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© Copyright 1999, Jim Loy
We live in a world of three dimensions. Well, we only perceive three dimensions. We can hypothesize many more dimensions. But, they are difficult to imagine.
Because of Einstein, we often call time the fourth dimension. Special relativity shows that time behaves surprisingly like the three spatial dimensions. The Lorenz equations show this. Length contracts as speed increases. Time expands as speed increases.
Scientists have been graphing time, as if
it were a length, for hundreds of years. To the left is a typical graph,
showing two things in motion at the same speed, one to the left and one to the
right. Time never behaves exactly like a spatial dimension. You cannot go
backward in time. And you normally cannot go forward at different rates. But,
there are surprising parallels. For some purposes, it is handy to call time a
fourth dimension. For other purposes, it is not.
Pretend, for a moment, that there are more than three spatial dimensions. What is a four or five-dimensional cube like? It is hard to visualize. But, we can make a few deductions about such an object. What if a 5-dimensional cube is 2 centimeters on a side, what is its 5-dimensional volume? Well, we can easily generalize from the first three dimensions. A 2x2 square is 4 (2x2) square centimeters in area. A 2x2x2 cube is 8 (2x2x2) cubic centimeters in volume. A 2x2x2x2x2 5-dimensional cube is 32 centimeters-to-the-5th-power in 5-dimensional volume. None of that can be visualized. But, it makes sense. What is the distance between two points in 5-space? You can easily deduce a 5-dimensional Pythagorean Theorem.
Addendum:
I once read in a science fiction story that time is the fourth dimension, and space is the fifth. That's pretty poor; space is the first three dimensions, and there may be more spatial dimensions that we cannot observe or interact with. One would expect a science fiction author to get the simplest science right.