arXiv subjects
Publications and source records attributed to Richard A. Mould.
A meaning is given to the state of a system that is consistent with the trans-coordinate physics previously proposed by the author. The collapse of such a state is described using the previously proposed q-rules. A Hamiltonian is defined for these states and it is shown that their square modulus is conserved. Keywords: invariance, state reduction, wave collapse.
An experiment is described that empirically distinguishes the previously proposed q-rules governing the collapse of a wave function, and contrasts it with the conventional idea of a collapse as well as the current leading theory of collapse advanced by Ghirardi and Pearle. Keywords: foundation theory, measurement, qRules, state reduction, wave collapse.
The q-rules are three auxiliary rules that guide the application of Schrodinger's equation. They are a set of instructions that describe how stochastic choices cause the wave to collapse and "start over" with new boundary conditions.
The auxiliary q-rules of quantum mechanics developed in other papers are applied to the problem of the location of material objects, both macroscopic and microscopic. All objects tend to expand in space due to the uncertainty in their momentum. The q-rules are found to oppose this perpetual expansion with a collapse mechanism that insures the dependable localization of objects in ordinary human experience.
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken from a novel limiting process are defined for a particle's wave function, allowing the particle's dynamic principle to operate locally without the use of coordinates. These differentials replace the covariant differentials of Riemannian geometry. With coordinates out of the way regional conservation principles and the Einstein field equation are no longer fundamentally defined; although they are constructible along with coordinate systems so they continue to be analytically useful. Gravity waves as presently understood are not defined, so we conclude that the gravitational detectors LIGO and Weber bar will not work. We assume that gravitons alone are fundamentally responsible for gravity. It is shown how gravitational uncertainty can be reconciled with the certainty of quantum mechanical dynamics. Keywords: covariance, invariance, geometry, gravitons, metric spaces, state reduction; 03.65.a, 03.65.Ta, 04.20.Cv
Quantum mechanics traditionally places the observer outside of the system being studied and employs the Born interpretation. In this and related papers the observer is placed inside the system. To accomplish this, special rules are required to engage and interpret the Schrodinger solutions in individual measurements. The rules in this paper (called the nRules) do not include the Born rule that connects probability with square modulus. It is required that the rules allow all conscious observers to exist inside the system without empirical ambiguity, reflecting our own unambiguous experience in the universe. This requirement is satisfied by the nRules. They allow both objective and observer measurements, so state reduction can occur with or without an observer being present. Keywords: brain states, consciousness, decoherence, epistemology, measurement, ontology, stochastic, state reduction, wave collapse.
We consider two straightforward rules that govern the stochastic choice in a single quantum mechanical event. They are shown to lead to absurd results if an objective state reduction is allowed to compete with an observer state reduction. Since the latter collapse is empirically verifiable, the existence of the former is thrown into question. Key Words: Born Interpretation, brain states, continuous observation, conscious observer, objective measurement, observer measurement, probability current, state reduction, wave collapse.
The effect of rule (4) on a series or parallel sequence of quantum mechanical steps is to insure that a conscious observer does not skip a step. This rule effectively places the observer in continuous contact with the system. Key Words: brain states, continuous observation, conscious observer, measurement, probability current, state reduction, wave collapse.
The author has proposed five rules that permit conscious observers to be included in quantum mechanics. In the present paper, these rules are applied to the observation of a non-local pair of correlated particles. Rule (4) again prevents an anomalous result. Two different kinds of relativistic state reduction are considered, where these differ in the way that they impose boundary conditions in Minkowski space. In response to a problem that arises in this context, we require the Lorentz invariance of stochastic hits. And finally, it is claimed that the rules proposed by the author are themselves relativistically covariant with some qualification. Key Words: brain states, boundary conditions, consciousness, decoherence, macroscopic superposition, probability current, von Neumann, wave collapse.
This paper elaborates on four previously proposed rules of engagement between conscious states and physiological states. A new rule is proposed that applies to a continuous model of conscious brain states that cannot precisely resolve eigenvalues. If two apparatus states are in superposition, and if their eigenvalues are so close together that they cannot be consciously resolved on this model, then it is shown that observation will not generally reduce the superposition to just one of its member eigenstates. In general, the observation of a quantum mechanical superposition results in another superposition. Key words: Brain states, consciousness, conscious observer, macroscopic superposition, measurement, state reduction, state collapse, von Neumann.
In a previous paper, the author proposed a quantum mechanical interaction that would insure that the evolution of subjective states would parallel the evolution of biological states, as required by von Neumann's theory of measurement. The particular model for this interaction suggested an experiment that the author has now performed wih negative results. A modified model is outlined in this paper that preserves the desirable features of the original model, and is consistent with the experimental results. This model will be more difficult to verify. However, some strategies are suggested.