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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:
The article currently says:
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:
But I'm not certain enough to make the edit. -- Jorend 17:35, 5 January 2007 (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)
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).
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, 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)
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)
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)
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)
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)
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)
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)
"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)
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)
Sorry Berrtus you are wrong! Thia was made very clear by Pascual Jordan in his 1964 Lecture on General Relativity (GR) in Hamburg and Carl Friederich von Weizsäcker in his lecture "das Raumproblem in der Relativitätstheorie": First General Relativity: There were contributions by Hilbert and especially Riemann and maybe others. But GR came into being exactly when the principle of equivalence (of inertial and gravitational mass) was reckognized, which immediately leads to the equivalence of gravitation and geometry. And this was Einstein. Secondly Special Relativity (SR): There undoubtedly were contributions by Lorentz, Minkowski, Poincare and the Austrian physicist Hasenörl. But SR comes into being exactly in one moment, namely when you take two special Lorentz transformations, say matrices, and multiply them to get a third special Lorentz transformation. Giving the resulting parameters in this third special Lorentz transformation a physical meaning is SR. Who has done this calculation and this interpretation has invented SR. Note that Einstein, although having mathematics in an outdated form available only, had a sense for mathematical beauty and elegance (how, was the content of Weizsäcker's lecture). 184.22.189.33 ( talk) 07:05, 18 February 2018 (UTC)
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)
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 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)
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:
And I think it does neither subject any good to be combined in one article and I would suggest therefore splitting it up.
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
But even after this the article is still to complicated. WillemienH ( talk) 13:02, 19 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)
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)
Yet another suggestion
Why isn't anyone using Quaternions here, or even attempted to provide some insights on the relation of Minkowski generalizations and the quaternions - e.g., an increase of dimensionality produces stretchings to become rotations under multiplication? Not a mathematician here but I think it would be very insightful to analyze the analogies. [EDIT] There is indeed a mention in this discussion about hyperbolic quaternions, but a quick read on them pointed further to /info/en/?search=Biquaternion as a more suitable algebra to represent the full Lorentz group.
Should Minkowski manifold redirect here? — Preceding unsigned comment added by 70.247.173.205 ( talk) 21:00, 28 February 2016 (UTC)
Again I have reverted ( [1]) this unsourced nonsense:
The signature (+,-,-,-) which has been adopted here has several physical implications. Principally it is positive for physically observable events and for the difference between two such events. The attempt to keep a Euclidean analogy by using the opposite signature fails completely.
- DVdm ( talk) 17:24, 1 September 2016 (UTC)|
References
@JFB80, since you don't understand groups, let's skip the Lorentz group. The end points of a meter stick at any given time in a particular Lorentz frame in which the meter stick is at rest are two events that are very much measurable. You simply record their spatial locations (xi) (you can use the meter stick itself for the purpose) and note the common time. Now take their difference and compute the interval,
This is positive with the (−, +, +, +) metric and negative with the (+, − ,− , −) metric. Right?
Is this a "physical implication" of any of the two conventions? No, putting in such an interpretation is nonsense – in any convention. What happens is that you get a sign flip in the definition of proper length in terms of the interval, illustrating a point (one of the bullets) I made in my first post.
By the way, this example illustrates that restriction of the (−, +, +, +) metric to space yields the Euclidean metric. (But this is not important.)
Moreover, your edit made the rest of the article inconsistent. The rest relies on the choice of the (−, +, +, +) metric for definiteness and preservation of (article) space. Spelling out both choices is just a waste of space since they are trivially related. If you feel religious about the (+, −, −, −) signature, by all means change, but do so consistently throughout and please, please don't add anything about physical implications. There aren't any. YohanN7 ( talk) 09:32, 5 September 2016 (UTC)
@JFB80. Finally you say something that is precise enough to be responded to properly, because it is not again of the sort not even wrong. This time it is finally clear. What you say is simply false or plainly wrong. This is an improvement over nonsense, a term that you probably don't like and a term that becomes unavoidable (of sorts) when you or anyone else is less than crystal clear. This is good.
