Space and Time Warps
Space and Time Warps
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In science fiction, space and time warps are a commonplace. They are used for rapid journeys around the galaxy, or for travel through time. But today’s science fiction, is often tomorrow’s science fact. So what are the chances for space and time warps.
The idea that space and time can be curved, or warped, is fairly recent. For more than two thousand years, the axioms of Euclidean geometry, were considered to be self evident. As those of you that were forced to learn Euclidean geometry
at school may remember, one of the consequences of
these axioms is, that the angles of a triangle, add up to a hundred and 80 degrees.
However, in the last century, people began to realize that
other forms of geometry were possible, in which the
angles of a triangle, need not add up to a hundred and 80
degrees. Consider, for example, the surface of the Earth.
The nearest thing to a straight line on the surface of the Earth, is what is called, a great circle.
These are the shortest paths between two points, so they are the roots that air lines use.
Consider now the triangle on the surface of the Earth, made up of the equator, the line of 0
degrees longitude through London, and the line of 90 degrees longtitude east, through Bangladesh. The two lines of longitude, meet the equator at a right angle, 90 degrees. The two lines of longitude also meet each other at the north pole, at a right angle, or 90 degrees. Thus one has a triangle with three right angles. The angles of this triangle add up to two hundred and seventy degrees. This is greater than the hundred and eighty degrees, for a triangle on a flat surface. If one drew a triangle on a saddle shaped surface, one would find that the angles added up to less than a hundred and eighty degrees. The surface of the Earth, is what is called a two dimensional space. That is, you can move on the surface of the Earth, in two directions at right angles to each other: you can move north south, or east west. But of course, there is a third direction at right angles to these two, and that is up or down. That is to say, the surface of the Earth exists in three-dimensional space. The three dimensional space is flat. That is to say, it obeys Euclidean geometry. The angles of a triangle, add up to a hundred and eighty degrees.
However, one could imagine a race of two dimensional creatures, who could move about on the surface of the Earth, but who couldn’t experience the third direction, of up or down. They wouldn’t know about the flat three-dimensional space, in which the surface of the Earth lives.
For them, space would be curved, and geometry would be non-Euclidean.
It would be very difficult to design a living being that could exist in only two dimensions.
Food that the creature couldn’t digest would have to be spat out the same way it came in. If there were a passage right the way through, like we have, the poor animal would fall
apart.
So three dimensions, seems to be the
minimum for life. But just as one can think
of two dimensional beings living on the
surface of the Earth, so one could imagine that the three dimensional space in which we live, was the surface of a sphere, in another dimension that we don’t see. If the sphere were very large, space would be nearly flat, and Euclidean geometry would be a very good approximation over small distances. But we would notice that Euclidean geometry broke down, over large distances. As an
illustration of this, imagine a team of painters, adding paint to the surface of a large ball. As the thickness of the paint layer increased, the
surface area would go up. If the ball were in a flat
three-dimensional space, one could go on adding
paint indefinitely, and the ball would get bigger and