Space-time uncertainty relation and operational definition of dimension

Abstract

Operational definition of space-time in light of quantum mechanics and general relativity inevitably indicates an intrinsic imprecision in space-time structure which has to do with space-time dimension as well. The operational dimension of space-time turns out to be a scale dependent quantity slightly smaller than four at distances $\gg l_P$. Close to the Planck length the deviation of space-time dimension from four becomes appreciable. The experimental bounds on the deviation of space-time dimension from four coming from the electron $\mathtt{g}-2$ factor, Lamb shift in hydrogen atom and the perihelion shift in the planetary motion are still far from the theoretical predictions.

5 pages

References in corpus (7)

• Effective Field Theory, Black Holes, and the Cosmological Constant
• A Generalized Uncertainty Principle in Quantum Gravity
• Entropy Bounds and Black Hole Remnants
• Quantum Measurement, Gravitation, and Locality
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Cited by in corpus (5)

• Light incoherence due to quantum-gravitational fluctuations of the background space
• Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space-time dimension
• Quantum-gravitational corrections to the hydrogen atom and harmonic oscillator
• Quantum-gravitational running/reduction of space-time dimension
• Random versus holographic fluctuations of the background metric. II. Note on the dark energies arising due to microstructure of space-time