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READING (5B)

• Before reading the passage, read its headline and say what you know about the problem. Discuss the problem with your partners. Then read the passage and And the facts supporting your ideas.

HOW MANY DIMENSIONS EXIST?

It is usually taken for granted that there are three dimensions of space and a single dimension of time. That is, any event that occurs anywhere in the universe can be assigned a location in space using three coordinates and a location in time using one. *But physicists and mathematicians have studied hypothetical worlds in which more or fewer dimensions exist, and so questions arise as to whether the usual belief about our world is strictly correct, and if so, whether we can find any reason for it being true. For example, we might consider the possibility that there are really four dimensions of space, but that for some reason, all of the phenomena that we usually observe have the same value for one of the space coordinates.

It has been known for a century that if the dimensionality of space were other than three, and if free motion were possible in all of the dimensions in the same way, then some of the known laws of physics would not obtain. Newton's inverse square law for the force of gravity is one such. This argument gives additional evidence that space is in fact three-dimensional, but does not explain why this is so. * Furthermore, it does not rule out the possibility

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that our world has more than the expected number of dimensions, but that most phenomena are restricted in how they can vary in the extra dimension.

Our approach to the question is to consider how spaces and times with different numbers of dimensions might behave. For example, one might find that the dimensionality of space and time can itself undergo evolution, and that the values familiar to us are the present result of that evolution. Such an approach would involve relations between the number of dimensions and other physical quantities such as the temperature of the universe. Through these relations, the dimensionality would be determined by these other quantities. Since dimensionality is usually taken to be a whole number, it might not be possible for a dimension to disappear through evolution. *Instead, what might happen through evolution is that some extra dimensions could become suppressed in comparisons with others. Our present picture of the expansion of the universe makes this idea much more plausible than it was once. Since everything was once much closer together than it is now, we can imagine that there are indeed more dimensions than we think. The expansion of the universe may have taken place asymmetrically, so that in one of the dimensions there has been little or no expansion, and the scale of distances in that dimension would still be as small as it was at the beginning of the universe.

If this idea is correct, it would mean that there really are more than the familiar number of dimensions. *It is intriguing to think that it might be possible to find some technological means to find and study the usually inaccessible dimensions. Very likely some phenomena would be different in a universe with more than four dimensions, even if there were no symmetry between the different dimensions. It would be of great interest to identify such phenomena and to see if they can be observed.

*Theoretical investigations have shown that if the general theory of relativity is set up in a space-time of more than four dimensions, and if the extents of the extra dimensions are made small and connected like a cylinder, then the resulting theory describes not only gravity, but also electromagnetism and other fields that have been introduced to describe subatomic particles. The extra dimensions in this case are associated not with space and time, but with the internal symmetries. Physicists are actively trying to unite space-time symmetries and internal symmetries in this way.

If other dimensions do exist, we would still want to account for the precise number through some more basic principles. In the type of theory just described, the total number of dimensions would be related through an internal symmetry to the number of quantum fields that exist. But we should still need to understand why precisely four dimensions have expanded while the others remained small. *The question of the dimensionality of space-time is ripe for more serious investigation.

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