• Aerts, D. (1982). Example of a macroscopical situation that violates Bell inequalities. Lettere al Nuovo Cimento, 34, pp. 107-111.

• Aerts, D. (1985). The physical origin of the Einstein Podolsky Rosen paradox. In G. Tarozzi and A. van der Merwe (Eds.), Open Questions in Quantum Physics: Invited Papers on the Foundations of Microphysics (pp. 33-50). Dordrecht: Kluwer Academic.

• Aerts, D. (1985). A possible explanation for the probabilities of quantum mechanics and a macroscopical situation that violates Bell inequalities. In P. Mittelstaedt and E. W. Stachow (Eds.), Recent Developments in Quantum Logic, Grundlagen der Exacten Naturwissenschaften, vol.6, Wissenschaftverlag (pp. 235-251). Mannheim: Bibliographisches Institut.

• Aerts, D. (1991). A mechanistic classical laboratory situation violating the Bell inequalities with 2sqrt(2), exactly 'in the same way' as its violations by the EPR experiments. Helvetica Physica Acta, 64, pp. 1-23.

  Abstract: We present a macroscopical mechanistic classical laboratory situation, and a classical macroscopical entity, and coincidence measurements on this entity, that lead to a violation of the Bell inequalities corresponding to these coincidence measurements. The violation that we obtain with these coincidence measurements is exactly the same as the violation of the Bell inequalities by the well known coincidence measurements of the quantum entity of two spin 1/2 particles in a singlet spin state. With this we mean that it gives rise to the same numerical values for the expectation values and the same numerical value 2sqrt(2) for the expression used in the Bell inequality. We analyze the origin of the violation, and can formulate the main difference between the violation of Bell inequalities by means of classical entities and the violation of Bell inequalities by means of quantum entities. The making clear of this difference can help us to understand better what the quantum-violation could mean for the nature of reality. We think that some classical concepts will have to be changed, and new concepts will have to be introduced, to be able to understand the reality of the quantum world.

• Aerts, D. (1998). The hidden measurement formalism: what can be explained and where paradoxes remain. International Journal of Theoretical Physics, 37, pp. 291-304. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0105126.

  Abstract: In the hidden measurement formalism that we develop in Brussels we explain the quantum structure as due to the presence of two effects, (a) a real change of state of the system under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement process. We show that the presence of these two effects leads to the major part of the quantum mechanical structure of a theory describing a physical system where the measurements to test the properties of this physical system contain the two mentioned effects. We present a quantum machine, where we can illustrate in a simple way how the quantum structure arises as a consequence of the two effects. We introduce a parameter epsilon that measures the amount of the lack of knowledge on the measurement process, and by varying this parameter, we describe a continuous evolution from a quantum structure (maximal lack of knowledge) to a classical structure (zero lack of knowledge). We show that for intermediate values of epsilon we find a new type of structure that is neither quantum nor classical. We analyze the quantum paradoxes in the light of these findings and show that they can be divided into two groups: (1) The group (measurement problem and Schrodingers cat paradox) where the paradoxical aspects arise mainly from the application of standard quantum theory as a general theory (e.g. also describing the measurement apparatus). This type of paradox disappears in the hidden measurement formalism. (2) A second group collecting the paradoxes connected to the effect of non-locality (the Einstein-Podolsky-Rosen paradox and the violation of Bell inequalities). We show that these paradoxes are internally resolved because the effect of non-locality turns out to be a fundamental property of the hidden measurement formalism itself.

• Aerts, D., Aerts, S., Broekaert, J. and Gabora, L. (2000). The violation of Bell inequalities in the macroworld. Foundations of Physics, 30, pp. 1387-1414. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0007044.

  Abstract: We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or in the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation.