Related papers: Numerical search for a fundamental theory
It is discussed and surveyed a numerical method proposed before, that alternative to the usual compression method, provides an approximation to the algorithmic (Kolmogorov) complexity, particularly useful for short strings for which…
Different observers do not have to agree on how they identify a quantum system. We explore a condition based on algorithmic complexity that allows a system to be described as an objective "element of reality". We also suggest an…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the…
Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as…
Several mathematical problems can be modeled as a search in a database. An example is the problem of finding the minimum of a function. Quantum algorithms for solving this problem have been proposed and all of them use the quantum search…
I review the reason for considering the prime purpose of the program of measurements of the fundamental parameters of cosmology to be the tests of cosmological models. I comment on the philosophy by which we are approaching this goal, offer…
First we consider pair-wise distances for literal objects consisting of finite binary files. These files are taken to contain all of their meaning, like genomes or books. The distances are based on compression of the objects concerned,…
Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…
The laws of physics have a set of fundamental constants, and it is generally admitted that only dimensionless combinations of constants have physical significance. These combinations include the electromagnetic and gravitational fine…
The observed constraints on the variability of the proton to electron mass ratio $\mu$ and the fine structure constant $\alpha$ are used to establish constraints on the variability of the Quantum Chromodynamic Scale and a combination of the…
It is conjectured that in the geometric formulation of quantum computing, one can study quantum complexity through classical entropy of statistical ensembles established non-relativistically in the group manifold of unitary operators. The…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
Precision spectroscopy has long played a central role in testing the foundations of physics, from the early insights that led to the development of quantum mechanics to the validation of quantum electrodynamics and the determination of…
Attempts to understand zero temperature phase transitions have forced physicists to consider a regime where the standard paradigms of condensed matter physics break down [1-4]. These quantum critical systems lack a simple description in…
A quantum mechanical search procedure to determine the real zeros of a polynomial is introduced. It is based on the construction of a spin observable whose eigenvalues coincide with the zeros of the polynomial. Subsequent quantum mechanical…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory.…
Cosmography is a phenomenological and relatively model-independent approach to cosmology, where physical quantities are expanded as a Taylor series in the cosmological redshift, or in related variables. Here we apply this methodology to…