We all have an intuitive sense of what a dimension is. There are only three perpendicular directions in which we might move, which we might designate as “up and down,” “left and right,” and “back and forth.” Try as we might, any other mode of movement could not be perpendicular to those three. We can’t run or jump into a spatial fourth dimension that is at right angles to the others. Therefore, our experience informs us that we live in a three-dimensional world.

Image credit: Wikimedia Commons user Falcorian.

Modern physics, however, treats space and time as a unified four-dimensional entity. Time is a funny kind of fourth dimension, though, because we traverse it simply by waiting, not by moving through a direction of motion. Moreover, in calculating the four-dimensional equivalent of distance, the spacetime interval — a generalization of the Pythagorean theorem relating the hypotenuse of a right triangle to its sides — the time variable picks up a minus sign in order for descriptions of motion to make sense.

The replacement of independent space and time with amalgamated spacetime can be traced back in physics to the work of Russian-German mathematician Hermann Minkowski.

Image credit: Spacetime Society, via http://www.spacetimesociety.org/minkowski.html.

Minkowski brilliantly determined in 1907 that Einstein’s equations of special relativity, developed two years earlier, naturally emerged from the properties of a special four-dimensional graph. While in Einstein’s theory time dilates and length contracts along the direction of motion for objects approaching the speed of light, Minkowski showed that the spacetime interval is invariant: it remains the same from all perspectives.

Image credit: Wikimedia Commons user Maschen, with different observers marking different times and different spatial locations. Yet the spacetime interval remains invariant (see below).

We can think of the spacetime interval as something like a garden sundial with a pointed metal needle.

Image credit: Wikimedia Commons user SEWilco.

As Earth turns with respect to the Sun the shadows of the needle transform, but the needle itself remains rigid. Similarly, length and time — shadows of spacetime — transform with respect to the motion of observers, while the spacetime interval does not vary.

Image credit: Maurice Quentin de La Tour.

Long before Minkowski formalized the notion of spacetime, however, it was discussed in essays and stories. As early as 1754, French mathematician Jean d’Alembert mentioned the idea of time as the fourth dimension in an encyclopedia article. In 1885, the journal Nature featured an article by a pseudonymous author called “S”, entitled “Four dimensional Space.”

It proposed that three-dimensional objects trace out fourth dimensional tracks as they change over time. As “S” wrote:

“We must … conceive that there is a new three-dimensional space for each successive instant of time; and, by picturing to ourselves the aggregate formed by the successive positions in time-space of a given solid during a given time, we shall get the idea of a four-dimensional solid, which we may call a sur-solid… Let any man picture to himself the aggregate of his own bodily forms from birth to the present time, and he will have a clear idea of a sur-solid in time-space.”

Image credit: Fair Use image obtained by Wikimedia Commons user DASHBot.

Perhaps the most famous fictional depiction of movement through the fourth dimension is The Time Machine, H.G. Wells’s popular novella published in 1895. In that book, Wells introduced to his readers the idea of time as a dimension and pondered why we cannot travel as freely in that dimension as we can in space.

“There are really four dimensions,” he wrote, “three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.”

Image credit: author unknown; of H.G. Wells, circa 1918.

Wells became exposed to the idea of time as the fourth dimension when he founded and edited a college paper, at what is now Imperial College, London, called the Science School Journal. He avidly read science topics of the times, including debates about dimensionality. When a fellow student, E.A. Hamilton Gordon, contibuted an article to the journal, entitled “Fourth Dimension,” Wells became interested in the subject. Soon thereafter he a wrote a short story about that theme, “The Chronic Argonauts,” and published it in the same journal. Several years later, he expanded the story and it became The Time Machine.

Wells emphasized in the novella that if time is a dimension like those of space, the past, present and future are all all part of the same unified entity and potentially accessible. In other words, if someone could somehow step out of space and time, he would see each person’s life as a complete, immutable thread, akin to a reel of film. Such an idea has come to be known as the block universe. As Wells described such a situation:

“Here is a portrait of a man at eight years old, another at fifteen, another at twenty-three, and so on. All are evidently sections, as it were, Three-Dimensional representations of his Four-Dimensional being, which is a fixed and unalterable thing.”

Although The Time Machine was widely read, there is no evidence linking its four-dimensional construct with Minkowski’s masterful suggestion about Einsteinian relativity. Nor is there evidence that Einstein and Wells ever discussed the fourth dimension — as integral as it was to the former’s theories and the latter’s stories. Einstein was well-read, but not particularly a fan of speculative fiction. Wells probably was unfamiliar with Einstein’s work until measurements taken during the 1919 solar eclipse helped confirm the general relativistic prediction that the path of starlight would be bent by massive objects such as the Sun — consequently making Einstein world-famous.