Talk:Minkowski space

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Comments:

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)

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)

Is Minkowski space a vector space or an affine space? There is no prefered 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)

Contents

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] Rant on merging

ARRGH Please someone explain how I was browsing through a series on "timelike hotopy" and clicked on a link to get the exact definition of "timelike" and was brought to this page of technical jargon. For the love of god, don't make wikipedia inaccessible by merging every single article that is remotely similar. Eventually there'll just be one god damn article and it won't say anything useful, no matter how much of the irrelevant stuff we have to search through. —Preceding unsigned comment added by 61.68.184.249 (talk) 17:40, 22 December 2006

I fully support this rant. Time-like and Space-like must not redirect here. They should either redirect to Spacetime#Space-time_intervals or have their own article which would combine explanations from Spacetime#Space-time_intervals and from Speed of light. --206.169.169.1 21:11, 20 June 2007 (UTC)

Agreed there should be an unmerge. I volunteer to work on it when I get some time, but any contributor should start. It is against nature for Wikipedia's introduction on time-like intervals to be so off-putting. One of the most important things which must change is using approachable variables such as Δt and Δx rather than the Minkowski vectors. For example:

A time-like interval is a description of the space-time distance between two events. In such calculations, space and time are related by the speed of light. In a time-like interval, the squared interval of the time component ((Δt)2)of separation measured between the two events is greater in magnitude than that of the spatial distance component, that is: (Δt)2 > (Δx)2.
In this case of time-like intervals, the calculated proper time (Δτ = [(Δt)2 − (Δx)2]1 / 2) is used to represent the separation of the events. Heathhunnicutt (talk) 08:01, 8 January 2008 (UTC)

[edit] Typos in "Causal structure"?

The article currently says:

  • V is timelike if and only if \eta_{\mu \nu}V^\mu V^\nu \, = V^\mu V_\mu < 0
  • U is spacelike if and only if \eta_{\mu \nu }U^\mu U^\nu \, = U^\mu U_\mu > 0
  • W is null (lightlike) if and only if \eta_{\mu \nu}W^\mu W^\nu \, =W^\mu W_\mu = 0

Isn't this wrong? The middle part of each math statement looks wrong to me; it gets the sign of the timelike component wrong. If it were really correct, the result would be that no vectors would be timelike.

I think what is intended is the inner product:

\eta_{\mu \nu}V^\mu V^\nu \, = \langle V, V \rangle < 0
\eta_{\mu \nu }U^\mu U^\nu \, = \langle U, U \rangle > 0
\eta_{\mu \nu}W^\mu W^\nu \, = \langle W, W \rangle = 0

But I'm not certain enough to make the edit. --Jorend 17:35, 5 January 2007 (UTC)

By definition \langle V, V \rangle = \eta_{\mu \nu}V^\mu V^\nu \, = V^\mu V_\mu .
The pont is that V_\mu = \eta_{\mu \nu}V^\nu \, . I think that everything is OK here.
XCelam 21:09, 5 January 2007 (UTC)

[edit] Minkowski's nationality

I wouldn't be sure if it is important but this article calls Minkowski a "German mathematician" while by clicking at the guy's surname you can easily learn that he's a "Lithuanian mathematician". The information should be either coherent or omitted, IMO. What is even funnier, it then reads that he was born "to a family of German, Polish, and Jewish descent" and in fact his family sounds rather Polish (it would be also quite a good Jewish or German surname, still it wouldn't as Lithuanian nowadays since they add those "-is" and "-as" suffices to all surnames or so it looks like; I've seen a plaque to Dzordzas Busas, the president of USA in Vilnius).