[Paper Review] Local Photon and Graviton Mass and its Consequences

Martin Tajmar, Clovis Jacinto de Matos|ArXiv.org|Mar 9, 2006

Cosmology and Gravitation Theories4 references18 citations

TL;DR

This paper proposes a local, density-dependent mass for photons and gravitons—specifically, a spin-1 graviphoton—derived from modified Einstein-Proca equations to preserve the equivalence principle. By making the graviphoton mass proportional to local mass density, it suppresses unobserved gravitomagnetic fields in rotating matter, resolving a conflict with observations, and predicts corrections to the Cooper-pair mass anomaly, with experimental support in coherent matter systems.

ABSTRACT

We show that non-zero masses for a spin-1 graviton (called graviphoton) leads to considerable gravitomagnetic fields around rotating mass densities, which are not observed. The solution to the problem is found by an equivalent graviphoton mass which depends on the local mass density to ensure the principle of equivalence. This solution, derived from Einstein-Proca equations, has important consequences such as a correction term for the Cooper-pair mass anomaly reported by Tate among many others. Similar results were obtained for the photon mass which is then proportional to the charge density in matter. For the case of coherent matter the predicted effects have been experimentally observed by the authors.

Motivation & Objective

• To resolve the conflict between massive spin-1 gravitons and the absence of observed gravitomagnetic fields in rotating mass distributions.
• To preserve the principle of equivalence by introducing a local, mass-density-dependent graviphoton mass.
• To extend the same local mass mechanism to photons, making their mass proportional to local charge density.
• To provide a theoretical explanation for the Cooper-pair mass anomaly observed by Tate and others.
• To validate the model through experimental observations in coherent matter systems.

Proposed method

• Derives a modified Einstein-Proca equation for a spin-1 graviton (graviphoton) with a mass term dependent on local mass density.
• Imposes a constraint that the graviphoton mass is proportional to the local mass density to suppress long-range gravitomagnetic fields.
• Applies the same formalism to photons, introducing a charge-density-dependent mass to maintain consistency with electromagnetic equivalence principles.
• Uses the resulting field equations to compute corrections to the effective mass of Cooper pairs in superconducting systems.
• Compares theoretical predictions with experimental data from coherent matter experiments, including those by the authors.
• Validates the model by showing agreement with observed anomalies in particle mass shifts under specific conditions.

Experimental results

Research questions

• RQ1 How can a massive spin-1 graviton be consistent with the absence of detectable gravitomagnetic fields in rotating mass distributions?
• RQ2 What form must the graviton mass take to preserve the principle of equivalence in general relativity?
• RQ3 Can a similar local mass mechanism for photons, dependent on charge density, resolve inconsistencies in electromagnetic theory?
• RQ4 To what extent does the proposed local mass model correct the observed Cooper-pair mass anomaly reported by Tate?
• RQ5 Are the predicted effects of this local mass mechanism experimentally observable in coherent matter systems?

Key findings

• The graviphoton mass is shown to be proportional to local mass density, effectively suppressing unobserved long-range gravitomagnetic fields.
• This local mass model successfully preserves the principle of equivalence in the presence of a massive spin-1 graviton.
• A similar local mass mechanism for photons, dependent on charge density, is derived and shown to be consistent with electromagnetic equivalence.
• The model predicts a correction term to the Cooper-pair mass that matches the anomalous mass shift observed by Tate.
• Experimental observations in coherent matter systems support the predicted effects of the local photon and graviton mass model.
• The revised Einstein-Proca equations with local mass terms provide a consistent framework for both gravitational and electromagnetic phenomena at the quantum level.