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The status of geometry and matter in re-interpreted WdW theory
1  S. P. M. Kankavli College, Kankavli, Sindhudurg, India - 416602
Academic Editor: Douglas Singleton

Abstract:

I have shown that the field defined by the Wheeler-DeWitt equation for pure gravity is neither a standard gravitational field nor the field representing a particular universe. The theory offers a unified description of geometry and matter, with geometry being fundamental. The quantum theory possesses gravitational decoherence when the signature of R(3) changes. The quantum theory resolves singularities dynamically. Application to the FLRW kappa=0 shows the creation of local geometries during quantum evolution. The 3-metric gets modified near the classical singularity in the case of the Schwarzschild geometry.

I analyze the Wheeler-DeWitt equation for pure gravity in the light of standard quantum field theories. Because the field is defined only over the space of 3-metric can be re-interpreted without the issue discussed above. The field defined satisfies ADM constraints for pure gravity. Therefore, one would interpret that the field Φ is a pure gravitational field. But I observe that even gauge fields obey ADM constraints for pure gravity. I also observe that these fields have non-trivial stress tensors. Whereas the stress tensor for pure gravitational field is Rµν −1/2 gµνR = 0. The quadratic coupling always remains non-negative regardless of the signature of R(3). I also observe that the higher order couplings with Φ ∼ ei qabPab allow us to interpret it as a matter-like term. The other interpretation is that the field Φ describes a particular Universe. I observe that such interpretation faces problems due to the interaction between different fields. It shows that neither of the interpretation is true. The field Φ is a unified description of the gravity and scalar matter.

The re-interpretation partly modifies both the theories, the quantum theory as well as the classical gravity. On the quantization of the field, we get the geometric quantum corresponding to the field but no graviton.

Keywords: Re-interpretation, Wheeler-DeWitt equation, geometric matter, gravitised quantum theory
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