Related papers: An electrical engineering perspective on naturalit…
An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}'…
More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
This is an essay in what might be called ``mathematical metaphysics.'' There is a fundamental duality that run through mathematics and the natural sciences. The duality starts as the logical level; it is represented by the Boolean logic of…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
We consider a notion of "numerosity" for sets of tuples of natural numbers, that satisfies the five common notions of Euclid's Elements, so it can agree with cardinality only for finite sets. By suitably axiomatizing such a notion, we show…
It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do…
Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…
The usual action integral of classical electrodynamics is derived starting from Lanczos's electrodynamics -- a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell's equations interpreted…
It is demonstrated that energy conservation allows for a straight derivation of Newtonian mechanics without an apriori definition of the concept of work. Furthermore it is shown that energy must be depicted as a function of position and…
Some of the basic concepts of topology are explored through known physics problems. This helps us in two ways, one, in motivating the definitions and the concepts, and two, in showing that topological analysis leads to a clearer…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…