Table of Contents
What is a tensor physically?
Answer. Tensors, defined mathematically, are simply arrays of numbers, or functions, that transform according to certain rules under a change of coordinates. In physics, tensors characterize the properties of a physical system, as is best illustrated by giving some examples (below).
What information is stored in a metric tensor?
A metric tensor is essentially used when distances are measured , it gives information about how to compute the distance between two given points and about the characteristics of space in the framework of any arbitrarily given system of coordinates .
What does metric mean in physics?
A metric, or distance function, is a function which defines a distance between elements of a set.
What is the formula for the metric tensor?
The metric tensor is such that the scalar product $\\sigma(u,v) = g_{\\alpha\\beta}u^{\\alpha}v^{\\beta}$; unless you’re always on an orthogonal basis, there is no requirement for the diagonal terms to vanish.$\\endgroup$ – gented Aug 7 ’16 at 0:24 Add a comment | 1 Answer 1 ActiveOldestVotes 27 $\\begingroup$
What are off-diagonal elements of the metric tensor?
At a single point, off-diagonal elements of the metric tensor simply say that your coordinate system is not orthogonal. For example, if you use $\\hat{x}$ and $\\hat{x} + \\hat{y}$ as your basis in the plane, the resulting metric has a cross term.
What is the physical meaning of tensors?
In simple words, tensors are used to represent physical properties of a given system which are associated with more than one generalized coordinates (Cartesian, Spherical and Cylindrical). I would like to take crystals as an example to explain the physical meaning of tensors.
Is the metric tensor $G_{\\alpha \\beta}}$ a diagonal matrix?
For certain metrics in general relativity, the metric tensor $g_{{\\alpha}{\\beta}}$ is not a diagonal matrix. For example, the Alcubierre metricis given by