Talk:Minkowski space

message: 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).
::No, it is neither of German nor of Jewish but only of Polish descent - as long as considering languages. Jews of Lithuania have such names! At his time intelectual people moved to Germany, entering the German-Jewish culture of Theoretical Physics. Nowadays they would migrate to the USA! Compare Eugen Wigner and in the film industry Billy Wilder. But many Jews arriving from else in central and east Europe choose their family names sounding local but being close to Hebrew - example Kohn. So you may search Hebrew for some Min-. 115.164.73.50 (talk) 04:36, 13 June 2020 (UTC)
replies: text: 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)
thread_title:  Minkowski's nationality 

message: 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. --ChetvornoTALK 11:14, 13 January 2009 (UTC)
thread_title:  Math markup 

message: 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)
thread_title:  With this new dimension 

message: 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)
replies: text: 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)
replies: text:  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)
replies: text:  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)
thread_title:  imaginary length? 

message: 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)
thread_title:  Minkowski norm  

message: 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)
replies: text: 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! --ChetvornoTALK 10:41, 28 August 2012 (UTC)
replies: text: 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)

text: I would like to see more graphical representations of concepts.  first figure looks like a good start than just using TEX data equations which are not vetted and not informative , this is a not a reference book! Juror1 (talk) 18:49, 23 February 2017 (UTC)
thread_title:  So, an article on Minkowski space! 

message: I  the article precise where it talks of the square of the (Minkowski) norm.  However, arguably the quantity  is actually more useful, as I think 's  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 ?  —Quondum 22:33, 26 February 2015 (UTC)
replies: text: 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)

text: 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)
replies: text:  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  is the primary invariant scalar associated with any vector , and is thus something that we should mention, just like we find  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 ", thus avoiding a name for it. —Quondum 04:34, 27 February 2015 (UTC)
replies: text: 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)
replies: text: Much better. Though now I'm realizing that the notation  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. ). When you came to this article, it  these inappropriate/inaccurate references ("norm-squared of a vector" and ), 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)
thread_title:  Naming: norm squared (or separation squared?) 

message: Should Minkowski manifold redirect here?  — Preceding unsigned comment added by 70.247.173.205 (talk) 21:00, 28 February 2016 (UTC)
replies: text: After Googling it, I do not see enough usage of that phrase to justify having any redirect. JRSpriggs (talk) 02:37, 29 February 2016 (UTC)

text: A Manifold is a special type of a Topological space. All manifolds are spaces, but not the other way around. Spirit Ethanol (talk) 18:21, 2 March 2016 (UTC)
thread_title:  Minkowski manifold 

message: Is the treatment of the terminology in the article of the terms
*Minkowski inner product
*Minkowski metric 
*Minkowski norm
acceptable? They have long been here in one or another form. They aren't standard, but there is no standard to use. YohanN7 (talk) 14:47, 5 October 2016 (UTC)
thread_title:  Terminology 

message: I removed the empty section "Geometry". 
Should we have one? I think (but I am just guessing here, not my field) it is the case that the restriction of the Minkowski metric to one sheet of two-sided hyperboloids in fact yields a true Riemannian metric. An idea is to pull this metric back via a parametrization and explicitly demonstrate the result. Perhaps then from there calculate the (presumably hyperbolic) distance function (a true metric). Suggestions? YohanN7 (talk) 14:53, 5 October 2016 (UTC)
thread_title:  Geometry 

message: The section on four-dimensional spacetime includes a useful note comparing time when thought of in a four-dimensional field as compared to "time itself" as when measured by a clock.  My edit was reverted, but its intent was to eliminate this identifying "time itself" to be the experience of time as when measured by a clock (aka, sequentially/linearly).  Newton might have considered time to be a sequence, but if Einstein proved anything, it is that Newton's understanding of linear time was insufficient and therefore could not be considered 'time itself.'  Rather, by showing that physical phenomena like gravity were best modeled in Minkowski Space, Einstein was arguing that it is this 4-d conceptualization of time that should be thought of as 'time itself' and that the sequential perception of time as perceived by humans is merely a local perception of "time itself" (4-d spacetime) as interpreted by the mind of a great ape.  My objection is only with that label; it is very useful to highlight how fundamentally different the two mathematical models of time are.  Schray (talk) 20:18, 23 January 2017 (UTC)
thread_title:  "time itself" 

message: It has been proposed that the section Geometry be split out.
*Neutral: I wrote that section. Before I wrote it, I probed (scroll a little, link works poorly) whether we should have the section, but no-one expressed an opinion. On the one hand, there has been requests for a geometry section, but on the other hand, those requests might have anticipated something less technical. On the third hand, with the section, there's an excellent spot to exhibit the connection between Minkowski space, De Sitter space, and Anti-de Sitter space. YohanN7 (talk) 08:49, 5 May 2017 (UTC)
thread_title:  Split proposal for section Geometry 

message: @YohanN7 Thanks for the improvements to the hide box, but I think a bit more is needed. The two choices in the first sentence should be tied explicitly to their respective signatures. Also the sentence "Arguments for the latter include that otherwise ubiquitous minus signs in particle physics go away." can be parsed two ways: "Arguments for the latter include that (otherwise ubiquitous) minus signs in particle physics go away."  and "Arguments for the latter include that, otherwise, ubiquitous minus signs in particle physics go away."  I think the first is the desired meaning, but I'd rather someone with more knowledge clarity the sentence.--agr (talk) 11:07, 13 July 2017 (UTC)
replies: text: But why don't you edit yourself? YohanN7 (talk) 12:01, 13 July 2017 (UTC)
replies: text: I just did. I was a little uncertain, that's all. I assume you'll correct me if I got it wrong. --agr (talk) 15:59, 14 July 2017 (UTC)
thread_title:  Metric signature 

message: If v and w are both future-directed time like four-vectors, then their norms and cross product are positive so what's the problem? Why "if defining ||v|| := sqrt(||v||^2) makes sense"? 
This needs a source reference. JFB80 (talk) 19:44, 24 April 2019 (UTC)
thread_title:  Reversed Triangle Inequality What is the meaning in the article? 

