University of Oxford, UK
Does Bohmian Theory Have to Be Nonlocal? New Directions for Analysing the Bell Theorem
The Penrose “Impossible” Triangle appears incomprehensible because we implicitly assume that any two arms become close near a common vertex. It is made comprehensible by relaxing this assumption i.e. by analysing in a more appropriate 3D metric. Analogously, it is shown that the Bell Theorem in quantum physics can be made comprehensible – that is to say, consistent with local realism – if the conventional Euclidean metric of state space is replaced by a more appropriate p-adic-like metric, reflecting some underpinning fractal state-space geometry. In this representation, the Bell Inequality is distant from all forms of the inequality that have been shown to be violated experimentally. Which is to say that the Bell Inequality has not be shown to be violated experimentally, even approximately! This result has implications for finding a locally causal version of the explicitly realistic Bohmian Theory. In this interpretation, the Bohmian quantum potential should be considered a coarse-grain representation of the underpinning fractal state-space geometry.