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DEAN HARTLEY

Science and Speculative Science in Folded Universe Series

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Addendum:

This novel is science fiction. That means it is a story with some connection to science, particularly speculative science. 

Physics

We experience three directional dimensions and one time dimension.  However, there is another dimension that effects us - it is an imaginary dimension.  This dimension is useful in describing electromagnetic radiation, which travels through space over time, yet requires this extra dimension.

Unit circle

We also have proof that space has a local curvature; light is bent as it passes through gravity wells.

gravity well

 

Mathematics

Mathematically, curvature can be positive, zero, or negative.  By convention, the surface of a sphere has positive curvature.  A saddle point has negative curvature.  You can think of the surface not having enough stuff to lie flat as you get further from your reference point.  The constant pi is the ratio of the diameter of a circle and its circumference.  On a sphere, this ratio is not constant and is less than pi.  For negative curvature, there is too much stuff for the surface to lie flat.  A circle drawn around a point on the inside of a torus would have a ratio greater than pi.  The brim of a typical cowboy hat has this feature.

spheresaddle point

 

Fiction

The fictional assumption is that our universe has generally negative curvature and thus has many folds.  In the one-dimensional view below, the universe is folded back and forth to fit into a small area.  The observed directional dimension follows the curve and the extra dimension is the imaginary dimension.  Thus, if you could travel along the imaginary dimension, you could skip lots of conventional space and get to a distant location more quickly.  The book assumes a method of doing this that matches a disk at our location with a disk at a distant location.  The math uses Dehn's lemma and the substitution of axes.  The physics is fictional.

sin 1 over x

The figure below shows how two different starts (four-pointed objects) might be easily accessible from the Sun (five-pointed object).

simple folds

 


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