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.

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 = √(a² + b²).

In our Universe, of course, we’re not restricted to living on a flat sheet of paper. We have not only the dimensions of length and width (or the x and y directions, if you prefer) to our Universe, but the third dimension, depth (or the z direction), as well. If you want to figure out what the distance is between any two points in space, it’s the exact same method as it was in two dimensions, except with one extra dimension thrown in. Whatever amount your two points are separated by in the x direction, the y direction, and the z direction, you can figure out the total distance between them just the same as earlier.

Only, because of the extra dimension, the distance between them — let’s call it d — is now going to be given by d = √(x² + y² + z²). This might look like a scary equation, but it just says that the distance between any two points is defined by the straight line connecting them: the line that accounts for the separation between your two points in all three dimensions: the x-direction, the y-direction, and the z-direction combined.

One of the interesting and important realizations about this relationship — the distance between two points being a straight line — is that it absolutely does not matter how you orient your visualization of the x, y, and z dimensions. You can either:

• change your coordinates so that the x, y, and z dimensions are in any (mutually perpendicular) directions you like, or
• rotate these two points by any amount in any direction,

and the distance between them will not change at all. Similarly, if you reflect those dimensions in a mirror, or flip them inside out, the overall distance between those two points still remains the same, even as their separation in any one dimension might be altered.

Sure, the individual components will change if you make transformations to the geometry for the line connecting those two points, as your definitions of length, width, and depth will change relative to one another for that line as those transformations occur. But the overall distance between those two points doesn’t change at all; that quantity of the distance between those points remains what we call “invariant,” or unchanging, regardless of how you rotate them.

Now, let’s not simply consider space, but time as well. You might think, “Well, if time is just a dimension, too, then the distance between any two points in spacetime will work the same way.” You could be forgiven for assuming, that if we represent the time dimension as t, the distance would then simply be described by a straight line connecting any two points through the three spatial dimensions as well as the time dimension. In mathematical terms, you might think that the equation for the separation between any two points would look something like d = √(x² + y² + z² + t²).

After all, this is pretty much the same change we made when we went from two dimensions to three dimensions, except this time we’re going from three dimensions to four dimensions. It’s a reasonable step to attempt, and describes exactly what reality would look like if we had four dimensions of space, rather than the three dimensions that we possess instead.

However, our four dimensions don’t include four dimensions of space; we have three dimensions of space and one dimension of time. And despite what your intuition may have told you, time isn’t “just another dimension.”

There are two ways that time, as a dimension, is different from space.

The first way is a small one: you can’t put space (which is a measurement of distance) and time (which is a measurement of, well, time) on the same footing without some way to convert one to the other. Fortunately, one of the great revelations that came along with Einstein’s theory of relativity was the existence of an important, fundamental connection between distance and time: the speed of light. This speed doesn’t only apply to light, but rather relates time and space through any particle, wave, or signal that travels through the Universe with zero rest mass.

That fundamental constant, the speed of light in a vacuum — 299,792,458 meters per second — tells us precisely how to relate our motion through space with our motion through time: by a multiple of that fundamental constant itself. When we use terms like “one light-year” or “one light-second,” we speak about distances in terms of time: the amount of distance that light travels in one year (or one second), for example. If we want to convert “time” into a distance, we need to multiply it by the speed of light in a vacuum.

The second way that time is fundamentally different from space, however, requires an enormous leap to understand: something that eluded the greatest minds of the late 19th and early 20th centuries.

The key idea is to imagine that we’re all moving through the Universe, through both space and time, simultaneously. If we’re simply sitting here, stationary, and not moving through space at all, then we move through time at a very specific rate at which we’re all familiar: one second per second. This is the rate that your clocks tick by as you remain stationary here on the surface of the Earth. As long as you’re stationary, or you remain in the same, constant frame of reference, this will indisputably be the rate that time passes according to your observations.

However — and this is the key point — as you move through space, and as you move through space faster and faster, you change the rate at which you move through time, which passes evermore slowly the faster you move through space. The other dimensions are not like this at all: your motion through the x dimension in space, for example, is completely independent of your motion through the y and z dimensions, up to a total rate of motion that maxes out at the speed of light in a vacuum. But it’s your total motion through space, and this is relative to any other observer, that determines your motion through time. The more you move through one of those (space or time), the less you consequently move through the other.

This is why Einstein’s relativity gives us concepts like time dilation and length contraction. If you move at very low speeds compared to the speed of light, you’ll hardly be able to notice these effects: time appears to move at one second per second for everyone, and lengths appear to be the same distance for everyone at speeds normally achievable on Earth.

But as you approach the speed of light — or rather, as you perceive an object where the relative speed between you and it begins to approach the speed of light — you’ll observe that distances become contracted along the direction of relative motion, and that clocks for the observer moving at different speeds from you appear to run at a slower (dilated) rate relative to your own clocks.

The reason underlying this, as realized by Einstein, was straightforward: it’s because the speed of light in a vacuum is fundamentally the same for all observers. If you imagine that a clock is defined by light bouncing back and forth between two mirrors, then watching someone else’s clock as they move close to the speed of light will inevitably result in their clock running slower than your own.

But there’s an even deeper insight here, which initially eluded even Einstein himself. If you treat time as a dimension, multiply it by the speed of light, and — here’s the big leap — treat it as though it were mathematically imaginary, rather than real, then we can define a “spacetime interval” (also known as the Einstein interval) the same way we defined distance earlier. Only, since the imaginary number i is just √(-1), this means that the spacetime interval is actually d = √(x² + y² + z² – c²t²). [Note the minus sign attached to the time coordinate!]

In other words, the transformation from “motion through or separation in space” to “motion through or separation in time” is also a rotation, but it’s a rotation not in the cartesian coordinates of space (where x, y, and z are all real numbers), but through the hyperbolic coordinates of spacetime, where if the space coordinates are real, then the time coordinate must be imaginary.

In a great twist of fate, the person who first put these puzzle pieces together was Einstein’s former teacher, Hermann Minkowski, who noted in 1907/8 that,

“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”

With Minkowski’s mathematical rigor behind it, the concept of spacetime was not only born, but was here to stay.

What’s remarkable about all of this is that Einstein, despite lacking the mathematical insight to understand exactly how the dimension of time was related to the three conventional dimensions of space, was still able to formulate a new view of reality with this key physical insight at its core. Increasing your motion through space decreased your motion through time, and increasing your motion through time decreased your motion through space. All measurements of space and time are only meaningful relative to the observer in question, and depend on the relative motion of the observer to the observed.

And yet, the spacetime interval remains invariant. No matter who is doing the observing or how quickly they’re moving, the combined motion of any object through spacetime is something all observers can agree on. In some ways, the success of relativity was made all the more impressive in light of Minkowski’s assessments of Einstein. Speaking to his (later) student, Max Born, Minkowski had the following to say,

“For me [relativity] came as a tremendous surprise, for in his student days Einstein had been a real lazybones. He never bothered about mathematics at all.”

Fortunately, in physics, the Universe itself — not anyone’s opinion — is the ultimate arbiter of scientific truth, and hence this revolutionary view of spacetime from the early 20th century has persisted ever since. Time is indeed another dimension, but it has some important fundamental differences relative to the more familiar three dimensions of space.

This article was first published in July of 2022. It was updated in September of 2026.

This article is featured on Big Think.