Related papers: Understanding quantum mechanics: a review and synt…
The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
We discuss experimental situations that consist of multiple preparation and measurement stages. This leads us to a new approach to quantum mechanics. In particular, we introduce the idea of multi-time quantum states which are the…
A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
This article presents recent progress in the theory of quantum measurement engines and discusses the implications of them for quantum interpretations and philosophical implications of the theory. Several new measurement engine designs are…
Quantum mechanics is a cornerstone of our current understanding of nature and extremely successful in describing physics covering a huge range of scales. However, its interpretation remains controversial since the early days of quantum…
Quantum mechanics is more than the derivation of straightforward theorems about vector spaces, Hilbert spaces and functional analysis. In order to be applicable to experiment and technology, those theorems need interpretation and meaning.…
In a recently proposed interpretation of quantum mechanics, U. Mohrhoff advocates original and thought-provoking views on space and time, the definition of macroscopic objects, and the meaning of probability statements. The interpretation…
In this contribution I review rigorous formulations of a variety of limitations of measurability in quantum mechanics. To this end I begin with a brief presentation of the conceptual tools of modern measurement theory. I will make precise…
We search for a possible mathematical formulation of some of the key ideas of the relational interpretation of quantum mechanics and study their consequences. We also briefly overview some proposals of relational quantum mechanics for an…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
A new quantum ontology of quantum mechanics has been proposed recently. This ontology is based on impossible to realize measurements which need to be performed repeatedly on the same single physical system or on the same pair of physical…
The status of locality in quantum mechanics is analyzed from a nonstandard point of view. It is assumed that quantum states are relative, they depend on and are defined with respect to some bigger physical system which contains the former…
We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
We discuss a reconstruction of standard quantum mechanics assuming indistinguishability right from the start, by appealing to quasi-set theory. After recalling the fundamental aspects of the construction and introducing some improvements in…
Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…
This article was written in response to a request from an editor of American Vedantist. It is shown that the idea that consciousness is essential to understanding quantum mechanics arises from logical fallacies. This may be welcome news to…