The Principle of Symmetry Reduction

Symmetry reduction, also referred to as symmetry breaking, is a decrease in the symmetry of a system, usually a result of some type of change in phase. In the context of cosmology, it refers to a "crystallization" of fundamental forces or an expansion of dimensions. To illustrate the principle of symmetry reduction, consider the rather symmetric example of liquid water. When, at low enough temperatures, it freezes into ice, its symmetry is drastically reduced - ice has many surface irregularities that cause it to have much less symmetry than water. The same principle applies to cosmology.

The Fundamental Forces

Symmetry reduction in cosmology often refers to the four fundamental forces. Sheldon Glashow, Abdus Salam, and Steven Weinberg showed that the quantum field theories of the weak and electromagnetic forces unite at high enough energy and temperature. Although very distinct in their current conditions - the weak force can scarcely be felt beyond the scale of the subatomic, and electromagnetism accounts for light, x-rays, TV, radio, and a number of other modern conveniences - they essentially dissolve into one another, taking on common properties, when subjected to high energies and temperatures. The point after the big bang (ATB) at which they crystallized is the point at which their symmetry was reduced. This has been shown to occur at about 10¹⁵K. It was later found that the strong force merges with the other nongravitational forces as well, yielding one "grand unified" force at temperatures above 10²⁸K and meaning that its symmetry reduction occurred when the early universe cooled below this temperature. (It should be noted that the exact merger of the three forces requires supersymmetry.)

String theory allows gravity to enter the grand unified force as well. With relatively simple choices of Calabi-Yau spaces into which the universe's extra dimensions could be curled, the four forces almost but not quite merge. Careful choice of Calabi-Yau remedies the problem, but this is in itself dangerous because no one knows how to predict the exact form of the correct Calabi-Yau (actually, Joyce manifold, a similar shape in seven dimensions).

However, Edward Witten has shown that the second superstring revolution provides another alternative answer. Witten carefully studied the properties of the forces as they varied with the string coupling constant. He found that the forces can be "prodded" into merging completely without intrduction of a specially chosen Calabi-Yau, but research on this question will continue.

Dimensional Symmetry Reduction

Another type of symmetry reduction involves dimensions and their expansion. A question long speculated upon by physicists involves the reason three spatial dimensions have expanded if there are eleven to choose from. Cumrun Vafa and Robert Brandenberger have studied the question and proposed an answer: wrapped strings constrict the dimensions they encircle, thereby prohibiting the dimensions from expanding. However, strings encircling dimensions can annihilate with antistrings, thus producing an unwrapped string and leaving the dimension free to expand. They imagined two points moving along a line - virtually guaranteed to encounter each other. However, if allowed to move in two dimensions (through a plane), there is little likelihood that they would collide. Similarly, are likely to collide when traveling in three spatial dimensions or less. (Click here for an advanced explanation.) The expansion of three spatial dimensions is dimensional symmetry reduction.

Symmetry Reduction and the Cosmological Constant

The cosmological constant is a term in Einstein's equations representing the inherent energy of vacuum. Today we know that it is zero or very close to it, although Einstein once tried to add the term in order to account for the fact that his equations implied the universe was expanding. (He later called the term "the greatest bludner of my life," although recent research may imply a very tiny constant.) Physicists have shown that the symmetry reduction associated with the four fundamental forces results in an influx of energy into the vacuum of space. In fact, when they tried to calculate the cosmological constant, they got a value 10¹⁰⁰ larger than the experimentally observed value of close to zero. Physicist Sindey Coleman has recently suggested that tiny Planck-sized wormholes are responsible for reducing the vacuum energy to experimentally observed levels.