Free Will as a Synchronized Stochastic Process Lennart Brocki lennart.brocki@uwr.edu.pl Having a free will is one of our most basic experience as human beings and yet it is at odds with virtually all other of our observations of nature and the physical laws we have derived from them. The evidence for the deterministic nature of physical laws, at least on the macroscopic scale, is overwhelming and there appears to be no room for free will. Therefore many authors declare free will to be an illusion, see for example [1–3]. Other authors defend free will by claiming that it is a high-level phenomenon that emerges from the physical processes but is autonomous from them and fundamental physical laws are simply not the appropriate framework to understand it [4]. A popular approach is also to use quantum mechanics and its stochastic nature to find loopholes in the physical laws that would allow for free will [5]. The problem with this approach is that due to quantum decoherence [6] the timescale of quantum processes is too small to have any bearing on the processes in the brain. Here I would like to present a new perspective to resolve the tension between the laws of nature and free will which is based purely on classical physics and turns the argument against free will around: the starting point is to accept free will as a fact and too allow for a modification of Newton's law of motion in a compatible way such that in this new perspective the determinism of the laws of nature is an illusion. Compatible here means that the modified theory is in agreement with all established observations. As will be discussed in more detail, at the core of my argument is a criticism of reductionism which will motivate the modification of Newton's law. The plan of this article is to first argue that just because determinism in classical theories (as opposed to quantum theories) holds on a microscopic scale it does not necesseraly have to hold for large numbers of interacting particles. The next step is to explain how non-deterministic corrections of the physical laws could arise in a consistent manner and finally to give a technical definition of free will as a synchronized stochastic process. All proposition made here are of course highly speculative and as of now there are no observations supporting them. Any classical theory is deterministic, this means that given initial conditions lead to a 2 unique evolution of the system in consideration. The behavior of the system from the far past to the far future is uniquely determined once the state of the system at any point of time is fixed. The evolution of a system is obtained by solving the underlying differential equations, that is Newton's law of motion. The resulting solutions describe the trajectories of the constituents, or particles, of the system in consideration. This method has been very succesful in predicting virtually any of our observations of nature, at least for length and energy scales close to the human scale. It is one of the basic assumptions of reductionism that the same law that accurately describes the interaction of a few particles also describes the interactions of a system that is far more complicated, with a number of constituents many orders of magnitudes larger. Reductionism has been so succesful in explaining nature that we accept its assumptions as completely natural and do not recognize them any more for what they really are: assumptions. Facing the profound tensions between the established laws of nature and the human mind it is my conviction that one should explore all possibilities, including a scrutiny of reductionism. My basic argument is that Newton's law does not necessarily exactly hold for a large number of interacting particles and that one can construct corrections to it such that the resulting theory is compatible with established observations while, at least theoretically, being testable by new experiments. I propose that for a large number of interacting particles Newton's law obtains nondeterministic corrections which are vanishing in the limit of a small number of particles. A more suitable perspective on this is that the more fundamental theory includes these non-deterministic corrections and it reduces to Newton's law in the limit of a small number of particles. In this sense the determinism of the physical laws would be an illusion which arises by assuming that the deterministic behavior of a small number of particles can be extrapolated all the way to the macroscopic world. My claim is at odds with the idea of reductionism and I understand the non-deterministic effects to be strongly emergent, in the sense that they can not be deduced from the laws that govern the evolution of a small number of interacting particles. In this sense the modification of Newton's law is compatible with the observations made concerning systems with few constituents, such as the solar system. What about compatability to macroscopic observations involving a large number of particles? The bridge that connects the microscopic laws of mechanics with macroscopic observations such as temperature and pressure is statistical physics. One of the central elements of statistical physics is the statistical ensemble, essentially a large 3 number of independent copies of the system. The statistical ensemble can be understood as a probability distribution over all possible states of the system and essentially encodes our lack of knowledge about the evolution of a macroscopic number of particles. In this picture we can understand the non-deterministic corrections as fluctuations around the state of the system as dictated by Newton's law. Notice that there is a subtle but crucial difference to usual thermal fluctuations. These are also effectively, that is due to a lack of our knowledge, described as non-deterministic or stochastic but in the usual theory thought to still arise from the deterministic microscopic laws. The fluctuations we are describing here are truly non-deterministic. It is natural to assume that these fluctuations are uncorrelated and in the statistical ensemble they therefore average out, such that the net behavior is equivalent to the one obtained considering the exact Newton's law. This can also be understood in analogy to how the non-deterministic behavior of quantum mechanics averages out to the classical behavior when considering macroscopic systems. Now one can ask why should such a modification of Newton's law even be considered if it always gives the same answer as the usual theory? There are, however, two important cases which have not been discussed yet in which deviations could possibly manifest themselves and become observable. The first case is a system with a number of constituents that is large enough such that the non-deterministic effects become significant but not too large such that their effects average out. Furthermore, the number should not be too large so that high-precision numerical predictions using Newton's law are feasible and can be tested against the observed behavior. In this way the proposed modification is at least theoretically testable. Since no such deviation has been reported so far the effect can be expected to be minute on the other hand I am not aware of any such high-precision tests of Newton's law for a large number of particles. The second case finally brings me to the definition of free will as a synchronized stochastic process. By this I mean that the brain could be capable of organizing the non-deterministic behavior of its constituents in such a way that, in cooperation with a connected body, it is able to act as an entity independent from the deterministic flow dictated by Newton's law. This synchronization of stochastic processes might seem to be an almost esoteric claim but in fact we see examples of this in nature. The most prominent example is life itself. Under an evolutionary pressure natural selection picks out certain random mutations and these mutations prevail over the sea of random fluctuations and become persistent. It is 4 thinkable that in the brain a similar Darwinian selective process takes place which is able to let certain non-deterministic fluctuations, which we can see in analogy to the aforementioned mutations, prevail over others. An important question is what could be the equivalent to the evolutionary pressure, i.e. survival until reproduction, in this context? A mechanism would be needed that allows, in some sense which is to be defined, certain non-deterministic events to obtain an advantage over others and to "reproduce" this event. To summarize, I have proposed a new perspective that could potentially resolve the tension between the deterministic laws of nature and free will purely on grounds of classical physics. I proposed that through a criticism of reductionism one can justify a modification of Newton's law of motion and introduce non-deterministic corrections which arise for systems with a large number of interacting particles. These corrections were shown to be compatible with established observations while, at least theoretically, being testable. In line with my criticism of reductionism I suggested a change in perspective which takes the modified theory to be the fundamental one. This fundamental theory reduces to Newton's law in the limit of a small number of particles. Finally, I have suggested that the brain could be capable of synchronizing the non-deterministic corrections in order to act independently of the deterministic flow of Netwon's law. This motivated my definition of free will as a synchronized stochastic process. [1] A. R. Cashmore, Proceedings of the National Academy of Sciences 107, 4499 (2010). [2] D. M. Wegner, The illusion of conscious will (MIT press, 2002). [3] G. D. Caruso, Free will and consciousness: A determinist account of the illusion of free will (Lexington Books, 2012). [4] C. List, Why free will is real (Harvard University Press, 2019). [5] J. Conway and S. Kochen, Foundations of Physics 36, 1441 (2006). [6] M. Tegmark, Physical review E 61, 4194 (2000).