There seems to be a fundamental issue that prevents one from applying truly reductionist concepts below the mesoscopic scale, the scale of molecules and molecular interactions. Note that we could also look at this scale separation as being at the level between classical mechanics and quantum mechanics. I'm going to separate the concept of physical reducibility from analytical reducibility and look at how each differs above or below this mesoscopic scale. I'm interested in feedback on concepts used in physics, especially below the mesoscopic scale, that would help flesh out an argument which essentially says, there is both a physical and analytical separation that exists in the world at this scale. Above this scale, we can easily reduce any system, but below this scale the systems are not reducible in a truly reductionist sense. Physical Reducibility - above mesoscopic scale Physical reducibility would be the ability to separate things physically into small chunks or volumes while maintaining some kind of causal affect on the volume which is independent of the causal affect’s source. In other words, physical reducibility can be obtained by replacing the causal affects that some finite volume has in one physical system with equal causal affects such as is done in a lab to reproduce the affect within some experimental volume. This can be as simple as reproducing a chemical reaction on a bench top that would otherwise occur elsewhere, such as deep in the ocean or within a chemical reactor in a refinery. Another example might be a fatigue test on a piece of aluminum for example. We don’t need to put an engine bracket from an aircraft into the actual aircraft and fly it around for thousands of hours under conditions of low temperature or salt spray to understand if it will crack. We can do this in a lab, in a test chamber. Such classical mechanical interactions can all be seen to be physically reducible simply by taking some small volume of a system and subjecting it to equivalent causal actions. The main reason we can duplicate a given volume like this is because the behavior of anything at the classical scale is due to an aggregate of molecules or atoms. Physical Reducibility - below mesoscopic scale On the other hand, we can’t do this with molecules or atoms. For example, we can’t physically separate out the nucleus and see how one atom might react to another by subjecting the nucleus to some kind of electrical field that simulates the electrons. We can’t physically separate the nucleus from the electrons in an atom, and duplicate the interaction of one part by subjecting it to causal actions so that the interaction with other atoms can be duplicated. Similarly, I believe it is impossible to separate out matter and apply causal actions on molecules like we do to large objects. We could take C2H6 for example, and make it CH4 by cutting a carbon bond, but I don’t know how we might then make the CH4 molecule ‘act like’ a C2H6 molecule. I don’t believe we can physically simulate one part (part A) of a molecule by removing part of it and subjecting it to intramolecular forces that are identical to those forces that part A would have been subjected to had it been actually attached to the remainder of the molecule. So for physical reducibility, we have the ability to reduce a system that operates at a classical scale but we don’t have the ability to reduce such a system below roughly the mesoscopic scale. Would you agree with this or not? How would you argue that such a physical separation exists? Any papers that might address this would be appreciated. Analytical Reducibility - above mesoscopic scale The second part of this is what I’ll call “analytical reducibility”. Just as classical mechanical structures such as an aircraft or chemical refinery can be physically reduced, we have concepts that allow analytical reduction. We can cut any classical level object up and apply FEA or CFD to it as is commonly done in engineering. In basic physics courses, we learn concepts such as “free body diagrams” which allow us so separate out a truss in a bridge for example, and apply forces and moments to the various points on the boundaries so that the remaining portion of the truss can be analytically solved for forces and moments. I’m unaware of any system that we can’t analytically reduce above the mesoscopic scale in this way. Analytical Reducibility - below mesoscopic scale Below the mesoscopic scale, I believe things get a bit more tricky. I don’t believe, but would like to hear comments, on if a molecule can be reduced to it’s constituent atoms or not. Can one for example, reduce the CH4 molecule to the equations governing those atoms, and then place some other boundary conditions on that model such that we have duplicated a C2H6 molecule? Perhaps another example might regard amino acid sequences which fold. Can one determine the bending moment at the fold simply by reducing all the atoms on one side of the hinge to a single set of equations such that the analysis of the folding point is accurate, or do we actually need to have all atoms calculated on both sides to understand how and where it will fold? Are there techniques that conceptually reduce a molecule at an arbitrary cut similar to a free body diagram? Can we argue that there is no analytical method to create 'boundry conditions' for parts of molecules or between molecules, and if not, why not? Where is the analytical separation if there is one? I've read Laughlin's paper "The Middle Way" which addresses some of these concerns indirectly. I've also read similar papers but nothing that really touches directly on the questions above. Suggestions for papers like these would be appreciated.