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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.

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