Talk:Minkowski space

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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 ($(\Delta t)^{2}$)of separation measured between the two events is greater in magnitude than that of the spatial distance component, that is: $(\Delta t)^{2}>(\Delta x)^{2}$.

In this case of time-like intervals, the calculated proper time ($\Delta \tau =[(\Delta t)^{2}-(\Delta x)^{2}]^{1/2}$) is used to represent the separation of the events. Heathhunnicutt (talk) 08:01, 8 January 2008 (UTC)

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)

I would propose to start with choosing a signature. As far as I can see for the signs chosen, the following phrase should start the second sentence: "Given the (+,-,-,-) signature ". 92.54.93.79 18:15, 30 May 2009 (UTC)

I also believe that the article should stick to one signature. In the Causal Structure section, the time/space-like inequalities seem to be defined using the (-+++) signature instead of (+---) which was used earlier in the article. I'm just been introduced to the subject, so whoever feels comfortable please make the appropriate changes. Mppf (talk) 22:02, 30 January 2011 (UTC)

As far as I can see, the article only refers to (+---) as a secondary possibility in some cases where (-+++) has already been used. Is there some exception to this which I have not noticed? Please be specific as to the section and paragraph, and give a quotation. JRSpriggs (talk) 09:42, 31 January 2011 (UTC)

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).

Pigeon-holing every person into categories of that kind is a nasty habit of WP. Since it isn't relevent to this article I removed it. But I recommend that you edit the main article on the person Minkowski, to make the opening more factually correct and preferably to remove the horrible implication from the lead that his nationality and ethnicity are the absolute most-important two defining facts for readers to first know about him. Cesiumfrog (talk) 23:50, 22 November 2010 (UTC)

Math markup

The equations in this article are written in HTML instead of the TeX math markup used for equations in most of Wikipedia. A number of the math symbols, such as the 'element of' symbol and some of the brackets, don't display in my IE7 browser, so I'll bet this page doesn't display correctly for a significant number of viewers. I think the equations should be rewritten in math markup. --Chetvorno^TALK 11:14, 13 January 2009 (UTC)

With this new dimension

With this new dimension, it can now be more likely for time travel to become a reality, the time dimension and wormholes. Albertgenii12 (talk) 20:38, 9 March 2009 (UTC)

imaginary length?

The inner product of a timelike vector with itself is negative. Does this mean that the length of a timelike vector is imaginary? I think this point needs to be clarified a little in the discussion of timelike and spacelike vectors.

Etoombs (talk) 03:23, 14 April 2010 (UTC)

You cannot define length from the Minkowski 'norm'. It is not a norm. It is a pseudo-norm, i.e. it looks like one but isnt.94.66.66.21 (talk) 11:25, 20 October 2010 (UTC)

It's worse than that. The article currently states the Minkowski norm ||v|| of a vector v, defined as ||v||² = η(v,v), need not be positive (and mentions some misnomers relative to pure mathematics). This makes no sense. If read literally this definition means that the Minkowski norm is double-valued (since any value for the norm itself can be multiplied by minus one and will still satisfy the definition) and is sometimes not even real but imaginary (since by that definition the norm is still proportional to the square root of the metric product that isn't positive definite). Is it possible that the intention was to identify the Minkowski norm with ||v||² (and NOT with ||v|| itself), in which case the norm would be real (not complex and not more than single-valued) and simply not always non-negative (as per the clause that follows the definition) however there would still be other differences (e.g., for spacelike vectors the norm itself would have units of length-squared rather than just length, and the symbol for the norm would have to always incorporate the superscript in order to remind to take its square root before applying formula derived for standard norms). Which is it? Cesiumfrog (talk) 23:42, 22 November 2010 (UTC)

Usually, the "norm" as it is defined in relativity is $\|v\|={\sqrt {|\eta (v,v)|}}$, which is just the proper length. I have changed the article to reflect this more standard usage. I think we should avoid using "norm" also to refer to $\|v\|^{2}$, even if it is typical to do so in informal treatments. Sławomir Biały (talk) 14:26, 7 December 2010 (UTC)

It might be worth adding that in his 1908 "Space and Time" lecture Minkowski never referred to a norm. The "Minkowski norm" is a later invention. Neither did he talk of orthogonality but used the term "normal" instead. He was much more careful than his modern commentators.JFB80 (talk) 18:48, 5 October 2011 (UTC)

