Space-time structure and measurement theory

George Svetlichny

The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of joint probabilities of events in space-time according to whether the separation is space-like or time-like, a relativistic nonlinear or stochastic quantum theory may be possible.

K. Datta

M. Toller

Hemant Kumar Kushwaha

This document presents the author’s preprint version of Total State–Space Coexistence Theory, a structural framework addressing time, probability, multiplicity, and experience. The work treats time as an ordering relation rather than a flowing entity, probability as a structural measure over coexisting outcomes, and experience as index-local access within a complete state-space. Classical paradoxes related to time, measurement, and single-history assumptions are handled through structural separation rather than elimination. This preprint is intended for academic reference and archival purposes.The formally published edition of this work is available via Amazon KDP in paperback and Kindle formats.

Dorje C. Brody, Lane P. Hughston

Abstract The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is endowed with a natural positive-definite Riemannian metric that accommodates the underlying geometry of the indefinite Minkowski space metric, together with its symmetry group. A unitary representation of the 15-parameter group of conformal transformations can then be constructed that acts upon the Hilbert space of square-integrable holomorphic functions on the future tube. These structures are enough to allow one to put forward a quantum theory of phase-space events. In particular, a theory of quantum measurement can be formulated in a relativistic setting, based on the use of positive operator valued measures, for the detection of phase-space events, hence allowing one to assign probabilities to the outcomes of joint space-time and four-momentum measurements in a manifestly covariant framework. This leads to a localization theorem for phase-space events in relativistic quantum theory, determined by the associated Compton wavelength.

Wolfram Schommers