- #1
kent davidge
- 933
- 56
I read from this page https://properphysics.wordpress.com...se-introduction-to-special-relativity-part-6/
that the basis vectors are the canonical basis vectors in any coordinate system. This seems to be wrong, because if that was the case the metric would be the identity matrix in any coordinate system, and we know that, for example, in spherical coordinates the metric has components ##\{1, r^2, r^2 \sin^2 \varphi \}##. So should I conclude that what is said on that page is wrong?
On the other hand, what is said on there seems to be more consistent with the inner product properties, because then a vector ##V = Ae_1 + Be_2## would have norm ##\sqrt{A^2 + B^2}## in any coordinate system.
So I'm not sure what conclusion I should draw from that page.
that the basis vectors are the canonical basis vectors in any coordinate system. This seems to be wrong, because if that was the case the metric would be the identity matrix in any coordinate system, and we know that, for example, in spherical coordinates the metric has components ##\{1, r^2, r^2 \sin^2 \varphi \}##. So should I conclude that what is said on that page is wrong?
On the other hand, what is said on there seems to be more consistent with the inner product properties, because then a vector ##V = Ae_1 + Be_2## would have norm ##\sqrt{A^2 + B^2}## in any coordinate system.
So I'm not sure what conclusion I should draw from that page.