You need to get acquainted with the concept of Lorentz observer. I'll not spell out the details, but a Lorentz observer is someone who has access to a complete record of spacetime events in his Lorentz frame. The concept requires "observers" at arbitrary points in space of the Lorentz frame in question, at rest relative to the coordinate system. These observers have synchronized clocks. They report to a main office. The Lorentz observer can read all their reports. Lorentz observers provably exist in principle (can be realized), see for example *Sard, R. D. (1970). Relativistic Mechanics - Special Relativity and Classical Particle Dynamics. New York: W. A. Benjamin.
ISBN
978-0805384918. {{
cite book}}
: Invalid |ref=harv
(
help) In particular, they can be realized in practice when it comes to noting the end points of a meter stick at an instant.
How accepted do you think special relativity would be if we could not measure the length of things at rest in our world?
Thus when you talk about undefined concepts such as "physically realizable events". not having understood the meaning of "Lorentz observer", then you will in the first place either be misunderstood or tossed off as being a crackpot. Invariably. Period. If you have a reference defining these things of yours, just burn it.
Finally, the "reversed Cauchy inequality and reversed triangle inequality" have analogues in the (−, +, +, +)) metric. The inequalities in this case reverse direction (to the standard direction) with the price being paid absolute signs. Thus the signatures each have imperfect versions of theorems that hold in true inner product spaces. Also, the section about causal ordering does not refer to the signature of the metric. It is an thereof independent concept. Nothing new under the sun.
I urge you to think twice or even ten times deeply before you proceed to respond. I don't wish to spend much more time on this and had in fact promised myself not to respond further because experience suggests that it is a total waste of time. I will respond, but only if I can see that you have read up on the basic concepts and use a language common to us both, free of your own definitions. YohanN7 ( talk) 06:57, 7 September 2016 (UTC)
The signature (+,-,-,-) which has been adopted here has several physical implications. Principally it is positive for physically observable events and for the difference between two such events. The attempt to keep a Euclidean analogy by using the opposite signature fails completely.
Perhaps that is what you have in mind? - DVdm ( talk) 09:11, 10 September 2016 (UTC)The actual form of ds above depends on the metric and on the choices for the X0 coordinate. To make the time coordinate look like the space coordinates, it can be treated as imaginary: X0 = ict (this is called a Wick rotation). According to Misner, Thorne and Wheeler (1971, §2.3), ultimately the deeper understanding of both special and general relativity will come from the study of the Minkowski metric (described below) and to take X0 = ct, rather than a "disguised" Euclidean metric using ict as the time coordinate.
I'm not too fond of this passage:
It is unusual to speak events as being timelike, etc. Is would not be a fully Lorentz invariant concept (i.e. not Poincaré invariant). It should be emphasized more that we are talking about intervals here, i.e. the interval between v and the origin (0, 0, 0, 0). This is a fully Lorentz invariant concept. For some 4-vectors, e.g the momentum 4-vector, this works automatically since there is an implicit derivative. But the event (0, 2.5 million light-years, 0, 0) referring to an event in the Andromeda galaxy 2000 years ago (according to us) is according to us spacelike, but the Andromedans might disagree.
What makes this confusion possible is the canonical identification of tangent spaces with the spacetime manifold itself. This does not work in general relativity. YohanN7 ( talk) 07:17, 8 September 2016 (UTC)
Perhaps this [8] is acceptable. There is absolutely nothing timelike, spacelike, or lightlike about events per se. But when one refers to events as vectors, then an origin is implied (we then have a coordinate system on the spacetime manifold). YohanN7 ( talk) 08:27, 29 September 2016 (UTC)
People, does someone have a specific proposal to change something, backed by a relevant source, to the article? If not, we are discussing our personal preferences and views of some aspect of the subject of the article, which is not allowed per the wp:talk page guidelines. If no one has a specific proposal, this discussion should be closed here. It can of course be continued on one of our user talk pages, like for instance User talk:JFB80#Spacetime metric sign convention. Thanks. - DVdm ( talk) 18:58, 2 October 2016 (UTC)
My tone of discussion isn't the best in my latest post. Well, there are reasons. That is, there were reasons. After my last reply, JFB80 went back and changed his post from downright offensive to more neutral words. This would suffice for someone else than me to take it to the higher powers. YohanN7 ( talk) 09:04, 3 October 2016 (UTC)
Is the treatment of the terminology in the article of the terms
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)
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)
This would work. I found a reference, the Lee book recently added to the ref list.
