Minkowski metric η_{μν}
E376582
The Minkowski metric η_{μν} is the flat spacetime metric of special relativity, describing a four-dimensional spacetime with Lorentzian signature that serves as the background for many formulations of relativistic physics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Minkowski metric | 2 |
| Minkowski metric η_{μν} canonical | 1 |
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
Lorentzian metric
ⓘ
bilinear form ⓘ flat metric ⓘ pseudo-Riemannian metric ⓘ spacetime metric ⓘ |
| associatedSpacetime | flat spacetime ⓘ |
| ChristoffelSymbolsInInertialCoords | zero ⓘ |
| compatibleConnection | Levi-Civita connection of flat spacetime ⓘ |
| componentsInStandardCoordinates |
diag(-1,1,1,1)
ⓘ
diag(1,-1,-1,-1) ⓘ |
| coordinateNames |
(t,x,y,z)
ⓘ
(x^0,x^1,x^2,x^3) ⓘ |
| coordinateSystem | inertial coordinates ⓘ |
| curvature | zero ⓘ |
| definedOn |
Minkowski space-time
ⓘ
surface form:
Minkowski spacetime
|
| definesInterval | ds^2 = η_{μν} dx^μ dx^ν ⓘ |
| determinant | -1 in standard units and coordinates ⓘ |
| determinesCausalStructure | lightlike, timelike, spacelike intervals ⓘ |
| dimension | 4 ⓘ |
| indexRange | μ,ν = 0,1,2,3 ⓘ |
| introducedBy | Hermann Minkowski ⓘ |
| invarianceGroup | Poincaré group ⓘ |
| isInvariantUnder |
Lorentz transformation
ⓘ
surface form:
Lorentz transformations
spacetime translations ⓘ |
| lightConeCondition | ds^2 = 0 ⓘ |
| lineElementForm |
ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2
ⓘ
ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 ⓘ |
| lowersIndicesOf |
four-vectors
ⓘ
tensors on Minkowski spacetime ⓘ |
| raisesIndicesOf |
four-vectors
ⓘ
tensors on Minkowski spacetime ⓘ |
| relatedConcept |
Minkowski interval
ⓘ
surface form:
Lorentz interval
energy-momentum four-vector ⓘ four-vector formalism ⓘ |
| RicciTensor | vanishes identically ⓘ |
| RiemannTensor | vanishes identically ⓘ |
| scalarCurvature | 0 ⓘ |
| signature |
(+,-,-,-)
ⓘ
(-,+,+,+) ⓘ Lorentzian ⓘ |
| spatialSubmetric | Euclidean metric on R^3 ⓘ |
| timeComponentSign |
negative in mostly-plus convention
ⓘ
positive in mostly-minus convention ⓘ |
| usedAsBackgroundIn |
linearized gravity
ⓘ
perturbative general relativity ⓘ |
| usedInTheory |
quantum field theory
ⓘ
relativistic classical field theory ⓘ special relativity ⓘ |
| usedToDefine |
invariant spacetime distance between events
ⓘ
proper time of timelike worldlines ⓘ |
| yearIntroducedApprox | 1908 ⓘ |
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Minkowski metric
this entity surface form:
Minkowski metric