Search results

The electromagnetic field at a point ''p'' (i.e. an event) of a Lorentzian spacetime is represented by a [[Real number|real]] bivector {{nowrap|1=''F'' = ''F''< ...]. To simplify the notation, we will assume the spacetime ''is'' Minkowski spacetime. This tends to blur the distinction between the tangent space at ''p'' and ...

...or current''', it is used in the geometric context of ''four-dimensional [[spacetime]]'', rather than separating time from [[three-dimensional space|three-dimen Using the [[Minkowski metric]] <math>\eta_{\mu\nu}</math> of [[metric signature]] {{nowrap|(+ − − ...

...eld energy of an [[electromagnetic field]], which must satisfy the (curved-spacetime) ''source-free'' [[Maxwell equations]] appropriate to the given geometry. ...l phenomena is a [[Lorentzian manifold]], which is interpreted as a curved spacetime, and which is specified by defining a [[metric tensor]] <math>g_{ab}</math> ...

...escription|Mathematical object that describes the electromagnetic field in spacetime}} ...tensor]] formulation of [[special relativity]] was introduced by [[Hermann Minkowski]]. The tensor allows related physical laws to be written very concisely, an ...

...theory]], a branch of modern [[string theory]], describes a 12-dimensional spacetime having two dimensions of time, giving it the [[metric signature]] (10,2).<r ...into a complex plane.<ref name="dinov" /> Introducing it into [[Minkowski spacetime]] allows a generalization of [[Kaluza–Klein theory]].<ref>{{cite book |last ...

...]] as a model for (3+1)-dimensional [[spacetime]], representing a point in spacetime via a [[paravector]] (3-dimensional vector plus a 1-dimensional scalar). ...rd algebra]] Cl_1,3('''R''') of the four-dimensional [[Minkowski spacetime]]. ...

...f> The stress–energy tensor describes the flow of energy and momentum in [[spacetime]]. The electromagnetic stress–energy tensor contains the negative of the cl ...{\mu\nu}</math> is the [[Metric tensor (general relativity)#Flat spacetime|Minkowski metric tensor]] of [[metric signature]] {{nowrap|(− + + +)}}. When using th ...

...Minkowski diagram (and a straight line is a [[geodesic]] in flat Minkowski spacetime), or the coordinate distance between the events in the inertial frame where ...cetime is "inertial", but in the local neighborhood of any point in curved spacetime we can define a "local inertial frame" in which the local speed of light is ...

...he most physical interest. We view <math>\mathbb R^n</math> as [[Minkowski spacetime]]. Since the [[gauge group]] of [[electromagnetism]] is <math>U(1)</math>, ...

...nother. However, this is not as general as [[Maxwell's equations in curved spacetime]] or non-rectilinear coordinate systems. ...nt of tensors]] and [[Einstein summation convention]] throughout and the [[Minkowski metric]] has the form {{math|diag(+1, −1, −1, −1)}}. Where the equations ar ...

...]]; the [[pseudo-Riemannian manifold]]s of [[general relativity]] describe spacetime with matter and gravity. 10 dimensions are used to describe [[superstring t ...sup>}} such small balls. This observation leads to the definition of the [[Minkowski dimension]] and its more sophisticated variant, the [[Hausdorff dimension]] ...

...t||the formulation in [[general relativity]]|Maxwell's equations in curved spacetime|the [[manifestly covariant]] formulation in [[special relativity]]|Classica ===Spacetime algebra=== ...

...undless [[four-dimensional]] [[Continuum (theory)|continuum]] known as ''[[spacetime]]''.<ref name="metafizika">{{cite journal|last1=Bunyadzade |first1=Konul |t ...ncept that space and time can be viewed as a single construct known as ''[[spacetime]]''. In this theory, the [[speed of light]] in [[vacuum]] is the same for a ...

where <math>\mu=\{0,1,2,3\}</math> denotes four indices of the [[spacetime]] and [[Einstein notation|Einstein's summation convention]] has been applie ...th>g^{\mu\nu}=\rm{diag}\{1,-1,-1,-1\}</math> is the metric tensor of the [[Minkowski space]]. ...

...Lectures on Physics }}</ref> and its [[motion (physics)|motion]] through [[spacetime]], along with related concepts such as [[energy]] and [[force]].<ref>{{cite ...ton|Sands|1963|p=I-2}}</ref> and its [[Motion (physics)|motion]] through [[Spacetime|space and time]], along with related concepts such as [[energy]] and [[forc ...

...stress–energy tensor]], into [[Einstein field equations]] that include the spacetime curvature.</ref> In fact, [[Albert Einstein]] developed special and general {{For|the equations in [[general relativity]]|Maxwell's equations in curved spacetime}} ...

...of [[special relativity]], and it turns out that the [[conformal group of spacetime]] includes the [[Lorentz group]] and the [[Poincaré group]] as subgroups. H ...esponds to the above Cayley metric (based on a real conic section), if the spacetime coordinates are identified with the above homogeneous coordinates ...

...tly depending on relative motion, and [[space]] and time are merged into [[spacetime]], where we live on a [[world line]] rather than a timeline. In this view t ===Einstein's physics: spacetime=== ...

...reference frame]]. Also conserved is the vector length ([[Minkowski space|Minkowski norm]]), which is the [[rest mass]] for single particles, and the [[invaria ...e with time) or asymptotically flat (that is, at an infinite distance away spacetime looks empty), then energy conservation holds without major pitfalls. In pra ...

{{Spacetime|cTopic=Types}} ...nto a single [[four-dimensional]] [[continuum (measurement)|continuum]]. [[Spacetime diagram]]s are useful in visualizing and understanding [[Special relativity ...