The Eleventh Dimension--String Theory, Supersymmetry and Super Gravity

In the mid ‘60s, physicists were struggling with the dichotomy between Relativity and Quantum Mechanics. Both theories beautifully described a part of nature—Relativity the large and massive, Quantum theory the tiny. Both had been proven in experiment and observation many times.

But there was no way apparently to bring the two together in a single encompassing theory of how the universe—large and small—worked.

During this time, several physicists, including Leonard Susskind, John Schwarz, Peter Higgs, Francois Englert, R. Bout and Gabriele Veneziano were grappling with two of the thorniest problems in subatomic physics. One was breaking quantum gauge symmetry. Gauge symmetry is required in the Standard Model for particles that carry the strong and weak forces, called gauge bosons. These particles have no mass. Symmetry says these particles behave the same no matter how their charge or rotation may change. But the math says symmetry can be broken, and if symmetry is broken, a massive boson will be created. It is named, although as yet undiscovered, after Peter Higgs—the Higgs boson.

The other problem deviling physicists was how the strong interaction held quarks together so tightly.

As it turned out, these two questions had the same answer.

In 1967 Steven Weinberg shows that the electromagnetic and weak forces are the same. The next year, Veneziano shows that the strong force depends on the resonance, or vibration, of the gluon boson which mediates the force. That concept, while it had problems mathematically, will cause a scientific upheaval.

For this work did bear fruit. Three of the four forces had been unified. Only gravity remained lost. But the work showed the particle—the graviton--that had to mediate gravity had to have no mass, and have a spin equal to 2—the other force mediating particles have a spin of 1. And of course it had to exert its force over extreme distances, whereas the weak and strong forces are exerted only over quantum distances.

Two years later, Yochiro Nambu, Susskind and Holger Nielson, working independently, found that Veneziano’s resonance could be explained by the quantum mechanics of relativistic vibrating strings of energy. Now these weren’t physical strings, the way subatomic particles are physical points. These were minuscule strings of energy, no longer, or smaller, than the Planck unit (1.616252(81)×10⁻³⁵ meters). Their vibrations, which were of infinite variety, created the subatomic zoo. Each subatomic particle, from quarks to electrons, was the result of a specific vibration of a string.

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Strings apparently permeated the space-time continuum, perhaps even creating it.

The good news about string theory was it did combine quantum theory and relativity. The bad news was, it required a universe of 26 dimensions and predicted a particle with a mass having an imaginary number—a tachyon. Physicists were not ready to deal with that concept yet.

But they were excited about another prediction this strange theory made. It predicted the vibrating strings would create a particle with no mass, with a spin of 2, that would exert force over extreme distances. String theory was the first theory to predict the graviton.

That prediction alone had every PhD candidate and grad student at the chalkboard working on the math of string theory to solve the Gordian knot of 26 dimensions and imaginary particles. The answer came from work done at about the same time of Nambu, Susskind and Nielson’s universe shattering theory.

A plethora of researchers had long been looking for a way to relate bosons and fermions (the particles that form matter). Where bosons have integer spins, fermions have half-integer spins.

We talked earlier about symmetry. These researchers developed a theory called sypersymmetry that linked the particles, but only at very high energies, not at energies seen in the normal quantum world. Yet, supersymmetry suffers from one failing. It does not include the graviton.

Physicists continued to work at ridding strings of those 26 dimensions and that pesky negative energy tachyon. Based on the famous quantum uncertainty principle, a localized system tends to have a non-vanishing “zero energy point.” But in supersymmetry, where the bosons and fermions are linked, the zero point energies are of opposite sign, and thus cancel each other out. There is no tachyon! But even more exciting, the graviton remains!

String theory without a tachyon became known as superstring theory or even a theory of super gravity. And those 26 dimensions? Well, supersymmetry, by linking bosons and fermions, reduces them to 10. A more manageable number to grasp.

But superstrings had its own curveball to throw.

It seems strings can be either open—with two end points like a line—or closed in a loop. When two open strings touch, they join to become one longer string. If the two end points touch each other, they join to form a closed string. So we have a theory of strings that include both open and closed strings.

However, if we consider only closed strings, we can never have open strings. If two closed strings contact, they form a single closed string.

The open string theory fits beautifully with quantum subatomic theory—at first glance. At low energies, there is the graviton, and exactly the proper gauge fields to form the photon, and all the proper bosons. Fermions are present as well and are of the proper ‘handedness.’

Ah, but all is not perfection with this so called Type I string theory. Besides requiring 10 dimensions, the symmetry group associated with the gauge particles is much larger than that found in the quantum world. And the particles are all massless, contrary to what we know of particles such as the electron and quarks.

In attempts to solve these problems, physicists worked to develop other string theories based on closed strings. Two came to the fore, called IIA and IIB. These had problems, however. They don’t have gauge particles and as a result fermions have no charge. Each had other problems as well, and they fell into disrepute until recently.

In their efforts to solve the problems with the Type II theories, physicists developed a hybrid “herterotic” theory. The excitation of closed strings appears like waves moving along the loop. Some move left and some move right, but they do not interfere with each other. The right moving waves are supersymmetric.

But the left moving waves have an exotic origin. It appears that these left moving waves are made up of tiny circles that are the missing 16 dimensions of the 26 dimension theory all curled up! This gives the left moving waves an additional 16 degrees of freedom in which to vibrate. And these extra degrees of freedom are manifested as gauge fields!

One question remained regarding the 16 dimensional circles. They created a torus as they moved around the string. But what size was the torus? It turned out there were two possible answers. One answer gives a gauge symmetry group similar to the Type I theory. The other gives a completely new fifth theory with a gauge symmetry group one-fourth the size of the other. This theory is called the E(8) x E(8) theory.

This theory became the toast of the string theory world for a time, because it was the one that seemed most prone to a process called compactification--that is compressing the sting’s 10 dimensions into the four we observe.

But further work developed new concepts such as membranes, manifolds…and an 11th dimension.

We talk about these in Part 2.

http://www.superstringtheory.com/basics/basic3.html

http://theory.tifr.res.in/~mukhi/Physics/string2.html

http://www.superstringtheory.com/basics/basic3.html

http://www.superstringtheory.com/history/history3.html