YohanN7 (
talk) 09:59, 6 October 2016 (UTC)
Done
Rest list:
To be honest, hyperbolic geometry is probably of less interest in special relativity than what special relativity is in hyperbolic geometry. Reason: The geodesics of H1(n)
R are not geodesics of flat spacetime (in the same way great circles on the sphere aren't geodesics of ℝ3). That said, I think it may be of value to the reader to see curved things embedded in flat spacetime like is now done.
YohanN7 (
talk) 14:21, 11 October 2016 (UTC)
Under "History", the following phrase appears, "In 1905, and later published in 1906...". The grammar might be improved.
The effort of 14:53 G.M.T. on 20/10/2016 seems to be wrong. — Preceding unsigned comment added by 92.26.14.17 ( talk) 10:09, 21 October 2016 (UTC)
In the section Pseudo-Euclidean metrics the following appears:
The links refer to positive definite quadratic forms and are not appropriate here. The material further down in the article on space-like and time-like vectors needs to precede this discussion. For space-like vectors orthogonality is right, but hyperbolic orthogonality applies between a time-like and space-like vector. Rgdboer ( talk) 01:59, 9 December 2016 (UTC)
Thank you YohanN7 for calling attention to the lack of naming reference. One has been supplied with online link. The author uses "inner product" including the indefinite case, not restricted as our inner product; we must use bilinear form. The author also develops hyperbolic numbers which clarifies the usage with orthogonality. In the interests of making Minkowski space a better article, the above comments were suggested to clarify the special nature of the temporal axis in orthogonality. Rgdboer ( talk) 02:11, 12 December 2016 (UTC)
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)
The statement The Minkowski inner product is defined as to yield the spacetime interval between two events when given their coordinate difference vector as argument. is wrong. The interval between x and y is sqrt(|<x-y,x-y>|), the norm, not the inner product. Shmuel (Seymour J.) Metz Username:Chatul ( talk) 20:58, 14 February 2017 (UTC)
Under Standard basis we have
Shouldn't it be
? — Preceding unsigned comment added by 147.91.66.6 ( talk) 08:43, 3 March 2017 (UTC)
It has been proposed that the section Geometry be split out.
@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)
The following paragraph intimating tetrad formalism, such as Newman-Penrose formalism and the construction of a complex null tetrad, subjects of general relativity, has been removed as this article deals strictly with flat spacetime.
Please discuss if you disagree. — Rgdboer ( talk) 02:50, 24 September 2017 (UTC)
User:JRSpriggs thinks that orthonormal "makes perfect sense in Minkowski space" according to his edit summary. But Othonormal only applies to inner product spaces, which Minkowski space is not. He re-instated the first three sentences, inappropriately. He should come here to discuss, or restore my edit. — Rgdboer ( talk) 23:07, 25 September 2017 (UTC)
Thank you for such a complete response. The indefinite inner product η that gives Minkowski space structure has null vectors that do not occur in inner product spaces. The following statement from the article has been tagged as it is unlikely that a reliable source will turn up:
What is important for η are the hyperbolic-orthogonal events that Minkowski used to define simultaneity in his space. Repeatedly this information has been inserted. (12 May 2006, 1 April 2008, 24 September 2017). It is very important to distinguish Minkowski space from four-dimensional Euclidean space where unit vectors and orthogonal basis mean something. These terms arise in linear algebra, and special relativity based on Minkowski space relies on linear algebra, but the subtlety of η requires special care, not imitation of inner product space.
Furthermore, linear algebra has sufficient language for special relativity, and the use of tensor algebra, manifolds, differential geometry, and tangent space is out of place and makes the article a headache for someone just looking to get started in relativity with this model. As learners use this resource, editors should keep in mind pedagogical principles like cognitive load, instructional scaffolding, and zone of proximal development. Inclusion of the unnecessary geometry runs counter to the needs of the learner. — Rgdboer ( talk) 21:45, 1 October 2017 (UTC)
Yes, as mentioned at WP:Technical#Put the least obscure parts of the article up front. But the article can be completely clear when differential geometry is left out. For perspective, consider this comment:
"[In 1912] Einstein realized that mathematics demanded much more than cursory acquaintance, that in fact his hopes for a generalization of special relativity could not be realized without a heavy dose of mathematics." (from Cornelius Lanczos (1972) "Einstein’s Path from Special to General Relativity", pages 5 to 19 of General Relativity: Papers in Honour of J.L. Synge, L. O’Raifeartaigh editor, Clarendon Press, see page 12) — Rgdboer ( talk) 21:49, 4 October 2017 (UTC)
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)
18:14, 7 November 2019 (UTC) JFB80 ( talk)
This article needs an introduction for lay readers. What is Minkowski space? Instead of starting with a lot of math and theory, how about explain whether this is the spacetime metric of the real universe, or just a mathematical construct used for calculations? I have yet to find a wiki article about spacetime metrics that even mentions which one we live in! 2601:441:4680:3230:ED26:3A73:A06E:9B5B ( talk) 03:24, 12 June 2019 (UTC)
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)
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)
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).
