The typical size of a string is near the Planck length, or 10 33 centimeter (less than a billionth of a billionth of the size of an atomic nucleus). In string theory, a leading approach to that unification, particles are in actuality one-dimensional objects, small vibrating loops or strands. The possibility of extra dimensions has also come to play a vital role in unifying general relativity and quantum mechanics. Thus, from a theory of gravity alone in five dimensions, we obtain a theory of both gravity and electromagnetism in four dimensions. The circumference determines the relative strengths of the electromagnetic and gravitational forces. That is, the equations governing its behavior are identical to those of electromagnetism. Amazingly, the angle field turns out to mimic an electromagnetic field living in the four-dimensional world. At every location within it, the angle and circumference have some value, just like two fields permeating spacetime and taking on certain values at each location. The large spacetime behaves according to ordinary four-dimensional general relativity. We can split this geometry into three elements: the shape of the four large spacetime dimensions, the angle between the small dimension and the others, and the circumference of the small dimension. General relativity would then describe the geometry of a five-dimensional spacetime. The three dimensions that we see are expanding and were once much smaller, so it is not such a stretch to imagine that there is another dimension that remains small today.Īlthough we cannot detect it directly, a small extra dimension would have important indirect effects that could be observed. Moreover, we already know from general relativity that space is flexible. If the extra spatial dimension is curled up into a small enough circle, it will have eluded our best microscopes-that is, the most powerful particle accelerators. Kaluza and Klein noticed that Einstein's geometric theory of gravity might provide this connection if an additional spatial dimension existed, making spacetime five-dimensional. Both fall off inversely proportional to the square of the distance from their source, so it was tempting to speculate that they were connected in some way. KALUZA AND KLEIN put forth their concept of a fifth dimension in the early part of the 20th century, when scientists knew of two forces-electromagnetism and gravity. What determines this shape? Recent experimental and theoretical developments suggest a striking and controversial answer that greatly alters our picture of the universe. In both the Kaluza-Klein conjecture and string theory, the laws of physics that we see are controlled by the shape and size of additional microscopic dimensions. The Kaluza-Klein idea has been resurrected and extended as a feature of string theory, a promising framework for the unification of quantum mechanics, general relativity and particle physics. The search for a unified theory is a central activity in theoretical physics today, and just as Einstein foresaw, geometric concepts play a key role. In fact, it was premature: physicists first had to understand the nuclear forces and the crucial role of quantum field theory in describing physics-an understanding that was only achieved in the 1970s. Einstein's search for a unified theory is often remembered as a failure. He was particularly attracted to work by German Theodor Kaluza and Swede Oskar Klein, which proposed that whereas gravity reflects the shape of the four familiar spacetime dimensions, electromagnetism arises from the geometry of an additional fifth dimension that is too small to see directly (at least so far). Given the success of replacing the gravitational force with the dynamics of space and time, why not seek a geometric explanation for the other forces of nature and even for the spectrum of elementary particles? Indeed, this quest occupied Einstein for much of his life. This surprising and beautiful idea has been confirmed by many precision experiments. The curvature of spacetime keeps the earth in its orbit around the sun and drives distant galaxies ever farther apart. When the apple falls, it is actually responding to this warping of time. The earth's mass, for example, makes time pass slightly more rapidly for an apple near the top of a tree than for a physicist working in its shade. Any massive body leaves an imprint on the shape of spacetime, governed by an equation Einstein formulated in 1915. According to Albert Einstein's theory of general relativity, gravity arises from the geometry of space and time, which combine to form spacetime.
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