Abstract

Heisenberg's microscope experiment for the determination of the position of an electron is fundamentally flawed because it does not define position in four dimensions, as an event in space-time. To rectify this the microscope is substituted for by an ideal radar system situated at the origin of a coordinate system, thereby defining a reference system. It is then demonstrated that the origin and resulting coordinate points have a minimum uncertainty due to the physical extension of the photon in space-time. Further analysis reveals that quantum mechanics may be characterized in general as the study of material processes for which the spatial extension of the photon must be taken into account.

Heisenberg described the mathematical relationship (Delta)p(Delta)x=h as the "uncertainty" principle to indicate that it expresses an observer's lack of knowledge of the wave function of a particle. Later interpretations have preferred the use of "indeterminacy" indicating that this is actually a property of the wave function. It is shown here that in order to define a reference system quantum-mechanically, both uncertainty and indeterminacy must be included, but as separate concepts. Uncertainty is expressed in the classically defined coordinates of the observer, while indeterminacy is defined in the coordinates of quantum mechanical state space.