Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given (...) probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise. (shrink)

A physical mechanical sequence is proposed representing measurement interactions ‘hidden' within QM's proverbial ‘black box'. Our ‘beam splitter' pairs share a polar angle, but head in opposite directions, so ‘led' by opposite hemisphere rotations. For orbital ‘ellipticity', we use the inverse value momentum ‘pairs' of Maxwell's ‘linear' and ‘curl' momenta, seen as vectors on the Poincare spherical surface. Values change inversely from 0 to 1 over 90 degrees, then ± inverts.. Detector polarising screens consist of electrons with the same vector (...) distributions, but polar angles set independently by A & B. The absorption/re-emission interaction process is modelled as surface vector additions at the angle of polar latitude of each interaction. This ‘collapse' of characteristic ‘wave values' is really then simply ‘re-polarisation', with new ellipticity. We then obtain the relation Cosθ at polarisers. We may simplify this to new ellipses with major/minor axis values. Considering as spherical orbital angular momentum rotation we invoke the unique quality of spheres to rotate concurrently on three axes! Rotating on y or z axes concurrent with x axis spin can return surface points to starting positions with non-integer x axis rotations, from half to infinity!. Second interactions at photomultiplier/ analysers are identical but at two orthogonal ‘channels'. Vector addition interactions at BOTH channel orientations normally produce a vector value of adequate amplitude to give a *click* from the MAJOR axis direction. At the ‘crossover' points at near circular polarity the orthogonal ‘certainty' is ~ 50:50, so both or neither channels may produce a ‘click'. The apparently unphysical but proved ‘Malus' law' relation; Cos2θ emerges physically from the 2nd set of interactions. The main departure from QM's assumptions are; That the original pair members each actually possessed two inverse momenta sets; ‘curl' and ‘linear'. Also that complex ‘vector additions' of those pairs occurs. Vector quantities allow A & B to reverse their OWN finding by reversing dial setting, reproducing experimental outputs without problematic ‘non-locality'. (shrink)

An appropriate kind of curved Hilbert space is developed in such a manner that it admits operators of $\mathcal{C}$ - and $\mathfrak{D}$ -differentiation, which are the analogues of the familiar covariant and D-differentiation available in a manifold. These tools are then employed to shed light on the space-time structure of Quantum Mechanics, from the points of view of the Feynman ‘path integral’ and of canonical quantisation. (The latter contains, as a special case, quantisation in arbitrary curvilinear coordinates when space is (...) flat.) The influence of curvature is emphasised throughout, with an illustration provided by the Aharonov-Bohm effect. (shrink)

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak assumptions, and (...) from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed. (shrink)

This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some inconsistencies (...) of the CI, and gives intuitive explanations of some previously mysterious quantum effects. (shrink)