It's each component of the four-vector that transforms, not the four-vector itself, it must be invariant under a certain transformation. For example, given a vector A, under a certain transformation, one always has:
A=A_{\mu}e^\mu = A^{'}_{\nu}e^{\mu^'}
This is exactly the invariance I mean...
What you are mentioning about is the Energy-Momentum four-vector p^{\mu} (p^0 =m_0 c^2, p^i). Not surprisingly, the four-vector is Lorentz invariant because one always has: p^{\mu}p_{\mu}=\sqrt{E^2 - p^2c^2}=m_{0}c^2 . The physics behind is the validity of the well-known equation E=mc^2 in the...
I'm studying General Relativity and facing several problems. We know that energy-momentum must be Lorentz invariant in locally inertial coordinates. I am not sure I understand this point clearly. What is the physics behind?
Thanks for your suggestion. As I understand, the principle of equivalence states that: in small enough regions of spacetime, the laws of physics reduce to those of special relativity; it is impossible to detect the existence of a gravitational field by means of local experiments. The scalar...
As I know, Einstein initially tried describe the gravitational interaction as mediated by a scalar field, but he later gave up this idea because it is incompatible with the Principle of Equivalence.I don't know how this idea is incompatible with the Principle of Equivalence. Please help me. Thanks