## Minkowski's Space-Time

Govindswaroop Rahangdale

Oct 28, 2020

### The views of space and time which I wish to lay before you have sprung from the soil of experimental physics and therein lie their strength. They are radical. Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and and only a kind of union of the two will preserve independent reality.

**– Hermann Minkowski, 1907**

Before Minkowski, Space-Time was considered two-dimensional space sheets that lay over each other vs. increasing the time axis. As Eddington had described in his book, space lies like sheets of paper stacked on a floor with time increasing in an axis towards the ceiling. Minkowski said that the time axis isn’t only in a particular direction but can be in any direction perpendicular to the stacks of paper sheets providing the freedom to decide what space is and what time is.

Minkowski’s Space-Time is a fictitious four-dimensional space in which every point is an EVENT. It is specified by three space coordinates and one time coordinate. Just as in Euclidean Geometry, a continuum of points defines a plane, the collection of all the events – past, present, and future – defines the space-time continuum. It represents a ONCE-AND-FOR-ALL picture of the universe. Nothing ‘happens’ in Minkowski’s Space-Time; for example, a physical particle is described as the locus of all the events that occur at the particle’s location at various times. Whatever goes on in the physical world can be characterized by ‘geometrical structures’ within space-time.

The interval between two events in Minkowski’s Space-Time is defined as

*where S represents the interval, t represents time cooredinates, (x, y, z) represents the space coordinates*

Minkowski said that this distance between two points in space-time is the same in all the inertial frames. It is a Lorentz invariant; the Lorentz transformation is just a rotation in space-time. A critical characteristic of the geometry of Minkowski’s four-dimensional space is Pseudo-Euclidean. The geometry of the special relativity in space-time is pseudo-euclidean.

Minkowski said that there is an objective geometry in space-time corresponding to a physical event independent of any particular observer. Roger Penrose said that “What Minkowski did was take ‘relativity out of the special relativity theory, and presented us with an ‘absolute’ picture of Spatio-temporal activity.” The activity and the geometrical structures in space-time are valid for all inertial observers, regardless of how space and time are defined. However, as arrogant as the great Albert Einstein was, he repeatedly scoffed at the theory, calling it ‘superfluous learnedness’ and unnecessary mathematics, obscuring the beauty of relativity theory.

In 1912-13, Einstein accepted this theory of Minkowski’s Space-time when he formulated his theory of gravitation and developed the profound General Theory Of Relativity. Minkowski’s theory of space-time played an essential role in Einstein’s General Theory of Relativity when considering gravity’s space-time geometry.