Related papers: Generalised Virial theorems in Classical and Quant…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
Several definitions for the average local value and local variance of a quantum observable are examined and compared with their classical counterparts. An explicit way to construct an infinite number of these quantities is provided. It is…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
We summarise and discuss some of our previous results, which show that Bohr's theory of the one-electron atom may be derived from the theory underpinning Quantum ElectroDynamics (QED) or vice versa, and that General Relativity may also be…
We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…
Quantum theory can be understood as pointing to an ontology of relations. I observe that this reading of quantum mechanics is supported by the ubiquity of relationality in contemporary fundamental physics, including in classical mechanics,…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal and Ville. We analyze the relationship between this formalism and geometry of the Galilei group, classical momentum…
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
In this note, we study the celebrated virial theorem for dissipative systems, both classical and quantum. The classical formulation is discussed and an intriguing effect of the random force (noise) is made explicit in the context of the…
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…
We generalize the virial theorem in f(R) modified gravity using the collisionless Boltzmann equation. We find supplementary geometric terms in the modified Einstein equation providing an effective contribution to the gravitational energy.…
Some consequences of a fully classical unified theory of gravity and electromagnetism are worked out for the electromagnetic sector such as the occurrence of classical light beams with spin and orbital angular momenta that are topologically…
We postulate the applicability of the general form-invariance principle in special relativity. It is shown that this principle holds in classical mechanics. Some examples of transformations between the reference frames which satisfy this…
Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we…
In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of…
Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…