The two most successful theories of physics are incompatible with determinism. On the one hand, quantum physics (quantum mechanics, quantum field theory, quantum electrodynamics, particle physics, etc.) are fundamentally indeterministic. On the other hand, both special and general relativity render the entirety of classical determinism obsolete: simultaneity is only defined locally, so "before" and "after" (requisite states for determinism) don't exist. Finally, the past century of research into nonlinear systems has shown that even within classical mechanics the classical linear causal model (every effect has a set of causes that precede it and are both necessary and sufficient to bring about it) irrelevant, incoherent, and false. Consider a model, simulation, or similar "realization" of a cell and the process of metabolic-repair, and let
f:
A→B be a function
"where
f is the process that takes input A and output B...The system Rosen uses for an example is the Metabolism-Repair or [M,R] system. The process, f, in this case stands for the entire metabolism goin on in an organism...The transition, f, which is being called metabolism, is a mapping taking some set of metabolites, A, into some set of products, B. What are the members of A? Really everything in the organism has to be included in A, and there has to be an implicit agreement that at least some of the members of A can enter the organism from its environment. What are the members of B? Many, if not all, of the memebers of A since the transitions in the reduced system are all strung together in the many intricate patterns or networks that make up the organism's metabolism. It also must be true that some members of B leave the organism as products of metabolism...In the context developed so far, the mapping, f, has a very special nature. It is a functional component of the system we are developing. A functional component has many interesting attributes. First of all,
it exists independent of the material parts that make it possible.
Reductionism has taught us that every thing in a real system can be expressed as a collection of material parts. This is not so in the case of functional components...Fragmentability is the aspect of systems that can be reduced to their material parts leaving recognizable material entities as the result. A system is not fragmentable is reducing it to its parts destroys something essential about that system. Since the crux of understanding a complex system had to do with identifying the context dependent functional components, they are by definition, not fragmentable". (pp.103-108; emphasis added; italics in original)
Mikulecky, D. C. (2005). The Circle That Never Ends: Can Complexity be Made Simple? In D. Bonchev & D. H. Rouvray (Eds.).
Complexity in Chemistry, Biology, and Ecology (
Mathematical and Computational Chemistry). Springer.