The Construction Interpretation: Conceptual Roads to Quantum Gravity

TL;DR

The paper advocates The Construction Interpretation as a methodology for building a theory of Quantum Gravity rather than a conventional interpretation, arguing that progress requires re-purposing foundations from quantum theory and General Relativity within a pluralistic, conceptually driven program. It lays out a seven-step framework and three defining elements for General Relativity, illustrating how GR motivates an interpretive stance via diffeomorphism invariance and beables. It then connects to Quantum Field Theory through an operational, operator-tensor formulation, discussing the physicality condition and related boundary/region-based perspectives, with the overarching aim of generalizing these concepts to a coherent road to Quantum Gravity. The work emphasizes bridging how GR’s structural insights can guide the construction of a quantum-gravitational theory that recovers GR and QFT in appropriate limits, while remaining open to multiple constructive paths. Finally, it sketches a quantum-theoretic approach that treats local operations and probabilities in a way compatible with a future quantum gravitational framework.

Abstract

In the first part of this paper I propose the Construction Interpretation of the Quantum. The main point of this interpretation is that (unlike previous interpretations) it is not actually an interpretation but rather a methodology aimed to encourage a conceptually driven construction of a theory of Quantum Gravity. In so doing we will, I hope, resolve the ontological problems that come along with Quantum Theory. In the second part of this paper I offer a particular perspective on the theory of General Relativity and set out a path of seven steps and three elements corresponding (more-or-less) to the path that Einstein took to this theory. In the third part I review a particular operational approach to Quantum Field Theory I have been developing - the operator tensor formulation. The physicality condition (this ensures that probabilities are between 0 and 1 and that choices in the future cannot effect the past) is discussed in some detail in this part and also in an appendix. In the fourth part of the paper I set out one particular conceptually driven possible road to Quantum Gravity. This approach works by establishing seven steps and three elements for a theory of Quantum Gravity that are analogous to those of General Relativity. The holy grail in this approach is to generalize the physicality conditions from Quantum Field theory to the new situation we find ourselves in in Quantum Gravity. Such conditions, in the present approach, would be analogous to the Einstein Field Equations. In the fifth part of the paper I propose the quantum equivalence principle whereby it is always possible to transform to a quantum reference frame such that we have definite causal structure in the vicinity of any given point. This equivalence principle suggests another possible road (albeit more speculative) to Quantum Gravity in even closer analogy to the path Einstein took to General Relativity.