Exact solutions in general relativity | Geometry | Lorentzian manifolds
In mathematical physics, Minkowski space (or Minkowski spacetime) (/mɪŋˈkɔːfski, -ˈkɒf-/) is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be implied by the postulates of special relativity. Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time may differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events. Because it treats time differently than it treats the 3 spatial dimensions, Minkowski space differs from four-dimensional Euclidean space. In 3-dimensional Euclidean space (e.g., simply space in Galilean relativity), the isometry group (the maps preserving the regular Euclidean distance) is the Euclidean group. It is generated by rotations, reflections and translations. When time is appended as a fourth dimension, the further transformations of translations in time and Galilean boosts are added, and the group of all these transformations is called the Galilean group. All Galilean transformations preserve the 3-dimensional Euclidean distance. This distance is purely spatial. Time differences are separately preserved as well. This changes in the spacetime of special relativity, where space and time are interwoven. Spacetime is equipped with an indefinite non-degenerate bilinear form, variously called the Minkowski metric, the Minkowski norm squared or Minkowski inner product depending on the context. The Minkowski inner product is defined so as to yield the spacetime interval between two events when given their coordinate difference vector as argument. Equipped with this inner product, the mathematical model of spacetime is called Minkowski space. The analogue of the Galilean group for Minkowski space, preserving the spacetime interval (as opposed to the spatial Euclidean distance) is the Poincaré group. As manifolds, Galilean spacetime and Minkowski spacetime are the same. They differ in what further structures are defined on them. The former has the Euclidean distance function and time interval (separately) together with inertial frames whose coordinates are related by Galilean transformations, while the latter has the Minkowski metric together with inertial frames whose coordinates are related by Poincaré transformations. (Wikipedia).
Minkowski Space-Time: Spacetime in Special Relativity
Includes discussion of the space-time invariant interval and how the axes for time and space transform in Special Relativity.
From playlist Physics
Minkowski Metric | Special Relativity
▶ Topics ◀ Euclidean/Minkowski Metric, Spacelike, Timelike, Lightlike ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on
From playlist Minkowski Diagrams
Minkowski Diagrams | Special Relativity
▶ Topics ◀ Minkowski Diagrams, Event, World Line, Special Relativity ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on P
From playlist Minkowski Diagrams
Moving Observers | Minkowski Diagrams | Special Relativity
▶ Topics ◀ Moving Observers, Tilted Axes ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on Patreon! https://www.patreon
From playlist Minkowski Diagrams
What is General Relativity? Lesson 5: The Catalogue of Spacetimes
What is General Relativity? Lesson 5: The Catalogue of Spacetimes - Minkowski Spacetime I invite you to download the Catalog of Spacetimes at : https://arxiv.org/abs/0904.4184 to use as a reference for the rest of the course.
From playlist What is General Relativity?
This is a basic introduction to Minkowski's inequality, which has many applications in mathematics. A simple case in the Euclidean space R^n is discussed with a proof provided.
From playlist Mathematical analysis and applications
Relativity 8 - the yardstick of spacetime
The final piece of the puzzle falls in place. Herman Minkowski showed that Special Relativity defines a spacetime invariant - the "proper time" - between two events. Einstein's insight into the equivalence between falling and floating allowed him to realize that this also applied to Genera
From playlist Relativity
Tutorial for Juan Maldacena lectures by Yiming Chen
PROGRAM KAVLI ASIAN WINTER SCHOOL (KAWS) ON STRINGS, PARTICLES AND COSMOLOGY (ONLINE) ORGANIZERS Francesco Benini (SISSA, Italy), Bartek Czech (Tsinghua University, China), Dongmin Gang (Seoul National University, South Korea), Sungjay Lee (Korea Institute for Advanced Study, South Korea
From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology (ONLINE) - 2022
QED Prerequisites Geometric Algebra 3: The symmetric part
In this lesson we begin unpealing the spacetime product of two 4-vectors. The spacetime product can be split into a symmetric and anti-symmetric part and it is critical to understand what each of these two parts represents. We begin with the symmetric part. lease consider supporting thi
From playlist QED- Prerequisite Topics
S.T. Yau - Geometry of spacetime and mass in general relativity [2018]
Slides for this talk: https://drive.google.com/open?id=1_WQg_5dgDIcUeO53NriLy79UZVFyHOzs Abstract: I shall discuss the role of geometry in creating the space time that is fundamental to the physics of general relativity. I shall also discuss fundamental concepts such as mass, linear momen
From playlist Mathematics
A Strange But Elegant Approach to a Surprisingly Hard Problem (GJK Algorithm)
In 1988, three engineers came together and developed one of the most clever solutions to the problem of detecting when two complex objects collide. Their solution, the Gilbert Johnson Keerthi (GJK) algorithm, named after the authors, made an incredible impact in the fields of robotics, con
From playlist Computer Graphics
The biggest ideas in the Universe - with Sean Carroll
Join Sean M Carroll as he explores deep questions about the cosmos, laying out the framework of classical physics from Euclid and Galileo to Newton and Einstein. Watch the Q&A for this video here: https://youtu.be/mtUG1cRYXvU Sean's latest book 'The biggest ideas in the Universe 1: Space,
From playlist Ri Talks
QED Prerequisites Geometric Algebra: Spacetime.
In this lesson we continue our reading of an excellent paper on Geometric Algebra and spacetime algebra. The paper can be found here: https://arxiv.org/abs/1411.5002 We will cover section 3.1 and begin section 3.2. This material includes our first expansion of the vector space of spacet
From playlist QED- Prerequisite Topics
Michael Eastwood: Twistor theory for LQG
Twistor Theory was proposed in the late 1960s by Roger Penrose as a potential geometric unification of general relativity and quantum mechanics. During the past 50 years, there have been many mathematical advances and achievements in twistor theory. In physics, however, there are aspirati
From playlist Mathematical Physics
Franz Schuster: Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms
The Blaschke–Santaló inequality is one of the best known and most powerful affine isoperimetric inequalities in convex geometric analysis. In particular, it is significantly stronger than the classical Euclidean Urysohn inequality. In this talk, we present new isoperimetric inequalities fo
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Anna Sakovich: On the mass of asymptotically hyperbolic manifolds and initial data set
HYBRID EVENT A complete Riemannian manifold is called asymptotically hyperbolic if its ends are modeled on neighborhoods of infinity in hyperbolic space. There is a notion of mass for this class of manifolds defined as a coordinate invariant computed in a fixed asymptotically hyperbolic en
From playlist Analysis and its Applications
Rainer Verch: Linear hyperbolic PDEs with non-commutative time
Motivated by wave or Dirac equations on noncommutative deformations of Minkowski space, linear integro-differential equations of the form (D + sW) f = 0 are studied, where D is a normal or prenormal hyperbolic differential operator on Minkowski spacetime, s is a coupling constant, and W i
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Poincaré Transformation | Special Relativity
▶ Topics ◀ Poincaré Trafo, Lorentz Trafo, Minkowski Space, Rotations, Boosts, Translations ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, y
From playlist Minkowski Diagrams