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href="http://dbpedia.org/resource/Four-vector">Four-vector</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> An Entity of Type: <a href="http://dbpedia.org/class/yago/Abstraction100002137">Abstraction100002137</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the (1/2,1/2) representation. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Standard_conf.png?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">Un quadrivector és un vector d'un espai vectorial real de quatre dimensions, anomenat espai de Minkowski, les components del qual es transformen igual que les coordenades espacials i temporals (t, x, y, z) sota rotacions espacials i canvis d'un sistema de referència inercial a un altre. El conjunt d'aquestes transformacions, anomenades transformacions de Lorentz, queda descrit per un conjunt de matrius 4×4, que forma l'anomenat grup de Lorentz. Els quadrivectors i l'espai de Minkowski permeten una formulació acurada i còmoda de la teoria de la relativitat. (ca)</li> <li style="display:none;">Čtyřvektor je analogie pojmu vektor používaná v teorii relativity. Prostor a čas podle ní tvoří jediný celek, čtyřrozměrný časoprostor. Každá vektorová veličina (trojice reálných hodnot) je přirozeně spojena s další číselnou veličinou, které říkáme časová složka čtyřvektoru tak, aby byl výsledný objekt nezávislý na vztažné soustavě. Formálněji je prvek čtyřrozměrného reálného vektorového prostoru, tzv. Minkowského prostoru (který je ve speciální teorii relativity totožný s časoprostorem). Složky čtyřvektoru se při Lorentzových transformacích, rotacích a , tedy při přechodu z jedné (zcela obecné) inerciální vztažné soustavy do jiné, transformují jako vektory. Tyto transformace tvoří uzavřenou spojitou grupu, tzv. Poincarého grupu. Čtyřvektory hrají roli v popisu fyzikálních veličin nezávislých na vztažné soustavě i v obecně křivém prostoročasu, který využívá obecná teorie relativity. Zde Minkowského prostor hraje roli tečného (vektorového) prostoru. Všechny zákony, které musí být nezávislé na vztažné soustavě, je potřeba formulovat pomocí rovnic mezi čtyřvektory, nebo čtyřtenzory. Tomuto požadavku se říká . (cs)</li> <li style="display:none;">في نظرية النسبية العامة، المتجه الرباعي هو جسم ذو أربعة مكونات، يتحول بطريقة محددة تحت تحويل لورنتز. المتجه الرباعي هو تحديدًا عنصر من الفضاء المتجهي رباعي الأبعاد، ويعتبر فضاءً تمثيليًا للتمثيل المعياري لمجموعة لورنتز، تمثيل (½,½). يختلف المتجه الرباعي عن المتجه الإقليدي في كيفية تحديد حجمه. التحويل الذي يحفظ هذا الحجم هو تحويل لورنتز، الذي يتضمن التدويرات المكانية والدفعات (تغير بسرعة ثابتة بالنسبة لإطار مرجعي قصوري). يصف المتجه الرباعي، على سبيل المثال، الموقع xμ في الزمكان الذي يسمى فضاء منكوفسكي، زخم رباعي للجسيم pμ، سعة الجهد الرباعي الكهرومغناطيسي Aμ(x) في النقطة x في الزمكان، وعناصر الفضاء الفرعي الممتدة بواسطة مصفوفات جاما داخل جبر ديراك. يمكن تمثيل مجموعة لورنتز بمصفوفات 4×4 Λ. يحسب تأثير تحويل لورنتز على المتجه الرباعي المخالف للتغير X (مثل الأمثلة المذكورة بالأعلى)، يعتبر متجهًا عموديًا بإحداثيات ديكارتية بالنسبة للإطار القصوري في الإدخالات، من خلال: (مضاعفة المصفوفة) إذ تشير مكونات الجسم إلى الإطار الجديد. فيما يتعلق بالأمثلة المذكورة في الأعلى، والتي تقدم كمتجهات مخالفة للتغير، توجد أيضًا متجهات متزامنة مقابلة xμ, pμ وAμ(x). تتحول هذه المتجهات وفقًا للقاعدة: وتشير T إلى منقولة مصفوفة. تختلف هذه القاعدة عن القاعدة التي في الأعلى. تتوافق مع التمثيل المزدوج للتمثيل المعياري. لكن بالنسبة لمجموعة لورنتز، تكون ازدواجية أي تمثيل مكافئة للتمثيل الأصلي. وبالتالي، الأجسام ذات المؤشرات المتغيرة هي متجهات رباعية أيضًا. ليس المتجه الرباعي مثالًا لشيء مكون من أربعة مكونات يمكن وصفه في النسبية الخاصة. بالمثل، يعرف الفرق بأنه قاعدة التحول في ظل تحولات لورنتز التي تُقدم بواسطة تمثيل آخر غير التمثيل المعياري. في هذه الحالة، تصبح القاعدة X = Π(Λ)X حيث Π(Λ) مصفوفة 4×4 غير Λ. تنطبق ملاحظات مماثلة على الأشياء ذات مكونات أكثر أو أقل، والتي توصف ضمن تحويلات لورنتز. يشمل هذا الحقول القياسية والسبينورات والموترات وموترات السبينور. يتناول المقال المتجهات الرباعية في سياق النسبية الخاصة. بالرغم من أن مفهوم المتجهات الرباعية يمتد إلى النسبية العامة أيضًا، تتطلب بعض النتائج المذكورة في هذا المقال تعديلًا في النسبية العامة. (ar)</li> <li style="display:none;">Un cuadrivector es la representación matemática en forma de vector de cuatro dimensiones de una magnitud vectorial en teoría de la relatividad. (es)</li> <li style="display:none;">Ein Vierervektor, ein Begriff der Relativitätstheorie, ist ein Vektor in einem reellen, vierdimensionalen Raum mit einem indefiniten Längenquadrat. Beispielsweise sind die Zeit- und Ortskoordinaten eines Ereignisses in der Raumzeit die Komponenten eines Vierervektors, ebenso die Energie und der Impuls eines Teilchens. In zwei gegeneinander bewegten Inertialsystemen lassen sich die Komponenten der beiden Vierervektoren durch eine Lorentz-Transformation ineinander überführen. (de)</li> <li>In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the (1/2,1/2) representation. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). Four-vectors describe, for instance, position xμ in spacetime modeled as Minkowski space, a particle's four-momentum pμ, the amplitude of the electromagnetic four-potential Aμ(x) at a point x in spacetime, and the elements of the subspace spanned by the gamma matrices inside the Dirac algebra. The Lorentz group may be represented by 4×4 matrices Λ. The action of a Lorentz transformation on a general contravariant four-vector X (like the examples above), regarded as a column vector with Cartesian coordinates with respect to an inertial frame in the entries, is given by (matrix multiplication) where the components of the primed object refer to the new frame. Related to the examples above that are given as contravariant vectors, there are also the corresponding covariant vectors xμ, pμ and Aμ(x). These transform according to the rule where T denotes the matrix transpose. This rule is different from the above rule. It corresponds to the dual representation of the standard representation. However, for the Lorentz group the dual of any representation is equivalent to the original representation. Thus the objects with covariant indices are four-vectors as well. For an example of a well-behaved four-component object in special relativity that is not a four-vector, see bispinor. It is similarly defined, the difference being that the transformation rule under Lorentz transformations is given by a representation other than the standard representation. In this case, the rule reads X′ = Π(Λ)X, where Π(Λ) is a 4×4 matrix other than Λ. Similar remarks apply to objects with fewer or more components that are well-behaved under Lorentz transformations. These include scalars, spinors, tensors and spinor-tensors. The article considers four-vectors in the context of special relativity. Although the concept of four-vectors also extends to general relativity, some of the results stated in this article require modification in general relativity. (en)</li> <li style="display:none;">En physique, un quadrivecteur est un vecteur à quatre dimensions utilisé pour représenter un événement dans l'espace-temps. Dans la théorie de la relativité restreinte, un quadrivecteur est un vecteur de l'espace de Minkowski, où un changement de référentiel se fait par des transformations de Lorentz (par covariance des coordonnées). En relativité restreinte, un quadrivecteurcol. 