Related papers: Classical Aspects of a Distributional 3+1 Foam Mod…
We show that quantum gravity yields exponentially growing gravitational waves. Without a mechanism to stop these modes from growing, the universe would go through a gravitational collapse. For Minkowski background, we propose a solution by…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
We conduct a detailed analysis of Nat'{a}rio's ``zero-expansion'' warp drive spacetime, focusing on scalar curvature invariants within the 3+1 formalism. This paper has four primary objectives: First, we establish the Petrov type…
A quantum mechanical model for an N + 1 dimensional universe arising from a quantum fluctuation is outlined. (3 + 1) dimensions are a closed infinitely-expanding universe and the remaining N - 3 dimensions are compact. The (3 + 1)…
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…
Suppose the usual description of spacetime as a 4-dimensional manifold with a Lorentzian metric breaks down at Planck energies. Can we still construct sensible theoretical models of the universe? Are they testable? Do they lead to a…
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…
We prove quantitative versions of the following statement: If a solution of the 1+1-dimensional wave equation has spatially compact support and consists mainly of positive frequencies, then it must have a significant high-frequency…
The physical phase of Causal Dynamical Triangulations (CDT) is known to be described by an effective, one-dimensional action in which three-volumes of the underlying foliation of the full CDT play a role of the sole degrees of freedom. Here…
{\sl A Hamiltonian framework for 2+1 dimensional gravity coupled with matter (satisfying positive energy conditions) is considered in the asymptotically flat context. It is shown that the total energy of the system is non-negative,…
Maxwells classic equations with fields, potentials, positive and negative charges in 3+1 spacetime are derived solely from the symmetry that is required by the Geometric Algebra of a 3+3 spacetime. The observed direction of time is…
In previous works, we suggested considering a (3+1)D quantum gravitational field as an evolution of a (2+1)D renormalized quantum gravitational field along the direction of the gravitational force. The starting point of the suggestion is a…
The generalized harmonic equations of general relativity are written in 3+1 form. The result is a system of partial differential equations with first order time and second order space derivatives for the spatial metric, extrinsic curvature,…
We suggest an alternative mathematical model for the electron in dimension 1+2. We think of our (1+2)-dimensional spacetime as an elastic continuum whose material points can experience no displacements, only rotations. This framework is a…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general…
An approximate model of a spacetime foam is presented. It is supposed that in the spacetime foam each quantum handle is like to an electric dipole and therefore the spacetime foam is similar to a dielectric. If we neglect of linear sizes of…
We illustrate the relationship between spin networks and their dual representation by labelled triangulations of space in 2+1 and 3+1 dimensions. We apply this to the recent proposal for causal evolution of spin networks. The result is…
This paper summarizes the motivations and results obtained so far in the frame of a particular non-linearization of Classical Electrodynamics, which was called Extended Electrodynamics. The main purpose pursued with this non-linear…
The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum…