The apparent incompatibility between foreknowledge and free will is traditionally formulated in terms of the implication of knowledge of a future event for the freedom of that event. This paper reexamines the problem using the notions of causal order and physical determination provided by modern physics. I consider measurements of two entangled particles at spacelike-separated events, where a measurement outcome is taken to be free if it is not determined by the previous history of the part of the universe accessible to it. Relativity allows the temporal order of the two measurements to be reversed between reference frames while preserving their causal independence. Quantum correlations nevertheless allow an observer at one measurement event to know the outcome at the other. I show that there is, therefore, a frame in which an observer possesses foreknowledge of a measurement outcome that remains free in this sense. The argument demonstrates that epistemic access to a future event need not be grounded in physical conditions that determine it.
The apparent incompatibility between foreknowledge and free will is traditionally formulated in terms of the implication of knowledge of a future event for the freedom of that event. This paper reexamines the problem using the notions of causal order and physical determination provided by modern physics. I consider measurements of two entangled particles at spacelike-separated events, where a measurement outcome is taken to be free if it is not determined by the previous history of the part of the universe accessible to it. Relativity allows the temporal order of the two measurements to be reversed between reference frames while preserving their causal independence. Quantum correlations nevertheless allow an observer at one measurement event to know the outcome at the other. I show that there is, therefore, a frame in which an observer possesses foreknowledge of a measurement outcome that remains free in this sense. The argument demonstrates that epistemic access to a future event need not be grounded in physical conditions that determine it.
Introduction The two theories that revolutionized physics in the twentieth century, relativity and quantum mechanics, are full of predictions that defy common sense. Recently, we used three such paradoxical ideas to prove “The Free Will Theorem” (strengthened here), which is the culmination of a series of theorems about quantum mechanics that began in the 1960s. It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle's response (to be pedantic—the universe's response near the particle) is not determined by the entire previous history of the universe. Our argument combines the well-known consequence of relativity theory, that the time order of spacelike separated events is not absolute, with the EPR paradox discovered by Einstein, Podolsky, and Rosen in 1935 and the Kochen–Specker Paradox of 1967 (see [5]). We follow Bohm in using a spin version of EPR and Peres in using his set of thirty-three directions, rather than the original configuration used by Kochen and Specker. More contentiously, the argument also involves the notion of free will, but we postpone further discussion of this to the last section of the chapter.
Most modern physical theories are formulated in terms of differential equations. As a result, if we know exactly the current state of the world, then this state uniquely determines all the future events - including our own future behavior. This determination seems to contradict the intuitive notion of a free will, according to which we are free to make decisions - decisions which cannot be determined based on the past locations and velocities of the elementary particles. In quantum physics, the situation is somewhat better in the sense that we cannot determine the exact behavior, but we can still determine the quantum state, and thus, we can determine the probabilities of different behaviors - which is still inconsistent with our intuition. This inconsistency does not mean, of course, that we can practically predict our future behavior; however, in view of many physicists and philosophers, even the theoretical inconsistency is somewhat troubling. Some of these researchers feel that it is desirable to modify physical equations in such a way that such a counter-intuitive determination would no longer be possible. In this paper, we analyze the foundations for such possible theories, and show that on the level of simple mechanics, the formalization of a free will requires triple interactions - while traditional physics is based on pairwise interactions between the particles.
In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an observer-independent statement. When events are defined with respect to quantum systems however, nothing guarantees that the causal relationship between A and B is definite. We propose to associate a causal reference frame corresponding to each event, which can be interpreted as an observer-dependent time according to which an observer describes the evolution of quantum systems. In the causal reference frame of one event, this particular event is always localised, but other events can be ‘smeared out’ in the future and in the past. We do not impose a predefined causal order between the events, but only require that descriptions from different reference frames obey a global consistency condition. We show that our new formalism is equivalent to the pure process matrix formalism (Araújo et al 2017 Quantum 1 10). The latter is known to predict certain multipartite correlations, which are incompatible with the assumption of a causal ordering of the events—these correlations violate causal inequalities. We show how the causal reference frame description can be used to gain insight into the question of realisability of such strongly non-causal processes in laboratory experiments. As another application, we use causal reference frames to revisit a thought experiment Zych et al (arXiv: 1708.00248 ) where the gravitational time dilation due to a massive object in a quantum superposition of positions leads to a superposition of the causal ordering of two events.
