Related papers: Quantum-Mechanical Dualities on the Torus
We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Is the universe digital or analog? In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. That quantum physics does so is no surprise. That classical physics…
In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…
We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
$P$-divisibility is a central concept in both classical and quantum non-Markovian processes; in particular, it is strictly related to the notion of information backflow. When restricted to a fixed commutative algebra generated by a complete…
The appearance of infinity together with collapsing quantum state due to the observation or interaction, which are two challenging features of quantum field theory, become very serious problems in quantum gravity as well as in quantum…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
Elementary particles in quantum mechanics (QM) are indistinguishable when sharing the same intrinsic properties and the same quantum state. So, we can consider quantum particles as non-individuals, although non-individuality is usually…
In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…
Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
This paper traces an intellectual journey or \textit{Way} (in the sense of a Tao) that starts with some unfinished work of Gian-Carlo Rota on making a logic of equivalence relations or partitions. Rota understood the category-theoretic…
In this essay a quantum-dualistic, perspectival and synchronistic interpretation of quantum mechanics is further developed in which the classical world-from-decoherence which is perceived (decoherence) and the perceived…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
Quantum mechanics in the Wigner-von Neumann interpretation is presented. This is characterized by 1) a quantum dualism between matter and consciousness unified within an informational neutral monism, 2) a quantum perspectivism which is…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
The Classical Twin Paradox is widely dealt in literature and neatly resolved. In addition, it is also well known that, when looking at two systems which are boosted relative to each other, the concept of the simultaneous effect of a quantum…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…