Three-dimensional space

Three-dimensional space is the representation of the physical universe in three spatial dimensions: length, width, and height. A location in three-dimensional space can be represented by a series of coordinates using these three measurements that corresponds to a specific point. Everything humans experience in the physical world occurs in three-dimensional space, though some scientists often include a fourth dimension—time—as a necessary part of the equation. Despite the fact that humans can only experience three dimensions, some scientists believe that there may be more dimensions present in the universe. A concept known as string theory suggests that there may be as many as ten or eleven dimensions that make up the physical universe.

Background

Matter and energy exist in what humans perceive to be a vast three-dimensional space called the universe. Modern scientists believe the universe was born about 13.8 billion years ago in a cataclysmic event known as the Big Bang. At that time, all the matter in the universe was condensed into an infinitesimally small point called a singularity. Suddenly, for reasons that remain unknown, this point began to violently expand outward, creating intense amounts of heat and energy. The early universe was so hot that electrons were unable to combine with atomic nuclei, creating a sort of electron haze that blocked light from shining. It was not until about 380,000 years after the Big Bang that the universe had cooled enough to allow the first light to break through. It took another 100 million years for the first stars and galaxies to form. Earth, our sun, and our solar system formed about 4.6 billion years ago—9 billion years after the big bang.

In the first fraction of a second after the Big Bang, the universe was so small, hot, and dense that the laws of physics as they are today did not exist. This incredibly small unit of time is called the Planck epoch, named after German physicist Max Planck who studied matter and energy on the scale of the very small. A Planck epoch is a unit of time measured at 10^-43 seconds. At this time, the universe was close to the size of a Planck length, the smallest possible length that can exist. A Planck length is measured at about 1.6 x 10^-35 meters. This length is so incredibly small that if an atom were blown up to the size of the known universe, a Planck length would be about the size of a single tree.

Overview

The concept of dimensions is a way to measure the physical reality of the world around us. A single fixed point has zero dimensions; it is observed only as having position or location. Points are often represented as dots, which technically have some small physical dimensions, but a true geometric point has no size whatsoever. If a point is moved in a forward or backward direction, it forms a line. The line has length, which is considered the first dimension, but has no width or height. If a one-dimensional line is extended right or left, it gains width and becomes two-dimensional. Two-dimensional objects can move about on a perfectly flat surface, but have no height whatsoever. Figures such as squares, circles, or triangles are examples of two-dimensional shapes. If the points on these two-dimensional shapes are moved at right angles up or down, this adds a third dimension, height (or depth). For example, if a square, which has length and width, is given height, it becomes a cube. A circle becomes a sphere.

In 1884, a British teacher named Edwin Abbott wrote a book to illustrate what three-dimensional space would look like to beings who lived in two-dimensional space. His work, called Flatland, imagined a world that was completely two-dimensional; it had length and width, but no height. The beings who lived in Flatland were perfectly flat and saw each other only as lined segments. They could move forward and back, or right and left, but had no idea the directions of up or down even existed.

The three-dimensional world would be a totally alien concept to a two-dimensional inhabitant of Flatland. If a being from three-dimensional space were to see Flatland, that being could look down and view the Flatlanders, but the Flatlanders could not see it. If this being were to actually touch down in Flatland, the inhabitants would only see the lined section where the visitor intersected with the flat surface. While the third dimension is obviously real, the inhabitants of Flatland would be unable to perceive its existence.

To measure points in three-dimensional space, each dimension is represented by a position on an axis. The first dimension is represented on what is called the x-axis, which is typically drawn as a single horizontal line. The second dimension is represented by the y-axis, drawn vertically at a right angle to the z-axis. The third dimension is represented on the z-axis, which adds height and provides a sense of scale and area. In mathematics, coordinate values provided for each of the three axes—x, y, and z—give the location of a specific point in three-dimensional space. On the surface of Earth, these specific locations are represented by the values of longitude, latitude, and altitude.

Scientists believe the origins of three-dimensional space occurred at the same time as the Big Bang, but they do not know the exact reason why. At the time of the Big Bang, the universe was confined to a single point. When it suddenly began expanding outward, it expanded in three physical dimensions. Theories suggest that something happened to limit this expansion to just three dimensions. One theory proposed by a group of European scientists is that the incredible heat generated by the Big Bang allowed space to expand from the zero-dimensional singularity into three-dimensional space. However, as soon as the universe began expanding, it also began cooling. In its earliest fractions of a second of existence, the universe may still have been white hot, but it had cooled enough to drop below the threshold needed for the creation of additional physical dimensions. According to the theory, this “locked” the universe into three physical dimensions.

Another theory, which may be supported by evidence from Japanese scientists, is that the universe at the time of the Big Bang was perfectly symmetrical and contained about ten physical dimensions. However, the matter and energy in the universe was highly unstable and could not hold itself together. The fabric that made up the infant universe may have “snapped” like a breaking rubber band, with three dimensions rapidly expanding, and other dimensions retreating backwards, or “curling up,” into the realm of the very small.

Though the reality of the physical world exists in three-dimensional space, many scientists believe that time should be considered a fourth dimension. For example, each of the three coordinates that designate a point in three-dimensional space needs to exist for a duration of time in order to be valid. Famed German physicist Albert Einstein considered time and the three dimensions of space to be intricately connected in a four-dimensional universe called the space-time continuum. Three-dimensional space combined with time can be represented mathematically as a four-dimensional model called Minkowski space, named for nineteenth-century German mathematician Hermann Minkowski.

While humans perceive the world in three-dimensional space, and can also perceive the passage of time, modern scientists have developed the idea that the universe contains more dimensions than humans can experience. Similar to how Edwin Abbott’s two-dimensional Flatlanders could not fully perceive the third dimension, beings who live in three-dimensional space would not be able to physically experience higher dimensions. However, scientists who adhere to an idea known as string theory believe they may have mathematical evidence such dimensions exist.

String theory suggests that all the matter in the universe is made up of one-dimensional strings of energy that vibrate at the subatomic level. When scientists tried to develop a unified theory that explained how all the physical laws of the universe worked, they had trouble finding a mathematical model that worked in three-dimensional space. However, when they used a ten-dimensional model, the math seemed to support a unified theory. Further theories suggest that the universe may even be made up of eleven dimensions. As of 2019, the existence of additional dimensions has not been scientifically proven, but many physicists believe the evidence points to their existence.

If the additional dimensions are real, scientists believe they may exist at the subatomic level, at sizes approaching the Planck length. At the time of the Big Bang, these dimensions may have curled up or contracted just as three-dimensional space began to expand. These dimensions would be real places with very strange properties and laws of physics. For example, some of the dimensions may contain alternate realities that can be slightly different from the world we know; while others could have an infinite number of possible realities where all conceivable futures, pasts, and presents exist.

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