On the Sharpness of Localization of Individual Events in Space and Time

Krzysztof Ruebenbauer

Rudolf Haag

Abstract Apparent paradoxes in Quantum Physics demand a sharp distinction between a "real part of the world" and the realm of possibilities. In the former we may distinguish individual elements (coarse events) relating to space-time, with causal connections between them respecting the relativistic locality principle. The latter, quantitatively described by probability assignments conditioned on existing facts and depending on the definition of equivalence classes of situations, cannot be subdivided in space-time categories. There are global correlations (Pauli principle...). The cut between the realms of facts and possibilities implies an evolutionary picture of the "real world" in which the (generalized) arrow of time assumes basic significance. Some deficiencies of existing theory are pointed out.

Eugene T. Gendlin, J. Lemke

Kurt Bräuer

Abstract The quantum mechanical model under consideration describes a particle beam under the influence of an oscillator. Bohm’s causal interpretation of quantum mechanics is used to calculate trajectories of the particles. Individual quantum events are defined by the intersection of the beam particle trajectories and the particle detector. The time sequence of individual quantum events is interpreted as a time series and is analyzed by linear and nonlinear methods, which involves reconstruction and investigation of the system in an embedding space. The Fourier amplitudes and the fill factors show white noise, however the Karhunen-Loeve components indicate the influence of the oscillator on the beam particles. In this model individual quantum events carry information which can be detected by the Karhunen-Loeve ex-pansion.

Ping Sheng

Djordje Minić, Hsiung Chia Tze

The geometric form of standard quantum mechanics is compatible with the two postulates: (1) the laws of physics are invariant under the choice of experimental setup and (2) every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite-dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics.