Saturday, February 11, 2012

14. Supersymmetry, String Theories, M-Theory

At and soon after the Big Bang the temperatures and energies were so high that there was only one fundamental interaction, and not four. As our universe cooled a little, symmetry-breaking transitions occurred and different interactions appeared one by one. New fields and matter arose as a result of these transitions. Since there was only radiation, and no matter, to start with, the present distinction between matter particles (fermions) and field particles (bosons) is also a result of broken symmetry. We call it SUPERSYMMETRY (SUSY). If supersymmetry could be restored by going to high enough temperatures or energies, the distinction between fermions and bosons would vanish.

As we go up the symmetry ladder, more and more 'dimensions' come into existence. Supersymmetry involves symmetry operations in a certain n-dimensional superspace, four of these dimensions being the spacetime coordinates we perceive in our world.

The most important new symmetry emerging from the supersymmetry description of Nature is that for every particle with spin J (a boson), there must be another particle with spin J±1/2 (a fermion). We would see a 'degeneracy' (sameness) if this supersymmetry could be realized by going to high-enough temperatures, and the masses of the two partner particles would become equal. But since the supersymmetry has got broken at the prevailing temperatures, the masses are different.

The standard model does not include quantization of the gravitational interaction, and its unification with the other three interactions. This means that additional broken symmetries need to be postulated and verified, with an attendant increase in the number of dimensions of the hyperspace in which the symmetry transformations operate. STRING THEORIES attempts to do that. They involve an extension of the conceptual framework of quantum field theory.

The uncertainty principle (cf. Part 3) is one reason why it is so hard to formulate a quantum theory of gravity (Einstein’s general theory of relativity is a wholly classical theory). The uncertainty principle applies to pairs of ‘conjugate parameters’. For example, the position of a particle along the x-axis and its momentum component along the same direction are one such pair of conjugate parameters. A second such pair is the value of a field and its rate of change. The more accurately one is determined, the more uncertain the value of the other becomes. This means that there is NO SUCH THING AS EMPTY SPACE: An empty space would mean that both the value of a field and its rate of change are exactly zero; and this is not allowed by the uncertainty principle.

Thus when we speak of vacuum in quantum physics, we really mean a space which has a certain minimum-energy state. This state is subject to quantum fluctuations, which means that pairs of (virtual) particles can make momentary appearances (within the limits prescribed by the uncertainty principle), and then disappear by merging into each other. There are infinitely many such virtual pairs possible, each having energy, implying that the vacuum state should have infinite energy. But an infinite-energy vacuum state would curve the universe to an infinitely small size, according to the general theory of relativity. This is not what actually happens, so our theory is plagued by an 'infinity problem' again.

In 1976 the idea of supersymmetry was put forward in this context. In supersymmetry theory, force particles (bosons) and matter particles (fermions) are symmetry-related, or rather supersymmetry-related. This scenario has the potential to solve the above infinity problem: It turns out that the infinities from matter-related virtual particles are all negative, while they are all positive for force-related virtual particles, so they can cancel each other out.

The notion of supergravity, which emerges when we invoke supersymmetry, has the potential to unify gravity with the other three interactions.

The idea of supersymmetry had actually originated earlier when string theories were being formulated. In string theories the elementary particles are envisaged, not as points, but rather as patterns of vibration that have length but no width (‘strings’). The various string theories are consistent only if spacetime has 10 dimensions, rather than 4. We see only four dimensions because the other six have 'curled up' into a space of very small size.

An analogy will help understand this. Consider a straw you use for drinking lemonade. Its surface is 2-dimensional: We need two numbers or coordinates for specifying the location of any point on it. But if the straw is extremely thin (say a million-million-million-million-millionth of an inch), it is practically 1-dimensional; the other dimension has just curled up into near-nothingness in terms of visibility.

Introduction of supersymmetry into a string theory leads to the idea of SUPERSTRINGS. Earlier, there appeared to be at least five different string theories (or rather superstring theories), and millions of ways in which the extra dimensions could be curled up. But many experts are now convinced that the five superstring theories, as also supergravity, are merely different approximations to a more fundamental theory called the M-THEORY, each superstring theory being valid in different (but overlapping) situations.

M-theory involves 11 dimensions instead of 10. It is this extra dimension which unifies the five string theories. Moreover, M-theory allows for not just strings (which are 1-dimensional objects), but also point particles, 2-dimensional membranes, etc., all the way up to 9-dimensional entities (called 'p-branes', with p running from 0 to 9). M-theory is the unique supersymmetric theory in 11 dimensions.

A crucial feature of M-theory is that its mathematics restricts the ways in which the dimensions of the internal space can be curled-up. Thus the theory comes up with unique (rather than arbitrary) values for the fundamental constants and the ‘apparent’ laws of physics corresponding to any particular mode of curling.

M-theory needs to be verified adequately. It is a beautiful theory. If confirmed, it may well be the long-coveted 'theory of everything' (TOE).