In General Relativity we see spacetime as a manifold; in this context vectors can't be defined on the manifold but need to be defined on the tangent space of the manifold. So each point of the manifold has its own tangent space and different vectors in different tangent spaces cannot be easily co...

As tide approaches in lower part of some rivers (e.g. Ganges), a several feet high tidal wave enters from the sea (making a great noise), and the water level suddenly rises as the wave proceeds. I would expect the water level to rise slowly and gradually, as the angle between the moon and the zen...

Let's think about the following quantities: Kinetic energy: $K=\frac{1}{2}mv^2$ Lorentz's Force: $\vec{F}=q\vec{E}+q\vec{v} \times \vec{B}$ This two quantities are not invariant under Galilean transformation. I have a couple of questions: Question one: In classical mechanics how do we deal with...