Lucien Hardy: Operational road to Quantum Gravity

The speaker introduces the concept of operational quantum theory, emphasizing its practicality and intuitiveness compared to other formulations. They discuss the use of density matrices, CP maps, and super operators in quantum theory, and propose an alternative approach called the operator tensor formulation. This approach is likened to a user interface with knob settings and outcomes, aiming to reformulate general relativity in a similar manner.

The paragraph explains how to represent quantum experiments both diagrammatically and symbolically. It discusses the use of boxes with inputs and outputs to describe operations and the calculation of joint probabilities using the operator tensor framework. The concept of operational continuity and the composition principle are introduced, which allows for the mathematical calculation to mirror the structural form of the operational description.

The speaker provides a brief overview of general relativity (GR) for non-experts, discussing the transition from special relativity to GR and the use of field equations. They highlight the issue of the Einstein field equations providing fewer independent equations than needed due to a fundamental identity, leading to a lack of unique solutions. The concept of observables in GR is also introduced, which are functions invariant under diffeomorphisms.

This paragraph delves into the conceptual challenges of GR, particularly the difficulty of associating reality with the manifold due to the invariance of the field equations under general coordinate transformations. The speaker discusses the idea of 'beables' as real things in the theory and the challenges of defining local reality on the manifold.

The speaker outlines two strategies for adopting an operational approach to GR: one involving the use of physical instruments as primitive objects, and the other focusing on the fields themselves. The chosen approach involves extracting operational objects directly from the field equations, inspired by a paper by Westman and San Diego, aiming to reformulate GR in an operational context.

The paragraph introduces the concept of operational space, where scalars derived from the fields are used to map solutions onto a surface within this space. The speaker discusses the idea of plotting each point of a manifold into operational space based on the scalar values, creating a surface that represents the solution to the field equations.

The speaker explains how to join solutions in operational space, ensuring that they match at the boundary. They discuss the process of defining boundary conditions and the importance of matching both the manifolds and the fields. The concept of 'tilde solutions' is introduced as a bookkeeping device to understand the structure of solutions independent of their specific representations.

This paragraph explores the notion of non-separability in GR, where the joining of two solutions can result in physically inequivalent solutions, leading to a natural notion of mixed solutions. The speaker provides an example involving a rotationally symmetric distribution of matter to illustrate how pure and mixed solutions can be conceptualized in GR.

The speaker introduces agency fields as a way to incorporate decisions made by entities within the spacetime, such as a captain steering a spaceship. They discuss the effective nature of these fields and how they can be used to describe the influence of choices on the evolution of the spacetime, highlighting the practicality of this approach in certain scenarios.

The paragraph discusses the extraction of scalars from agency fields to describe the choices made by entities within the spacetime. The speaker outlines how these choices can be coordinated within a vast fleet of spaceships, forming a dust fluid, and how the agency fields can be used to control the decisions of the captains, effectively influencing the physics of the situation.

The speaker introduces the concept of a Tao field, which indicates the forward time direction at each point in spacetime. They discuss the challenges of incorporating time direction in the effective notions of GR and the need to reconcile the time symmetry of GR with the effective introduction of agency fields.

The paragraph explains how agency fields can be used to extract scalars that describe the choices made by entities, which can then be incorporated into the physics of the situation. The speaker discusses the idea of a global strategy for coordinating the actions of a vast fleet of spaceships, represented as a dust fluid, and how the agency fields can be used to control these actions effectively.

The speaker outlines three approaches to quantum gravity: the abstract, ontological, and principled approaches. They discuss the potential of operational GR to give rise to quantum theory and the possibility of extracting principles that could bridge both theories to construct a unified theory of quantum gravity.

The paragraph discusses the construction of time and agency within the operational framework of GR. The speaker provides an example of how to construct a clock using two immiscible fluids and how the interaction between these fluids can be witnessed in operational space, illustrating the primitive thought processes that can be built within this framework.

The speaker concludes with open questions regarding the status of agency fields and their physical dependence. They acknowledge the tentative nature of work on quantum gravity and the challenges of finding local scriptures on a manifold, suggesting that the operational approach to GR may offer new insights and directions for research.