- #1
Jokar
- 17
- 3
Suppose there are two reference frames. One is rotating with respect to another with rotational velocity ##\omega##.
Now if in one of the reference frames the vector potential is $$(1, 0, 0, 0)$$ then in the other reference frame it will be $$(\sqrt{1-(\omega r)^2}, 0, \omega r, 0)$$.
Now in the first reference frame the electric field is zero. But in the second reference frame
$$E = \frac{d\phi}{dr} = \frac{\omega^2 r}{\sqrt{1-(\omega r)^2}} $$ .
Now we know if $$F_{\mu\nu} = 0$$ then under coordinate transform also it will remain zero. So why are we getting the electric field?
Now if in one of the reference frames the vector potential is $$(1, 0, 0, 0)$$ then in the other reference frame it will be $$(\sqrt{1-(\omega r)^2}, 0, \omega r, 0)$$.
Now in the first reference frame the electric field is zero. But in the second reference frame
$$E = \frac{d\phi}{dr} = \frac{\omega^2 r}{\sqrt{1-(\omega r)^2}} $$ .
Now we know if $$F_{\mu\nu} = 0$$ then under coordinate transform also it will remain zero. So why are we getting the electric field?