Minkowski's Space and Time (1908): Time as the Fourth Dimension

Minkowski’s “Space and Time” is the lecture that turned time into the fourth dimension of physics. On 21 September 1908, in Cologne, the mathematician Hermann Minkowski showed that Einstein’s special relativity is simplest when space and time are joined into a single four-dimensional world, which we now call spacetime.

What the lecture found

• One four-dimensional world. Minkowski argued that the laws of physics only ever give us a four-dimensional “world” of events, each labeled by three space coordinates and one time coordinate. How that world splits into “space” and “time” depends on how the observer is moving.
• No single space and no single time. Observers in relative motion slice spacetime differently, so there are, in his words, infinitely many “spaces”, just as there are infinitely many planes in ordinary three-dimensional space.
• World lines and light cones. He described the history of every particle as a line through spacetime (a world line), and the reach of light from any event as a cone, the “fore-cone” and “after-cone” that physicists now call the light cone.
• A “world postulate”. He proposed renaming the principle of relativity the postulate of the absolute world, because what stays the same for every observer is the four-dimensional geometry, not lengths or durations taken separately.

How Minkowski did it

Minkowski started from the Lorentz transformations, the equations that connect the measurements of two observers moving relative to each other. He showed that they behave like rotations in a four-dimensional space in which time is treated as a coordinate on the same footing as the three of space, with one sign difference. That sign is what makes spacetime different from a plain four-dimensional room: the “distance” between two events can be zero for points joined by a light ray, and it separates events that can influence each other from events that cannot.

The lecture was mostly geometry and diagrams. It contained no new experiment. Its power was in reorganizing a known theory so that its consequences became visible at a glance.

Why it mattered

Minkowski opened with the line that made the lecture famous. In our translation from the German: “From this hour on, space by itself and time by itself are to sink fully into shadows, and only a kind of union of the two will preserve independence.”

Einstein built on this language. When he completed general relativity in 1915, gravity became the curvature of Minkowski’s four-dimensional spacetime. Every result in modern cosmology, from the expanding universe to black holes and gravitational waves, is written in this four-dimensional framework. The flat spacetime with no gravity is still called Minkowski space.

The lecture also changed how people talk about dimensions. When physicists say we live in four dimensions, they mean three of space and one of time, as Minkowski laid out. When they discuss extra dimensions, as Theodor Kaluza did in 1921, they mean dimensions beyond these four.

What we know now

Spacetime as a four-dimensional whole is not a hypothesis. It is the structure of both special and general relativity, which have passed every experimental test so far. In 2017, the neutron star merger GW170817 showed that gravitational waves and light travel at the same speed across 130 million light-years, a direct check on spacetime’s geometry. A 2018 analysis of the same event found that gravitational waves behave as they should in 3 + 1 spacetime dimensions.

Our explainer on the fourth dimension puts Minkowski’s idea next to the hypotheses of extra dimensions that came after it.

Who wrote it

Hermann Minkowski was a German mathematician who, in the lecture itself, credits Lorentz and Einstein for the physics he set out to reorganize. He gave the lecture at the 80th meeting of German natural scientists and physicians in Cologne. He died suddenly on 12 January 1909, a few months later, before he could develop the program further; the editor’s note to the printed lecture mourns him as taken at the height of his life and work.

Read the original

Minkowski, H. (1909). “Raum und Zeit.” Physikalische Zeitschrift 10, 104-111; also printed in the Jahresbericht der Deutschen Mathematiker-Vereinigung 18, 75-88 (1909). The German text is free to read on Wikisource, and an English translation is also on Wikisource. The paper has no DOI.

Questions people ask

Who said time is the fourth dimension?

Hermann Minkowski made the idea precise in his 1908 lecture “Space and Time”, which joined the three dimensions of space and the one of time into a single four-dimensional spacetime. It became the standard way physicists describe space and time.

Is time really the fourth dimension?

In relativity, yes. Events need four numbers to be located, three for place and one for time, and observers in motion mix them differently. Time is not just another direction, though: one sign in the geometry differs, which is why you can move freely in space but only forward in time.

What is Minkowski spacetime?

Minkowski spacetime is the flat four-dimensional spacetime of special relativity, with no gravity. Its geometry decides which events can influence each other (those inside each other’s light cones) and which cannot. General relativity curves this spacetime wherever there is mass and energy.