Gravity and quantum theory: Domains of conflict and contact

Abstract

There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit (observer dependent) thermal properties and possess a heat density. This suggests that spacetime, like matter, has microscopic degrees of freedom and its long wavelength

Microscopic origin of Einstein's field equations and the raison d'être for a positive cosmological constant

“…This suggests that: (a) One should not possibly consider the metric as dynamical, since in the absence of matter the metric disappears altogether from the effective action. (This point of view -viz., that the metric is not a dynamical variable and should not be varied in any action principle -has been stressed in the previous literature on the emergent gravity paradigm [2,9].) (b) In the complete theory of quantum spacetime and matter, it is very likely that matter and metric will emerge together.…”

“…Incredibly enough, there exists a very simple model which achieves this goal. The ingredients of this model are well motivated by the two clues [2] we have about quantum gravity; viz. the (i) nature of the cosmological constant problem and (ii) the thermodynamics of null surfaces.…”

“…We will treat the connection Γ i jk and the metric g ab to be independent variables in the spirit of the Palatini approach. 2 The space(time) is treated as a C ∞ , 4-dimensional Euclidean manifold with the metric, connection and the vector field defined as at least C 2 , C 1 and C 2 functions respectively. (The connection and the metric are treated as independent a priori.)…”

“…The convergence of the path integral requires the tensor M ab , treated as a matrix, to have positive definite 2 Note: (a) The measure dV = √ g d 4 x/L 4 is the natural choice for integration domain in Euclidean 4-space, in which we will work. However, the analysis goes through unhindered even if we choose a sub-region like, for e.g., a lower dimensional hypersurface embedded in the d = 4 space, with appropriate proper volume.…”

From the black hole conundrum to the structure of quantum gravity

“…A natural platform for this description is Euclidean gravitational path integral, 25,26,37,40 which treats the black hole as a quasi-static system. In this method, a state (ket) Ψ⟩ is given as a functional Ψ[φ i (x)] of field configurations on an equaltime hypersurface S 0 .…”