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Area of Science:

  • Theoretical Physics
  • Quantum Gravity

Background:

  • Quantum gravity (QG) theories are inherently non-deterministic due to quantum mechanics.
  • Current QG theories often rely on a multiverse spacetime representation.
  • A Heisenberg Generalized Uncertainty Principle (GUP) is crucial for deterministic QG.

Purpose of the Study:

  • To establish a physical realizability condition for quantum gravity theories.
  • To investigate the implications of a covariant Heisenberg GUP for spacetime structure.
  • To identify QG theories compatible with fundamental physical principles.

Main Methods:

  • Derivation of a Heisenberg GUP from first principles.
  • Formulation of the GUP in covariant 4-tensor form.
  • Introduction of the "quantum covariance criterion" for physical realizability.

Main Results:

  • The Heisenberg GUP imposes a "quantum covariance criterion" for physically admissible spacetimes.
  • Most current QG theories (e.g., string theory, loop quantum gravity) fail this criterion.
  • Theories with a universe representation, where variational and metric tensors differ, satisfy the GUP and criterion.

Conclusions:

  • A universe representation offers a viable alternative for quantum gravity theories.
  • The quantum covariance criterion acts as a selection rule for viable QG models.
  • Satisfying the Heisenberg GUP is essential for a physically realizable quantum gravity theory.