Possible violation of the optical theorem in LHC experiments

The optical theorem allowing the determination of the total cross section for a hadron-hadron scattering from the imaginary part of the forward elastic scattering amplitude is believed to be an unavoidable consequence of the conservation of probability and of the unitary S matrix. This is a fundamental theorem which contains not directly measurable imaginary part of the forward elastic scattering amplitude. The impossibility of scattering phenomena without the elastic channel is considered to be a part of the quantum magic. However if one takes seriously the idea that the hadrons are extended particles one may define a unitary S matrix such that one cannot prove the optical theorem. Moreover data violating the optical theorem do exist but they are not conclusive due to the uncertainties related to the extrapolation of the differential elastic cross-section to the forward direction. These results were published several years ago but they were forgotten. In this paper we will recall these results in an understandable way and we will give the additional arguments why the optical theorem can be violated in high energy strong interaction scattering and why it should be tested and not simply used as a tool in LHC experiments.