Invariant: Any physical quantity is invariant when its
value remains unchanged under coordinate or symmetry transformations
. Covariant: The term covariant is usually used when the equations of physical systems are unchanged under coordinate transformations.
What does covariant form mean?
Form-invariant” (surely less common in fundamental physics!) means that “form doesn’t change” for the same reason. The term “covariant” is linguistically “co” and “variant” which means “
together change
” – covariant objects change together with others i.e. in the same way as others.
What does covariant mean in physics?
In physics, the principle of covariance
emphasizes the formulation of physical laws using only those physical quantities the measurements of which the observers in different frames of reference could unambiguously correlate
.
What is a covariant equation?
In general relativity, a manifestly covariant equation is
one in which all expressions are tensors
. The operations of addition, tensor multiplication, tensor contraction, raising and lowering indices, and covariant differentiation may appear in the equation.
What is form invariance?
Form Invariance of Maxwell’s Equations:
The Pathway to Novel Metamaterial Specifications for Electromagnetic Reshaping
. … Constitutive parameters of the anisotropic material are determined to appropriately reflect the consequences of the coordinate transformation on the electromagnetic fields.
Why do we need covariant and Contravariant?
Associated with any coordinate system is a natural choice of coordinate basis for vectors based at each point of the space, and covariance and contravariance are particularly
important for understanding how the coordinate description of a vector changes by passing from one coordinate system to another
.
Which is a covariant return type?
In object-oriented programming, a covariant return type of a method is
one that can be replaced by a “narrower” type when the method is overridden in a subclass
. … This usually implies that the return types of the overriding methods will be subtypes of the return type of the overridden method.
What is covariant in Java?
The covariant return type in java,
allows narrowing down return type of the overridden method
. This feature will help to avoid down casting on the client side. It allows programmer to program without the need of type checking and down casting. The covariant return type always works only for non-primitive return types.
What is tensor calculus used for?
Tensor calculus has many applications in physics, engineering and computer science including
elasticity
, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning.
What is covariance of electrodynamics?
Lorentz-covariance of the equations of electrodynamics is a mathematical fact which is essentially
based “on the form of the differential equation for the propagation of waves with the velocity of light
.” … of light {V > c).
Are Maxwell’s equations covariant?
It is stated in many textbooks that Maxwell’s equations are
manifestly covariant when written down in tensorial form
. We recall that tensorial form of Maxwell’s equations does not secure their tensorial contents; they become covariant by postulating certain transformation properties of field functions.
What is invariant and covariant in Java?
Covariant would mean that
a List<String> is a subtype of List<Object>
, contravariant that a List<Object> is a subtype of List<String> and invariant that neither is a subtype of the other, i.e. List<String> and List<Object> are inconvertible types.
Are Maxwell’s equations Lorentz invariant?
In other words, its basic laws, as summarized by the four Maxwell equations plus Lorentz’s force law, are
form- invariant under Lorentz transformations
, i. e. under transformations from one inertial frame to another.
What is another word for invariant?
In this page you can discover 26 synonyms, antonyms, idiomatic expressions, and related words for invariant, like:
changeless
, constant, regular, unchanging, unvarying, equable, invariable, same, uniform, orthogonal and polynomial.
Why is invariant important?
An invariant is a property of your data that you expect to always hold. Invariants are important
because they allow you to separate business logic from validation
—your functions can safely assume that they’re not receiving invalid data.
What is meant by Galilean invariance?
Galilean invariance is a cornerstone of classical mechanics. It states that
for closed systems the equations of motion of the microscopic degrees of freedom do not change under Galilean transformations to different inertial
frames.
