The Anthropic Principle

As an example of the power of the Anthropic Principle, consider the number of directions in space. It is a matter of common experience that we live in three-dimensional space. That is to say, we can represent the position of a point in space by three numbers. For example, latitude. longitude and height above sea level. But why is space three-dimensional? Why isn't it two, or four, or some other number of dimensions, hke in science fiction? In fact, in M-theory space has ten dimensions (as well as the theory having one dimension of time), but it is thought that seven of the ten spatial directions are curled up very small, leaving three directions that are large and nearly flat. It is like a drinking straw. The surface of a straw is two-dimensional. However, one direction is curled up into a small circle, so that from a distance the straw looks like a one-dimensional line.

Why don't we live in a history in which eight of the dimensions are curled up small, leaving only two dimensions that we notice? A two-dimensional animal would have a hard job digesting food. If it had a gut that went right through, like we have, it would divide the animal in two, and the poor creature would fall apart. So two flat directions are not enough for anything as implicated as intelligent life. There is something special about three space dimensions. In three dimensions, planets can have stable orbits around stars. This is a consequence of gravitation obeying the inverse square law, as discovered by Robert Hooke in 1665 and elaborated on by Isaac Newton. Think about the gravitational attraction of two bodies at a particular distance. If that distance is doubled, then the force between them is halved. If the distance is tripled then the force is divided by nine, if quadrupled, then the force is divided by sixteen and so on. This leads to stable planetary orbits. Now lets think about four space dimensions. There gravitation would obey an inverse cube law. If the distance between two bodies is doubled, then the gravitational force would be divided by eight, tripled by twenty-seven and if quadrupled, by sixty-four. This change to an inverse cube law prevents planets from having stable orbits around their suns. They would either fall into their sun or escape to the outer darkness and cold. Similarly, the orbits of electrons in atoms would not be stable, so matter as we know it would not exist. Thus although the multiple-histories idea would allow any number of nearly flat directions, only histories with three flat directions will contain intelligent beings. Only in such histories will the question be asked, "Why does space have three dimensions?"

Notes:

Folksonomies: anthropic principle

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 Brief Answers to the Big Questions
Books, Brochures, and Chapters>Book:  Hawking , Stephen (2018), Brief Answers to the Big Questions, Retrieved on 2019-03-02
Folksonomies: science popular science