Related papers: What is the Mathematical Structure of Quantum Spac…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
On the basis that the universe is a closed quantum system with no external observers, we propose a paradigm in which the universe jumps through a series of stages. Each stage is defined by a quantum state, an information content, and rules…
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
By virtue of harmonic maps on two-dimensional spheres (S$^{2}$), a topological quantization in spacetime is proposed. The discrete character of all physical quantities follows naturally. A Schwarzschild black hole, non-black hole and…
In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
We propose a mathematically concrete way of modelling the suggestion that in quantum gravity the spacetime disappears, replacing it with a discrete approximation to the causal path space described as an object in a model category. One of…
A new concept of the constitution of Nature is proposed. The constructed submicroscopic quantum mechanics is deterministic and is characterised by elementary excitations of the space net that is treated as the tessellation of balls, or…
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…
We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. In Section 2, we introduce topos theory,…
Quantum gravity is known to be mostly a kind of metaphysical speculation. In this brief essay, we try to argue that, although still extremely difficult to reach, observational signatures can in fact be expected. The early universe is an…
We review certain emergent notions on the nature of spacetime from noncommutative geometry and their radical implications. These ideas of spacetime are suggested from developments in fuzzy physics, string theory, and deformation…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to…
The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using…
Loop quantum gravity is a perspective candidate for the quantum theory of gravity. However, there is a conceptual controversy in it: having started from the Einstein-Hilbert action and describing spacetime without matter, we can hardly…
We examine spectrum of the physical volume operator within the non-standard loop quantum cosmology. The spectrum is discrete with equally distant levels defining a quantum of the volume. The discreteness may imply a foamy structure of…
We derive the black hole solutions with horizons of non-trivial topology and investigate their properties in the framework of an approach to quantum gravity being an extension of Bohm's formulation of quantum mechanics. The solutions we…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
The idea that spacetime geometry is built from quantum entanglement has been widely accepted in the last years. But how exactly the geometry is related with quantum states is still unclear. In this note, based on the idea of deep learning,…