According to Wikipedia:
"In mathematical physics, Minkowski space or Minkowski spacetime (named after the mathematician Hermann Minkowski) is the mathematical space setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold for representing a spacetime.
In theoretical physics, Minkowski space is often contrasted with Euclidean space. While a Euclidean space has only spacelike dimensions, a Minkowski space also has one timelike dimension. The isometry group of a Euclidean space is the Euclidean group and for a Minkowski space it is the Poincaré group.
The spacetime interval between two events in Minkowski space is either space-like, light-like ('null') or time-like."
More views on Minkowski space are welcome! - Sundar
Suppose light propagates instantaneously and along straight rays, then whatever you see belongs to the current moment of time as Rene' Descartes believed. But as it is not so, you have to agree that everything you see belongs to the past, the farther the older. Then time cannot be divided from the space. If time is the fourth dimension, what geometry the space-time could have? You cannot add it the same way as one of spatial ones. Then you can assume that time is somewhat spacial, maybe, it is imaginary. Well, if you try it, you obtain so-called Minkowski space which in fact was introduced by J. d'Alembert in XVIII century when studying waves propagation (he also discovered the first relativistic-covariant operator (d'Alembertian) and relativistic covariant equation (d'Alembert equation). He also introduced the light cone (characteristic cone) and relativistic causality principle (d'Alembert principle). I think, the best way is to follow historical development of ideas.
Suppose light propagates instantaneously and along straight rays, then whatever you see belongs to the current moment of time as Rene' Descartes believed. But as it is not so, you have to agree that everything you see belongs to the past, the farther the older. Then time cannot be divided from the space. If time is the fourth dimension, what geometry the space-time could have? You cannot add it the same way as one of spatial ones. Then you can assume that time is somewhat spacial, maybe, it is imaginary. Well, if you try it, you obtain so-called Minkowski space which in fact was introduced by J. d'Alembert in XVIII century when studying waves propagation (he also discovered the first relativistic-covariant operator (d'Alembertian) and relativistic covariant equation (d'Alembert equation). He also introduced the light cone (characteristic cone) and relativistic causality principle (d'Alembert principle). I think, the best way is to follow historical development of ideas.
He provided rigorous criteria for inertial and accelerated motion – a free particle, which moves by inertia, is a straight timelike worldline in Minkowski spacetime, whereas the timelike worldline of an accelerating particle is clearly different – it is curved (i.e. deformed). That the concept of acceleration acquires a sharply prominent character.
He was not in line with Einsteins modern theory of gravitation, saw a confusing link of physics and geometry
http://www.minkowskiinstitute.org/mip/MinkowskiFreemiumMIP2012.pdf
Minkowski space-time is another way to describe special relativity, invented by the Polish mathematician Hermann Minkowski. It uses a view of the world we now call Minkowski Space, which elegantly describes special relativity as a consequence of the makeup and mixture of space and time. Minkowski treated space and time as two interlinked pieces of the same whole. In Minkowski space, we give each point (or event) a position in space and a position in time. In Minkowski space, people and objects exist at all times, but move between places. The line representing someone or something’s path through space and time is called a worldline. If an object is stationary, the worldline is vertical. If an object is moving, the worldline is at an angle, and the slope of the line is based on the speed at which the object is moving. Because nothing can travel faster than light, the light cones in Minkowski space determine what events in the past can affect current events and what events in the future can be affected by the present
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