Monday, 10 October 2005

Quantum Gravity: Strings

String theory is the most known approach to quantum gravity. It started as a tentative to describe the strong interaction in the 60's, but soon after QCD was discovered and shown to be the correct approach. Strings went forgotten for some time and were rediscovered by Green and Schwarz in the 80's. One of the main flaws of strings in the description of the strong force turned out to be what called the attention to it as a possible theory to describe QG: in the spectrum of the theory you always had a spin-2 massless boson that was undesirable in the description of strong interactions. But, if a graviton exists, it should be exactly a spin-2 massless boson, and so the idea that strings could describe QG was born. And gravitons are not the only particle that appears in the spectrum of the theory, other particles with lower spin appear too and so strings were believed to describe not only gravity, but all other interactions.

Okay, but what does the theory say? First, you must keep in mind that string theory is just a tentative theory, and not very successful yet. The theory appears to be consistent and appears to give general relativity and quantum mechanics in the correct limits, but it is not rigorously proved yet. Worse, the theory cannot predict anything testable yet, although it can be tested in principle (if not, it would not be a scientific theory). Well, let me give an idea of the picture of the universe painted by strings. String theory has a simple underlying idea that changes everything. In ordinary quantum mechanics, elementary particles are considered points in space, i.e., they are 0-dimensional. In string theory, they're supposed to be tiny strings, little 1-dimensional objects. Note that strings are not made of something, in fact, they're the fundamental stuff that makes everything.

Okay, you have 1-dimensional objects, but now you need to know how they move. As string theory must agree with relativity in the correct limit (the limit where the string seems to be a point), the movement of the string is supposed to behave in an analogous way as the particle in relativity. The particle in relativity traces a curve in space that is a geodesic, i.e., it is the short path from one point to the other with the distance given by some metric defined by the mass-energy distribution in the space. But as the string is 1-dimensional, instead of a minimal path we define that the string will move such that it traces a minimal area from one position to the other. This is the fundamental principle of strings. After defining this, you can do some calculations. But this description is not a quantum description yet and then you need to apply some mathematical rules that characterize quantum systems and you get what people call the Bosonic Strings, because this kind of string gives only bosons during the calculations.

Well, the universe is not only composed by bosons, which are the particles responsible by the interactions (strong, weak, EM and gravity), but by fermions too. Fermions are the particles that compose matter. Quarks and leptons (which include electrons). You include fermions in string theory by adding a kind of symmetry in Nature named supersymmetry. It is a principle that says that to every boson there exists a corresponding fermion. This hypothesis is a fundamental component of string theory, but it has not been proved yet in experiments. If it turn out to be wrong, string theory is probably wrong too.

The last curious feature of strings is the hypothesis that the universe has not 4 dimensions, but more. This comes from a mathematical problem that requires that, in order to string theory to be well defined, you need that the number of dimensions in the universe must be a specific number: 10. The problem is that we only experiment 4 dimensions in our daily lives and string theorists had to adapt and old trick first developed by Theodor Kaluza and Oskar Klein in the past to reduce the number of dimensions perceived by us, a theory that appropriately has the name of Kaluza-Klein Theory. The best way we devised till now is by means of a mathematical process where the extra-dimensions are wrapped in a geometrical cosntruct named a Calabi-Yau manifold, which is represented in the picture in the beginning of this post. This hypothesis has not been tested too. That is because our technology cannot probe the distances necessary to do the tests, but soon it will be possible. If we cannot find these extra dimensions, again string theory will be wrong.

String theory is ambitious. The idea is to describe all interactions in a unified framework. This ambition has a drawback: the theory is exceedingly complicated and to this date you cannot calculate anything numerically to compare with experiments. The predictions of extra dimensions and supersymmetry are important to strings, but even if they're found, they will not be sufficient to prove the theory for you can have other theories with these principles. A recent result of strings was the calculation of the entropy of a special kind of black hole with the correct factor given by the Bekenstein-Hawking formula. But as black holes are not experimental facts yet, it is just a marginal success.

Theoretical developments of strings lead in the past years to a myriad of new possibilities and mathematical techniques. Now it is believed that strings are part of a much more (to this date undefined) complex theory called M-Theory. Strings are not the only component of the theory now, but you have objects of any dimensionality called branes. But as the time passes and predictions and experimental observations do not happen, the scientific community is becoming more and more suspicious of the correctness of string theory. This has led to new theories of quantum gravity alternatives to strings. If they're related to it somehow, nobody knows. In the end, the answer is always with the only one who knows the correct laws: Nature.

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