Talk:Minkowski space

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. On this issue we can ascertain the facts. From what I have been able to determine Poincare came up with a far more general mathematical description of relativity theory than Einstein did before Einstein published his results. Further Einstein did not give proper attribution to Poincare although Einstein had read Poincare's results. However, I must also say that Einstein did put forth the relativity postulates more forcefully, although even he did not totally abandon the aether. Most likely the theory was a collaborative effort. But I see Lorentz- Poincare - Minkowski as the men who truly developed this theory especially in the mathematical details and generalizations. Einstein was more like the Carl Sagan of special relativity. §— Preceding unsigned comment added by Berrtus (talk • contribs) 09:52, 18 April 2013 (UTC)

(ec)

Please sign your talk page messages with four tildes (~~~~). Thanks.

We don't have to attribute the genuine authors of the theory. We have to reflect what the world says. This is just an encyclopedia, not a textbook, or a forum where we can put things straight, or straighter, or curved along the results of our personal research or someone else's fringe viewpoints. And this talk page is where we are supposed to discuss the content and format of the article, not a place where we make challenges — see also wp:TPG - DVdm (talk) 10:02, 18 April 2013 (UTC)

Einstein realized that this new symmetry between space and time applied to everything, not merely to electromagnetic phenomena. He discarded the old 3+1 way of thinking entirely; and noticed the importance of the fact that simultaneity is relative to the state of motion of the observer rather than an absolute relationship.

He was also the first to appreciate the fact that the equality of gravitational mass and inertia (i.e. the equivalence principle) is the defining property of gravity and that it implies that spacetime is curved. JRSpriggs (talk) 10:00, 18 April 2013 (UTC)

"We don't have to attribute the genuine authors of a theory." I disagree. At least if we have substantial evidence of who they are. "We have to reflect what the world says." I disagree especially if we have substantial evidence to the contrary, or if we do we should mention it. Going along with a known false status-quo is simply not acceptable. I think it is unfair to personalize this or to say that it is a fringe viewpoint. Those are just personal attacks. I disagree that proper attribution of a theory is an inappropriate topic for the talk page. Someone might rightly simply change the page to say the Lorentz - Poincare - Minkowski theory of special relativity, but I did not do that. So none of what you said gets to the actual issue. I see your comments as mostly personal and off issue.

As to the comment that Einstein was the first to apply his theory to everything. Please correct me if I have this wrong but was it not Poincare that applied this to Maxwells equations? And on gravitational mass that is general relativity. please note my comments are on special relativity. But thanks for the on issue comments! — Preceding unsigned comment added by Berrtus (talk • contribs) 10:29, 18 April 2013 (UTC)

Please note it was Poincare who developed the synchronization procedure for clocks (simultaneity) Berrtus (talk) 10:40, 18 April 2013 (UTC)

We don't have to correct you if you have this wrong. This is an article talk page where we discuss the article, not a chat room where we discuss a tangent of the subject. See wp:talk page guidelines. - DVdm (talk) 10:46, 18 April 2013 (UTC)

Berrtus, if you have reliable sources that Poincare, Lorentz, and Minkowski are more responsible for Special Relativity than Einstein, then the issue can be discussed. Otherwise it's WP:OR. --Chetvorno^TALK 15:14, 18 April 2013 (UTC)

And not just some rant from the incorrigible plagiarist please — read about our wp:UNDUE policy. - DVdm (talk) 16:22, 18 April 2013 (UTC)

Berrtus' opinion that Lorentz and Poincaré deserve more credit for the theory of relativity than does Einstein is not at all an original viewpoint. See Relativity priority dispute. Red Act (talk) 07:52, 27 May 2013 (UTC)

lorentz transformation's importance

it seems to me a lot of people are incorrectly stating that Minkowski's Raum Und Zeit paper showed that Lorentz' transformation was invariant.

This is not true. DVDm has forced me to post here, but it's quite clear in the link I posted in the edit (page 293).

Minkowski's geometric theory of spacetime was far more general than what lorentz was doing. He states that there is an equivalence, but that does not mean Lorentz' transformation is invariant.

