Time is a fundamentally different type of dimension than space

One of the most common questions we can ask about any two distinct locations is, “What’s the shortest distance between those two points?” By default, most of us will give the same answer that Archimedes gave more than 2,000 years ago: a straight line. If you take a flat sheet of paper and put two points down on it absolutely anywhere, you can always connect those two points with any line, curve, or geometrical path you can imagine. So long as the paper remains flat, uncurved, and doesn’t have any topological uncanniness to it, the straight line connecting those two points will indeed be the shortest way to connect them.

This is precisely how spaces work in even our three-dimensional Universe: as long as space is flat, the shortest distance between any two points is a straight line. This is true regardless of how or whether you rotate, orient, or position those two points. However, our Universe isn’t only made up merely of three dimensions of space, it is more fully described by four dimensions of spacetime.

It’s easy to look at that and say, “Oh, well, three of them are space and one of them is time, and that’s where we get spacetime,” and while that’s true, it doesn’t provide the full story. After all, the shortest distance between two spacetime events is no longer a straight line. Here’s the science, and mathematics, of why.

Normally, we measure the distance between two points by the distance traveled, such as that along the line connecting points A and B. But the shortest distance between them is a straight line directly connecting A to B, which isn’t always possible dependent on your physical boundary conditions. This applies to spatial distances only, not to separations in both space and time.

For most of us, our first exposure to the idea of a straight line being the shortest distance between two points comes from a place we might not quite recognize: the Pythagorean theorem. You might remember the Pythagorean theorem as a fundamental rule about right triangles: that if you square each of the short sides and add them together, their sum is equal to the square of the long side, or hypotenuse. In math terms, if the short sides are**a**and**b**while the long side is**c**, then the equation relating them is**a² + b² = c²**: the Pythagorean theorem in its most common modern form.

The meaning changes, however, if you think about what this means not from the perspective of pure mathematics alone, but rather in terms of distances. It means that if you move through one of your spatial dimensions by a certain amount (where **a**, for example, might represent the horizontal x-dimension) and then move through a perpendicular dimension by another amount (where **b**, then, can represent the vertical y-dimension), then the distance between where you began and where you wound up is equal to**c**, as defined by the Pythagorean theorem’s **a² + b² = c²**. In other words, the distance between any two points on a plane, where those points are separated by**a**in one dimension and**b**in a perpendicular dimension, is**c**, where**c**= √(**a**² +**b**²).