Lecture

Lorentz-Minkowski Spacetime

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In course

MATH-115(b): Advanced linear algebra II

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux du sujet. ...

Description

This lecture introduces the concept of Lorentz-Minkowski spacetime, a pseudo-Riemannian manifold of dimension 1+d with a quadratic form defining the spacetime interval. It explores the interpretation of the speed of light as the maximum propagation velocity of a signal in interactions, and the concept of spacetime intervals. The lecture also covers the Lorentz group, isometries, and the principle of special relativity. The instructor discusses the causal structure of events, the invariance of physical quantities under Lorentz transformations, and the concept of spacetime intervals for different types of events.

Instructor

Marc Troyanov

Expertise Differential Geometry Geometric Analysis Teaching & PhD Past EPFL PhD Students Olivier Mermoud, Khaled Gafaiti, Serguei Timochine, Stephen Ducret, Ratiba Djelid, Zahra Sinaei, Luc Genton, Adrien Giuliano Marcone, Guillaume Buro, Bruno Luiz Santos Correia Courses Advanced linear algebra II MATH-115(b) The purpose of this course is to introduce some basic notions of linear algebra and to rigorously prove the main results in the field.

Official source

Ontological neighbourhood

Physics

Relativity: Special relativity

Mathematics

Algebra: Linear algebra

Related concepts (32)

Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe).

Spacetime diagram

A spacetime diagram is a graphical illustration of objects' locations in space at various times, especially in the special theory of relativity. Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without mathematical equations. The history of an object's location through time traces out a line or curve on a spacetime diagram, referred to as the object's world line. Each point in a spacetime diagram represents a unique position in space and time and is referred to as an event.

Type system

In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type (for example, integer, floating point, string) to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term.

Type safety

In computer science, type safety and type soundness are the extent to which a programming language discourages or prevents type errors. Type safety is sometimes alternatively considered to be a property of facilities of a computer language; that is, some facilities are type-safe and their usage will not result in type errors, while other facilities in the same language may be type-unsafe and a program using them may encounter type errors.

Spacetime topology

Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing local as well as global aspects of spacetime. The study of spacetime topology is especially important in physical cosmology. There are two main types of topology for a spacetime M. As with any manifold, a spacetime possesses a natural manifold topology.

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