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 VOL. 23, NO. 18MARCH 27, 1998 

Prof. Brian Greene:

A Universe of at Least 10 Dimensions

String Theory Finally Reconciles Theories of Relativity and Gravity


String theory requires at least six extra spatial dimensions tightly curled-up to microscopic size. Here we see two such dimensions, curled-up into tiny spheres.

Physicists have spent much of the 20th century answering three major questions and redefining space and time in ways that contradict human intuition.

  The three questions, all of which deal with the nature of the universe, are:

  • Why can’t you run away from a light beam and diminish its approach speed?

  • If the sun were to explode, would you feel the gravitational impact on the Earth’s orbit before you saw the explosion eight minutes later?

  • Why are the two major theories in physics—one dealing with stars and galaxies, the other with atoms and subatomic particles, both proved time and time again—mutually incompatible?

  The answers to these questions have not been easy for physicists to find or for lay people to comprehend. Albert Einstein demonstrated that time slows at great speeds and that space is warped. The current “master theory” of particle physics holds that all matter is composed of tiny vibrating strings, which is easier to accept than the theory’s requirement that there need to be at least six more spatial dimensions in addition to time and the three spatial dimensions that we can perceive.

  The question of how there can be at least 10 dimensions and probably 11 dimensions when there only appear to be four was one of the issues explored by Professor of Mathematics and Physics Brian Greene in a Graduate School of Arts and Sciences’ Dean’s Distinguished Lecture, “Space And Time Since Einstein,” delivered Mar. 12 at the University Club. Greene, who is also writing a book on the subject, The Elegant Universe, to be published in January 1999 by W.W. Norton, described the three central conflicts that have driven physics in the 20th century.

  The first conflict, which concerns motion and the speed of light, arose in the early 1900s. When an ordinary object such as a baseball or snowball is thrown at us, we can run away from it, causing the speed with which it approaches us to decrease. But if you try to run away from a beam of light, you cannot make it approach you any slower.

  “Light will always approach you at 186,000 miles per second whether you run away from it, run toward it or stand still,” said Greene. “Einstein resolved the paradox by showing that our intuition regarding space and time was wrong, that our conception of motion—the distance something travels divided by the time it takes to get there—was incorrect.”

  Einstein’s Special Theory of Relativity explained that the speed of light is a constant and that at great speeds, time slows down (relatively speaking) and space becomes distorted.

  But in solving the paradox, Einstein came into conflict with another towering figure of physics, Isaac Newton and his Theory of Gravity, which holds that the gravitational force is transmitted instantaneously—or faster than the speed of light.

  “If the sun were to explode,” said Greene, “we would not know about it visually for eight minutes because it would take eight minutes for light from the explosion to reach us from the sun. According to Newton, however, the gravitational disturbance would immediately cause our orbit to abruptly change. So, the influence of gravity, in Newton’s Theory, is transmitted much faster than light. Einstein knew that nothing could exceed the light speed, and for the next decade he struggled to resolve this conflict.

  “His answer is the General Theory of Relativity, by which he showed us how gravity is transmitted through the warping of space, and if you look closely at how the space warps travel, much like ripples in a pond, you find they travel at light speed. And so, gravity is transmitted at exactly the same speed as light.

WHAT MATTER IS MADE OF—As explained by Brian Greene, above, all matter consists of atoms which are themselves composed of electrons swarming around a central nucleus. String theory adds a new ultramicroscopic layer by declaring that subatomic particles actually consist of tiny loops of vibrating energy, “strings.”

  “In actuality, then, if the sun were to explode, we would not know about it immediately by an abrupt change in our orbital motion. Instead, exactly when we saw the explosion, we would feel it.”

  Einstein’s General Theory of Relativity, which is applicable to things very big—gravity, stars, galaxies—became one of the two pillars upon which 20th century physics is based. The second pillar is Quantum Mechanics, which describes the microscopic structure of the world—atoms and subatomic particles.

  “Each of these pillars has been tested for accuracy,” said Greene. “Each comes through with flying colors, and yet, the two theories are mutually incompatible. And that has been the driving conflict in physics for the last half century.

  “The heart of Quantum Mechanics is summarized by (Werner) Heisenberg’s Uncertainty Principal and that tells us that there are certain features of the microscopic world that we cannot know with total precision. It’s not a limit of technology; there are just some complimentary things we can’t know simultaneously.

  “For example, Heisenberg showed us that when you look at smaller and smaller regions of space, the amount of energy embodied in that space is known with less and less precision. There is a tremendous amount of roiling, hot, kinetic energy bound up in every little morsel of space and the smaller the morsel the more the energy.

  “If you’ve got a lot of energy in tiny distances, it means that space is incredibly frothy and wildly undulating, and these undulations are so violent that they completely destroy Einstein’s Geometrical Model of Space, the central principle of General Relativity. On large scales, such as that of galaxies and beyond, these microscopic kinetic undulations average out to zero; we don’t see them. Only when we focus on microscopic distances, do we become aware of the tumult that is going on and realize that it is so severe that Einstein’s theory falls apart.”

  The conflict continued for half a century until the development of Super String Theory, which reconciles Quantum Mechanics with the General Theory of Relativity.

  “If you examine microscopic particles the way people did in the early part of the century, you come to the conclusion that the elementary constituents of nature are little dots that have no further internal structures,” explained Greene. “String Theory tells us that if you were to probe inside these dots with a precision not possible with our present technology, you would find each has a little vibrating loop, a vibrating filament of energy, inside of it. And the difference between one particle of matter and another, according to Super String Theory, is the pattern of vibration that the string is undergoing. Different particles can be compared to different notes that an ordinary vibrating violin string can play—electrons, photons, quarks.

  “String Theory also holds that there is a smallest possible distance in the world, the size of the string. And this distance is just large enough that the pernicious small scale quantum undulations predicted by Heisenberg’s Uncertainty Principle are avoided. Some people feel cheated with this explanation. What it means is that the problem we thought was there was not there at all.”

  String Theory may also lead to a Unified Theory in which all the principles and theories of physics can be distilled into a single overarching statement. String Theory holds that absolutely everything is a manifestation of a single object—a string. When it vibrates one way, it looks like an electron. When it vibrates another way, it looks like a photon. All the particles and all the forces are part of a single unified concept.

STRINGS IN ACTION—Two string loops interact by joining together into a third string.

  “Super String Theory has its own remaking of space-time,” said Greene. “It requires that it have more than three space dimensions.”

  If strings can only vibrate north and south, east and west, up and down, there are not enough variations to account for all the particles and forces. The equations of String Theory require at least six more spatial dimensions.

  Greene used an example of a garden hose to explain why we don’t see these additional dimensions. From a distance, the hose looks like a straight line, and if an ant lived on the hose, it could move up and down its length. But if you move closer to the hose, you realize it has another dimension, its girth, and the ant could walk around the hose as well.

  Dimensions, therefore, would come in two types: those that are long and visible and those that are tiny and curled up, existing only on the microscopic level of strings.

  “String Theory has the capacity to describe not only how the universe is, but how it got to be the way it is,” said Greene. “It may give us an explanation of why there is space and why there is time. In the same way that cloth is made of thread woven together in a pattern, some theorists have suggested that strings themselves are the threads of space and time. Space and time themselves may be the result of an enormous number of little vibrating strings all coalescing together and vibrating in a particular coherent pattern.

  “If so, you can imagine a state of the universe when the strings have not coalesced in that manner, and space and time have not yet been formed. And it is possible that the universe could return to that state.”

  Could strings also coalesce into another kind of universe?

  “In principle,” said Greene, “it is possible.”