ON SOME DIFFICULTIES CONCERNING HEISENBERG UNCERTAINTY AND QUANTUM-MECHANICAL RELATIONS

By examining the Heisenberg matrix mechanics with its commutation rela tions and the Schrodinger rules connecting the Heisenberg matrices to the Schrodinger wave theory, a consistent quantum theory emerges. Howe ver, it is maintained here that this self-consistent structure leaves open the question of the interpretation of local ''uncertainty,'' beca use the Heisenberg theory Is necessarily discontinuous by its construc tion, whereas Schrodinger's work uses continuous variables. The views of Einstein, Podolsky, and Rosen (EPR) are shown to address the issue of local ''uncertainty'' in the Schrodinger sense; consequently, it is argued that much of the critique leveled against EPR may be averted, and a reconciliation of the views of Heisenberg, Schrodinger, and othe rs, such as Feynman, is possible, because the above open nature of the Heisenberg Schrodinger theory does provide a possibility that local r ealism and local discontinuity need not be viewed in a mutually exclus ive manner. As such, local and global wave function Schrodinger operat ors are distinguished, and it is deduced that uncertainty as developed by Robertson from Schrodinger's operator assignment is of a global na ture, because the Heisenberg matrix formulation is of a global nature, and the Schrodinger operator assignments were postulated to harmonize with Heisenberg mechanics. To counter the possibly biased view of Hei senberg, that (his) theory dictates what may be measured, and with wha t precision - thereby possibly denying thepivotal and independent role of experiment in judging theories - a principle for ''isotropic'' var iables is presented, where it is stated that if no uncertainty is impl ied in the measurement of the classical variables, then no uncertainty is expected for the corresponding quantum mechanical variable, where this principle may be experimentally refuted in principle. This princi ple is also postulated to cater to the open nature of the Heisenberg-S chrodinger formalism, because it is maintained here that the algebraic Heisenberg calculus is quite distinct from the physical developments of intrinsic ''uncertainty,'' so that any repudiation of measurement u ncertainty does not in any way jeopardize the profound algebraic calcu lus of Heisenberg. From the Einstein discussion it is concluded that t he concept of uncertainty derived from conjugate operators obtains onl y for fixed eigenvalues. It is proved from a theorem that local uncert ainty does not obtain for both nondegenerate and degenerate conjugate operators.