Space-time

From the theory of relativity, space and time were found to be interwoven and inseparable. Space cannot be defined without a consideration of time. The measured rate of the passage of time will be slowed-down by the warping of space-time.

Gravity could be defined as the effect from the curvature of spacetime. Spacetime could be defined as the difference between a perfectly Euclidian (i.e., straight line, right angle, checkerboard grid) type of universe, and a curved or slightly bent reference frame. (Hint: Try drawing only perfect, 90o squares to completely cover the surface of an orange, or of a basketball. The geometric results suggests how curved spacetime differs from linear, or straight space.)

A useful analogy would be: imagine the shortest path between two dots painted on the surface of a ball. Unless the dots were on any perfect diameter, located at the exact opposite sides of the ball, there would be many different-lengthed paths between those two points. There will be at least one path on the surface of the ball which is the shortest. Many curved paths could exist which would eventually connect the two dots. To a dot or a period travelling along any given path, the shortest path may not be very obvious.

If we would enlarge the size of the ball, and shrink the distance between the two points, the ratio of path-length curvature to straight line-through the ball path-length would decrease. The surface curvature would exist until the two points merged or until the surface of the sphere flattened out totally. In a similar way, the shortest path which we can chose in our local "almost-flat" space-time would still possess some space-time curvature if a gravitational field existed anywhere in the universe.

Just for comparison purposes, consider the ratio of curving or of warping of a diagram drawn on the surface of a ball compared to the same diagram drawn flat on an uncurved 2 dimensional sheet of paper. View the drawing on the ball from an external 3D (3 axes) reference frame then view the 2 dimensional flat diagram. Imagine a straight line "short cut" through the body of the ball, directly between the two ends of the diagram. This path, in this real-life situation would symbolize the difference in our imagination between the path of a real-time light beam passing through curved vs. uncurved spacetime.

Although the short-cut, in this situation, would be obvious to a person situated in our 3 dimensional existence, to any period confined on the surface of the ball, the barrier to fully understanding the nature of the curvature would be almost insurmountable. In addition, the curvature of the "two-dimensional" surface of the ball would be unsuspected and almost undetectable if the sphere size encompassing the curvature was greatly increased.

In our universe, the slowdown in time could be attributed to the warping or the bending of space-time. The increased (or out- of-dimension) path length a ray of light would need to traverse in "bent" space-time would be analogous to our example above using two and three dimensions. To a four dimensional (or more) being, the path could be checked, and gravitationally curved (or time- warped) lightbeam pathlength would be found to be slightly longer than a similar distance in a section of space-time with no gravitational curvature1.

The hypothetical, multi-dimensional dwelling beings could view our situation in our gravitationally-spacetime-curved "3-dimensional" universe as an increase in the effective volume of spacetime occupied by a fixed amount of our matter-energy. If we keep the total energy content constant, and spread-out the energy contents into the larger, 4 (or more) dimensional volume, our only alternative is to effectively decrease the apparent "3-dimensional" energy in our volume of space(time). Since we cannot detect this increased (hyper)volume, we would conclude (and rightly-so, from our vantage point) that the 3-dimensional energy in the volume of spacetime which we can detect, had decreased.

The three dimensional viewpoint in the above situation cannot be short-changed, thanks for the most part, due to the law of conservation of energy. From our limited 3 dimensional viewpoint, we will detect the kinetic energy of the matter increasing by the same amount of energy it "apparently" loses due to 4-dimensional dilution.