What is Minkowski space?

Minkowski space is a four-dimensional mathematical structure that combines three spatial dimensions with time into a single framework. It is fundamental in the theory of special relativity, formulated by Albert Einstein. The key features of Minkowski space include: 1. **Flat Geometry**: Unlike curved spaces in general relativity, Minkowski space is flat. This means that it can be described by the familiar rules of Euclidean geometry in three spatial dimensions combined with a fourth dimension for time. 2. **Metric**: The distance (or interval) between two points (events) in Minkowski space is defined using a specific metric, often written as: \[ ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 \] Here, \( c \) is the speed of light, \( dt \) is the time interval, and \( dx, dy, dz \) are the spatial intervals in the three dimensions. This form of the metric incorporates the principle of relativity and shows how time and space are interrelated. 3. **Worldlines**: Objects moving through Minkowski space can be represented as worldlines, which are continuous lines traced out by the object's position in spacetime as it moves through time. Different types of worldlines indicate different types of motion (e.g., at rest, moving at constant speed, or accelerating). 4. **Causality**: Minkowski space allows for the distinction between different types of events based on their causal relationship. Events can be classified as "timelike," "spacelike," or "lightlike" depending on whether they can influence each other or not, based on their separation in spacetime. 5. **Lorentz Transformations**: Transformations between different inertial frames in Minkowski space are given by Lorentz transformations, which account for relative motion and ensure that the speed of light remains constant in all reference frames. Minkowski space lays the groundwork for our understanding of relativistic physics and provides a framework for more complicated structures, such as those found in general relativity.