Covariant meaning in physics
In the field of physics, the adjective covariant is often used informally as a synonym for invariant. For example, the Schrödinger equation does not keep its written form under the coordinate transformations of special relativity. Thus, a physicist might say that the Schrödinger equation is not covariant. In contrast, the … See more In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a See more The general formulation of covariance and contravariance refer to how the components of a coordinate vector transform under a change of basis (passive transformation). … See more In a finite-dimensional vector space V over a field K with a symmetric bilinear form g : V × V → K (which may be referred to as the metric tensor), … See more In category theory, there are covariant functors and contravariant functors. The assignment of the dual space to a vector space is a standard example of a contravariant functor. Some constructions of multilinear algebra are of "mixed" variance, which … See more In physics, a vector typically arises as the outcome of a measurement or series of measurements, and is represented as a list (or See more The choice of basis f on the vector space V defines uniquely a set of coordinate functions on V, by means of $${\displaystyle x^{i}[\mathbf {f} ](v)=v^{i}[\mathbf {f} ].}$$ The coordinates on V are therefore contravariant in the … See more The distinction between covariance and contravariance is particularly important for computations with tensors, which often have mixed … See more WebJan 23, 2024 · the metric is the very thing we’re solving for, so (2) is diffeomorphism invariant by construction. When Einstein first introduced GR, he emphasized the background independence (“no prior geometry”) under the guise of general covariance. But as alluded above, all laws of physics, properly formulated, are generally covariant!
Covariant meaning in physics
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WebApr 6, 2024 · Technically contravariant vectors are in one vector space, and covariant vectors are in a different space, the dual space. But there is a clear 1-1 correspondence between the space and its dual, and we tend to think of the contravariant and covariant vectors as different descriptions of the same vector. Share. Cite. WebMar 20, 2012 · The covariant derivative describes the gradient of a vector field (i.e., the effect of applying the gradient vector operator) to the vector, and properly includes the partial derivatives along the coordinate directions of both the vector components and the coordinate basis vectors. Mar 15, 2012. #5. pervect.
WebI am trying to understand the meanings of "covariant transformation" and "contravariant transformation" and how they are related. I have read the related Wikipedia article and still feel I cannot state, with mathematical precision, the definition of these terms.. The Wikipedia article states that a covariant transformation, in the context of a vector space, … WebMar 5, 2024 · Figure 5.7.4. At P, the plane’s velocity vector points directly west. At Q, over New England, its velocity has a large component to the south. Since the path is a geodesic and the plane has constant speed, the velocity vector is simply being parallel-transported; the vector’s covariant derivative is zero.
WebMar 21, 2024 · Covariant definition: a variant that changes leaving interrelations with another variant (or variants)... Meaning, pronunciation, translations and examples WebSep 1, 2015 · covariant: [adjective] varying with something else so as to preserve certain mathematical interrelations.
WebOct 3, 2024 · 322. 68. It seems most people say that a vector is either contravariant or covariant. To me it seems like contra/covariance is a property of the components of a vector (with respect to some basis) and not of the vector itself. Any basis {b i } has a reciprocal basis {b i } and any vector can be expressed with respect to either basis, …
WebHowever, in physics, we tend do ignore the basis vectors and only look at the components. And so many physicists have the sloppy tendency to say that vectors transform contravariantly. So a vector is actually A=A i e*i*. Same situation with covectors. A covector is contravariant. It's components are covariant. Physics texts call covectors ... franklin township public schoolWebIn physics, a covariant transformation is a rule that specifies how certain entities, such as vectors or tensors, change under a change of basis.The transformation that describes the new basis vectors as a linear combination of the old basis vectors is defined as a covariant transformation.Conventionally, indices identifying the basis vectors are placed as lower … bleached wheat bundleWebAug 30, 2016 · The "covariant" in "covariant derivative" should really be "invariant". It is a misnomer, but we are stuck with it. It is not the same "covariant" as that of a "covariant vector", and therefore, there is no "contravariant derivative". Armed with this, Wikipedia should fill in the rest for you :) bleached westminsterWebMar 5, 2024 · The Geodesic Equation. Recognizing ∂ κ T μ d x κ d λ as a total non-covariant derivative, we find. (5.8.2) ∇ λ T μ = d T μ d λ + Γ κ ν μ T ν d x κ d λ. This is known as the geodesic equation. There is a factor of two that is a common gotcha when applying this equation. The symmetry of the Christoffel symbols Γ κ ν μ = Γ ... franklin township school board electionWebMar 18, 2007 · ObsessiveMathsFreak. 406. 8. The covariant derivative (of a vector) is the rate of change of a vector in a paticular direction. If your vector field was V and the direction W, you would write it as: That really all there is to it. But, as zenmaster99 mentioned, if you are in a curvilinear coordinate system, then you have some additional ... franklin township police department njWebDefine covariant. covariant synonyms, covariant pronunciation, covariant translation, English dictionary definition of covariant. adj. 1. Physics Expressing, exhibiting, or … bleached wheat flour nutritionWebNov 5, 2024 · Intuitively also it makes sense. The velocity of an object can be expressed as n meters per second, (meaning the object travels n meters in a second), or as 1/n seconds per meter (meaning the object takes 1/n seconds to travel a meter). In the first way it will be a contravariant vector, and in the second way it will be covariant. bleached wheat paint color