Talk:Minkowski space/Archive 1

Archive 1

What is the genus of Minkowski space?

This could use some colloquialization. -- ESP 04:28 21 Jul 2003 (UTC)

I'm not sure about calling Minkowski space non-Euclidean. Standard usage is to call spaces with curvature non-Euclidean. Minkowski space is flat (the curvature tensor is zero). Bartosz 07:18, 21 Aug 2003 (UTC)

I know that Minkowski distance is a generalization of Euclidian distance. I don't know if this can help. Hugo Dufort 03:13, 18 November 2006 (UTC)

Work in progress

I started expanding this page and then ran out of time. It's in a rather half-baked state right now. A lot more needs to be said. I'll expand it when I find more time. -- Fropuff 01:53, 2004 Mar 16 (UTC)

OK, if you expand this article, but please note that even physics (e s p e c i a l l y physics) uses examples of Minkowski spaces which are not of type R⁴: Indeed the point with the Pauli-matrices (together with the two-dimensional identity matrix), with the the four Dirac matrices and with the four Duffin-Kemmer-Petiau matrices is, that they are in a natural way Minkowski spaces (of dimension 4 and signature +---), i.e. real vector spaces whose basis elements are complex matrices: "In a natural way" means: With respect to the natural symmetric non-degenerate bilinar form trace(AB)-trace(A)trace(B) on any vector space of square matrices. — Preceding unsigned comment added by 141.89.80.203 (talk) 14:56, 4 October 2011 (UTC)

Vector or affine?

Is Minkowski space a vector space or an affine space? There is no preferred origin. Phys 00:13, 21 Aug 2004 (UTC)

Depends on who you read. Naber (ref. in article) defines it as a vector space, though I've seen it defined as an affine space as well. I guess it really depends on the context you use it in. As a model for flat spacetime one should properly think of it as an affine space. As the set of momentum four-vectors one should regarded it as a vector space. To be pedantic we should distinguish between the two. — Fropuff 01:32, 2004 Aug 21 (UTC)

Revamping of relativity pages

I've changed the signature of the metric in the article to that of trace +2; reason: the general relativity pages (and hence this one) are undergoing a major revision in terms of style and consistency, as set out in CH's GTR Wikiproject. At the moment there are only 3 people who have signed up for this massive project, and we are looking for more. I know that there are some knowledgable people working on maths and physics articles, and their assistance would be very welcome in the project. ---Mpatel (talk) 13:55, August 28, 2005 (UTC)

Signature

Is it worth noting that many (at least many physicists) use the + - - - signature? (there are a number of articles in Wikipedia using this metric) Threepounds 04:44, 27 November 2005 (UTC)

Minkowski reference?

A quote from Minkowski (1908) is given, but there is no reference for Minkowski (1908).

The link to Scott Walter's paper says, among other things, that there are at least four drafts of the manuscript Minkowki wrote to be found in the archive at Gottingen ! Rgdboer 22:27, 24 June 2006 (UTC)

Minkowski metric

Minkowski metric redirects here. This is apparently a class of metric spaces, but this doesn't seem to be discussed in the article. Does anybody have some more information? — brighterorange (talk) 01:15, 8 August 2006 (UTC)

The Minkowski "metric" is not a metric, in the standard sense of the word (a real function which is symmetric, positive definite, separates points, and satisfies the triangle inequality). Nor does it qualify as any of the common generalizations (pseudometric, ultrametric, quasimetric). It is a pseudo-Riemannian metric tensor, and in that sense it can be called a metric, which is the justification of the usage. -lethe ^{talk +} 01:33, 8 August 2006 (UTC)

Does the Minkowski "metric" induce a natural topology on Minkowski spacetime? —Keenan Pepper 04:04, 8 August 2006 (UTC)

Orthogonal basis not appropriate

The link to orthogonal basis refers to a space with positive definite inner product, a situation that does not hold in Minkowski space. Rgdboer 22:36, 28 August 2006 (UTC) On the other hand, orthogonal group includes the context of the general quadratic form, something compatible with the bilinear form taken in the article. Naturally η is the invariant needed when Minkowski space is subjected to transformation.Rgdboer 22:12, 29 August 2006 (UTC)

Use in Machine Learning

The Minkowski distance between two points in a n-dimensional space is used in various AI applications, for instance in automated data clustering & classification, and in non-supervised machine learning. In Machine Learning, objects may have n attributes, each one defined as a dimension (some attributes define an orthonormal space, others define a sparse or non-orthonormal space, others are qualitative and non-ordered, others may have unknown/absurd values, ...). When attributes are compared, a distance metric is required; however, the euclidian distance is not always the best method. Since the Minkowski distance is a parametrable generalization of Euclidian distance, it offers more flexibility. The choice of a particular Minkowski metric (of order m) is a tricky question, and is sometimes chosen by the programmer, sometimes by a heuristic procedure, sometimes by a dynamic (adaptative) process. Here is a sample resource on the subject: http://www.ucl.ac.uk/oncology/MicroCore/HTML_resource/distances_popup.htm . I am the author of a partitional data clustering technique named CLARISSE, which uses Minkowski distances (an article on the subject was published at the ITS-2002 conference), however the article doesn't give fine details about the distance metrics. A second article, which I started writing in 2002, was supposed to cover the distance metrics and go in depth with the partition heuristics; ultimately it was not published because I was overworked & couldn't finish the experiments. Here is a reference to a paper with similar scope but from a different author http://www.actapress.com/PaperInfo.aspx?PaperID=13275 . -- Hugo Dufort 22:09, 17 November 2006 (UTC)