Related papers: A Possible Mathematical Structure for Physics
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
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…
We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are…
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…
The idea that possible configurations of a physical system can be represented as points in a multidimensional configuration space ${\cal C}$ is explored. The notion of spacetime, without ${\cal C}$, does not exist in this theory. Spacetime…
Basic concepts of theoretical particle physics, including quantum mechanics and Poincar\'e invariance, the leptonic mass spectrum and the proton mass, can be derived, without reference to first principles, from intrinsic properties of the…
A new kind of duality between the deep structures of spacetime and matter is proposed here, considering two partial orders which incorporate causality, extensity, and discreteness. This may have surprising consequences for the emergence of…
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…
We set out a fundamental ontology of atomism in terms of matter points. While being most parsimonious, this ontology is able to match both classical and quantum mechanics, and it remains a viable option for any future theory of cosmology…
Quantum theory and Lorentz structure are the twin pillars of fundamental physics today. With quantum theory kept and Lorentz structure replaced by Euclidean Jordan algebra --- a more fundamental structure, one naturally arrives at the…
We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are…
String theory is changing the relationship between mathematics and physics. The central role is played by the phenomenon of duality, which is intrinsic to quantum physics and abundant in string theory.
In our previous arXiv papers ("The Information and the Matter", v1, v5; more systematically the informational conception is presented in the paper "The Information as Absolute", 2010) it was rigorously shown that Matter in our Universe -…
We introduce an approach to the foundations of physics that is more in line with the foundations of mathematics. The idea is to examine current theories and find a set of starting physical assumptions that are sufficient to rederive them,…
Every physical theory has (at least) two different forms of mathematical equations to represent its target systems: the dynamical (equations of motion) and the kinematical (kinematical constraints). Kinematical constraints are…
Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as…
The representations of the world around in physics built with help of causality are analyzed and seems incomplete. The observer's causal representations form a closed logical system, i.e. the compact group related to cause-effect chains.…
The logic--linguistic structure of quantum physics is analysed. The role of formal systems and interpretations in the representation of nature is investigated. The problems of decidability, completeness, and consistency can affect quantum…
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…