In the debate whether ‘hidden variables’ could exist underneath quantum probabilities, the ‘no hidden-variables’ position is at present favored. In this article I attempt to provide a more equilibrated verdict, by pointing towards the heuristic and explanatory power of the hidden-variables hypothesis, in particular in its deterministic form. I argue that this hypothesis can answer three foundational questions, whereas the opposing thesis (‘no hidden variables’) remains entirely silent for them. These questions are: 1) How to interpret probabilistic correlation ? (a question considered by Kolmogorov “one of the most important problems in the philosophy of the natural sciences”, and first analysed by Reichenbach); 2) How to interpret the Central Limit Theorem ?; and 3) Are there degrees of freedom that could unify quantum field theories and general relativity, and if so, can we (at least qualitatively) specify them ? It appears that only the hidden-variables hypothesis can provide coherent answers to these problems; answers which can be mathematically justified in the deterministic case. This suggests that the hidden-variables hypothesis should be considered a legitimate candidate as a guiding, unifying principle in the foundations of physics.
In the debate whether ‘hidden variables’ could exist underneath quantum probabilities, the ‘no hidden-variables’ position is at present favored. In this article I attempt to provide a more equilibrated verdict, by pointing towards the heuristic and explanatory power of the hidden-variables hypothesis, in particular in its deterministic form. I argue that this hypothesis can answer three foundational questions, whereas the opposing thesis (‘no hidden variables’) remains entirely silent for them. These questions are: 1) How to interpret probabilistic correlation ? (a question considered by Kolmogorov “one of the most important problems in the philosophy of the natural sciences”, and first analysed by Reichenbach); 2) How to interpret the Central Limit Theorem ?; and 3) Are there degrees of freedom that could unify quantum field theories and general relativity, and if so, can we (at least qualitatively) specify them ? It appears that only the hidden-variables hypothesis can provide coherent answers to these problems; answers which can be mathematically justified in the deterministic case. This suggests that the hidden-variables hypothesis should be considered a legitimate candidate as a guiding, unifying principle in the foundations of physics.
Introduction To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements. It seems interesting to ask if this statistical element be thought of as arising, as in classical statistical mechanics, because the states in question are averages over better defined states for which individually the results would be quite determined. These hypothetical ‘dispersion free’ states would be specified not only by the quantum mechanical state vector but also by additional ‘hidden variables’ – ‘hidden’ because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate. Whether this question is indeed interesting has been the subject of debate. The present paper does not contribute to that debate. It is addressed to those who do find the question interesting, and more particularly to those among them who believe that ‘the question concerning the existence of such hidden variables received an early and rather decisive answer in the form of von Neumann's proof on the mathematical impossibility of such variables in quantum theory.’ An attempt will be made to clarify what von Neumann and his successors actually demonstrated. This will cover, as well as von Neumann's treatment, the recent version of the argument by Jauch and Piron, and the stronger result consequent on the work of Gleason. It will be urged that these analyses leave the real question untouched.
In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of "hidden" variables, developed in a previous paper. We find that in principle, these "hidden" variables determine the precise results of each individual measurement process. In practice, however, in measurements that we now know how to carry out, the observing apparatus disturbs the observed system in an unpredictable and uncontrollable way, so that the uncertainty principle is obtained as a practical limitation on the possible precision of measurements. This limitation is not, however, inherent in the conceptual structure of our interpretation. We shall see, for example, that simultaneous measurements of position and momentum having unlimited precision would in principle be possible if, as suggested in the previous paper, the mathematical formulation of the quantum theory needs to be modified at very short distances in certain ways that are consistent with our interpretation but not with the usual interpretation.We give a simple explanation of the origin of quantum-mechanical correlations of distant objects in the hypothetical experiment of Einstein, Podolsky, and Rosen, which was suggested by these authors as a criticism of the usual interpretation.Finally, we show that von Neumann's proof that quantum theory is not consistent with hidden variables does not apply to our interpretation, because the hidden variables contemplated here depend both on the state of the measuring apparatus and the observed system and therefore go beyond certain of von Neumann's assumptions.In two appendixes, we treat the problem of the electromagnetic field in our interpretation and answer certain additional objections which have arisen in the attempt to give a precise description for an individual system at the quantum level.
Hardy presented a famous argument that shows that there exist no hidden variables in quantum mechanics. His argument is called Hardy's paradox. The commentaries and discussions on Hardy's paradox have been ordinarily presented for deterministic hidden variables, and it has not been discussed whether a similar paradox will occurs in probabilistic hidden variables. So, first, I will show that Hardy's argument can also be applied to probabilistic hidden variables. After that, I discuss the common cause of a correlation, which has been actively discussed in the philosophy of science in recent years. That is because requiring the common cause of a quantum correlation is mathematically equivalent to introducing a probabilistic hidden variable to explain the correlation. Some researchers argued that in the non-existence proof of hidden variables, the existence of a common common-cause to multiple correlations is tacitly assumed, however that is unreasonably strong. According to their idea, it is sufficient if there exists a respective common-cause of each correlation. However, it will be revealed that at least as far as Hardy's paradox is concerned, merely weakening the common common-cause requirement to the respective common-cause requirement does not help to construct a local model.
Probability theory as a physical theory is, in a sense, the most general physics theory available, more encompassing than relativity theory and quantum mechanics, which comply with probability theory. Taking this simple fact seriously, I argue that probability theory points towards superdeterminism, a principle that underlies, notably, ‘t Hooft’s Cellular Automaton Interpretation of quantum mechanics. Specifically, I argue that superdeterminism offers a solution for: (1) Kolmogorov’s problem of probabilistic dependence; (2) the interpretation of the Central Limit Theorem; and (3) Bell’s theorem. Superdeterminism’s competitor, indeterminism (“no hidden variables”), remains entirely silent regarding (1) and (2), and leaves (3) as an obstacle rather than a solution for the unification of quantum mechanics and general relativity. This suggests that, if one wishes to stick to the standard position in physics and adopt the principles with the highest explanatory power, one should adopt superdeterminism and reject indeterminism. Throughout the article precise questions to mathematicians are formulated to advance this research.
The primary criterion of adequacy of a probabilistic causal analysis is that the causal variable should render the simultaneous phenomenological data conditionally independent. The intuition back of this idea is that the common cause of the phenomena should factor out the observed correlations. So we label the principle the common cause criterion . If we find that the barometric pressure and temperature are both dropping at the same time, we do not think of one as the cause of the other but look for a common dynamical cause within the physical theory of meteorology. If we find fever and headaches positively correlated, we look for a common disease as the source and do not consider one the cause of the other. But we do not want to suggest that satisfaction of this criterion is the end of the search for causes or probabilistic explanations. It does represent a significant and important milestone in any particular investigation. Under another banner the search for common causes in quantum mechanics is the search for hidden variables. A hidden variable that satisfies the common cause criterion provides a satisfactory explanation “in classical terms” of the quantum phenomenon. Much of the earlier discussion of hidden variables in quantum mechanics has centered around the search for deterministic underlying processes, but for some time now the literature has also been concerned with the existence of probabilistic hidden variables. It is a striking and important fact that even probabilistic hidden variables do not always exist when certain intuitive criteria are imposed.
What does quantum physics tell us about the nature of reality, specifically the parts of reality we do not directly perceive called hidden variables? One may think it could tell us a lot because of our enhanced technological sensing abilities that delve into the realms that quantum physics covers so well. Surprisingly, it seems to surround us in a deeper mystery rather than reveal more of nature's secrets. It seems that we cannot escape from philosophical consideration when dealing with what is hidden in quantum physics. In Part I we will look at how Epistemology and Ontology bear upon Hidden Variables. In Part II we will consider Hidden Variables in the light of Contextuality, and Non-Classicality. Inevitably questions of subjectivity and objectivity arise in dealing with states of observation. How should we think about these states? Perhaps it is a question of the meaning associated with our knowledge of a state-that is, a question of ontology or epistemology. The issue of ontic and epistemic states is particularly important when considering hidden variables in quantum physics because, as one may argue, the interpretation of quantum states as either ontic or epistemic will naturally lead to different assumptions about how reality is constructed; if it is constructed or not. It also raises the question of what attributes we are able to observe simultaneously and that brings contextuality into the discussion. If it turns out that reality is constructed contextually what does that imply about ontological realism? If on the other hand reality is constructed non-contextually what does that imply about ontological realism? Many implications can arise when considering these questions from a quantum physical point of view. In this paper I shall discuss how quantum physics provides some answers to these questions by considering quantum physical states and their measurements.