M. Srednicki in his book "QFT" has mentioned in page 4 that
" ... we get an infinite number of spatial derivatives acting on $\psi (x,t)$; this imples that equation $$i\hbar\frac{\partial}{\partial t}\psi (x,t)=+\sqrt{-\hbar^2c^2 \bigtriangledown^2+m^2 c^4}\psi(x,t)$$ is not local in space."
What does the author mean by locality? I would really appreciate if someone could explain to me about this concept and this problem.
The author has also mentioned on page 7 that
" ... the norm of a state is not in general time indepedent. Thus probability is not conserved. Thus the Klein-Gordon does not obey quantum mechanics".
Can anyone tell me why the probability is not conserved? Why the norm of a state, $$\langle \psi ,t|\psi ,t\rangle =\int d^3 x\langle \psi ,t,x\rangle \langle x|\psi ,t\rangle =\int d^3 x \psi^* (x)\psi (x)$$ is not in general time indepedent? I really want to know the details and have tried to understand them but unfortutaley I couldn't.
