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Minimum Spacetime Length and the Thermodynamics of Spacetime.

Valeria Rossi1,2, Sergio L Cacciatori1,2, Alessandro Pesci3

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Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

Emergent gravity theories link entropy and spacetime geometry using thermodynamics. A minimum spacetime length, implemented via a quantum metric, explains gravity

Keywords:
emergent gravityhorizon thermodynamicsminimum lengthquantum gravity

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • Thermodynamics

Background:

  • Emergent gravity theories connect spacetime geometry with entropy through a thermodynamic perspective.
  • Macroscopic gravity properties are viewed as statistical outcomes of spacetime's discrete small-scale structure and information content.

Purpose of the Study:

  • To review how quantum gravity theories generally imply a minimum spacetime length.
  • To describe a method for implementing this structure independently of quantum fluctuation details.
  • To discuss how microscopic entropy can generate gravitational field equations via thermodynamics.

Main Methods:

  • Review of quantum gravity theories predicting a minimum spacetime length.
  • Implementation of a discrete spacetime structure using a bi-tensorial quantum metric qαβ(x,x').
  • Application of a thermodynamic variational principle to derive gravitational field equations.

Main Results:

  • Quantum gravity theories generally support a minimum spacetime length.
  • A bi-tensorial quantum metric provides a finite geodesic distance, ensuring a discrete spacetime structure.
  • The proposed framework successfully derives gravitational field equations from entropy and thermodynamics.

Conclusions:

  • A discrete spacetime structure with a minimum length is a general feature of quantum gravity.
  • The bi-tensorial quantum metric offers a robust way to implement this structure.
  • Thermodynamic principles applied to microscopic degrees of freedom can explain emergent gravity.