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)
DaveJWhitten ( talk) 16:45, 1 April 2021 (UTC) As I was reading, this sentence popped up:
This can be expressed in terms of the sign of η(v, v) as well, which depends on the signature.
I didn't see any definition for it earlier in the article.
Twice anon 99.239.158.18 ( talk · contribs · deleted contribs · logs · filter log · block user · block log) removed well known and sourced content ( [9], [10]), which I restored for the reasons given ( [11], [12]). Anon warned on their user talk for edit warring. Comments from others welcome. - DVdm ( talk) 00:26, 13 February 2021 (UTC)
The source (Landau & Lifshitz) says twice on page 4 that Minkowski space-time is a "fictitious four-dimensional space". On the other side, the relativity postulates are based on experiments done in the physical reality. The physical reality can't create itself fictitious things, because all fictitious things are created by imagination in the human mind. Therefore the statement in the article is incorrect and not supported by the source. 176.222.34.111 ( talk) 05:01, 19 March 2021 (UTC)
A lot of talk about a flat spacetime, but no definition of 'flatness' to be found (I think). What do you mean with 'flat'? — Preceding unsigned comment added by Koitus~nlwiki ( talk • contribs) 20:11, 15 August 2021 (UTC)
In section "Causal structure" the image "Subdivision of Minkowski spacetime" has a misleading terminology: "absolute future" and "absolute past". A better terminology is used in the Wikipedia article "Causal structure": "causal future" and "causal past". Johanwiden ( talk) 14:59, 13 March 2024 (UTC)
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)
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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:
The article currently says:
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:
But I'm not certain enough to make the edit. -- Jorend 17:35, 5 January 2007 (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)
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).
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, 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)
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)
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)
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)
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)
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)
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)
"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)
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)
Sorry Berrtus you are wrong! Thia was made very clear by Pascual Jordan in his 1964 Lecture on General Relativity (GR) in Hamburg and Carl Friederich von Weizsäcker in his lecture "das Raumproblem in der Relativitätstheorie": First General Relativity: There were contributions by Hilbert and especially Riemann and maybe others. But GR came into being exactly when the principle of equivalence (of inertial and gravitational mass) was reckognized, which immediately leads to the equivalence of gravitation and geometry. And this was Einstein. Secondly Special Relativity (SR): There undoubtedly were contributions by Lorentz, Minkowski, Poincare and the Austrian physicist Hasenörl. But SR comes into being exactly in one moment, namely when you take two special Lorentz transformations, say matrices, and multiply them to get a third special Lorentz transformation. Giving the resulting parameters in this third special Lorentz transformation a physical meaning is SR. Who has done this calculation and this interpretation has invented SR. Note that Einstein, although having mathematics in an outdated form available only, had a sense for mathematical beauty and elegance (how, was the content of Weizsäcker's lecture). 184.22.189.33 ( talk) 07:05, 18 February 2018 (UTC)
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)
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 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)
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:
And I think it does neither subject any good to be combined in one article and I would suggest therefore splitting it up.
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
But even after this the article is still to complicated. WillemienH ( talk) 13:02, 19 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)
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)
Yet another suggestion
Why isn't anyone using Quaternions here, or even attempted to provide some insights on the relation of Minkowski generalizations and the quaternions - e.g., an increase of dimensionality produces stretchings to become rotations under multiplication? Not a mathematician here but I think it would be very insightful to analyze the analogies. [EDIT] There is indeed a mention in this discussion about hyperbolic quaternions, but a quick read on them pointed further to /info/en/?search=Biquaternion as a more suitable algebra to represent the full Lorentz group.
Should Minkowski manifold redirect here? — Preceding unsigned comment added by 70.247.173.205 ( talk) 21:00, 28 February 2016 (UTC)
Again I have reverted ( [1]) this unsourced nonsense:
The signature (+,-,-,-) which has been adopted here has several physical implications. Principally it is positive for physically observable events and for the difference between two such events. The attempt to keep a Euclidean analogy by using the opposite signature fails completely.
- DVdm ( talk) 17:24, 1 September 2016 (UTC)|
References
@JFB80, since you don't understand groups, let's skip the Lorentz group. The end points of a meter stick at any given time in a particular Lorentz frame in which the meter stick is at rest are two events that are very much measurable. You simply record their spatial locations (xi) (you can use the meter stick itself for the purpose) and note the common time. Now take their difference and compute the interval,
This is positive with the (−, +, +, +) metric and negative with the (+, − ,− , −) metric. Right?
Is this a "physical implication" of any of the two conventions? No, putting in such an interpretation is nonsense – in any convention. What happens is that you get a sign flip in the definition of proper length in terms of the interval, illustrating a point (one of the bullets) I made in my first post.
By the way, this example illustrates that restriction of the (−, +, +, +) metric to space yields the Euclidean metric. (But this is not important.)
Moreover, your edit made the rest of the article inconsistent. The rest relies on the choice of the (−, +, +, +) metric for definiteness and preservation of (article) space. Spelling out both choices is just a waste of space since they are trivially related. If you feel religious about the (+, −, −, −) signature, by all means change, but do so consistently throughout and please, please don't add anything about physical implications. There aren't any. YohanN7 ( talk) 09:32, 5 September 2016 (UTC)
@JFB80. Finally you say something that is precise enough to be responded to properly, because it is not again of the sort not even wrong. This time it is finally clear. What you say is simply false or plainly wrong. This is an improvement over nonsense, a term that you probably don't like and a term that becomes unavoidable (of sorts) when you or anyone else is less than crystal clear. This is good.
You need to get acquainted with the concept of Lorentz observer. I'll not spell out the details, but a Lorentz observer is someone who has access to a complete record of spacetime events in his Lorentz frame. The concept requires "observers" at arbitrary points in space of the Lorentz frame in question, at rest relative to the coordinate system. These observers have synchronized clocks. They report to a main office. The Lorentz observer can read all their reports. Lorentz observers provably exist in principle (can be realized), see for example *Sard, R. D. (1970). Relativistic Mechanics - Special Relativity and Classical Particle Dynamics. New York: W. A. Benjamin.
ISBN
978-0805384918. {{
cite book}}
: Invalid |ref=harv
(
help) In particular, they can be realized in practice when it comes to noting the end points of a meter stick at an instant.
How accepted do you think special relativity would be if we could not measure the length of things at rest in our world?
Thus when you talk about undefined concepts such as "physically realizable events". not having understood the meaning of "Lorentz observer", then you will in the first place either be misunderstood or tossed off as being a crackpot. Invariably. Period. If you have a reference defining these things of yours, just burn it.
Finally, the "reversed Cauchy inequality and reversed triangle inequality" have analogues in the (−, +, +, +)) metric. The inequalities in this case reverse direction (to the standard direction) with the price being paid absolute signs. Thus the signatures each have imperfect versions of theorems that hold in true inner product spaces. Also, the section about causal ordering does not refer to the signature of the metric. It is an thereof independent concept. Nothing new under the sun.
I urge you to think twice or even ten times deeply before you proceed to respond. I don't wish to spend much more time on this and had in fact promised myself not to respond further because experience suggests that it is a total waste of time. I will respond, but only if I can see that you have read up on the basic concepts and use a language common to us both, free of your own definitions. YohanN7 ( talk) 06:57, 7 September 2016 (UTC)
The signature (+,-,-,-) which has been adopted here has several physical implications. Principally it is positive for physically observable events and for the difference between two such events. The attempt to keep a Euclidean analogy by using the opposite signature fails completely.
Perhaps that is what you have in mind? - DVdm ( talk) 09:11, 10 September 2016 (UTC)The actual form of ds above depends on the metric and on the choices for the X0 coordinate. To make the time coordinate look like the space coordinates, it can be treated as imaginary: X0 = ict (this is called a Wick rotation). According to Misner, Thorne and Wheeler (1971, §2.3), ultimately the deeper understanding of both special and general relativity will come from the study of the Minkowski metric (described below) and to take X0 = ct, rather than a "disguised" Euclidean metric using ict as the time coordinate.
