I agree with you. This is my interpretation for a long time. And, also, is it true that we can not simultaneously determine the position of the momentum of a particle? But this, by itself, is already a form of terminism! So, if you want another interpretation, it's wanting to invent the wheel.
Hello.
I ask for solution help from the integral below, where y and x represent angles in a metric of a spherical, 2-D surface. He was studying how to obtain the geodesic curves on the spherical surface, the sphere of radius r = 1, to simplify. The integral is the end result. It is enough, now...
Tensor of Riemann. Geometric interpretation.The Riemann tensor gives the variation of a vector displaced parallel in a closed loop, say a small rectangle formed by geodesic sides, (δa) and δb) first, starting from a vertex A and going to another vertex in the diagonal, B; then starting from the...
The distinction only disappears in Euclidean spaces. In the general case of curved spaces, unidirectional forms and vectors have fundamentally different geometric properties! The clearest example of this is Grad (f), which is often mistaken for a vector, but is not a vector.
A beautiful, intelligible, complete and objective explanation of this important subject can be found on pages 52 the 56 of B.Schutz's Geometric Methods of Mathematical Physics.
Indeed, not only by modern mathematical approach, simple and intuitive, but also by good teaching used, the work of B.Schutz is suitable not only for beginners but for veterans in general relativity as well as teachers of matter. It is a work, in my opinion, simply wonderful.
Imagine the free fall of a body toward the earth, like falling off a ladder, or an astronaut in a spaceship orbiting the Earth. Both are in free fall situation. A fixed observer on the Earth's surface, notice the astronaut or body in free fall with an acceleration g. Already for a comoving...
Olá,
Very good your answer. And add the following relevant data: one can not draw straight lines in curved spaces as required by Cartesian rectilinear systems!
On the surface of a sphere, it is still a shortest distance curve. Hence the convenience of curvilinear coordinate systems.
Hello,
After best thinking, concludes that ε², ε being the geodesic tiny parallelogram side, the right of which is made parallel displacement of vector w, is the area of that parallelogram infinisitesimal so that w'can be compared at the same point where w giving w'-w as a vector. Do ε tend to...
Someone could detail how ε² fall within the definition of a tensor, as follows:
Eq.(5) at http://arxiv.org/pdf/gr-qc/0103044v5.pdf)
Thanks for explanation above.
Thanks, DrGreg.
Now, the correct text.
Difference between the metric and the metric tensor.
1) Metric: is a quadratic relationship involving the squares of the differences between the coordinates of two nearby points in space-time, which allows calculating the geometrical properties of...