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Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…
Physical systems are often simulated using a stochastic computation where different final states result from identical initial states. Here, we derive the minimum energy cost of simulating a complex data set of a general physical system…
This paper studies the energy decoherence of an interacting quantum system. It first reviews the experiments that motivated the postulates of quantum mechanics. It then discusses a decoherence that occurs dynamically in a closed system.…
From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…
The distinction between sciences is becoming increasingly more artificial -- an approach from one area can be easily applied to the other. More exciting research nowadays is happening perhaps at the interfaces of disciplines like Physics,…
Energy concepts are fundamental across the sciences, yet these concepts can be fragmented along disciplinary boundaries, rather than integrated into a coherent whole. To teach physics effectively to biology students, we need to understand…
The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…
Single particle models are sufficient for many topics in introductory physics courses, but become misleading when applied to situations involving changes in internal energy. This paper merges two parallel attempts to reform the teaching of…
It is indicated that principal models of computation are indeed significantly related. The quantum field computation model contains the quantum computation model of Feynman. (The term "quantum field computer" was used by Freedman.) Quantum…
This article is a short review on the concept of information. We show the strong relation between Information Theory and Physics, beginning by the concept of bit and its representation with classical physical systems, and then going to the…
Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity". To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
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…
We discuss the concept of energy packets in respect to the energy transported by electromagnetic waves and we demonstrate that this physical quantity can be used in physical problems involving relativistic effects. This refined concept…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum…
Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, $\mathbb{R}_+^4$ and $(-L/2,L/2)^4$, are considered where different types…