1''s.v.''_quadrivecteur_2-0" class="reference">chap. 1er,_sect._1.1,_§ 1.1.1_3-0" class="reference"> (ou 4-vecteur)col. 1''s.v.''_quadrivecteur_2-1" class="reference">chap. 1er,_sect._1.1,_§ 1.1.1_3-1" class="reference"> est un vecteurcol. 1''s.v.''_quadrivecteur_2-2" class="reference">chap. 1er,_sect._1.1,_§ 1.1.1_3-2" class="reference"> appartenant à l'espace vectoriel associé à l'espace affine qu'est l'espace-tempschap. 1er,_sect._1.1,_§ 1.1.1_3-3" class="reference">chap. 8,_introd._4-0" class="reference">. Un quadrivecteur a quatre composantescol. 1''s.v.''_quadrivecteur_2-3" class="reference">chap. 3,_sect._1,_§ 3_5-0" class="reference">chap. 2,_sect._III,_§ III.1_6-0" class="reference"> homogènes en dimensionchap. 2,_sect._III,_§ III.1_6-1" class="reference">. Exprimés dans une base vectorielle donnée de l'espace-temps de Minkowski, on parle de quadrivecteurs contravariants. À partir de cette base et du produit scalaire de l'espace de Minkowski, on construit une autre base vectorielle, dite covariante, permettant d'écrire le produit scalaire de manière allégée. Exprimés dans cette seconde base, les quadrivecteurs sont dits covariants. Dans la théorie de la relativité générale, un quadrivecteur est un quadrivecteur de l'espace tangent de la variété de dimension quatre de cette théorie. Un quadrivecteur est un tenseur d'ordre 1 (il n'y a qu'un indice). Le terme quadrivecteur est dû au physicien théoricien allemand Arnold Sommerfeld (1864-1951)chap. 1er,_sect._1.6,_n. histor._7-0" class="reference">. (fr)</li> <li style="display:none;">Dalam relativitas khusus, vektor empat (disebut juga vektor-4) adalah suatu objek dengan empat komponen, yang akan bertransformasi dengan cara tertentu di bawah transformasi Lorentz. Secara spesifik, vektor empat adalah anggota dari ruang vektor empat dimensi yang dianggap sebagai ruang representasi dari , yaitu representasi (½,½). Vektor empat berbeda dengan vektor Euklides dalam bagaimana besar vektornya ditentukan. Transformasi yang tidak mengubah besar tersebut adalah transformasi Lorentz, yang terdiri di antaranya dari dan boost Lorentz (perubahan ke kerangka acuan inersia lain yang hanya berbeda suatu kecepatan konstan).:ch1 Vektor empat menggambarkan, di antaranya, posisi xμ dalam ruang waktu yang dimodelkan sebagai ruang Minkowski, momentum empat partikel pμ, amplitudo dari Aμ(x) pada titik x dalam ruang waktu, dan anggota subruang yang direntang oleh di dalam . Grup Lorentz bisa direpresentasikan dengan matriks 4×4 Λ. Transformasi Lorentz pada vektor empat X (seperti contoh di atas), yang dianggap sebagai sebuah vektor kolom yang berisi koordinat Kartesius terhadap kerangka acuan inersia, dituliskan sebagai (perkalian matriks) di mana komponen dari objek akhir adalah koordinat terhadap kerangka yang baru. Terkait dengan contoh vektor kontravarian di atas, terdapat yang bersesuaian xμ, pμ dan Aμ(x). Vektor-vektor kovarian tersebut bertransformasi mengikuti aturan di mana T melambangkan . Aturan ini berbeda dari aturan yang sebelumnya. Aturan tersebut melambangkan dari representasi standar. Akan tetapi, untuk grup Lorentz dual dari representasi manapun dengan representasi yang aslinya. Jadi objek dengan indeks kovarian juga merupakan vektor empat. Untuk contoh objek empat komponen yang berperilaku baik dalam relativitas khusus tetapi bukan merupakan vektor empat, lihat . Definisinya mirip, perbedaannya adalah aturan transformasi di bawah transformasi Lorentz dituliskan sebagai representasi selain representasi standar. Dalam kasus ini, aturannya adalah X′ = Π(Λ)X, di mana Π(Λ) adalah matriks 4×4 yang bukan Λ. Perbedaan serupa berlaku pada objek lain yang berperilaku baik di bawah