It seems to me that Minkowski was making a small reference to the lorentz transformation, and everyone else decided this meant he was providing additional strength to Lorentz' hypothesis. this is incorrect.

Minkowski's paper simply was showing the geometric properties necessary to establish a full axiomatic system for a geometric theory of gravitation.

The lorentz transformation does not have any *mathematically* valid interpretations of geometry. Minkowski's paper is providing a *geometric* basis for a relativistic theory, complete with the conditions (like the sum of the squares of the measures should total to 1).— Preceding unsigned comment added by 174.3.213.121 (talk • contribs) 22:42, 22 November 2014‎ (UTC)

Please sign your talk page messages with four tildes (~~~~). Thanks.

Nowhere it was written "that Lorentz' transformation was invariant.". The article said that Maxwell's equations are invariant under a Lorentz' transformation. I don't think that our interpretation of the text that you quoted really matters here—see wp:NOR. - DVdm (talk) 09:56, 23 November 2014 (UTC)

you shouldn't be citing minkowski directly after an interpretation. all references to original work should be cited in place for clarity--i.e., to "bookend" any reference to previous work.— Preceding unsigned comment added by 174.3.213.121 (talk • contribs) 05:12, 24 November 2014‎ (UTC)

What? What do you mean? What is "bookend"? JRSpriggs (talk) 09:47, 24 November 2014 (UTC)

Naming: norm squared (or separation squared?)

I made the article precise where it talks of the square of the (Minkowski) norm. However, arguably the quantity v² is actually more useful, as I think JRSpriggs's edit seems to be suggesting (I'd agree that the square of the Minkowski norm doesn't merit being mentioned). Can we find a suitable name for this ubiquitous quantity – or more correctly, of the scalar value ⟨v,v⟩? —Quondum 22:33, 26 February 2015 (UTC)

The article says "The Minkowski norm of a vector v is defined by $\|v\|={\sqrt {|\eta (v,v)|}}$", so saying that the norm squared is $v^{2}=\eta _{\mu \nu }v^{\mu }v^{\nu }=-(v^{0})^{2}+(v^{1})^{2}+(v^{2})^{2}+(v^{3})^{2}$ is obviously wrong, because the latter can be negative, so I was puzzled by JRSpriggs' reversal of my correction. So it is because he does not realize/agree that norm squared means the square of the norm?. - Patrick (talk) 00:29, 27 February 2015 (UTC)

If v² is supposed to be a variable it should be written as such, just a letter. If v is the variable it should be defined explicitly, "v² = .." has two solutions. - Patrick (talk) 01:32, 27 February 2015 (UTC)

v is the four-vector we're dealing with, not something that we're solving for. JRSpriggs's comment "there is no basis for talking about absolute values here; the absolute value of this has no physical meaning or significance" is valid: the square of the Minkowski norm has no particular utility, other than when its square root (i.e. the Minkowski norm itself) is needed. The problem was the mismatch between the text and the formula, and the revert restored the mismatch. So I put it into a correct, if somewhat useless state. The ideal edit would restore the formula to without the absolute value, but would match the words to the formula. The quantity v² ≝ ⟨v,v⟩ is the primary invariant scalar associated with any vector v, and is thus something that we should mention, just like we find ds² = g_μνdx^μdx^ν occurring everywhere. The sign of the square is significant: it distinguishes spacelike from timelike vectors. My problem is that I do not know what the name for this is: not absolute value, not magnitude, not norm. Penrose, for example, simply seems to refer to "the quantity v²", thus avoiding a name for it. —Quondum 04:34, 27 February 2015 (UTC)

Earlier I encountered in the article: "the norm-squared of a vector v is $v^{2}=\eta _{\mu \nu }v^{\mu }v^{\nu }=-(v^{0})^{2}+(v^{1})^{2}+(v^{2})^{2}+(v^{3})^{2}$" and corrected that into a correct statement about the square of the previously defined norm $\|v\|={\sqrt {|\eta (v,v)|}}$, but it seems now that what was meant was v² ≝ ⟨v,v⟩ = $\eta _{\mu \nu }v^{\mu }v^{\nu }=-(v^{0})^{2}+(v^{1})^{2}+(v^{2})^{2}+(v^{3})^{2}$, and no statement about the square of the norm was intended, "norm-squared" was apparently just a poor formulation. I removed it, added the definition of v^2, and restored the original formula. - Patrick (talk) 09:22, 27 February 2015 (UTC)

