In the early stages of the famous debates between Einstein and Bohr on the foundations of quantum mechanics, Einstein attempted to devise thought experiments aiming at showing that arbitrarily accurate predictions of incompatible physical quantities was possible, in violation of Heisenberg's uncertainty principle. Bohr was able to defend quantum mechanics from those attacks by showing that a careful application of the uncertainty principle to the experimental apparata as well as the measured system lead to consistent results. Could Bohr have given an independent argument for the irreducible unpredictability implied by the uncertainty principle?
The celebrated 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the ontological concepts of locality and determinism. However, nothing can be concluded from Bell's theorem alone about locality by itself or determinism by itself--it is possible to reproduce quantum-mechanical predictions with deterministic models which violate locality as well as indeterministic models which satisfy locality. On the other hand, there's almost universal agreement that the epistemic form of locality--signal locality, or the impossibility of faster-than-light communication--must hold in a relativistic universe. By making a similar distinction between determinism and the epistemic concept of predictability, I show that signal locality plus the bare observed phenomena of Bell inequality violations lead to the remarkable conclusion that Nature is fundamentally unpredictable. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the principle of relativity, regardless of any postulates of quantum mechanics.
In the early stages of the famous debates between Einstein and Bohr on the foundations of quantum mechanics, Einstein attempted to devise thought experiments aiming at showing that arbitrarily accurate predictions of incompatible physical quantities was possible, in violation of Heisenberg's uncertainty principle. Bohr was able to defend quantum mechanics from those attacks by showing that a careful application of the uncertainty principle to the experimental apparata as well as the measured system lead to consistent results. Could Bohr have given an independent argument for the irreducible unpredictability implied by the uncertainty principle?
The celebrated 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the ontological concepts of locality and determinism. However, nothing can be concluded from Bell's theorem alone about locality by itself or determinism by itself--it is possible to reproduce quantum-mechanical predictions with deterministic models which violate locality as well as indeterministic models which satisfy locality. On the other hand, there's almost universal agreement that the epistemic form of locality--signal locality, or the impossibility of faster-than-light communication--must hold in a relativistic universe. By making a similar distinction between determinism and the epistemic concept of predictability, I show that signal locality plus the bare observed phenomena of Bell inequality violations lead to the remarkable conclusion that Nature is fundamentally unpredictable. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the principle of relativity, regardless of any postulates of quantum mechanics.
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational interpretation of the non-signalling theorem. We here argue that the non-signalling theorem must instead be viewed as an epistemic, operational theorem i.e. one that refers exclusively to what epistemic agents can, or rather cannot, do. That is, we emphasize that the non-signalling theorem is a theorem about the operational inability of epistemic agents to signal information. In other words, as a proper principle, the non-signalling theorem may only be employed as an epistemic, phenomenological, or operational principle. Critically, our argument emphasizes that the non-signalling principle must not be used as an ontic principle about physical reality as such, i.e. as a theorem about the nature of physical reality independently of epistemic agents e.g. human observers. One major reason in favor of our conclusion is that any definition of signalling or of non-signalling invariably requires a reference to epistemic agents, and what these agents can actually measure and report. Otherwise, the non-signalling theorem would equal a general "no-influence" theorem. In conclusion, under the assumption that the non-signalling theorem is epistemic (i.e. "epistemic non-signalling"), the search for deterministic approaches to quantum mechanics, including NHVTs and an emergent quantum mechanics, continues to be a viable research program towards disclosing the foundations of physical reality at its smallest dimensions.
By implicitly assuming that all possible Bell-measurements occur simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty Principle. This assumption is made in the original form of Bell's inequality, in Wigner's probability inequalities, and in the ``nonlocality without inequalities'' arguments. The introduction of time into derivations of these variants of Bell's theorem results in extra terms related to the time order of the measurements used in constructing correlation coefficients. Since the same locality assumptions are made in the Heisenberg-compliant derivations of this paper, only time-independent classical local hidden variable theories are forbidden by violations of the original Bell inequalities; time-dependent quantum local hidden variable theories can satisfy this new bound and agree with experiment. We further point out that factorizable wavefunctions have been used to describe some EPR experiments and can be used to describe others. These will generate local de Broglie-Bohm trajectories in the description of the data. This second, independent, line of argument also shows that violation of Bell's inequality is only evidence that Heisenberg's Uncertainty Principle cannot be ignored.