Minkowski norm

Minkowski norm redirects here. But that seems to be something different. At least, there seems to be a totally different notion of Minkowski norm, which is related to Finsler spaces.--Trigamma (talk) 22:07, 7 May 2010 (UTC)

ict picture and rotation

How should we present the elaboration of the x0 = ict picture? It is mentioned briefly in one paragraph, but I think it's worth presenting fully because of its beauty and the transformation-as-(ordinary)-rotation picture. What do you think? CecilWard (talk) 02:55, 23 December 2011 (UTC)

You may put it into a separate section near the end of the article. JRSpriggs (talk) 04:15, 24 December 2011 (UTC)

I don't think that's a good idea. As it is so obsolete, giving it a section of its own would i.m.o. give wp:undue weight to it, and it is already prominently mentioned in the history section. - DVdm (talk) 10:17, 24 December 2011 (UTC)

I wrote the historical note and think the complex Minkowski representation important. It is in several respects much clearer than the standard affine space view and deserves a separate page to itself. It is one form of the hyperbolic theory of special relativity. The standard view is horribly muddled in this article which should be rewritten in simpler form without tensors.JFB80 (talk) 16:14, 24 December 2011 (UTC)

I don't see how it would help: in one sense it's mathematically no different from more modern ways of doing things which being modern have much more theory and sourcing behind them, as it produces the same results so must involve the same calculations. But it's also potentially confusing: complex rotations, as described at e.g. Rotation (mathematics)#Complex numbers, are usually Euclidian. These are non-Euclidian and so far from ordinary. That can be explained away but again it ends up duplicating mathematics that is already there.--JohnBlackburne^words_deeds 17:25, 24 December 2011 (UTC)

I disagree and as I said before think the complex space method deserves a special page. (a) The method used in this article is just Minkowski's 2nd method of the 1908 'Space and Time' lecture expressed in terms of 'Minkowski norm' (not used by Minkowski and unsatisfactory) with a hint of tensor notation. I'm not clear on what could be these 'more modern ways with more theory and sourcing' you talk about. I am not of course saying that they shouldn't be also described. It's not one or the other.

(b) The method you prefer does not produce the same results as the complex space method. You say the complex space method produces a non-Euclidean result. So it should – perfectly correct. I did remark that it is a form of the hyperbolic space theory of special relativity. Your final remark is: 'they can explained away but again it ends up duplicating mathematics that is already there'. I don't believe it. How and where?JFB80 (talk) 19:57, 27 December 2011 (UTC)

So, an article on Minkowski space!

Alright...so here are my thoughts. Hopefully they're helpful!

First off, as has been pointed out, this article is much too technical much too soon, jumping into terms, axioms, and derivations without even definitions. Reading this now, knowing what a Minkowski space is to a reasonable extent, I can understand the material, and it seems that it has definitely been put forward correctly. However, it most certainly has not been put forward introductorily! If I didn't know what a Minkowski space was, what context its terms were in, or what kind of elements it had, I suspect I would be rather lost. Now, obviously the article can't be self-contained, but it can be much more reader-friendly, even through simply defining terms and using more well-known objects to define things at first (and later telling us that such a structure has a name). I'm referring, of course, to the sudden technical punch that begins the discussion on structure—'a nondegenerate symmetric bilinear form with signature (-,+,+,+)' or similar. While fine if you're familiar with the terms, this is quite unnecessarily intimidating to one without such previous familiarity. These terms do help to pick Minkowski space out of a broader, more general class of spaces, but that is not a helpful initial definition—rather, we should build up Minkowski space from more-likely-to-be-familiar and more accessible vector-related notions. Also, I think putting Minkowski space in a mathematical relativistic context early on (perhaps after the initial definitions) is important—after all, that's why this specific space has an entire page! Also, I've noticed that this page doesn't focus much on defining the particular term "Minkowski metric"—even though the term is a misnomer, as said in the article, it is quite common, and one looking for a good definition of "Monkowski metric" on Wikipedia, having been redirected to this page, would have to be halfway through the Structure section to notice it, and even there it's rather hidden as a secondary name for "Minkowski inner product" (and only for the fact that it's a misnomer). As the article shows, this space is interesting precisely because of its inner product/metric—however, it's not clear at all what's so interesting about this "metric" from the article, even though it's properly defined. This article should focus on defining the Minkowski "inner product"/"metric" in context and from more basic structures, and on exploring its relevant ramifications and interpretations in physics in (reasonably) commonly accessible terms. For instance, the section on Lorentz transformations doesn't explain how these are physically relevant or what they represent to the extent an article so important to relativity should. So, if it's alright with you who have been working on this page, I'll set about organizing and expanding this page in the immediate future—note that I'll maintain at least all of the information already put forth (just organized differently). (And note that I'm also responding positively to the "Rant on merging" section which is in this Talk page.) Just wanted to bring this up on the Talk page before I changed the page! (Of course, if I don't get a response, I'll just start—it can always be undone if someone finds an objection, after all.) Anyway! I hope what I plan to do will help the page!

