[Paper Review] Spin-compatible construction of a consistent quantum gravity model from minimum information

Pierre-André Mandrin|arXiv (Cornell University)|Aug 8, 2014

Black Holes and Theoretical Physics7 references3 citations

TL;DR

This paper proposes a background-independent quantum gravity model—Minimum Information Quantum Gravity (MIQG)—that derives general relativity and quantum field theory from thermodynamic principles, quantum number conservation, and maximal entropy per imposed degree of freedom. Using the tetrad formalism, it derives a spin-compatible action where torsion arises from fermionic spin, unifying gravity and matter without requiring a fundamental spacetime or variational principle at the microscopic level.

ABSTRACT

This article shows in detail the computations made for the poster presented at the Symposium "Frontiers of Fundamental Physics" in July 2014. As was shown in a previous publication, a quantum gravity formulation exists on the basis of abstract quantum number conservation, the laws of thermodynamics, unspecific interactions, and locally maximising the ratio of resulting degrees of freedom per imposed degree of freedom of the theory. The first law of thermodynamics was evaluated by imposing boundary conditions on small volumes of optimised dimension (3+1). As a consequence, no explicit microscopic quantum structure was required in order to recover all well established physics as special cases (Quantum Field Theory, QFT, and General Relativity, GR) and compute all measurable quantities. This article presents the generalised action in terms of tetrads and shows how this action may be related to the spin of generalised matter fields, especially for fermionic matter.

Motivation & Objective

• To develop a consistent quantum gravity model based solely on thermodynamic principles and minimal microscopic input.
• To show that general relativity and quantum field theory emerge as special cases of this framework.
• To establish a spin-compatible formulation of gravity and matter using the tetrad formalism.
• To demonstrate that fermionic matter induces torsion in the connection, linking spin to geometric structure.

Proposed method

• Derives the gravitational action using the tetrad formalism and Legendre transformation to express dynamics in terms of conjugate variables.
• Applies the principle of maximizing degrees of freedom per imposed degree of freedom to derive the general action.
• Introduces generalized stress and current densities via boundary variations and applies Gauss’ theorem to obtain bulk terms.
• Uses the formalism to derive a total action that includes gravity, matter, and interactions, with spin coupling through the connection 1-form.
• Relies on thermodynamic variables (entropy, temperature) and macroscopic observables rather than spacetime or Hamiltonian dynamics.
• Demonstrates that the action reduces to the Palatini action in the absence of torsion and to Einstein-Cartan theory when fermionic spin is present.

Experimental results

Research questions

• RQ1 Can a consistent quantum gravity model be constructed from thermodynamic principles and minimal information without assuming a spacetime background?
• RQ2 How can fermionic spin be naturally incorporated into a geometric quantum gravity framework?
• RQ3 What is the general form of the action for gravity and matter when derived from entropy maximization and quantum number conservation?
• RQ4 How do standard theories like general relativity and quantum field theory emerge as limiting cases of this framework?
• RQ5 What is the relationship between torsion in the connection and the spin of fermionic matter fields?

Key findings

• The total action derived is spin-compatible, with torsion arising naturally from the presence of fermionic matter with net spin.
• The formalism reproduces the Palatini action in the absence of torsion and reduces to Einstein-Cartan theory when fermionic spin is included.
• Fermionic matter fields couple to the connection 1-form in a way that directly relates the non-Lorentz part of the connection to spin.
• The theory reproduces quantum field theory in the limit of negligible gravitational fields, with second quantization emerging from macroscopic variational principles.
• The derivation does not require a fundamental spacetime or variational principle at the microscopic level, with dynamics arising from thermodynamic behavior.
• The tetrad formalism is essential for consistently describing all types of matter, especially fermions, in the unified framework.