Related papers: From nothing to something: discrete integrable sys…
A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum…
The Heisenberg uncertainty principle is one of the most famous features of quantum mechanics. However, the non-determinism implied by the Heisenberg uncertainty principle --- together with other prominent aspects of quantum mechanics such…
The experience from Quantum Information has lead us to look at Quantum Theory (QT) and the whole Physics from a different angle. The information-theoretical paradigm---"It from Bit'---prophesied by John Archibald Wheeler is relentlessly…
Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and quantum physics. Essential tools for its…
There is natural association of entropy with gravitational systems on one hand and partition of natural numbers on the other hand. We show that given a partition of natural numbers, it is possible to directly associate a metric with it.…
It is suggested that the Einstein equation can be derived from Landauer's principle applied to an information erasing process at a local Rindler horizon and Jacobson's idea linking the Einstein equation with thermodynamics. When matter…
We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in this respect, namely quad-graphs, the cellular…
Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using simple thought experiments, that quantum theory follows from decompositional equivalence…
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
To explain conceptual gap between classical/quantum and other, hypothetical descriptions of world, several principles has been proposed. So far, all these principles have not explicitly included the uncertainty relation. Here we introduce…
Incompleteness theorems of Godel, Turing, Chaitin, and Algorithmic Information Theory have profound epistemological implications. Incompleteness limits our ability to ever understand every observable phenomenon in the universe.…
What does it mean for a causal structure to be `unknown'? Can we even talk about `repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary,…
In these lectures I propose to push Einstein's principle of coordinate independence to the extreme in order to restrict the possible form of fundamental equations of motion in physics. I start from nearly tautological system theoretic…
We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to…
Environmentally-induced superselection or "einselection" has been proposed as an observer-independent mechanism by which apparently classical systems "emerge" from physical interactions between degrees of freedom described completely…
At the mesoscopic scales --- which interpolate between the macroscopic, classical, geometry and the microscopic, quantum, structure of spacetime --- one can identify the density of states of the geometry which arises from the existence of a…
The Friedmann equations of universe dynamics describe the infinite number of the Friedmannian models of universe. The consistent and distinguished relativistic, classical-mechanical, quantum-mechanical and formal-logical analysis of the…
After more than a century since its birth, Quantum Theory still eludes our understanding. If asked to describe it, we have to resort to abstract and ad hoc principles about complex Hilbert spaces. How is it possible that a fundamental…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
In our previous arXiv papers (more systematically the informational conception is presented in the paper "The Information as Absolute", 2010) it was rigorously shown that Matter in our Universe - and Universe as a whole - are some…