Related papers: Operational quantum theory without predefined time
It is brought forward that viable theories of the physical world that have no variable at all that can play the role of time, do not exist; some notion of time is one of the very first ingredients a candidate theory should possess. Almost…
We develop a notion of quantum observable for the general boundary formulation of quantum theory. This notion is adapted to spacetime regions rather than to hypersurfaces and naturally fits into the topological quantum field theory like…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
In modern physics, one of the greatest divides is that between space-time and quantum fields, as the fiber bundle of the Standard Model indicates. However on the operational grounds the fields and spacetime are not very different. To…
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime.…
Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantum circuits. The class of quantum…
The causal set approach to quantum gravity is based on the hypothesis that the underlying structure of spacetime is that of a random partial order. We survey some of the interesting mathematics that has arisen in connection with the causal…
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
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…
There is a deep structural link between acausal spacetimes and quantum theory. As a consequence quantum theory may resolve some "paradoxes" of time travel. Conversely, non-time-orientable spacetimes naturally give rise to electric charges…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within…
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…
In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems…
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of…
Our common understanding of the physical world deeply relies on the notion that events are ordered with respect to some time parameter, with past events serving as causes for future ones. Nonetheless, it was recently found that it is…
This paper outlines a mathematical framework of quantum probability in which the time asymmetry in describing measuring processes is avoided. The main objects of the framework are hyperfinite operations, which are constructed by using…