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