In this paper, a new conserved current for Klein-Gordon equation is derived. It is shown, for 1 + 1-dimensions, the first component of this current is non-negative and reduces to |φ| 2 in nonrelativistic limit. Therefore, it can be interpreted as the probability density of spinless particles. In addition, main issues pertaining to localization in relativistic quantum theory are discussed, with a demonstration on how this definition of probability density can overcome such obstacles. Our numerical study indicates that the probability density deviates significantly from |φ| 2 only when the uncertainty in momentum is greater than m0c.

We show that the Born's rule is incompatible with Lorentz symmetry of the Square Root Klein-Gordon equation (Salpeter equation). It has been demonstrated that the Born rule must be modified in relativistic regime if one wishes to keep the Salpeter equation as the correct equation for describing quantum behavior.

We have shown that the Born rule (ρ = |ψ| 2 ) is inconsistent with Lorentz symmetry of the Salpeter equation (square root Klein-Gordon equation). So we find relativistic modification of the Born rule as) , which is consistent with Lorentz symmetry of this equation.