## Abstract

In the area of the foundations of quantum mechanics a true industry appears to have developed in the last decades, with the aim of proving as many results as possible concerning what there cannot be in the quantum realm. In principle, the significance of proving ‘no-go’ results should consist in clarifying the fundamental structure of the theory, by pointing out a class of basic constraints that the theory itself is supposed to satisfy. In the present paper I will discuss some more recent no-go claims and I will argue against the deep significance of these results, with a two-fold strategy. First, I will consider three results concerning respectively local realism, quantum covariance and predictive power in quantum mechanics, and I will try to show how controversial the main conditions of the negative theorem turn out to be—something that strongly undermines the general relevance of these theorems. Second, I will try to discuss what I take to be a common feature of these theoretical enterprises, namely that of aiming at establishing negative results for quantum mechanics in absence of a deeper understanding of the overall ontological content and structure of the theory. I will argue that the only way toward such an understanding may be to cast in advance the problems in a clear and well-defined interpretational framework—which in my view means primarily to specify the ontology that quantum theory is supposed to be about—and after to wonder whether problems that seemed worth pursuing still are so in the framework.

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## Notes

It might be called ‘Non-local determinism’, since the actual outcomes are well determined by the pre-existing properties of the systems but possibly also in a non-local way.

As a matter of fact, the Leggett-type of theories are ‘realistic’ hidden variable theories that are assumed to be non-local by accepting the condition usually called

*outcome independence*but dropping the further condition called*parameter independence*(according to the Shimony revision of the terminology introduced in Jarrett 1984: see my Laudisa 2008 for details). I wish also to stress that in presenting the Leggett framework I skip several technical details that, although deserving attention, are inessential to the present discussion.Bell also mentions an especially restrictive assumption of the von Neumann theorem, an assumption which makes the von Neumann formulation much stronger with respect to the non-contextual formulations given by Gleason, Jauch-Piron, Bell and Kochen-Specker, and hence even less plausible.

It has still to be stressed how much confusion in the debates concerning the meaning of the Bell theorem derives from insisting on the requirement that the supposed local extension of quantum theory (an extension that the Bell theorem proves to be impossible) has to be also a

*hidden variable*theory.In fact, that quantum theory is ‘complete’ in this sense is a

*postulate*of the theory and not a theorem that can be proved within the theory.We put technical details aside, but the interested reader may consult the

*Supplementary Information*attached to the main paper, which is presented in a rather qualitative form.We wish to stress that we refer to Bohmian mechanics for exemplifying and explanatory reasons, without claiming any apriori superiority for it with respect to competing views on the foundations of quantum mechanics. True, we feel that the Bohmian framework is able to address foundational issues with a clarity and crispness that are often rare in current debates but this has to do with a personal—as such, highly debatable—philosophical taste.

A last critical remark. The authors claim that FR involves the lightcone structure of the relativity theory just to provide a meaning to the idea of spacetime random variable, and “does not involve any assumptions about relativity theory” (p. 2). First, assuming the lightcone structure

*is*basically assuming relativity theory. Second, taking seriously the fact that the spacetime which is the arena of quantum measurements is at least a special-relativistic spacetime is essential in several respects: otherwise awkward properties would hold for QM, first of all signalling across distant regions since in a non-relativistic spacetime no limit to the travel of information can be postulated.The issue of free will assumptions in a quantum-mechanical context is in itself a highly delicate one, whose discussion clearly goes well beyond the scope of the present paper. For a recent formulation of a specific and detailed critical argument against the plausibility of the Colbeck-Renner FR assumption, see Ghirardi, Romano 2013.

Two further examples worth mentioning in the context of the present paper are the Conway and Specker’s

*Free Will Theorem*(Conway and Kochen 2006), criticized among others by Tumulka 2007 and Goldstein et al. 2010, and the Hardy’s*Quantum ontological excess baggage theorem*(Hardy 2004), criticized by Yong 2010.

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Laudisa, F. Against the ‘no-go’ philosophy of quantum mechanics.
*Euro Jnl Phil Sci* **4**, 1–17 (2014). https://doi.org/10.1007/s13194-013-0071-4

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DOI: https://doi.org/10.1007/s13194-013-0071-4