transformasi Lorentz tetapi memiliki banyak komponen yang berbeda, di antaranya adalah , , dan spinor-tensor. (in)</li> <li style="display:none;">In relatività ristretta il quadrivettore, o tetravettore, rappresentato da una quadrupla di valori, è un vettore dello spaziotempo di Minkowski. Nelle trasformazioni di coordinate tra due sistemi di riferimento inerziali il quadrivettore rispetta le trasformazioni di Lorentz e le sue componenti si trasformano rispetto alla base standard dello spaziotempo di Minkowski come la differenza tra le rispettive coordinate spaziali e temporali. L'insieme delle rotazioni, traslazioni e cambi di coordinate tra due sistemi di riferimento inerziali alle quali sono soggetti i quadrivettori è il gruppo di Poincaré. (it)</li> <li style="display:none;">사차원 벡터(四次元vector, 독일어: Vierervektor, 영어: four-vector) 또는 네성분 벡터(-成分vector)는 로런츠 변환 아래 벡터로서 변환하는 값이다. 사차원 위치 나 사차원 운동량 따위가 있다. 실수 네 개의 성분으로 구성되어 있다. (ko)</li> <li style="display:none;">Een viervector is een elementair wiskundig object in de (speciale) relativiteitstheorie. Het is een uitbreiding van het begrip vector in de klassieke natuurkunde. Net zoals een gewone natuurkundige vector een natuurkundige grootheid is die onafhankelijk van het coördinatenstelsel betekenis heeft, en afhankelijk van het coördinatenstelsel wordt gegeven door drie coördinaten, zo is een viervector een natuurkundige grootheid die ook onafhankelijk van het coördinatenstelsel betekenis heeft, en afhankelijk van het inertiaalstelsel wordt gegeven door een scalar en een vector, die bij elkaar gerepresenteerd worden door vier coördinaten. (nl)</li> <li style="display:none;">物理学の、特に相対性理論における4元ベクトル（よんげんべくとる、英語: four–vector ）とは、ミンコフスキー空間またはローレンツ多様体上の 4 次元のベクトルである。より具体的には、時間に対応する物理量と空間に対応する 3 次元ベクトルをまとめて 4 次元時空上のベクトルとして表示したものである。ベクトルということで太字で表されたり、3次元のベクトルと区別するため細字のままのこともある。4元ベクトルの添え字は μ, ν などギリシャ文字を使用することが多い。i, j などラテン文字の添え字は、しばしば空間成分のみを表す意図で用いられる。添え字の上付き・下付きによって、後述する反変ベクトルと共変ベクトルを区別する。 (ja)</li> <li style="display:none;">Czterowektor – wektor o czterech współrzędnych należący do czasoprzestrzeni, która jest przestrzenią 4-wymiarową (dokładniej przestrzenią wektorową pseudoeuklidesową). Archetypem wszystkich 4-wektorów jest 4-wektor położenia. Na jego podstawie definiuje się wszystkie inne 4-wektory. (pl)</li> <li style="display:none;">Na relatividade, quadrivetor é um vetor no espaço de Minkowski (tetradimensional e real) que, sob uma transformação de Lorentz, comporta-se como as coordenadas espaço-temporais t, x, y e z. (pt)</li> <li style="display:none;">4-вектор — це аналог тривимірного вектора в чотиривимірному просторі-часі, складеному змінними ct та x, y, z звичайного простору. В цьому визначенні t — час, c — швидкість світла. При переході від звичайних векторів тривимірного простору до 4-векторів основні рівняння фізики набирають простішої форми. (uk)</li> <li style="display:none;">4-вектор (четы́ре-ве́ктор, четырёхве́ктор) — вектор в четырёхмерном пространстве Минковского, а в более общем случае — вектор в искривлённом четырёхмерном пространстве-времени. Компоненты любого 4-вектора, описывающего физическую систему, при переносе или повороте системы отсчёта, а также при переходе из одной системы отсчёта в другую преобразуются по одному и тому закону, задаваемому преобразованием системы отсчёта.В 4-векторе одна временна́я компонента и три пространственных. Пространственные компоненты составляют обычный пространственный трёхмерный вектор, компоненты которого могут быть выражены в декартовых, цилиндрических, сферических и в любых других пространственных координатах. * В современных обозначениях временно́й компоненте обычно соответствует индекс 0 (то есть она считается нулевой компонентой), пространственным — 1, 2, 3 (совпадающим с x, y, z; обычно, по умолчанию и если возможно, это обычные прямоугольные декартовы координаты). В старой литературе часто используется соглашение (восходящее к Минковскому), по которому временна́я компонента считалась не нулевой, а четвёртой. * Иногда бывает удобно приписывать временно́й компоненте 4-вектора чисто мнимый характер (всегда умножать действительную временну́ю компоненту на мнимую единицу). Такое представление 4-векторов было исторически введено первым и иногда используется и в современной литературе. * 4-векторы (их компонентное представление) могут быть записаны в контравариантной и (или) ковариантной форме (см. ниже), которые не всегда совпадают, а в случае действительного представления (без мнимой единицы) всегда различаются между собой, хотя в большинстве случаев случаях это различие подчиняется весьма простому правилу. (ru)</li> <li style="display:none;">在相對論裏，四維向量（four-vector）是實值四維向量空間裏的矢量。這四維向量空間稱為閔考斯基時空。四維向量的分量分別為在某個時間點與三維空間點的四個數量。在閔考斯基時空內的任何一點，都代表一個「事件」，可以用四維向量表示。從任意慣性參考系觀察某事件所獲得的四維向量，通過勞侖茲變換，可以變換為從其它慣性參考系觀察該事件所獲得的四維向量。本文章只思考在狹義相對論範圍內的四維向量，儘管四維向量的概念延伸至廣義相對論。在本文章內寫出的一些結果，必須加以修改，才能在廣義相對論範圍內成立。 (zh)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail">dbo:thumbnail</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/Standard_conf.png?width=300" href="http://commons.wikimedia.org/wiki/Special:FilePath/Standard_conf.png?width=300">wiki-commons:Special:FilePath/Standard_conf.png?width=300</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageID">dbo:wikiPageID</a> </td><td class="col-10 text-break"><ul> <li>226424 (xsd:integer)</li> </ul></td></tr><tr class="even"><td class="col-2"><a 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href="http://dbpedia.org/class/yago/Content105809192">yago:Content105809192</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Idea105833840" href="http://dbpedia.org/class/yago/Idea105833840">yago:Idea105833840</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/PsychologicalFeature100023100" href="http://dbpedia.org/class/yago/PsychologicalFeature100023100">yago:PsychologicalFeature100023100</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Quantity105855125" href="http://dbpedia.org/class/yago/Quantity105855125">yago:Quantity105855125</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Tensor105864481" href="http://dbpedia.org/class/yago/Tensor105864481">yago:Tensor105864481</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Variable105857459" href="http://dbpedia.org/class/yago/Variable105857459">yago:Variable105857459</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Vector105864577" href="http://dbpedia.org/class/yago/Vector105864577">yago:Vector105864577</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment">rdfs:comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">Un quadrivector és un vector d'un espai vectorial real de quatre dimensions, anomenat espai de Minkowski, les components del qual es transformen igual que les coordenades espacials i temporals (t, x, y, z) sota rotacions espacials i canvis d'un sistema de referència inercial a un altre. El conjunt d'aquestes transformacions, anomenades transformacions de Lorentz, queda descrit per un conjunt de matrius 4×4, que forma l'anomenat grup de Lorentz. Els quadrivectors i l'espai de Minkowski permeten una formulació acurada i còmoda de la teoria de la relativitat. (ca)</li> <li style="display:none;">Un cuadrivector es la representación matemática en forma de vector de cuatro dimensiones de una magnitud vectorial en teoría de la relatividad. (es)</li> <li style="display:none;">Ein Vierervektor, ein Begriff der Relativitätstheorie, ist ein Vektor in einem reellen, vierdimensionalen Raum mit einem indefiniten Längenquadrat. Beispielsweise sind die Zeit- und Ortskoordinaten eines Ereignisses in der Raumzeit die Komponenten eines Vierervektors, ebenso die Energie und der Impuls eines Teilchens. In zwei gegeneinander bewegten Inertialsystemen lassen sich die Komponenten der beiden Vierervektoren durch eine Lorentz-Transformation ineinander überführen. (de)</li> <li style="display:none;">In relatività ristretta il quadrivettore, o tetravettore, rappresentato da una quadrupla di valori, è un vettore dello spaziotempo di Minkowski. Nelle trasformazioni di coordinate tra due sistemi di riferimento inerziali il quadrivettore rispetta le trasformazioni di Lorentz e le sue componenti si trasformano rispetto alla base standard dello spaziotempo di Minkowski come la differenza tra le rispettive coordinate spaziali e temporali. L'insieme delle rotazioni, traslazioni e cambi di coordinate tra due sistemi di riferimento inerziali alle quali sono soggetti i quadrivettori è il gruppo di Poincaré. (it)</li> <li style="display:none;">사차원 벡터(四次元vector, 독일어: Vierervektor, 영어: four-vector) 또는 네성분 벡터(-成分vector)는 로런츠 변환 아래 벡터로서 변환하는 값이다. 사차원 위치 나 사차원 운동량 따위가 있다. 실수 네 개의 성분으로 구성되어 있다. (ko)</li> <li style="display:none;">Een viervector is een elementair wiskundig object in de (speciale) relativiteitstheorie. Het is een uitbreiding van het begrip vector in de klassieke natuurkunde. Net zoals een gewone natuurkundige vector een natuurkundige grootheid is die onafhankelijk van het coördinatenstelsel betekenis heeft, en afhankelijk van het coördinatenstelsel wordt gegeven door drie coördinaten, zo is een viervector een natuurkundige grootheid die ook onafhankelijk van het coördinatenstelsel betekenis heeft, en afhankelijk van het inertiaalstelsel wordt gegeven door een scalar en een vector, die bij elkaar gerepresenteerd worden door vier coördinaten. (nl)</li> <li style="display:none;">物理学の、特に相対性理論における4元ベクトル（よんげんべくとる、英語: four–vector ）とは、ミンコフスキー空間またはローレンツ多様体上の 4 次元のベクトルである。より具体的には、時間に対応する物理量と空間に対応する 3 次元ベクトルをまとめて 4 次元時空上のベクトルとして表示したものである。ベクトルということで太字で表されたり、3次元のベクトルと区別するため細字のままのこともある。4元ベクトルの添え字は μ, ν などギリシャ文字を使用することが多い。i, j などラテン文字の添え字は、しばしば空間成分のみを表す意図で用いられる。添え字の上付き・下付きによって、後述する反変ベクトルと共変ベクトルを区別する。 (ja)</li> <li style="display:none;">Czterowektor – wektor o czterech współrzędnych należący do czasoprzestrzeni, która jest przestrzenią 4-wymiarową (dokładniej przestrzenią wektorową pseudoeuklidesową). Archetypem wszystkich 4-wektorów jest 4-wektor położenia. Na jego podstawie definiuje się wszystkie inne 4-wektory. (pl)</li> <li style="display:none;">Na relatividade, quadrivetor é um vetor no espaço de Minkowski (tetradimensional e real) que, sob uma transformação de Lorentz, comporta-se como as coordenadas espaço-temporais t, x, y e z. (pt)</li> <li style="display:none;">4-вектор — це аналог тривимірного вектора в чотиривимірному просторі-часі, складеному змінними ct та x, y, z звичайного простору. В цьому визначенні t — час, c — швидкість світла. При переході від звичайних векторів тривимірного простору до 4-векторів основні рівняння фізики набирають простішої форми. (uk)</li> <li style="display:none;">在相對論裏，四維向量（four-vector）是實值四維向量空間裏的矢量。這四維向量空間稱為閔考斯基時空。四維向量的分量分別為在某個時間點與三維空間點的四個數量。在閔考斯基時空內的任何一點，都代表一個「事件」，可以用四維向量表示。從任意慣性參考系觀察某事件所獲得的四維向量，通過勞侖茲變換，可以變換為從其它慣性參考系觀察該事件所獲得的四維向量。本文章只思考在狹義相對論範圍內的四維向量，儘管四維向量的概念延伸至廣義相對論。在本文章內寫出的一些結果，必須加以修改，才能在廣義相對論範圍內成立。 (zh)</li> <li style="display:none;">في نظرية النسبية العامة، المتجه الرباعي هو جسم ذو أربعة مكونات، يتحول بطريقة محددة تحت تحويل لورنتز. المتجه الرباعي هو تحديدًا عنصر من الفضاء المتجهي رباعي الأبعاد، ويعتبر فضاءً تمثيليًا للتمثيل المعياري لمجموعة لورنتز، تمثيل (½,½). يختلف المتجه الرباعي عن المتجه الإقليدي في كيفية تحديد حجمه. التحويل الذي يحفظ هذا الحجم هو تحويل لورنتز، الذي يتضمن التدويرات المكانية والدفعات (تغير بسرعة ثابتة بالنسبة لإطار مرجعي قصوري). (ar)</li> <li style="display:none;">Čtyřvektor je analogie pojmu vektor používaná v teorii relativity. Prostor a čas podle ní tvoří jediný celek, čtyřrozměrný časoprostor. Každá vektorová veličina (trojice reálných hodnot) je přirozeně spojena s další číselnou veličinou, které říkáme časová složka čtyřvektoru tak, aby byl výsledný objekt nezávislý na vztažné soustavě. (cs)</li> <li>In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the (1/2,1/2) representation. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). (en)</li> <li style="display:none;">En physique, un quadrivecteur est un vecteur à quatre dimensions utilisé pour représenter un événement dans l'espace-temps. Dans la théorie de la relativité restreinte, un quadrivecteur est un vecteur de l'espace de Minkowski, où un changement de référentiel se fait par des transformations de Lorentz (par covariance des coordonnées). Dans la théorie de la relativité générale, un quadrivecteur est un quadrivecteur de l'espace tangent de la variété de dimension quatre de cette théorie. Un quadrivecteur est un tenseur d'ordre 1 (il n'y a qu'un indice). (fr)</li> <li style="display:none;">Dalam relativitas khusus, vektor empat (disebut juga vektor-4) adalah suatu objek dengan empat komponen, yang akan bertransformasi dengan cara tertentu di bawah transformasi Lorentz. Secara spesifik, vektor empat adalah anggota dari ruang vektor empat dimensi yang dianggap sebagai ruang representasi dari , yaitu representasi (½,½). Vektor empat berbeda dengan vektor Euklides dalam bagaimana besar vektornya ditentukan. Transformasi yang tidak mengubah besar tersebut adalah transformasi Lorentz, yang terdiri di antaranya dari dan boost Lorentz (perubahan ke kerangka acuan inersia lain yang hanya berbeda suatu kecepatan konstan).:ch1 (in)</li> <li style="display:none;">4-вектор (четы́ре-ве́ктор, четырёхве́ктор) — вектор в четырёхмерном пространстве Минковского, а в более общем случае — вектор в искривлённом четырёхмерном пространстве-времени. Компоненты любого 4-вектора, описывающего физическую систему, при переносе или повороте системы отсчёта, а также при переходе из одной системы отсчёта в другую преобразуются по одному и тому закону, задаваемому преобразованием системы отсчёта.В 4-векторе одна временна́я компонента и три пространственных. Пространственные компоненты составляют обычный пространственный трёхмерный вектор, компоненты которого могут быть выражены в декартовых, цилиндрических, сферических и в любых других пространственных координатах. (ru)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label">rdfs:label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">المتجه الرباعي (ar)</li> <li style="display:none;">Quadrivector (ca)</li> <li style="display:none;">Čtyřvektor (cs)</li> <li style="display:none;">Vierervektor (de)</li> <li style="display:none;">Cuadrivector (es)</li> <li>Four-vector (en)</li> <li style="display:none;">Quadrivecteur (fr)</li> <li style="display:none;">Vektor empat (in)</li> <li style="display:none;">Quadrivettore (it)</li> <li style="display:none;">4元ベクトル (ja)</li> <li style="display:none;">사차원 벡터 (ko)</li> <li style="display:none;">Czterowektor (pl)</li> <li style="display:none;">Viervector (nl)</li> <li style="display:none;">Quadrivetor (pt)</li> <li style="display:none;">4-вектор (ru)</li> <li style="display:none;">4-вектор (uk)</li> <li style="display:none;">四維矢量 (zh)</li> </ul></td></tr><tr class="even"><td 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