Reformulation of Max Born’s Theory for Information Science

It is shown that there is a contradiction within conventional quantum mechanics [K. Nagata, Int J Theor Phys (2009), DOI: 10.1007/s10773-009-0158-z] based on the Born statistical formula. We investigate whether the Born statistical formula meets our physical world. We derive a proposition concerning a quantum expec-tation value under the assumption of the existence of the orientation of reference frames in N spin-1/2 systems. This assumption intuitively depictures our physical world. The quantum predictions within the formalism of the Born statistical for-mula violate the proposition with a magnitude that grows exponentially with the number of particles. The Born statistical formula cannot depicture our physical world with a violation factor that grows exponentially with the number of particles. The Born statistical formula cannot meet our physical world. We reformulate the Born statistical formula. PACS: 03.65.Ta, 03.67.Lx, 03.65.Ca