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Past and future blurring at fundamental length scale.

M J Neves1, C Farina, M V Cougo-Pinto

  • 1Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Urca, Rio de Janeiro, RJ, 22290-180, Brasil.

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The study introduces κ-deformed Green functions, revealing blurred causality and a smeared light cone. This suggests a fundamental length scale (q) where spacetime points become fuzzy regions, supporting Heisenberg's concept.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Spacetime Structure

Background:

  • Causality and light cone structure are fundamental in relativistic physics.
  • Deformed theories explore modifications to standard spacetime concepts.
  • Heisenberg proposed a fundamental length scale, suggesting a fuzzy spacetime.

Purpose of the Study:

  • To investigate the implications of κ-deformation on Green functions.
  • To analyze the causality properties and light cone structure in κ-deformed theories.
  • To explore the physical interpretation of the deformation parameter q.

Main Methods:

  • Derivation of κ-deformed retarded and advanced Green functions.
  • Analysis of causality conditions within the deformed framework.
  • Examination of the light cone structure in the presence of the deformation.

Main Results:

  • The κ-deformed Green functions exhibit blurred causality over a length scale q = 1/(2κ).
  • A smearing of the light cone is observed in the deformed theory.
  • The results indicate a departure from point-like spacetime events.

Conclusions:

  • The parameter q, derived from κ-deformation, represents a fundamental length scale.
  • This scale suggests that spacetime points are not precise but rather fuzzy regions.
  • The findings align with Heisenberg's early ideas on spacetime quantization and fuzzy geometry.