Much better. Though now I'm realizing that the notation v² is inappropriate in this context (it is used, and correctly at that, in contexts such as geometric algebra, where the metric tensor is implicit in the product of two vectors, as well as in vector contexts where the "inner product" between vectors is denoted as some operator, e.g. u · v). When you came to this article, it already had these inappropriate/inaccurate references ("norm-squared of a vector" and v²), and your stumbling over them has highlighted this. You have already removed the first problem; I've now removed the second. —Quondum 15:36, 27 February 2015 (UTC)

Splitting off Minkowski geometry

Following on a discussion at Talk:Hyperbolic geometry#Lorentzian ≠ hyperbolic To me this article seems to be about a couple of different (and only loosly related) subjects:

• minkowski geometry an affine geometry a geometrical subject

• a description of minkowski space-time a special relativity subject

And I think it does neither subject any good to be combined in one article and I would suggest therefore splitting it up.

• A more basic geometrical article on minkowski geometry including the basic 2 dimensional case ,axiomatics, similarities and differences in relation to Euclidean geometry and other more geometrical relevancies. (any reference to time would not occur on this page) see for example http://www.dynamicgeometry.com/General_Resources/Advanced_Sketch_Gallery/Beyond_Euclid/Minkowskian_Geometry.html

• an space time article on minkowski space, part of the series on special relativity, no i am not nowledgable enough to say what should change here, maybe it should even be split in more articles.

To be honnest on the talk page of hyperbolic geometry this idea was rejected, so now I am trying it here, (this is also the better place to discuss it) WillemienH (talk) 09:29, 7 July 2015 (UTC)

I think what I mean with minkowski geometry is more the geometry of the minkowski plane ( a kind of Benz plane) not that I understand it all (I just stumbled upon it) but the pictures seem similar. WillemienH (talk) 21:08, 7 July 2015 (UTC)

Very quiet here :) , maybe my suggestion was to radical, but still the article is to complex, could we change the structure a bit?

my suggestions

• split the geometry of the physics (maybe we also could use a section on 3 dimensional minkowski space (I am thinking about a 3 d space with a signature (+ + -) , just to bridge the gap between minkowski plane 2- dimensional planeand this page 4 dimensional spacetime.
• more consistency the minskowski metric really seems to use the wrong signature

now: $\pm \left[c^{2}(t_{1}-t_{2})^{2}-(x_{1}-x_{2})^{2}-(y_{1}-y_{2})^{2}-(z_{1}-z_{2})^{2}\right]$ should this not be $\left[-c^{2}(t_{1}-t_{2})^{2}+(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}+(z_{1}-z_{2})^{2}\right],$ yes just to keep to the right signature.

But even after this the article is still to complicated.WillemienH (talk) 13:02, 19 July 2015 (UTC)

On the first point, I don't know what you mean by "geometry of the physics". There is little geometry in the article, unless you promote pretty much every structure in the article to fall into the confines of geometry (which is an entirely acceptable POV). Concepts as straight lines, angles, length etc are, in the article, undefined. This should perhaps change with additions to the new empty subsection called "Geometry". Edit: To be clearer, both the former and this version tackles Minkowski space in an almost entirely algebraic fashion. I believe the foundation should be algebraic because it follows the most easily from the postulates. We also have an article on Pseudo-Euclidean space. Minkowski geometry is a special case of that, and perhaps you should look there for material to split off.

On the second point, there is no such thing as the "correct signature". It is made abundantly clear in the article. The article takes on a neutral POV (hence the ±) with respect to the signature, except in the very last section where a choice is made explicit for preservation of space.

