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Quantum Gravitational Force Between Polarizable Objects.

L H Ford1, Mark P Hertzberg1, J Karouby1

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Quantum corrections to gravity reveal a new force between polarizable objects. This two-graviton exchange effect, analogous to atomic forces, depends on object polarizability and distance.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • Gravitational Interactions

Background:

  • General relativity as a low-energy effective field theory allows quantum corrections.
  • Quantum effects, like Casimir-Polder and London-van der Waals forces, are known for atomic interactions.

Purpose of the Study:

  • To compute a quantum correction to the gravitational potential between two distant polarizable objects.
  • To investigate the force arising from induced quadrupole moments due to two-graviton exchange.

Main Methods:

  • Calculating the quantum force from induced quadrupole moments via two-graviton exchange.
  • Analyzing the shift in vacuum energy of metric fluctuations due to object polarizability.
  • Computing the potential energy across various distances, including far (retarded) and near regimes.

Main Results:

  • A novel quantum gravitational force is derived.
  • The potential energy in the far-distance regime is V(r)=-3987ℏcG²α₁Sα₂S/(4πr¹¹).
  • α₁S and α₂S represent the static gravitational quadrupole polarizabilities of the objects.

Conclusions:

  • Quantum mechanics introduces corrections to classical gravitational forces.
  • The derived force provides a new mechanism for gravitational interaction between massive bodies.
  • Estimates for the magnitude of this quantum gravitational effect are provided.