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String Theory, the ultimate theory?

The Standard Model

In the standard model of particle physics, particles are considered to be points moving through space, tracing out a line called the 'world line'. To take into account the different interactions observed in nature, one has to provide particles with more degrees of freedom than only their position and velocity, such as mass, electric charge, colour (which is the "charge" associated with the strong interaction) or spin.

The standard model was designed within a framework known as Quantum Field Theory (QFT), which gives us the tools to build theories consistent both with quantum mechanics and the special theory of relativity. With these tools, theories were built which describe with great success three of the four known interactions in nature: Electromagnetism, and the Strong and Weak nuclear forces.

Furthermore, a very successful unification between Electromagnetism and the Weak force was achieved (Electroweak Theory) and promising ideas put forward to try to include the Strong force. But unfortunately the fourth interaction, gravity, as described by Einstein's General Relativity (GR), does not seem to fit into this scheme. Whenever one tries to apply the rules of QFT to GR, one gets results that make no sense.

The usual domains of general relativity and quantum mechanics are quite different. General relativity describes the force of gravity and hence is usually applied to the largest and most massive structures, including stars, galaxies, black holes and even, in cosmology, the universe itself. Quantum mechanics is most relevant in describing the smallest structures in the universe such as electrons and quarks.

In most ordinary physical situations, therefore, either general relativity or quantum mechanics is required for a theoretical understanding, but not both. There are, however, extreme physical circumstances that require both of these fundamental theories for a proper theoretical treatment.

Prime examples of such situations are space-time singularities such as the central point of a black hole or the state of the universe just before the big bang. These exotic physical structures involve enormous mass scales (thus requiring general relativity) and extremely small distance scales (thus requiring quantum mechanics).

Unfortunately, general relativity and quantum mechanics are mutually incompatible. Any calculation that simultaneously uses both of these tools yields nonsensical answers. The origin of this problem can be traced to equations that become badly behaved when particles interact with each other across minute distance scales on the order of 10-33cm - the Planck length.

Another problem with this model is that one has to assume the existence of distinct forces and their carriers. Einstein hoped that there would be a 'unified' theory in which all known forces would emerge out of a single one in some way. Electricity and magnetism used to be thought of as two forces, but now we know they are different aspects of the same (electro-magnetic) force. Could the same type of unification hold for the four forces that are today viewed as distinct?

String theory is currently the most promising example of a candidate unified theory. We do not yet know whether it correctly describes nature, but it seems to be a theory that broadly describes a world similar to ours and is endowed with beauty and consistency to an astonishing degree.

Strings

The physical idea is utterly simple. Instead of many types of elementary point-like particles, physicists postulate that in nature there is a single variety of string-like object. The string is not 'made up of anything', rather, it is basic and other things are made up of it. As with musical strings, this basic string can vibrate, and each vibrational mode can be viewed as a point-like elementary particle, just as the modes of a musical string are perceived as distinct notes!

String theory solves the deep problem of the incompatibility of the two fundamental theories (GR and QFT) by modifying the properties of general relativity when it is applied to scales on the order of the Planck length. Modern accelerators can only probe down to distance scales around 10-16cm and hence these loops of string appear to be point objects.

However, the string theoretic hypothesis that they are actually tiny loops changes drastically the way in which these objects interact on the shortest of distance scales. This modification is what allows gravity and quantum mechanics to form a harmonious union.

There is a price to be paid for this solution, however. It turns out that the equations of string theory are self-consistent only if the universe contains, in addition to time, nine spatial dimensions. As this is in gross conflict with the perception of three spatial dimensions, it might seem that string theory must be discarded. This is, however, not true.

Multiple String Theories

There is, however, more than one string theory. These theories are classified according to whether or not the strings are required to be closed loops and whether or not the particle spectrum includes fermions (particles that makes up matter). In order to include fermions in string theory, there must be a special kind of symmetry called supersymmetry, which means for every boson (particle that transmits a force) there is a corresponding fermion. So supersymmetry relates the particles that transmit forces to the particles that make up matter.

String theories that incorporate bosons only are no longer popular as they require 26 space-time dimensions and a particle with imaginary mass known as the tachyon. There are quite a few superstring theories that make sense mathematically that only require ten dimensions. A few of the differences between them include theories with closed loops only and others with closed loops that can break into open strings.

Theories with massless fermions only spinning one way (chiral) and string theories, which are heterotic, meaning right moving and left moving strings, differ. Different combinations of the above properties leave us with 5 (mathematically) plausible theories.

M-Theory

There was a difficulty in studying these theories: physicists and mathematicians did not have tools to explore the theories over all possible values of the parameters in the theories. Each theory was like a large planet of which we only knew a small island somewhere on the planet. But over the last four years, techniques were developed to explore the theories more thoroughly, in other words, to travel around the seas in each of those planets and find new islands. And only then it was realised that those five string theories are actually islands on the same planet, not different ones! Thus there is an underlying theory of which all string theories are only different aspects. This was called M-theory.

One of the islands that was found on the M-theory planet corresponds to a theory that lives not in 10 but in 11 dimensions. This seems to be telling us that M-theory should be viewed as an 11 dimensional theory that looks 10 dimensional at some points in its space of parameters. Such a theory could have as a fundamental object a membrane, as opposed to a string. Like a drinking straw seen at a distance, the membranes would look like strings when we curl the 11th dimension into a small circle.

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Author: Astronomy Today Staff

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