On your third point, please tell me exactly what you find too complicated. Verdicts as "article too complicated" are useless. In the process, I suggest that you bring up the latest version side by side with the version just prior to my edits (that I gather from my talk page that you fancied more). Then you can compare section by section, and tell me which section/paragraph/sentence has not improved. Note that some statements from the old version are totally gone. I found those too unclear to keep. The intention is to reformulate some of these and restore them, some in the geometry section. Please keep in mind that things should be presented as simply as possible, but no simpler than that. YohanN7 (talk) 14:05, 19 July 2015 (UTC)

For example: I find what is said about the quadratic form η(v, v) and just $\eta$ very confusing.

it says $u\cdot v=\eta (u,v)$ , but also $x\cdot y=x^{\mathrm {T} }[\eta ]y,$

are η(v, v) and $\eta$ the same thing?

Also how to combine "$\eta (u,v)=0\quad \forall v\in M\Rightarrow u=0\qquad {\text{(non-degeneracy)}}$ " and " Two vectors v and w are said to be orthogonal if η(v, w) = 0. " (so Two vectors are said to be orthogonal iif one of them = 0?) and later " they are to be mutually orthogonal vectors { e₀, e₁, e₂, e₃ } such that$-\eta (e_{0},e_{0})=\eta (e_{1},e_{1})=\eta (e_{2},e_{2})=\eta (e_{3},e_{3})=1.$"

somewhere I am missing something or getting confused.

You do explain there are two different signatures (very well) but just use only one signature in the article (it is a bit like driving on the right and driving on the left they are both safe, but only if everybody stays at the same side) WillemienH (talk) 05:55, 20 July 2015 (UTC)

I took the liberty of indenting your reply. It is our way of keeping track of who is responding to what. I'll work backwards through your points.

• As I tried to demonstrate above, the article is neutral with respect to the signature. It is therefore you see the ± in places. With a particular choice, the ± wouldn't be there. I also added a note in the article to that effect in response to your first post. The sole exception is the last section, to save space. A choice is there made explicit. To get the other choice, flip sign (−→+, +→ −) in (the matrix representation of) η. I honestly don't know how to make this more clear.
• The non-degeneracy condition says in words that no vector is orthogonal to every vector. Each vector can be orthogonal to some vectors, but not all unless it is itself the null vector. The way this is formulated is standard. Maybe the explanation in words should go in?
• It is mentioned (in the "intro" section of "Mathematical structure") that the metric tensor, the bilinear form, the Minkowski inner product are all the same object, and that it is good to keep that in mind. You can also add the quadratic form to that list since the polarization identity allows you to pass back and forth between a bilinear form and a quadratic form. But that would be an unusual way of promoting a quadratic form to a full blown tensor. The matrix [η] also refers to the same object. It, however, is basis-dependent. This does not mean different appearance in cartesian coordinates for different inertial frames, but it means different appearance in, say, spherical coordinates. I am emphasizing this because it is the major key to all of special relativity. The invariance of the interval (now first thing of substance in lead) forces coordinate transformations between inertial systems to take the form of Lorentz transformation. These are exactly the ones that preserves the interval, or , equivalently the bilinear (or quadratic) form with the matrix η being what it is in these coordinates.

I see a spot or two where I can use a better notation and a better formulation. For instance, η(v, v) and η are not really exactly the same thing. One of them is the metric tensor/bilinear form/Minkowski inner product/quadratic form when given two equal arguments, i. e. a number that it prodces, while the other is the metric tensor/bilinear form/Minkowski inner product/quadratic form, i. e. a function that will produce a number when fed arguments. (Standard notational abuse in physics, but not math.) I'll make a small edit (in due time).

You have not mentioned the involvement of tangent spaces in the article. I thought that this may be the major obstacle for understanding for most, since the topic of manifolds, from which this concept stems is almost always introduced later than introductory special relativity. The rationale for introducing tangent spaces (which I kept from the previous version) at all here is that it facilitates comparison with general relativity. Another rationale is that the article is not only aimed at the beginning relativist/geometer/whatever. It is (in an ideal state) supposed to be a reference for people familiar with the subject, but perhaps being rusty needing to look up some definition (this article is very much not there yet). Do you think that tangent spaces are treated in a comprehensible fashion? YohanN7 (talk) 09:40, 20 July 2015 (UTC)

