Minkowski Space

Minkowski space or Minkowski spacetime is mainly named after the mathematician Hermann Minkowski. It is actually a mathematical formulation in which Einstein’s theory of relativity is formulated. It is a four-dimensional manifold which represents space-time and the four dimension are three dimensions of space with a single dimension of space.

This is Minkowski space in mathematical physics but in theoretical physics, Minkowski space is mainly constructed with Euclidean space. Euclidean space has only space-like dimensions and Minkowski space similarly has only one time-like dimension. In Minkowski space, the space-time interval is mainly either space-like or light-like or time-like.

Structure of Minkowski Space

The structure of the Minkowski space is a four-dimensional vector space that is equipped with a non-degenerate and the signature is (-,+,+,+). In Minkowski space, the elements are called events or four-vectors.

Lorentz Transformation and Symmetry

The Poincare group is the group of all isometric of Minkowski space-time including boosts, rotations, and translations. The Lorentz group is the subgroup of isometric which leaves the origin fixed and includes the boosts and rotations. Members of this subgroup are called Lorentz transformation. Among the simplest Lorentz transformation is a Lorentz boost. All four-vectors in Minkowski space transformation according to the same formula under Lorentz transformations. Minkowski diagrams illustrate Lorentz transformation.

Causal Structure

In the theory of relativity, we mainly use the Minkowski space. In the case of Minkowski space, the set of all null vectors at an event continues the light cone of that event. All the notions are independent of the frame of reference. Minkowski space generally denotes relativity of simultaneity since this hyperplane depends on v. In the plane spanned by v and such a win the hyperplane, the relation of w to v is hyperbolic-orthogonal. Once a direction of time is chosen then time-like and null vectors can be further decomposed into various types.

For time-like vectors, we have future-directed time-like vectors whose first component is positive and past directed time-like vectors whose first component is negative. All the null vectors in Minkowski space are generally classified into three types as the zero vector whose components are in 0,0,0,0 basis, future-directed null vectors whose first component is positive, and past directed null vectors whose first components is negative. An orthonormal basis for Minkowski space necessarily consists of one time-like and three space-like unit vectors. If someone wishes to work with non-orthonormal bases it is possible to have other combinations of vectors in space-time.

FAQs about Minkowski Space

Q.1 In everyday life how many dimensions do we live in?

Answer: In everyday life, we live in a space of three dimensions which are height, width, and depth.

Q.2: What are the dimensions that a human can see?

Answer: Humans are 3D creatures but we can only see two dimensions.

Q.3: Can a human eye see one dimension?

Answer: A human eye can visualize two dimensions but cannot see one or zero dimension without the help of two-dimension objects which represents them.