I'm not too fond of this passage:
It is unusual to speak events as being timelike, etc. Is would not be a fully Lorentz invariant concept (i.e. not Poincaré invariant). It should be emphasized more that we are talking about intervals here, i.e. the interval between v and the origin (0, 0, 0, 0). This is a fully Lorentz invariant concept. For some 4-vectors, e.g the momentum 4-vector, this works automatically since there is an implicit derivative. But the event (0, 2.5 million light-years, 0, 0) referring to an event in the Andromeda galaxy 2000 years ago (according to us) is according to us spacelike, but the Andromedans might disagree.
What makes this confusion possible is the canonical identification of tangent spaces with the spacetime manifold itself. This does not work in general relativity. YohanN7 ( talk) 07:17, 8 September 2016 (UTC)
Perhaps this [8] is acceptable. There is absolutely nothing timelike, spacelike, or lightlike about events per se. But when one refers to events as vectors, then an origin is implied (we then have a coordinate system on the spacetime manifold). YohanN7 ( talk) 08:27, 29 September 2016 (UTC)
People, does someone have a specific proposal to change something, backed by a relevant source, to the article? If not, we are discussing our personal preferences and views of some aspect of the subject of the article, which is not allowed per the wp:talk page guidelines. If no one has a specific proposal, this discussion should be closed here. It can of course be continued on one of our user talk pages, like for instance User talk:JFB80#Spacetime metric sign convention. Thanks. - DVdm ( talk) 18:58, 2 October 2016 (UTC)
My tone of discussion isn't the best in my latest post. Well, there are reasons. That is, there were reasons. After my last reply, JFB80 went back and changed his post from downright offensive to more neutral words. This would suffice for someone else than me to take it to the higher powers. YohanN7 ( talk) 09:04, 3 October 2016 (UTC)
Is the treatment of the terminology in the article of the terms
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)
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)
This would work. I found a reference, the Lee book recently added to the ref list.
YohanN7 (
talk) 09:59, 6 October 2016 (UTC)
Done
Rest list:
To be honest, hyperbolic geometry is probably of less interest in special relativity than what special relativity is in hyperbolic geometry. Reason: The geodesics of H1(n)
R are not geodesics of flat spacetime (in the same way great circles on the sphere aren't geodesics of ℝ3). That said, I think it may be of value to the reader to see curved things embedded in flat spacetime like is now done.
YohanN7 (
talk) 14:21, 11 October 2016 (UTC)
Under "History", the following phrase appears, "In 1905, and later published in 1906...". The grammar might be improved.
The effort of 14:53 G.M.T. on 20/10/2016 seems to be wrong. — Preceding unsigned comment added by 92.26.14.17 ( talk) 10:09, 21 October 2016 (UTC)
In the section Pseudo-Euclidean metrics the following appears:
The links refer to positive definite quadratic forms and are not appropriate here. The material further down in the article on space-like and time-like vectors needs to precede this discussion. For space-like vectors orthogonality is right, but hyperbolic orthogonality applies between a time-like and space-like vector. Rgdboer ( talk) 01:59, 9 December 2016 (UTC)
Thank you YohanN7 for calling attention to the lack of naming reference. One has been supplied with online link. The author uses "inner product" including the indefinite case, not restricted as our inner product; we must use bilinear form. The author also develops hyperbolic numbers which clarifies the usage with orthogonality. In the interests of making Minkowski space a better article, the above comments were suggested to clarify the special nature of the temporal axis in orthogonality. Rgdboer ( talk) 02:11, 12 December 2016 (UTC)
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)
The statement The Minkowski inner product is defined as to yield the spacetime interval between two events when given their coordinate difference vector as argument. is wrong. The interval between x and y is sqrt(|<x-y,x-y>|), the norm, not the inner product. Shmuel (Seymour J.) Metz Username:Chatul ( talk) 20:58, 14 February 2017 (UTC)
Under Standard basis we have
Shouldn't it be
? — Preceding unsigned comment added by 147.91.66.6 ( talk) 08:43, 3 March 2017 (UTC)
It has been proposed that the section Geometry be split out.
@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)
The following paragraph intimating tetrad formalism, such as Newman-Penrose formalism and the construction of a complex null tetrad, subjects of general relativity, has been removed as this article deals strictly with flat spacetime.
