# Hermann Minkowski Pioneers the Concept of a Four-Dimensional Space-Time Continuum

# Hermann Minkowski Pioneers the Concept of a Four-Dimensional Space-Time Continuum

*Overview*

There is no doubt that Albert Einstein's (1879-1955) relativity theory changed the way we view the universe. Less well known is the extent to which Einstein's thinking was influenced by his former professor, Hermann Minkowski (1864-1909). Minkowski was the first to propose the concept of a four-dimensional space-time continuum, now a popular phrase in science fiction. Minkowski later became an influential proponent of Einstein's theories, helping them to gain acceptance despite their radical view of physics and the universe. Although Einstein consolidated work from many physicists and mathematicians in constructing his theory, Minkowski's contributions are noteworthy because of his influence over the young Einstein and physicists of his day.

*Background*

For millennia, mathematicians recognized that space could be divided into three dimensions—length, width, and height. These form the basis of Euclid's (330?-260? b.c.) geometry and virtually all subsequent geometry. In fact, it was not until 1826 that Russian mathematician Nicolai Lobachevsky (1793-1856) developed the first non-Euclidean geometry; that is, the first geometry not based on Euclid's postulates. For example, Euclid theorized that straight lines intersect only at a single point. However, in some non-Euclidean geometries, lines may intersect each other multiple times. Consider, for example, the surface of a sphere, on which all nonparallel lines must intersect each other twice.

Another long-established notion was that time was separate from any other phenomenon in the universe. For centuries, time was more of a philosophical concept than a physical one, something for philosophers to ponder rather than scientists to compute. With the ascendance of the physical sciences in the seventeenth and eighteenth centuries, time began to acquire its current meaning, but it was still considered something apart from the rest of the physical universe, something not well understood.

In the latter part of the nineteenth century, this concept of time began to evolve further, coming even closer to our current concept. At the turn of the century, Minkowski first proposed the interwoven nature of space and time being, stating: "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." This amazing concept influenced Einstein, who would carry it to heights not considered by Minkowski or any others of that time.

Explaining this conception of space-time is actually not difficult, when we view it with the advantage of a century's hindsight. Consider, for example, taking a trip. If you travel from New York to Chicago you go not only through physical space, but through time as well, because it takes a finite amount of time to make this journey. The trip cannot be viewed simply as movement through space, but must be seen as movement through time, as well. Similarly, if you traveled at the speed of light from the Earth to the Moon you would traverse a quarter million miles of physical space and a second and a half of temporal space. Even if you didn't move at all you'd travel through the time dimension.

Minkowski's conceptualization of space-time was a set of four axes, the familiar *x, y,* and *z* axes of high-school geometry class and a fourth, *t *axis, upon which time is marked. In this system, then, your trip from New York to Chicago would take you along all four axes; standing perfectly still would still take you along the *t* axis, moving into the future without moving physically through space. It should also be noted that movement along the *t* axis is not time travel, at least not as long as the rate of movement is exactly the same as the rate that time normally flows. Although parts of relativity theory address ways to change the rate at which time flows along this axis, these are not yet significant from the standpoint of human experience.

*Impact*

The impact of Minkowski's conception of spacetime is hard to describe briefly because of its influence on Einstein's thinking and the subsequent impact of relativity theory. However, it is safe to say that his work influenced philosophy, physics, and popular culture during the mid-to late-twentieth century.

From the philosophical point of view, Minkowski's work led to some interesting and, in some cases, unsettling results. As mentioned above, for millennia time had been the province of philosophers as much as physicists, and theories abounded as to the reasons time existed, its nature, and why we perceive it the way we do. To see time treated like any of the physical dimensions was shocking to many who had spent time speculating about the nature of time and who had treated it as something special for so long.

Also shocking was that, unlike the physical dimensions, time had special properties. Chief among them was that it could only be traveled in one direction, and at only a given rate of speed. True, as later relativity theory was to show, the rate at which time passed was related to the observer's frame of reference, but the key issue was that, to the observer, time always passed at the same rate and it was the rest of the universe that seemed to experience time at a faster or slower rate, depending on the observer's velocity relative to the rest of the universe. These points, as much physical as philosophical, were very disturbing to many, and it took years until they were widely accepted. In fact, only after the widespread acceptance of Einstein's work was Minkowski's notion of space-time taken to be an accurate description of our universe.

In the world of physics, Minkowski's work, and its effect on Einstein's, was even more revolutionary. By showing time to be an inseparable part of space-time, Minkowski not only inspired parts of Einstein's work, but also helped set the stage for further levels of abstraction such as string theory in physics. In this theory, all elementary particles are viewed as vibrating "loops" that occupy no fewer than 11 physical dimensions, most of which are "compactified," or shrunken to the point of being unnoticeable. Virtually every aspect of string theory depends on looking at the universe in a vastly different way than in previous centuries—a way made possible in part by Minkowski's uniting the visible dimensions of space with the invisible dimension of time.

Minkowski not only changed modern physics, he greatly influenced the theory of relativity, which describes the rate at which time passes, and how this rate changes. At relatively low speeds, such as those we experience in our daily lives, this change is not noticeable. However, at high speeds (approaching the speed of light), these changes are very evident. This is because the speed of light appears to be the same to an observer, regardless of the observer's speed. So, for example, if you were in a rocket traveling at nearly the speed of light and you shined a light in the direction the rocket is traveling, you would not see the beam crawl towards the front of the rocket. Instead, you would see the beam move at the same speed as if you were standing still. That same beam of light seen by a stationary observer would also seem to move at the speed of light. In short, two observers, looking at the same beam of light will see it move at exactly the same rate, regardless of their speed relative to each other or the beam of light. The only way that this can happen is if time for the rapidly moving observer slows down so that, with respect to him or her, the beam seems to be moving at its "normal" speed. This prediction has been proven with a very high degree of accuracy in experiments performed in space and on earth and is held to be generally true throughout the universe.

Finally, Minkowski's conceptualization of space and time as inseparable has become part of the popular culture. In fact, the term "space-time continuum" has become a staple of science fiction and, in this guise, has become part of the vocabulary for many people who otherwise have no knowledge of physics. As a punch line in jokes, a plot gimmick in science fiction movies and books, or a phrase used to impress people at parties, it has entered the lexicon and is familiar to virtually everyone who reads or keeps up with the media. This widespread usage does not seem to have improved the general public's understanding or appreciation of theoretical physics, but then, a large number of people can also quote Einstein's famous equation, *E* = *mc*^{2} without understanding it or its importance, either. However, simply knowing the term and understanding that it has something to do with physics and the universe is more than anyone in previous centuries knew, which is a significant step forward in the public's understanding and appreciation of physics. From this standpoint, Minkowski's work still influential.

**P. ANDREW KARAM**

*Further Reading*

Naber, Gregory L. *The Geometry of Minkowski Space-Time:**An Introduction to the Mathematics of the Special Theory of Relativity.* New York: Springer-Verlag, 1992.

Schutz, John W. *Foundations of Special Relativity: Kinematic Axioms for Minkowski Space-Time.* New York: Springer-Verlag, 1973.

Thompson, Anthony C. *Minkowski Geometry.* Cambridge: Cambridge University Press, 1996.

Weaver, Jefferson Hane, ed. *The World of Physics: A Small**Library of the Literature of Physics from Antiquity to the Present.* Vol. 2. New York: Simon and Schuster, 1987.

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# Hermann Minkowski Pioneers the Concept of a Four-Dimensional Space-Time Continuum

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