story. When you view the bad movie on the screen, you then put special eyeglasses: each eye has a polarizer oriented differently and picks up only the image from the corresponding video feed. So, your brain receives two different images, slightly off from each other in perspective - just so that it appears you are immersed in the movie's scene. It's a very simple idea that capitalizes on the fact that there are two degrees of freedom in light and one can package two images in the same beam; and separate things out once again with polarizers in front of your eyes. Unfortunately, all this physics will not improve the quality of some of these recent 3d movies.

The first video demonstrates the basic physics of light polarization. The second video talks about 3D TV technology.

 

Monday
Nov082010

How To Mutate A Physicist

The deep universe is littered with violent astrophysical events: exploding stars (supernovae), colliding galaxies, merging black holes tearing the fabric of space-time, crazy fast spinning pulsars, movies by Quentin Tarantino… these events can create powerful shockwaves that kick intergalactic or stellar gas particles to immense speeds and energies. These particles - often simply protons (i.e. Hydrogen atom nuclei), but sometimes also X-rays and atoms like Carbon - attain unimaginably large energies. They are all around us, so energetic that they pass through our bodies and much of the Earth's rock layers. We call them collectively and cryptically "cosmic rays".

Cosmic rays - unlike the neutrinos of my previous post - do occasionally interact with organic matter (i.e. biological cells) and play an important role in the evolution of life on Earth: they can help mutate DNA when they penetrate a cell, and mutations are a key ingredient in the process of evolution. What is quite astounding about cosmic rays is their extremely high energies. Physicists often measure energies in "electron Volts" - some useful unit of energy related to the more familiar ones such as Joules or Calories. To put things in perspective, the largest particle accelerator built by the pitiful human race generates particles with energies around several trillions of electron Volts. Cosmic ray particles have been detected with energies around a million times more… but not much more than that. Lower energy cosmic rays - in the thousands of trillions of electron Volts range - can be detected directly through detectors raised to the edge of the atmosphere with balloons; higher energy ones are seen indirectly through showers of particles they generate when they collide with the Earth's atmosphere. Much is not known or understood about these mysterious visitors from outer space. But in the past few decades, we have started tracking them down actively and aggressively.

The first video features the late celebrated science narrator Carl Sagan and gives a great overview of the subject. The second video is part 1 of a 3 part series that goes into more details.