Thanks for your explanations , I do think I miss interpreted the non-degenerate condition. I guess I still needs to learn more. I did put an hatnote refering more to Pseudo-Euclidean space. Maybe better to copy bits to there (and start subsections on 2 dimensional and 3 dimensional Pseudo-Euclidean spaces). Maybe I am getting more and more confused: There seem to be two unrelated types of hyperbolic plane (the "2 dimensional plane in hyperbolic geometry" and the " hyperbolic plane as Isotropic quadratic form") two or even more unrelated types of Minkowski plane (the Benz plane one, the affine geometry one, and maybe even more see http://math.stackexchange.com/q/1352447/88985 ) on introspection this article seems to be about the four "dimensional" Isotropic quadratic form and I am just getting confused.

I don't like the always indent one more indenting structure, my ideas is to keep it less indented, just the op (original poster) has no indention, the first reply-er gets one intention, the second reply-er gets 2 indentions, and reply ers keep their indention level as they go along, it is just a much more efficient use of screenspace . (but I guess you don't agree with this) Thanks for your eplanation, ps I am still looking forward to your reply at Talk:Hyperbolic geometry#GA nomination and archivingthat is all for now.WillemienH (talk) 16:27, 21 July 2015 (UTC)

Someone with better knowledge of geometry should chip in. My knowledge is limited. But it does include the fact that "Minkowski geometry" is somewhat of a misnomer. The Minkowski metric is a pseudo-Riemannian metric (standard terminology). But it is not Riemann that is pseudo, it is the geometry. Only when you restrict to certain subsets (hyperboloids of dimension one less than spacetime) you get a space with a true geometry (including lengths, angles and all). See surfaces of transitivity of spacetime. YohanN7 (talk) 18:34, 21 July 2015 (UTC)

You can interpret that as the hyperboloid (and hence the other model spaces) being isometrically embedded in spacetime when given the metric induced by the Minkowski metric. YohanN7 (talk) 18:59, 21 July 2015 (UTC)

Instead of Minkowski space why not use 4D Euclidean space with meters=i*c*seconds?

Einstein shows in Appendix 2 of "Relativity" that Minkowski space is formally equal to 4D Euclidean space if you make the simple substitution meters=i*c*seconds where i*c, not c, is the exact and universal conversion factor between meters and seconds that needs to be incorporated into Planck units to make them a lot simpler by removing several of the "units" altogether, not just making the constants "1". A lot of contradicting talk over "speed" in special relativity examples crop up from not doing this because not using this more strictly makes people think c is a constant and "speed" is a variable (speed is unitless if you take meters and seconds being equal seriously, so it can't be a physical measurement) when the opposite follows Occam's razor more closely. If you let c be defined for a particular reference frame, then length, meters, mass, and entropy do not change for any reference frame. Wouldn't 1 physical quantity varying instead of 4 be nicer? Lorentz transformations would no longer be needed in theory if the experimenters insert the Lorentz adjustment when they measure in meters, mass, and I think entropy. Seconds could remain the same. Ywaz (talk) 13:09, 9 August 2015 (UTC)

I found your reference to Relativity here. Making the analogy to 4-D Euclidean space is helpful,(and in-source) but your point about making the speed of light frame-dependent is not in the source. (WP:OR)

What frame is a photon tied to if its speed is dependent on a frame? The speed of the source object? Destination? Something else? The speed of light in a frame would change depending on the observation frame as well. A reliable source might bring some more specificity on the math here. Forbes72 (talk) 04:16, 2 September 2015 (UTC)

Why give Einstein credit when he is merely restating what Minkowski had previously done? Minkowski in 1907 had taken units with c=1 which is equivalent to what you are proposing isnt it? The attempt to interpret Minkowski space as Euclidean is flawed because it just is not Euclidean. JFB80 (talk) 04:39, 5 September 2015 (UTC)

ict is out of fashion. It used to be popular for introductory texts, but rarely for the advanced texts, and never in general relativity. It deserves mention though, as an existing variation. YohanN7 (talk) 12:57, 29 September 2015 (UTC)

Minkowski manifold

Should Minkowski manifold redirect here?