Consider the two principles: A QFT of spin-2 particles (gravitons) cannot transmit information faster than the speed of light by special relativity. (Let's make an assumption that such a theory can exist). In GR we can have a metric of space-time in which shortens distances between two points to...

Writing the product $$ \mathbf{T} = \mathbf{A}^\text{T}\boldsymbol{\eta}\mathbf{A}\tag1 $$ in Einstein index notation I get: $$ T_{\mu\nu} = (A^\text{T})^{\alpha}_{\,\,\mu}\eta_{\alpha\beta}A^{\beta}_{\,\,\nu}=A_{\mu}^{\,\,\alpha}\eta_{\alpha\beta}A^{\beta}_{\,\,\nu}\tag2 $$ Assuming $\boldsymbol...

Consider a Hamiltonian $H_N$ on a finite system with the following properties: It has a unique ground state The first excited energy level has a degeneracy $N$ (there are $N$ eigenstates for the first excited eigenvalue). The question I have is the following: Is it possible for such a hamiltoni...