相关论文: The Mathematical Universe in a Nutshell
The theory that all processes in the universe are computational is attractive in its promise to provide an understandable theory of everything. I want to suggest here that this pancomputationalism is not sufficiently clear on which problem…
The physical models of a successful unified theory about the Universe must operate in different phase of matter evolution and different fields of physics. The attempts to build such wide range theory as a bunch of theories developed for…
The triumphs of the Standard Model of Particle Physics call attention upon an old idea, that the so-called vacuum is an accessible physical medium, and not just a tautology. I take this idea as a serious working hypothesis, and I suggest a…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
The paper presents several quantum models constructed with the formalism of algebraic geometry. The Universe is presented as a presheaf on the "space of ultimation" (i.e. the branching future) with values in certain category which enhances…
Despite the success of modern physics in formulating mathematical theories that can predict the outcome of experiments, we have made remarkably little progress towards answering the most fundamental question of: why is there a universe at…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by…
Merely by existing, all physical systems register information. And by evolving dynamically in time, they transform and process that information. The laws of physics determine the amount of information that a physical system can register…
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
The development of science and technology has progressively demonstrated the ability of humankind to understand and manipulate the physical world, and it has also shown some fundamental limitations to predictability of physical events. This…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
We have already shown how a modified Friedmann equation, originating from a model of the Universe built from a certain $W_3$ algebra, is able to explainthe difference between the Hubble constants extracted from CMB data and from local…
The role of mathematics in physical sciences is discussed, particularly how higher mathematics found applications in empirical problems. Several examples are given to illustrate this role.
In this paper we work out a multiverse scenario whose physical characteristics enable us to advance the following the conjecture that whereas the physics of particles and fields is confined to live in the realm of the whole multiverse…
According to observations, in our Universe for gravitational phenomena in a Newtonian approximation the Newtonian non-modified relations are valid. The Friedmann equations of universe dynamics describe infinite number of relativistic…
I discuss some compelling suggestions about particles which could be the dark matter in the universe, with special attention to experimental searches for them.
A basic modern picture of the universe is given here. The lectures start from the historical ideas of a static universe. Then I move on to Newtonian cosmology and derive the main cosmological equations in the framework of Newtonian…
This contribution presents the cosmological models with extra dimensions that have been recently elaborated, which assume that ordinary matter is confined on a surface, called brane, embedded in a higher dimensional spacetime.