clifford_a-_pickover_surfing_through_hyperspacebookfi-org

84 surfing through hyperspace
dimensional. A hypersphere's surface is three-dimensional. Many physicists
in the late 1800s thought forces like gravity and electromagnetism
could be transmitted by vibrations of a hypersphere."
Sally tosses the bone to you. "You already told me Einstein proposed
the surface of a hypersphere as a model of our universe. It would be finite
but boundaryless, like the surface of a ball. It's an interesting theory."
You catch the bone with a deft flick of your wrist and toss it onto a chair.
You reach into a cabinet and remove two tennis balls.
Sally stares at your balls. "Why is it so hard to imagine our space as
hyperspherical?"
You throw one of the balls to Sally. "The curvature of our 3-D universe
would be in the direction of the fourth dimension. Our 'straight
lines' would actually be curved, but in a direction unknown to us. This
would be similar to a creature living on the two-space surface of a sphere.
Lines that appeared straight to him would actually be curved. Parallel
lines could actually intersect, just as longitude lines (which seem parallel
at the equator) intersect at the poles. This curvature could be hard to
detect if his, or our, universe were large compared to the local curvature.
In other words, only if the radius of the hypersphere (whose hypersurface
forms our 3-D space) were very small, could we notice it."
Sally plays with the ball, studying its smooth surface. "What would
happen if we lived in a hypersurface of a hypersphere whose radius was
the size of a football stadium?"
"In such a small universe, if you run in a straight line, you'd return to
your starting point very quickly. In any direction you looked, you'd see
yourself" (Fig. 4.2a). You pause dramatically before launching into a
more intriguing line of thought. "The idea that our 3-D space is the surface
of the hypersphere is seriously considered by many responsible scientists.
This idea suggests another, even wilder possibility."
"Yes?"
"Sally, consider Flatland existing as a surface of a sphere. Pretend the
surface of the tennis ball in your hand is Flatland. Three dimensions permit
the possibility of many separate, spherical Flatlands floating in 3-D
space. Think of many floating bubbles in which each bubble's surface is
an entire universe for Flatlanders. Similarly, there could be many hyperspherical
universes floating in 4-D space" (Fig. 4.2b).
Sally nods. "If there are many hyperspherical universes, why can't we
escape from our hypersphere and explore these other universes?"