Unification of Physics
Many physicists have long argued the conceptual simplicity of the Universe, and have sought to explain its workings in a manner consistent with that simplicity. In the late sixteenth century Italian astronomer and physicist Galileo Galilei demonstrated that mathematical laws describe Earthly physical phenomena. In the early seventieth century English physicist and mathematician Sir Isaac Newton proved the universality of those physical laws. Ever since, the history of theoretical physics has shown an evolution towards greater simplicity, an evolution towards a description of nature in terms of fewer, and more logically coherent, ideas.
This unification of physical theory is largely due to the realization that a few unifying principles apply to nature as a whole. These principles, which transcend all branches of physics, point to a concise fundamental structure of the world, and can be expressed simply: nature is both economical and symmetrical.
Open any physics text, and one is confronted with scores of equations, English physicist and mathematician Sir Isaac Newton's laws of motion and gravity, Scottish physicist James Clerk Maxwell's equations, Austrian physicist Erwin Schrödinger's equation, German-American physicist Albert Einstein's relativity equations, and the list seems endless. Yet, every one of them can be derived by invoking a single principle, first enunciated in 1834 by the Irish mathematician Sir William Rowan Hamilton, the principle of least action.
As with most notions in physics with abstract principles, a simple example taken from the realm of mechanics can suffice for exposition. A particle travels from point A to point B. Imagine an infinite number of different paths over which the particle may travel on its journey between those two points. How does nature choose the unique path actually taken? For each path, a particular mathematical function, called the action, takes a numerical value. The actual path is the one that yields the minimum value; the action evaluated over any path other than the actual path is larger. In the same manner, consider what will be the electric field surrounding a particular charge distribution, or what will be the temperature change in a gas as it expands. In each of these cases, the actual result will be the one that minimizes the action associated with that process. It is a simple idea, and is pervasive in nature.
Various geometrical figures contain a familiar symmetry. The mathematical definition of that symmetry is invariance under a symmetry transformation. The letter A is reflection invariant, since it is identical to its mirror image. Rotate a square by 90 degrees (or any multiple of 90 degrees), and it remains a square; it is rotation invariant under those transformations. The same definition holds for mathematical expressions. When the laws of physics are expressed mathematically they are symmetrical; they are invariant under a large number of symmetry transformations. Those invariances have remarkable consequences. For example, if the laws are translation invariant (which means that the laws here are the laws everywhere), then momentum must be conserved. If the laws are time translation invariant (which means that the laws now are the laws at any time), then energy must be conserved.
But what are the symmetries that physical law obeys? Identifying the proper symmetries leads to uniquely defined unified theories, in which a single mathematical model encompasses what had previously been thought to be unrelated phenomena. For example, try to write down a Lorentz invariant theory of the electric field, and two things happen. First, there is one, and only one set of Maxwell's equations that satisfies the symmetry requirement. It must be accepted, or give up the symmetry requirement altogether. Second, that model must, by necessity, describe the magnetic field as well. Thus, if physical law is Lorentz invariant, then Maxwell's theory of electromagnetism, which unites electricity and magnetism, must be the correct description of those phenomena; there is no other choice.
In the 1950s, physicists began exploring the quantum field theories that possessed a symmetry called local gauge invariance. Consider English physicist Paul Dirac's (1902-1984) quantum theory of the electron. Modify it so that it will be invariant under a particular set of symmetry transformations, and one result is the quantized form of Maxwell's unified theory, quantum electrodynamics (QED). In 1967, both Steven Weinberg and Abdus Salam independently realized that the field theory invariant under a larger group of symmetry transformations unites electromagnetism and the weak nuclear force to form what is now understood as the electroweak interaction. The search for the ultimate symmetry group which would unite all four forces in nature (the strong nuclear force, the weak nuclear force, the electromagnetic force, and gravity) was on. Thus far, a more comprehensive unifying theory remains elusive.
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