Related papers: Towards a Derivation of Space
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
We argue that quantum theory is a low-energy effective theory which emerges from some sub-quantum level theory which is of an undulatory and translocal character. We show the close connection of quantum theory with both gravity and the…
A notion of time is fundamental in the study of dynamical systems. Time arises as a standalone dynamical system and also in solutions or trajectories as a special kind of map between systems. We characterize time by a universal property and…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
Random walks of particles on a lattice are a classical paradigm for the microscopic mechanism underlying diffusive processes. In deterministic walks, the role of space and time can be reversed, and the microscopic dynamics can produce quite…
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
There is a formal analogy between the evolution of the universe, when this is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm,…
In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dynamics necessarily looks as though it is performing inference…
Shape is an important feature of physical systems although very seldom it is addressed in the framework of a quantitative description approach. In this paper we propose to interpret the shape of things as a physical manifestation of the…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
We define a random walk of a particle in $\mathbb{R}^3$ where the space is rotating. The particle is not glued to the space and will collide with it at random times, resulting in changes in its velocity and direction. After many collisions,…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
We propose that dark matter is not yet another new particle in nature, but that it is a remnant of quantum gravitational effects on known fields. We arrive at this possibility in an indirect and surprising manner: by considering retarded,…
A spinfoam model of 3D gravity non-minimally coupled with a scalar field is studied. By discretization of the scalar field, the model is worked out precisely in a purely combinational way. It is shown that the quantum physics of the scalar…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
The cosmological constant problem can be understood as the failure of the decoupling principle behind effective field theory, so that some quantities in the low-energy theory are extremely sensitive to the high-energy properties. While this…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…