Lightlike | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-06-05

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Minkowski_space


00:03:02 1 History
00:03:11 1.1 Four-dimensional Euclidean spacetime
00:06:50 1.2 Minkowski space
00:10:23 2 Mathematical structure
00:11:37 2.1 Tangent vectors
00:16:38 2.2 Metric signature
00:17:13 2.3 Terminology
00:19:09 2.4 Pseudo-Euclidean metrics
00:24:20 2.5 Minkowski metric
00:30:40 2.6 Standard basis
00:32:34 2.6.1 Raising and lowering of indices
00:36:11 2.6.2 The formalism of the Minkowski metric
00:37:03 3 Lorentz transformations and symmetry
00:40:04 4 Causal structure
00:40:37 4.1 Chronological and causality relations
00:44:15 4.2 Reversed triangle inequality
00:44:38 5 Generalizations
00:46:29 5.1 Generalized Minkowski space
00:47:19 5.2 Curvature
00:47:58 6 Geometry
00:48:25 6.1 Preliminaries
00:49:34 6.2 Hyperbolic stereographic projection
00:50:49 6.3 Pulling back the metric
00:54:58 7 See also
00:55:29 8 Remarks
00:56:34 9 Notes
01:04:46 10 References
01:04:55 11 External links



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9260120817389981
Voice name: en-US-Wavenet-C


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In mathematical physics, Minkowski space (or Minkowski spacetime) 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 an immediate consequence of the postulates of special relativity.Minkowski space is closely associated with Einstein's theory of special 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 amended 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.
In summary, Galilean spacetime and Minkowski spacetime are, when viewed as manifolds, actually the same. They differ in what further structures are defined on them.  The former has the Euclidean distance function and time (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.