Please discuss if you disagree. — Rgdboer ( talk) 02:50, 24 September 2017 (UTC)
User:JRSpriggs thinks that orthonormal "makes perfect sense in Minkowski space" according to his edit summary. But Othonormal only applies to inner product spaces, which Minkowski space is not. He re-instated the first three sentences, inappropriately. He should come here to discuss, or restore my edit. — Rgdboer ( talk) 23:07, 25 September 2017 (UTC)
Thank you for such a complete response. The indefinite inner product η that gives Minkowski space structure has null vectors that do not occur in inner product spaces. The following statement from the article has been tagged as it is unlikely that a reliable source will turn up:
What is important for η are the hyperbolic-orthogonal events that Minkowski used to define simultaneity in his space. Repeatedly this information has been inserted. (12 May 2006, 1 April 2008, 24 September 2017). It is very important to distinguish Minkowski space from four-dimensional Euclidean space where unit vectors and orthogonal basis mean something. These terms arise in linear algebra, and special relativity based on Minkowski space relies on linear algebra, but the subtlety of η requires special care, not imitation of inner product space.
Furthermore, linear algebra has sufficient language for special relativity, and the use of tensor algebra, manifolds, differential geometry, and tangent space is out of place and makes the article a headache for someone just looking to get started in relativity with this model. As learners use this resource, editors should keep in mind pedagogical principles like cognitive load, instructional scaffolding, and zone of proximal development. Inclusion of the unnecessary geometry runs counter to the needs of the learner. — Rgdboer ( talk) 21:45, 1 October 2017 (UTC)
Yes, as mentioned at WP:Technical#Put the least obscure parts of the article up front. But the article can be completely clear when differential geometry is left out. For perspective, consider this comment:
"[In 1912] Einstein realized that mathematics demanded much more than cursory acquaintance, that in fact his hopes for a generalization of special relativity could not be realized without a heavy dose of mathematics." (from Cornelius Lanczos (1972) "Einstein’s Path from Special to General Relativity", pages 5 to 19 of General Relativity: Papers in Honour of J.L. Synge, L. O’Raifeartaigh editor, Clarendon Press, see page 12) — Rgdboer ( talk) 21:49, 4 October 2017 (UTC)
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)
18:14, 7 November 2019 (UTC) JFB80 ( talk)
This article needs an introduction for lay readers. What is Minkowski space? Instead of starting with a lot of math and theory, how about explain whether this is the spacetime metric of the real universe, or just a mathematical construct used for calculations? I have yet to find a wiki article about spacetime metrics that even mentions which one we live in! 2601:441:4680:3230:ED26:3A73:A06E:9B5B ( talk) 03:24, 12 June 2019 (UTC)
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)
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)
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).
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)
DaveJWhitten ( talk) 16:45, 1 April 2021 (UTC) As I was reading, this sentence popped up:
This can be expressed in terms of the sign of η(v, v) as well, which depends on the signature.
I didn't see any definition for it earlier in the article.
Twice anon 99.239.158.18 ( talk · contribs · deleted contribs · logs · filter log · block user · block log) removed well known and sourced content ( [9], [10]), which I restored for the reasons given ( [11], [12]). Anon warned on their user talk for edit warring. Comments from others welcome. - DVdm ( talk) 00:26, 13 February 2021 (UTC)
The source (Landau & Lifshitz) says twice on page 4 that Minkowski space-time is a "fictitious four-dimensional space". On the other side, the relativity postulates are based on experiments done in the physical reality. The physical reality can't create itself fictitious things, because all fictitious things are created by imagination in the human mind. Therefore the statement in the article is incorrect and not supported by the source. 176.222.34.111 ( talk) 05:01, 19 March 2021 (UTC)
A lot of talk about a flat spacetime, but no definition of 'flatness' to be found (I think). What do you mean with 'flat'? — Preceding unsigned comment added by Koitus~nlwiki ( talk • contribs) 20:11, 15 August 2021 (UTC)
In section "Causal structure" the image "Subdivision of Minkowski spacetime" has a misleading terminology: "absolute future" and "absolute past". A better terminology is used in the Wikipedia article "Causal structure": "causal future" and "causal past". Johanwiden ( talk) 14:59, 13 March 2024 (UTC)
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)