相关论文: Some minor examples on discrete geometry

A monistic framework is set up where energy is the only fundamental substance. Different states of energy are ordered by a set of scalar qunatum-phase-fields. The dual elements of matter, mass and space, are described as volume- and…

We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…

A Planck scale inflationary era -- in a quantum gravity theory predicting discreteness of quantum geometry at the fundamental scale -- produces the scale invariant spectrum of inhomogeneities with very small tensor-to-scalar ratio of…

One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Various approaches towards developing such a theory of quantum gravity are pursued, but the lack of…

A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…

This work investigates in which form quantities with Planck dimensions occur already in the common quantum theory with local Lorentz symmetry. Since such Planck quantities as Planck length or Planck mass involve the Planck constant h, the…

Real world quantum systems are open to perpetual influence from the wider environment. Quantum gravitational fluctuations provide a most fundamental source of the environmental influence through their universal interactions with all forms…

Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, these extraordinarily small effects may in fact have a real and significant influence on our world. A calculation suggests that the minute…

The aim of this note is to address the low energy limit of quantum field theories with a minimal length scale. The essential feature of these models is that the minimal length acts as a regulator in the asymptotic high energy limit which is…

It is shown that in the model [3,4] of quantum mechanics besides probability amplitudes, the Planck constant and the Fock space, the cosmological constant also appear in the natural way. The Poisson brackets are generalized for the case of…

All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…

Assuming the holographic principle, the gravitational force can be formulated thermodynamically as an entropic force, but the mechanism by which the attraction between two masses occurs is not clear. The physical basis for the holographic…

The mechanism of low energy physics formation in the framework of multidimensional gravity is discussed. It is shown that a wide set of parameters of a primary theory could lead to the observable Universe. Quantum fluctuations of extra…

More recently, we have proposed a set of noncommutative space that describes the quantum gravity at the Planck scale [J. Phys. A: Math. Theor. 53, 115303 (2020)]. The interesting significant result we found is that, the generalized…

I describe a constructive foundation for Quantum Mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a…

In General Relativity, gravity around a black hole is universally regarded as an attractive force. However, quantum effects may significantly alter this classical picture and thus affect the dynamics of test particles. In this work, we…

We consider gravitational scattering of point particles with Planckian centre-of-mass energy and fixed low momentum transfers in the framework of general relativity and dilaton gravity. The geometry around the particles are modelled by…

We analyze the recent proposal of measuring a quantum gravity phenomenon in the lab by entangling two particles gravitationally. We give a generally covariant description of this phenomenon, where the relevant effect turns out to be a…

We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the…

Models for deterministic quantum mechanics of Cartan-Randers type are introduced, together with the fundamental notions of the concentration of measure theory. We explain how the application of the concentration of measure to Cartan-Randers…