I grew up reading stories about Superman and Batman during the Golden Age of comics when these superheroes fought villains and beings not only from outer space and here on earth, but from other dimensions as well. This early introduction to visualizing more than just the four dimensions of space-time left me with a desire to find out if these other dimensions were really real or just science fiction or fantasy. In the last 25 years the concepts of other dimensions have become a mainstay in movies and television that deal with these same categories. Words such as subspace, warp-drive, hyperdrive, hyperspace, warpspace, multiverse, multidimensional, and super-space are familiar terms to followers of science fiction. But the concept of other dimensions, like many aspects that were once only part of science fiction, has become part of mainstream science. In both superstring and supersymmetry, additional dimensions play a key role in the theory.

In the 1970s, the success of gauge symmetry in understanding the interaction between forces and particles encouraged theorists to attempt to find a geometrical description of everything in terms of one great symmetry, or supersymmetry. This supersymmetry, or SUSY for short, utilizes two main concepts to unify the four forces and all of the elementary particles:

- The addition of four other dimensions to the already existing four dimensions of space-time to give us a total of eight dimensions.
- Each real world particle has a corresponding superpartner that interacts with it and which mediates the movement from four dimensions to eight dimensions and vice versa.

**Gauge symmetry** is a concept used in field theory (like in an electromagnetic field) to describe a field for which the equations describing the field do not change when some operation is applied to all particles everywhere in space. Remember that in science, symmetry is a property that means it's the same at all times and all places. The term “gauge” simply means to measure. The point is that fields with gauge symmetry can be remeasured from different places without affecting their properties.

Let's look at these two features in a little more detail. As mentioned earlier, nature has seemingly divided herself into two main classifications of particles, matter particles or fermions and force particles or bosons. In geometric terms, the key difference between these two kinds of particles is the spin rotation. In the previous discussion on spin, we saw that fermions need 720 degrees or two rotations in order to get back to where it started. But bosons have to rotate only once or just 360 degrees to get back to where it started. SUSY is a kind of symmetry that unites these two different patterns of behavior in one geometric framework.

Supersymmetry works by attaching another four dimensions to the four dimensions of ordinary space-time. The resulting eight-dimensional geometry, which is known as superspace, provides the needed room for the extra rotation that a fermion needs to get back to its original starting configuration. However, these extra dimensions are not space or time dimensions and are different than the dimensions I'll be talking about in the next section on string theory. The extra dimensions are mathematical/geometrical constructs that utilize the mathematics of SUSY to rotate particles in and out of the extra four dimensions. Let me explain.

The assigned values of ^{1}/_{2} spin or 1 spin reflect the relationship that particles have to 360-degree rotation. In other words, a value of 1 means that it takes 1 complete rotation of the particle to complete 360 degrees. And just in case you didn't know, there are 360 degrees in a circle. The fermions, which only have a spin of ^{1}/_{2}, means that even though they rotate 360 degrees, which is one complete rotation in the normal sense, they are only “halfway” to the point where they first started from. They have to complete another whole rotation, or 720 degrees altogether to get back to the point where they started.

In the mathematics of SUSY, there is an operation that is equivalent to rotation in the everyday world. But instead of rotating an object in four-dimensional space-time, this operation rotates an object from the usual four-dimensional space-time into the eight-dimensional geometry inhabited by fermions. And of course, there is an equivalent operation that rotates an object out of eight-dimensional geometry inhabited by fermions back into the everyday geometry four-dimensional space-time. What this means is that it is possible to transform bosons into fermions and fermions into bosons, and what we see as two different kinds of particles is an illusion created by geometry.

If this is a little confusing, I hope to make it less so by the time we're through. In our discussion above, rotating fermions in this way would not produce any of the known bosons. Within the structure of this theory, none of the known bosons correspond to the rotated versions of known fermions, and none of the known fermions correspond to rotated versions of known bosons. So if supersymmetry is to apply to the real world, there must be a supersymmetric particle, also called a superpartner, or a sparticle, for every known type of boson and every known type of fermion. This of course doubles the number of varieties of particles in the world. The following is a table of some of the known particles and their corresponding sparticles.

Besides the predictions in supersymmetry for all of the superpartners, there is a prediction for another particle related to the “mechanism” that is responsible for the symmetry breaking. The currently favored mechanism is known as the *Higgs field*, after Peter Higgs of the University of Edinburgh. The Higgs field acts as a sort of “party pooper” in that when it achieves its lowest energy state (which all systems like to achieve), it breaks the symmetry. The prediction is that the Higgs field is carried by a massive particle, known as the Higgs Boson, sometimes affectionately called the “God particle.” The discovery of this particle is currently one of the goals of the huge accelerators. If found, this particle would open the doors to revealing how symmetry was first broken shortly after the big bang and lead to a firm foundation upon which can be built the “primary” theory.

Known Particles That Transmit Forces and Their Possible Superpartners | |||
---|---|---|---|

Name | Spin | Superpartner | Spin |

Graviton | 2 | Gravitino | ^{3}/_{2} |

Photon | 1 | Photino | ^{1}/_{2} |

Gluon | 1 | Gluino | ^{1}/_{2} |

W^{+,-} | 1 | Wino^{+,-} | ^{1}/_{2} |

Z^{0} | 1 | Zino | ^{1}/_{2} |

Higgs | 0 | Higgsino | ^{1}/_{2} |

Known Particles That Make Up Matter and Their Possible Superpartners | |||
---|---|---|---|

Name | Spin | Superpartner | Spin |

Electron | ^{1}/_{2} | Selectron | 0 |

Muon | ^{1}/_{2} | Smuon | 0 |

Tau | ^{1}/_{2} | Stau | 0 |

Neutrino | ^{1}/_{2} | Sneutrino | 0 |

Quark | ^{1}/_{2} | Squark | 0 |

And as with other broken symmetries in particle physics, the implication is that at higher energies, or in other words, at distances much closer to the point of expansion, there was a complete symmetry. In this case, the complete symmetry would show that each type of boson was accompanied by a fermion superpartner and vice versa. The reason why the symmetry is broken is assumed to be that the supersymmetric partners are much more massive than the counterparts we know today, and could be manufactured only at very high energies. So the search is on to find these massive particles in the most powerful particle accelerators we have.

To put this theory in a nutshell, if that's really possible, it could go something like this. Supersymmetry is the idea, or hypothesis, that the equations of the TOE will remain unchanged even if fermions are replaced by bosons, and vice versa. The replacement occurs in the equations, not for fermions or bosons in the real world. But by showing how these particles interact, even just mathematically, gravity, along with the other three forces, because of the particles that carry them, becomes unified with the matter particles. The broken symmetry, which reflects the structure of the everyday world around us, is again unified under the geometrical/mathematical-particle/sparticle model of supersymmetry.

Excerpted from The Complete Idiot's Guide to Theories of the Universe © 2001 by Gary F. Moring. All rights reserved including the right
of reproduction in whole or in part in any form. Used by
arrangement with **Alpha Books**, a member of Penguin Group
(USA) Inc.

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