We argue that the concepts of "freedom of choice" and of "causal order" are intrinsically linked: a choice is considered "free" if it is correlated only to variables in its causal future. We discuss the implications of this to Bell-type scenarios, where two separate measurements are carried out, neither of which lies in the causal future of the other, and where one typically assumes that the measurement settings are chosen freely. Furthermore, we refute a recent criticism made by Ghirardi and Romano in [arXiv:1301.5040] and [arXiv:1302.1635] that we used an unphysical freedom of choice assumption in our previous works, [Nat. Commun. 2, 411 (2011)] and [Phys. Rev. Lett. 108, 150402 (2012)].
This work presents a conceptual and semi-formal analysis of quantum entanglement, locality, and determinism, motivated by a thought experiment involving double-slit measurements performed on entangled particles at spacelike separation. While quantum correlations appear instantaneous, the paper demonstrates that no superluminal information transfer or causal influence is required to explain observed outcomes.Building upon the Einstein–Podolsky–Rosen framework and Bell’s theorem, the study distinguishes between local dynamical processes and nonlocal informational correlations encoded in the global quantum state. It argues that measurement outcomes are locally realized yet globally constrained, leading to an effectively deterministic universal description while preserving epistemic uncertainty for observers.The paper reframes quantum nonlocality as a manifestation of global consistency rather than physical influence, offering insights into the relationship between realism, free will, and relativistic causality. The discussion is interpretational in nature and does not introduce new experimental claims, aiming instead to clarify foundational assumptions underlying quantum theory.This work is intended for researchers and students interested in quantum foundations, the philosophy of physics, and the conceptual structure of modern physical theories.
The idea that events are equipped with a partial causal order is central to our understanding of physics in the tested regimes: given two pointlike events A and B , either A is in the causal past of B , B is in the causal past of A , or A and B are space-like separated. Operationally, the meaning of these order relations corresponds to constraints on the possible correlations between experiments performed in the vicinities of the respective events: if A is in the causal past of B , an experimenter at A could signal to an experimenter at B but not the other way around, while if A and B are space-like separated, no signaling is possible in either direction. In the context of a concrete physical theory, the correlations compatible with a given causal configuration may obey further constraints. For instance, space-like correlations in quantum mechanics arise from local measurements on joint quantum states, while time-like correlations are established via quantum channels. Similarly to other variables, however, the causal order of a set of events could be random, and little is understood about the constraints that causality implies in this case. A main difficulty concerns the fact that the order of events can now generally depend on the operations performed at the locations of these events, since, for instance, an operation at A could influence the order in which B and C occur in A ’s future. So far, no formal theory of causality compatible with such dynamical causal order has been developed. Apart from being of fundamental interest in the context of inferring causal relations, such a theory is imperative for understanding recent suggestions that the causal order of events in quantum mechanics can be indefinite. Here, we develop such a theory in the general multipartite case. Starting from a background-independent definition of causality, we derive an iteratively formulated canonical decomposition of multipartite causal correlations. For a fixed number of settings and outcomes for each party, these correlations form a polytope whose facets define causal inequalities. The case of quantum correlations in this paradigm is captured by the process matrix formalism. We investigate the link between causality and the closely related notion of causal separability of quantum processes, which we here define rigorously in analogy with the link between Bell locality and separability of quantum states. We show that causality and causal separability are not equivalent in general by giving an example of a physically admissible tripartite quantum process that is causal but not causally separable. We also show that there are causally separable quantum processes that become non-causal if extended by supplying the parties with entangled ancillas. This motivates the concepts of extensibly causal and extensibly causally separable (ECS) processes, for which the respective property remains invariant under extension. We characterize the class of ECS quantum processes in the tripartite case via simple conditions on the form of the process matrix. We show that the processes realizable by classically controlled quantum circuits are ECS and conjecture that the reverse also holds.