Categories of Nonlocality in EPR Theories and the Validity of Einstein’s Separation Principle as Well as Bell’s Theorem

Abstract

Work on quantum entanglement is currently emphasizing the nonlocal nature of theories that attempt to explain spatially separated Einstein-Podolsky-Rosen (EPR) correlation experiments. It is frequently claimed that nonlocal instantaneous influences, or equivalently a breakdown of Einstein’s separation principle, are a signature property of (quantum) entanglement. This paper presents a categorization of the various forms of nonlocality in physical theories. It is shown that, even for Einstein’s theory of relativity, correlations of spatially separated measurements cannot be explained without the involvement of some nonlocal or global knowledge and facts. Instantaneous Influences at a distance are, however, in a special category of nonlocality and, as is well known, Einstein called them spooky. Following a separation of nonlocalities into four distinctly different categories 0, 1, 2, 3, with number 3 corresponding to theories containing instantaneous influences at a distance, I show that any theory of EPR experiments must be at least in category 1 or 2 and does not need to be in category 3. In particular, the Bell theorem, valid for category 0 theories, may be violated for categories 1 and 2 and does not require category 3 theories. Category 0 enforces Bell’s theorem. However, it does not apply to relativistic theories of space like separated measurements.