Related papers: On the assumptions underlying KS-like contradictio…
We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables which is a consequence of the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on…
Fully revealing the mathmatical structure of quantum contextuality is a significant task, while some known contextuality theories are only applicable for rank-1 projectors. That is because they adopt the observable-based definitions. This…
Contextuality is a key feature of quantum mechanics, as was first brought to light by Bohr and later realised more technically by Kochen and Specker. Isham and Butterfield put contextuality at the heart of their topos-based formalism and…
We present two geometric proofs of the Kochen-Specker theorem. A quite similar argument has been used by Cooke, Keane, and Moran, as well as by Kalmbach in her book to derive the Gleason theorem.
The notorious Wigner's friend thought experiment (and modifications thereof) has in recent years received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In…
Theoretical physics has faced many challenges since the advent of quantum mechanics. Recently, Frauchiger and Renner have presented a no-go theorem, which makes quantum mechanics more controversial. However, from our perspective, the…
The Kochen-Specker theorem states that a 3-dimensional complex Euclidean space admits a finite configuration of projective lines such that the corresponding quantum observables (the orthogonal projectors) cannot be assigned with 0 and 1…
We present a systematic, constructive analysis of Kochen-Specker contextuality, emphasizing the foundational importance of complete orthogonal bases (contexts). First, in three dimensions, we generate a complete inventory of 165 rays and…
The structure of a complete lattice formed by closed linear subspaces of a Hilbert space (i.e., a Hilbert lattice) entails some unreasonable consequences from the physical point of view. Specifically, this structure seems to contradict to…
In this paper we consider theories in which reality is described by some underlying variables. Each value these variables can take represents an ontic state (a particular state of reality). The preparation of a quantum state corresponds to…
In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper "scrambling" of two…
Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S^2, can be colored so that the contradiction with hidden…
A recent no-go theorem (Frauchiger and Renner, 2018) establishes a contradiction from a specific application of quantum theory to a multi-agent setting. The proof of this theorem relies heavily on notions such as 'knows' or `is certain…
The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism, the essence of the theorem is the lack of a joint probability distributions for some experiment settings. In this…
We present an elementary proof of a reduced version of Gleason's theorem and the Kochen-Specker theorem to provide a novel perspective on the relation between both theorems. The proof is based on a set of linear equations for the values of…
In the topos approach to quantum theory of Doering and Isham the Kochen-Specker Theorem, which asserts the contextual nature of quantum theory, can be reformulated in terms of the global sections of a presheaf characterised by the Gelfand…
Unspeakable coherence is a key feature separating quantum and classical physics. Modelled as asymmetry with respect to a continuous transformation generated by a physically relevant observable, such as the Hamiltonian or angular moment,…
We show that a reduced form of the structural requirements for deterministic hidden variables used in Bell-Kochen-Specker theorems is already sufficient for the no-go results. Those requirements are captured by the following principle: an…
Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present…
A thought experiment is described and the probability of a particular type of results is predicted according to the quantum formalism. Then, the assumption is made that there exists a particle that travels from the source to one of the…