Related papers: Computability and Physical Theories
The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming…
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories.The algebraic tools…
After a long technical and consequently philosophical disgression about the necessity of the construction presented in this book, a logically consistent and precise theory of quantum gravity is presented. The construction of this theory…
General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper we build a framework for probabilistic theories with non-fixed causal…
We comment on the fact that certain mathematical models that have been proposed in the quantum gravity literature, may not be subject to experimental checks, even if they turn out to be mathematically well defined. This means that they…
Quantum theory is incredibly successful, explaining the microscopic world with great accuracy, from the behaviour of subatomic particles to chemical reactions to solid-state electronics. There is not a single experimental finding…
Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field…
Quantum theory was radically different from the theories of nature which came before it. One key difference was its use of complex numbers. This opened a longstanding debate over whether quantum theory fundamentally requires complex numbers…
We review some of the well-known features of quantum cosmology, such as the factor ordering problem, the wave function and the density matrix, for a dark energy dominated universe, where analytical solutions can be obtained. For the…
Anthropic models can give testable predictions, which can be confirmed or falsified at a specified confidence level. This is illustrated using the successful prediction of the cosmological constant as an example. The history and the nature…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
We show that the quantum computational speedup of quantum algorithms is due to their teleological character, their being evolutions toward a goal (the solution of the problem) with an attractor in the very goal they will produce in the…
Suspicions that the world might be some sort of a machine or algorithm existing ``in the mind'' of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
When one takes into account gravitation, the measurement of space and time cannot be carried out with infinite accuracy. When quantum mechanics is reformulated taking into account this lack of accuracy, the resolution of the measurement…
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…
The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However,…