Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
What Is Computable? What Is Feasibly Computable? A Physicist's Viewpoint, Vladik Kreinovich, Olga Kosheleva
What Is Computable? What Is Feasibly Computable? A Physicist's Viewpoint, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
In this paper, we show how the questions of what is computable and what is feasibly computable can be viewed from the viewpoint of physics: what is computable within the current physics? what is computable if we assume -- as many physicists do -- that no final physical theory is possible? what is computable if we consider data processing, i.e., computations based on physical inputs? Our physics-based analysis of these questions leads to some unexpected answers, both positive and negative. For example, we show that under the no-physical-theory-is-perfect assumption, almost all problems are feasibly solvable -- but not all of …
Towards A Physics-Motivated Small-Velocities Approximation To General Relativity, Vladik Kreinovich, Olga Kosheleva
Towards A Physics-Motivated Small-Velocities Approximation To General Relativity, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
In the general case, complex non-linear partial differential equations of General Relativity are very hard to solve. Thus, to solve the corresponding physical problems, usually appropriate approximations are used. The first approximation to General Relativity is, of course, Newton's theory of gravitation. Newton's theory is applicable when the gravitational field is weak and when all velocities are much smaller than the speed of light. Most existing approximations allow higher velocities, but still limit us to weak gravitational fields. In this paper, he consider the possibility of a different approximation, in which strong fields are allowed but velocities are required to …
We Live In The Best Of Possible Worlds: Leibniz's Insight Helps To Derive Equations Of Modern Physics, Vladik Kreinovich, Guoqing Liu
We Live In The Best Of Possible Worlds: Leibniz's Insight Helps To Derive Equations Of Modern Physics, Vladik Kreinovich, Guoqing Liu
Departmental Technical Reports (CS)
To reconcile the notion of a benevolent and powerful God with the actual human suffering, Leibniz proposed the idea idea that while our world is not perfect, it is the best of possible worlds. This idea inspired important developments in physics: namely, it turned out that equations of motions and equations which describe the dynamics of physical fields can be deduced from the condition that the (appropriately defined) action functional is optimal. In practice, this idea is not always very helpful in physics applications: to fully utilize this fact, we need to how the action, and there are many possible …
Analysis Of Random Metric Spaces Explains Emergence Phenomenon And Suggests Discreteness Of Physical Space, Olga Kosheleva, Vladik Kreinovich
Analysis Of Random Metric Spaces Explains Emergence Phenomenon And Suggests Discreteness Of Physical Space, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, systems follow the pattern set by the second law of thermodynamics: they evolve from an organized inhomogeneous state into a homogeneous structure-free state. In many other practical situations, however, we observe the opposite emergence phenomenon: in an originally homogeneous structure-free state, an inhomogeneous structure spontaneously appears. In this paper, we show that the analysis of random metric spaces provides a possible explanation for this phenomenon. We also show that a similar analysis supports space-time models in which proper space is discrete.
Towards The Possibility Of Objective Interval Uncertainty In Physics. Ii, Luc Longpre, Olga Kosheleva, Vladik Kreinovich
Towards The Possibility Of Objective Interval Uncertainty In Physics. Ii, Luc Longpre, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Applications of interval computations usually assume that while we only know an interval containing the actual (unknown) value of a physical quantity, there is the exact value of this quantity, and that in principle, we can get more and more accurate estimates of this value. Physicists know, however, that, due to uncertainty principle, there are limitations on how accurately we can measure the values of physical quantities. One of the important principles of modern physics is operationalism -- that a physical theory should only use observable properties. This principle is behind most successes of the 20th century physics, starting with …