What Is the Difference Between 4-D & 3-D?

By J.T. Barett
Mathematicians use hypercubes to describe four dimensions of space.
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Although relativity, space-time and multiple dimensions can be heady subjects, the basics are fairly straightforward. From traditional science and everyday experience, you can treat the world as a three-dimensional place having width, depth and height. However, in the early 1900s, Albert Einstein and others theorized that time -- previously thought to be a completely separate phenomenon -- is a fourth dimension.

Three Spatial Dimensions

Ordinary objects and the space they inhabit have three dimensions you can easily see and measure. When you want to know how much space an object takes up, you measure it, plug the numbers into a formula that applies to the shape and get the object’s volume. For example, a marble has a radius of 1 centimeter, and the formula for the shape, a sphere, is 4/3 * pi * radius^3. The marble has a volume of 4.12 cubic centimeters. Since space has three dimensions, you can explore it by moving up and down, side to side, and forward and backward.

Four Dimensional Space-Time

Einstein’s Theory of Relativity joins time to the familiar three dimensions to create a four-dimensional universe. The idea came about because three dimensions no longer seemed sufficient to describe new scientific observations. For example, time passes slightly more slowly on the surface of the earth than at the top of a tall skyscraper; this is because the earth’s mass “bends” space-time, and it bends less the farther you move away. Although you can move freely in three dimensions, you are stuck moving “forward” in the time dimension.

Four Spatial Dimensions

Mathematicians regularly work with dimensions and have names for imaginary objects with dimensional properties. A point, for example, has zero dimensions; it has no width, depth or height. A line has one dimension, and a plane has two. A cube has three dimensions, and cubes have familiar counterparts in everyday life -- boxes, ice cubes and even grains of salt. Mathematicians propose a four-dimensional “cube” called a hypercube or tesseract. A corner of a cube has angles that go into three dimensions, but a tesseract’s go into four. Because it occupies four spatial dimensions, you cannot make a “real” tesseract in three-dimensional space, although you can represent it as an image. The idea of the tesseract helps students grasp the ideas of higher dimensions.

More Dimensions?

Three dimensions are obvious; four are a stretch. How can there possibly be more? Scientists have theories about the nature of the universe that require up to 11 dimensions to explain. For example, in superstring theory, all known phenomena come from tiny string-like objects smaller than an electron that vibrate in 11 dimensions. Still other theories look at our 4-dimensional universe as a tiny part of a larger object that has 10 or 11 dimensions, holding that our universe grew from or is attached to it.

About the Author

Chicago native J.T. Barett has a Bachelor of Science in physics from Northeastern Illinois University and has been writing since 1991. He has contributed to "Foresight Update," a nanotechnology newsletter from the Foresight Institute. He also contributed to the book, "Nanotechnology: Molecular Speculations on Global Abundance."