—Trmwiki (talk) 07:51, 28 August 2012 (UTC)

I agree. Glad to see someone who believes like I do, that we've got to stop those complaints by the public that "the only people who understand WP articles are the ones who write them"! I'm an engineer so my level of comfort is the Lorentz transformations, but the higher math is a little unfamiliar. From my perspective, what I'd most like to see explained for the general reader is the crucial difference between "distance" in Euclidean space and "interval" in Minkowski space, which is now expressed by that cryptic phrase: "(-,+,+,+) signature" Most people get the idea of a spacetime created by adding a time dimension to the 3 space dimensions (although that could also use a little explaining, maybe bringing in the idea of a worldline). But the article doesn't explain anything about how the Minkowski metric creates the light cone structure at an event, dividing spacetime into future and past causally connected regions and noncausally connected region. It discusses it in mathematical terms in "Causal structure" but not lay terms, except for the good diagram. Also as you say the Lorentz transformations, and why the speed of light is a universal speed limit. BTW, my feeling is most of the existing article is good and should be kept, just additional sections could be added giving nontechnical explanations. Cheers! --Chetvorno^TALK 10:41, 28 August 2012 (UTC)

I would like to a comment because in my opinion the article certainly needs to be rewritten. Principally I think an article about Minkowski space should pay some attention to what Minkowski actually said which the main part of the article does not do. Minkowski talked about two different space-time representations (as I tried briefly to explain in the historical remarks) .His first was complex Minkowski space, using (x, y, z, ict) and pseudo-Euclidean ideas (orthogonality, distance etc) His second was affine Minkowski space using (x, y, z, t) with affine geometry (oblique axes not preserving angles). Almost all the WP article is written about someone else's creation called Minkowski space which mixes and muddles the two using some of the ideas of affine Minkowski space together with a Euclidean style pseudo-metric (plus some fancy notation to go with it) Pseudo-metric only works in complex Minkowski space. Affine space was essential to Minkowski's 2nd presentation (the 'Space and Time' one usual nowadays) because he showed how the Lorentz transformation could be understood in terms of a skewing of axes. So he never referred to orthogonality but always to conjugate directions. And the space time diagram and the ideas of the light cone structure i.e. 'time-like', 'space-like' were presented by Minkowski in an affine way too even though the diagram in the article shows them looking Euclidean which their definition doesn’t depend on. So why not at least take a look at Minkowski's 'Space and Time' lecture on http://en.wikisource.org/wiki/Space_and_Time ?JFB80 (talk) 04:54, 5 September 2012 (UTC)

Incorrect though Popular Attribution: "Einstein's theory of special relativity"

Although interested in the relativity theory and history of it I am not an expert. However, based on my research the statement "Einstein's theory of special relativity" is vastly misleading. I point to the Articles on the Poincare group, the Lorentz Transformation and Minkowski Spacetime. From what I can determine Einstein played zero role (other than popularization) in the development of the theory of special relativity. Far more prominent was Poincare who developed the theory to a level that Einstein never even managed to copy. In fact Poincare did state the principle of relativity before Einstein and he developed it in terms of a beautiful and far more general mathematical theory involving groups. Poincare did acknowledge Lorentz for the famous Lorentz transformations central to the theory. I therefore suggest Poincare-Lorentz special theory of relativity with mention of the work by Minkowski. Little or no credit goes to Einstein. Apparently Einstein may have played some role in the development of general relativity but there again Hilbert was involved. However, Einstein did successfully predict the advancement of the perihelion of Mercury, however, this is general and not special relativity. — Preceding unsigned comment added by Berrtus (talk • contribs) 08:33, 17 April 2013 (UTC)

The world seems to disagree with that point of view. Check Google scholar and Google books. - DVdm (talk) 08:56, 17 April 2013 (UTC)

Admittedly, you are correct. The world disagrees with the point of view that I put forth. But luckily this is not an issue of popular agreement (for the population is vastly deceived in many areas) On this issue we can ascertain the facts. Let me put it this way: Can anyone find anything in special relativity that Einstein came up with first? If it was all developed by Poincare and Lorentz it doesn't matter what the world thinks. We have to attribute the genuine authors of the theory. So I make the challenge: Those wanting to attribute special relativity to Einstein must actually find something he did BEFORE Poincare did it. And from my research you cannot. (Except popularizing the theory) But Poincare and Lorentz did Publish!§