Recent experiments allow one to conclude that Bell-type inequalities are indeed violated; thus, it is important to understand what this means and how we can explain the existence of strong correlations between outcomes of distant measurements. Do we have to announce that Einstein was wrong, Nature is non-local and non-local correlations are produced due to quantum magic and emerge, somehow, from outside space-time? Fortunately, such conclusions are unfounded because, if supplementary parameters describing measuring instruments are correctly incorporated in a theoretical model, then Bell-type inequalities may not be proved. We construct a simple probabilistic model allowing these correlations to be explained in a locally causal way. In our model, measurement outcomes are neither predetermined nor produced in an irreducibly random way. We explain why, contrary to the general belief, the introduction of setting-dependent parameters does not restrict experimenters' freedom of choice. Since the violation of Bell-type inequalities does not allow the conclusion that Nature is non-local and that quantum theory is complete, the Bohr-Einstein quantum debate may not be closed. The continuation of this debate is important not only for a better understanding of Nature but also for various practical applications of quantum phenomena.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
Bell's Theorem prescribes that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. However the theorem presupposes that distanced physical systems become spatially disconnected. This presupposition, although in agreement with our intuition, has never been confirmed experimentally. As a result Bell's Theorem prohibits only temporal locality, but not spatial locality between distanced particles. Here, I show that any local-deterministic relativity theory that violates Lorentz's contraction for distancing bodies cannot be forbidden by Bell's inequality. I further show that the predictions of a recently proposed local and deterministic Information Relativity Theory, are consistent with quantum theory and quantum thermodynamics, and reproduce the same results for key quantum phenomena, including matter-wave duality, quantum criticality and phase transition, formation of Bose-Einstein condensate, and quantum entanglement. The theory assumes that observers who are in inertial motion with respect to each other with relative velocity v, communicate information about physical observables using an information carrier with known velocity (vc) which satisfies vc > v. No other presumptions are made. For velocities satisfying v << vc all the theory transformations reduce to Galileo-Newton laws. The theory is simple and is also beautiful due to its Golden Ratio symmetries. More importantly, the theory is scale independent with respect to the investigated physical systems' dimensions and the velocity of the information carrier, which renders it applicable to the dynamics of moving bodies in all inertial physical systems.
The first round of the Einstein–Bohr debates took place when Einstein challenged Bohr’s principle of complementarity at the Solvay conference in 1927 and Bohr successfully defended it. The most serious challenge, however, came in 1935 when a paper by Einstein, Podolsky, and Rosen (EPR) argued that quantum mechanics was incomplete through a gedanken experiment motivating an approach based on hidden variables. In this chapter, EPR’s arguments about the incompleteness of quantum mechanics and Bohr’s reply to them are presented. The ultimate answer came almost 30 years later, almost ten years after Einstein’s death, and was nothing that Einstein would have expected. Bell’s inequality and the subsequent Bell-CHSH inequality, that are satisfied by all theories based on the “self-evident truths” of reality and locality are discussed. The startling results that quantum mechanics violates Bell’s inequality and the experimental results are in agreement with the prediction of quantum mechanics are presented.
By implicitly assuming that all measurements occur simultaneously, Bell's Theorem only applied to local theories that violated Heisenberg's Uncertainty Principle. By explicitly introducing time into our derivation of Bell's theorem, an extra term related to the time-ordering of actual measurements is found to augment (i.e. weaken) the upper bound of the inequality. Since the same locality assumptions hold for this rederivation as for the original, we conclude that only {\em classical} measurement-order independent local hidden variable theories are constrained by Bell's inequality; time dependent, non-classical local theories (i.e. theories respecting Heisenberg's Uncertainty Principle) can satisfy this new bound while exceeding Bell's limit. Unconditional nonlocality is only expected to occur with Bell parameters between 22 and 4. This weakening of Bell's inequality is seen for the quantum Bell operator (squared) as an extra term involving the commutators of {\em local} measurement operators. We note that a factorizable second-quantized wavefunction can reproduce experimental measurements; because such wavefunctions allow local de Broglie-Bohm hidden variable modelling, we have another indication that violation of {\em Bell's} inequality does not require an acceptance of non-locality.