message: The space-time interval defined in the section '2.5 Minkowski metric' is (a) unsourced (b) inconsistent with the referenced Wikipedia article 'spacetime interval'  (c) disagrees with the standard works of Minkowski himself, Sard and Landau & Lifschitz. I hope that there will not be violent objections (as has happened in the past) if I change it to make it consistent with these sources.JFB80 (talk) 09:13, 21 January 2020 (UTC)
thread_title:  Minkowski metric again 

message: I propose making changes in the order of the topics so there is an introductory part and a development part. The introductory part will be straightforward explanation of the basic ideas from Minkowski and will include causal relations and the definition and properties of norm and bilinear product. Then the development part will include other topics such as tensors, pseudo-metric spaces  and hyperbolic geometry. Hopefully this will make the article easier for an inexperienced person (and maybe others) to understand as requested in the editorial remarks at the top of the page. Any comments? JFB80 (talk) 07:02, 28 January 2020 (UTC)
replies: text: Comments above from 2017 are re-affirmed. Further, the historic place of Minkowski space (1908) is between hyperbolic quaternions and general relativity. The enunciation of a cosmology marks the concept as a new paradigm, with analytic geometry and linear algebra as supporting structure. Readiness for non-Euclidean geometry was a further support, and was made explicit in usage as a metric-velocity space with kinematic geometry. Your note that order is wrong can be seen especially in the section on motions of Minkowski space: links are given first to Poincare group, then to Lorentz group, and next to Lorentz transformation – opposite to natural. Furthermore, a link could be made to history of Lorentz transformations where much of the linear algebra is reviewed. An early link to isotropic quadratic form should be made since this is not a metric space. — Rgdboer (talk) 02:11, 29 January 2020 (UTC)
replies: text:  Thank you for your comments. After some experimenting I begin to realize the difficulties. It needs considerable rewriting and deleting. Quite a lot of work!  JFB80 (talk) 21:47, 29 January 2020 (UTC)

text: Yes, a daunting task. The necessity of Minkowski space may be appreciated by recalling that A Treatise on Electricity and Magnetism used four coordinates without acknowledging their structure. Further, the finitude of light speed was long realized but slow to be put into geometry. As mentioned, English algebraists had anticipated Minkowski space structure but refrained from making a cosmology (any mathematical model deceives by inherent limitation). Given the importance of WP:SOURCES, one notes that Wolfgang Rindler is not yet cited, and the spur that Minkowski space has given to philosophy is shown by Minkowski space at PhilPapers. — Rgdboer (talk) 21:39, 30 January 2020 (UTC)
replies: text: A further point which needs to be made clear because it is the cause of misunderstandings is that there is a difference between the physics and the mathematics views. Relativity requires all signals to travel at a speed less than that of light. This limits attention to time-like vectors and certain properties then apply which are not valid for space-like vectors. The mathematicians do not put this relativity requirement and aim at a theory covering both time-like and space-like events  This is more difficult and needs a different, more abstract approach.JFB80 (talk) 20:41, 11 February 2020 (UTC)
thread_title:  Reordering of topics in the article 

message: For defining a Minkowski space, there is no need to introduce a basis. So the definition of a Minkowski space runs as follows:
A Minkowski space is a pair of a real four-dimensional vector space together with a symmetric bilinear form which is non-degenerate and has a signature of (1,3). Thats the physical concept in the language of mathematics. Mathematically it makes sense to generalize it to 1+n dimensions, i.e. the signature becomes (1,n).
The rest is deduction. Why that? Because there are two standard examples in physics. One is what in this article is taken for Minkowski space, namely a R4 in pseudo-orthogonal coordinates, and a second one - which even may be more fundamental in physics: namely the hermitian matrices of a two-dimensional Hilbert space (with respect to the standard real bilinear form for matrices). In physics there are two more examples - the Dirac and the Duffin-Kemmer-Petiau matrices.
Since physics needs differentiation there must be a topology, defined entirely in terms of such a Minowski structure. Which? .2001:E68:442D:54F1:F506:2A05:AC7B:B7AB (talk) 14:46, 3 February 2020 (UTC)
replies: text: Doesn't the Lorentz group come into it? JFB80 (talk) 19:44, 3 February 2020 (UTC)
thread_title:  ununderstandable for mathematicians 

message: I have removed the template too technical, the reason being that it should be possible for quite a few to understand the ingress. That the rest of the article is not so easy to grasp is another matter, Wikipedia should not shy away from diving into hard to grasp content. Ulflarsen (talk) 13:14, 25 February 2020 (UTC)
replies: text: This is the first time I have heard of the lead referred to as the "ingress", if that is what you mean. JRSpriggs (talk) 20:36, 25 February 2020 (UTC)
thread_title:  Removed template: Too technical 

message: DaveJWhitten (talk) 16:45, 1 April 2021 (UTC)
thread_title:  Meaning of η(v,v) ?? 

message: In section "Causal structure" the greek symbol "eta", is used without explanation or reference.
Add a named link "scalar product" at the use of symbol "eta". "scalar product" is defined later on in the article. Johanwiden (talk) 10:17, 14 March 2024 (UTC)
replies: text: I have know added the forward link to section "Scalar product". Johanwiden (talk) 13:22, 9 May 2024 (UTC)
thread_title:  Add a forward reference to definition of "scalar product" at first use of symbol for scalar product