4,358 research outputs found
Algebraic Quantum Mechanics and Pregeometry
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra
Aspects of Objectivity in Quantum Mechanics
The purpose of the paper is to explore different aspects of the covariance of (mostly) non-relativistic quantum mechanics. First, doubts are expressed concerning the claim that gauge fields can be 'generated' by way of imposition of (local) gauge covariance of the single-particle wave equation. Then a brief review is given of Galilean covariance in the general case of external fields, and the connection between Galilean boosts and gauge transformations. Under time-dependent translations (and hence non-instantaneous boosts) the geometric phase associated with Schrödinger evolution is non-invariant, and the significance of this result is briefly analysed. The covariance properties of Schrödinger dynamics are then brought to bear on certain versions of the modal interpretation of quantum mechanics. The conclusion that it is only relational properties that can be considered coordinate- or gauge-independent elements of reality is reinforced by appeal to the theory of quantum reference frames due to Aharonov and Kauffher. (This paper appeared in "From Physics to Philosophy", J. Butterfield and C. Pagonis (eds.), Cambridge University Press (1999); pp. 45-70.
On A New Formulation of Micro-phenomena: Basic Principles, Stationary Fields And Beyond
In a series of essays, beginning with this article, we are going to develop a
new formulation of micro-phenomena based on the principles of reality and
causality. The new theory provides with us a new depiction of micro-phenomena
assuming an unified concept of information, matter and energy. So, we suppose
that in a definite micro-physical context (including other interacting
particles), each particle is enfolded by a probability field whose existence is
contingent upon the existence of the particle, but it can locally affect the
physical status of the particle in a context-dependent manner. The dynamics of
the whole particle-field system obeys deterministic equations in a manner that
when the particle is subjected to a conservative force, the field also
experiences a conservative complex force which its form is determined by the
dynamics of particle. So, the field is endowed with a given amount of energy,
but its value is contingent upon the physical conditions the particle is
subjected to. Based on the energy balance of the particle and its associated
field, we argue why the field has a probabilistic objective nature. In such a
way, the basic elements of this new formulation, its application for some
stationary states and its nonlinear generalization for conservative systems are
discussed here.Comment: 35 pages, 5 figures, 3 appendice
On geometric relativistic foundations of matter field equations and plane wave solutions
In this paper, we start from the geometric relativistic foundations to define
the basis upon which matter field theories are built, and their wave solutions
are investigated, finding that they display repulsive interactions able to
reproduce the exclusion principle in terms of its effects in a dynamical way,
then discussing possible consequences and problems.Comment: 11 page
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