相关论文: Quantum Quandaries: a Category-Theoretic Perspecti…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
A four dimensional generally covariant field theory is presented which describes non-dynamical three geometries coupled to scalar fields. The theory has an infinite number of physical observables (or constants of the motion) which are…
The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic…
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…
Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical…
I take non-locality to be the Michaelson Morley experiment of the 21st Century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but emergent from entangled coherent…
We study the apparent tension between locality and unitarity for symmetries in quantum field theory. This emerges in the context of categorical symmetries where symmetry operators are generically non-invertible. We argue that locality…
We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum…
At present, quantum theory leaves unsettled which quantities ontologically, physically exist in a quantum system. Do observables such as energy and position have meaningful values only at the precise moment of measurement, as in the…
A quantum physical projector is proposed for generally covariant theories which are derivable from a Lagrangian. The projector is the quantum analogue of the integral over the generators of finite one-parameter subgroups of the gauge…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of light $c$ not being infinite calls for a redefinition of space-time on large and cosmological scales,…
The problem of time in canonical quantum gravity is related to the fact that the canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to…
According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…
Cirelli, Mani\`{a} and Pizzocchero generalized quantum mechanics by K\"{a}hler geometry. Furthermore they proved that any unital C$^{*}$-algebra is represented as a function algebra on the set of pure states with a noncommutative…
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and…
We relate three-dimensional loop quantum gravity to the combinatorial quantisation formalism based on the Chern-Simons formulation for three-dimensional Lorentzian and Euclidean gravity with vanishing cosmological constant. We compare the…