Quasi-set theory was developed to deal with collections of indistinguishable objects. In standard mathematics, there are no such kind of entities, for indistinguishability (agreement with respect to all properties) entails numerical identity. The main motivation underlying such a theory is of course quantum physics, for collections of indistinguishable (’identical’ in the physicists’ jargon) particles cannot be regarded as ’sets’ of standard set theories, which are collections of distinguishable objects. In this paper, a rationale for the development of such a theory is presented, motivated by Heinz Post’s claim that indistinguishability of quantum entities should be attributed ’right at the start’.Quasi-set theory was developed to deal with collections of indistinguishable objects. In standard mathematics, there are no such kind of entities, for indistinguishability (agreement with respect to all properties) entails numerical identity. The main motivation underlying such a theory is of course quantum physics, for collections of indistinguishable (’identical’ in the physicists’ jargon) particles cannot be regarded as ’sets’ of standard set theories, which are collections of distinguishable objects. In this paper, a rationale for the development of such a theory is presented, motivated by Heinz Post’s claim that indistinguishability of quantum entities should be attributed ’right at the start’.

Boletim da Sociedade Paranaense de MatemáticaJun 29, 200912 citations

Indistinguishability, the Pauli Principle (Quantum Mechanics)

Springer eBooksJan 20, 20060 citations

Algebraic aspects of quantum indiscernibility

Décio Krause, Hércules de Araújo Feitosa

Quasi-set theory was proposed as a mathematical context to investigate collections of indistinguishable objects. After presenting an outline of this theory, we define an algebra that has most of the standard properties of an orthocomplete orthomodular lattice, which is the lattice of the closed subspaces of a Hilbert space. We call the mathematical structure so obtained $\mathfrak{I}$ -lattice. After discussing, in a preliminary form, some aspects of such a structure, we indicate the next problem of axiomatizing the corresponding logic, that is, a logic which has $\mathfrak{I}$ -lattices as its algebraic models. We suggest that the intuitions that the `logic of quantum mechanics' would be not classical logic (with its Boolean algebra), is consonant with the idea of considering indistinguishability right from the start, that is, as a primitive concept. In other words, indiscernibility seems to lead `directly' to $\mathfrak{I}$ -lattices. In the first sections, we present the main motivations and a `classical' situation which mirrors that one we focus on the last part of the paper. This paper is our first study of the algebraic structure of indiscernibility within quasi-set theory.Quasi-set theory was proposed as a mathematical context to investigate collections of indistinguishable objects. After presenting an outline of this theory, we define an algebra that has most of the standard properties of an orthocomplete orthomodular lattice, which is the lattice of the closed subspaces of a Hilbert space. We call the mathematical structure so obtained $\mathfrak{I}$-lattice. After discussing, in a preliminary form, some aspects of such a structure, we indicate the next problem of axiomatizing the corresponding logic, that is, a logic which has $\mathfrak{I}$-lattices as its algebraic models. We suggest that the intuitions that the `logic of quantum mechanics' would be not classical logic (with its Boolean algebra), is consonant with the idea of considering indistinguishability right from the start, that is, as a primitive concept. In other words, indiscernibility seems to lead `directly' to $\mathfrak{I}$-lattices. In the first sections, we present the main motivations and a `classical' situation which mirrors that one we focus on the last part of the paper. This paper is our first study of the algebraic structure of indiscernibility within quasi-set theory.

arXiv:0902.3184Feb 18, 20090 citations

Dynamical quantum indistinguishability

Kostya Trachenko

arXiv:2104.07422Annals of PhysicsApr 22, 20223 citations

Quantum Identity and Indistinguishability

Holger Lyre

Springer eBooksJan 1, 20181 citation

Which Version of Quantum Mechanics is the Right One

Jiří Souček

In this article we consider four versions of quantum mechanics (QM), which form four different theories and which have the same experimental consequences (one of them is the standard QM). We consider six fundamental problems as criteria for the evaluation of these theories. The most successful is the modified QM introduced in [1] and described in the axiomatic form in [2], which solves all six problems. The least successful is the standard QM, which does not solve any of considered problems. (It seems that the standard QM is unable to solve any of these problems.) Other two theories solve some of problems and did not solve some other problems. On the base of this result we recommend to abandon the standard QM and to accept the modified QM as the right QM, since both variants have the same experimental content and the differences rest only in theoretical considerations.In this article we consider four versions of quantum mechanics (QM), which form four different theories and which have the same experimental consequences (one of them is the standard QM). We consider six fundamental problems as criteria for the evaluation of these theories. The most successful is the modified QM introduced in [1] and described in the axiomatic form in [2], which solves all six problems. The least successful is the standard QM, which does not solve any of considered problems. (It seems that the standard QM is unable to solve any of these problems.) Other two theories solve some of problems and did not solve some other problems. On the base of this result we recommend to abandon the standard QM and to accept the modified QM as the right QM, since both variants have the same experimental content and the differences rest only in theoretical considerations.

May 1, 20151 citation

\mathfrak{I}

-lattice. After discussing, in a preliminary form, some aspects of such a structure, we indicate the next problem of axiomatizing the corresponding logic, that is, a logic which has

\mathfrak{I}

-lattices as its algebraic models. We suggest that the intuitions that the `logic of quantum mechanics' would be not classical logic (with its Boolean algebra), is consonant with the idea of considering indistinguishability right from the start, that is, as a primitive concept. In other words, indiscernibility seems to lead `directly' to

\mathfrak{I}

-lattices. In the first sections, we present the main motivations and a `classical' situation which mirrors that one we focus on the last part of the paper. This paper is our first study of the algebraic structure of indiscernibility within quasi-set theory.