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.
Mathematically, the physical quantities must transform covariantly, that is, under a certain representation of the group of coordinate transformations between admissible frames of reference of the physical theory. This group is referred to as the covariance group.
The principle of covariance does not require invariance of the physical laws under the group of admissible transformations although in most cases the equations are actually invariant. However, in the theory of weak interactions, the equations are not invariant under reflections (but are, of course, still covariant).
In Newtonian mechanics the admissible frames of reference are inertial frames with relative velocities much smaller than the speed of light. Time is then absolute and the transformations between admissible frames of references are Galilean transformations which (together with rotations, translations, and reflections) form the Galilean group. The covariant physical quantities are Euclidean scalars, vectors, and tensors. An example of a covariant equation is Newton's second law,
where the covariant quantities are the mass of a moving body (scalar), the velocity of the body (vector), the force acting on the body, and the invariant time .
In special relativity the admissible frames of reference are all inertial frames. The transformations between frames are the Lorentz transformations which (together with the rotations, translations, and reflections) form the Poincaré group. The covariant quantities are four-scalars, four-vectors etc., of the Minkowski space (and also more complicated objects like bispinors and others). An example of a covariant equation is the Lorentz force equation of motion of a charged particle in an electromagnetic field (a generalization of Newton's second law)
where and are the mass and charge of the particle (invariant 4-scalars); is the invariant interval (4-scalar); is the 4-velocity (4-vector); and is the electromagnetic field strength tensor (4-tensor).
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".
In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries.
This course is the basic introduction to modern cosmology. It introduces students to the main concepts and formalism of cosmology, the observational status of Hot Big Bang theory
and discusses major
Biology is becoming more and more a data science, as illustrated by the explosion of available genome sequences. This course aims to show how we can make sense of such data and harness it in order to
We study the spatial structure of soil moisture fields within savanna ecosystems, whose persistence is vital because it is the driver of the entire ecological structure and function. These include changes in the physical and biogeochemical conditions of th ...
In many sensing and control applications, data are represented in the form of symmetric positive definite (SPD) matrices. Considering the underlying geometry of this data space can be beneficial in many robotics applications. In this paper, we present an e ...
2017
,
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the backgrou ...