For an approximate continuity of structure between Newtonian and Bohmian Mechanics

Abstract

Structural Realism (SR) endorses a notion of continuity of structure across different theories that needs clarification (Worrall 1989). In light of this, my contribution aims to provide an example of such continuity. More specifically, my talk concerns Newtonian and Bohmian Mechanics and raises the question of whether it is possible to see a continuity of structure between the two theories in case we endorse Ontic Structural Realism (OSR). In the first part, I present SR and OSR. In a nutshell, while SR claims that there is continuity of structure and not of content (Worrall 1989) between shifts of different Scientific Theories, OSR advances the bolder claim that all that really exists is structure (Ladyman 1998) and that, for this reason, we have to re-conceptualize objects in terms of the relations they entertain (French and Ladyman 2003). These relations are spelled out by the laws of the theory through mathematical equations. In light of this, two theories present a continuity of structure when the laws remain invariant. However, this is hardly ever the case, since often the equations of one theory reappear as limiting cases of another one. In this case the continuity of structure is only approximate. In the second part,I present the case of the shift between Newtonian and Bohmian Mechanics. Bohmian Mechanics seems to be the most suitable quantum theory that can account for a continuity from Newtonian Mechanics to the quantum domain, since both theories share a primitive ontology that consists of particles in motions. However, if we re-conceptualize the ontology according to OSR, in order to detect a continuity between the two theories, we need a continuity of structure. Hence, the question is whether or not the two theories rely on the same structure. Both theories present a non-local dynamics according to which each particle position depends simultaneously on all the other particles’ positions of the system. Hence, it seems that both ontologies present the same underlying structure. However, contrary to Esfeld (forthcoming), I claim that it is not the case. Indeed, I show that the structure relating all the particles of the system is reducible to many one-to-one relations in Newtonian Mechanics, but not separable in Bohmian Mechanics (Hubert forthcoming). Hence, I argue that while for the Newtonian case the structure is simply non-local, in the Bohmian case it is holistic, since in the latter the whole is prior to the parts. My final question is whether it is still possible to recover a continuity of structure between the two theories. I claim that the answer is up to the physicists working in the classical limit of Bohmian mechanics. In case it is possible to regard the Newtonian laws as limiting cases of the Bohmian laws when some quantity goes to zero (for example Q or ћ as was suggested in the literature (Allori et al. 2002, Holland 1993)), then we can still talk of a continuity. However, this continuity is only approximate, since the two theories do not share the same dynamical structure.