Quantum Gravity

The constrained Hamiltonian formalism is the basis for canonical quantization techniques. However, there are disagreements surrounding the notion of a gauge transformation in such a formalism. The standard definition of a gauge transformation in the constrained Hamiltonian formalism traces back to Dirac: a gauge transformation is a transformation generated by an arbitrary combination of first-class constraints. On the basis of this definition, Dirac argued that one should extend the form of the Hamiltonian in order to include all of the gauge freedom. However, Pitts (2014) argues that in some cases, a first-class constraint does not generate a gauge transformation, but rather "a bad physical change". Similarly, Pons (2005) argues that Dirac's analysis of gauge transformations is "incomplete" and does not provide an account of the symmetries between solutions. Both authors conclude that extending the Hamiltonian in the way suggested by Dirac is unmotivated. If correct, these arguments could have implications for other issues in the foundations of the constrained Hamiltonian formalism, including the Problem of Time. In this talk, I use a geometric formulation of the constrained Hamiltonian formalism to show that one can motivate the extension to the Hamiltonian independently from consideration of the gauge transformations, and I argue that this supports the standard definition of a gauge transformation without falling prey to the criticisms of Pitts (2014) and Pons (2005). Therefore, in order to maintain that first-class constraints do not generate gauge transformations, one must reject the claim that the constrained Hamiltonian formalism is fully described by the geometric picture; I suggest two avenues for doing so.

The success of the AdS/CFT correspondence motivates a holographic approach for spacetime beyond AdS, including our own universe. One possible method involves using an asymptotically-AdS holography and introducing a finite radial cutoff by inserting an End-of-World (EoW) brane. However, previous studies have shown that this leads to nonlocal effects on the boundary and violates entanglement sub-additivity. In this work, we address these issues by examining a two-particle scattering process through the lens of holographic quantum tasks. Our findings suggest that connectedness of entanglement wedge does indeed require nonlocal domain of dependence, but that violation of sub-additivity can be avoided. We also discuss an important question that arises from our results, namely whether the non-locality on the EoW brane is real or apparent. We argue that it is the latter. This talk is based on ongoing work with Takato Mori.

For the last ten years I have been documenting various scenarios for the early universe in a YouTube series called ‘Before the Big Bang”. Having interviewed many of the leader figures of the field including Stephen Hawking, Roger Penrose, Alan Guth (and hosted debates between them), this will be a broad survey of inflation, it’s suggested prequels and alternatives. I shall highlight the strengths and weaknesses of the various proposals and give an inside track of the claims and counter claims in attempts to move beyond the standard Big Bang model.

Singularities in general relativity and quantum field theory are often taken not only to motivate the search for a more-fundamental theory (quantum gravity), but also to characterise this new theory and shape expectations of what it is to achieve. In this talk, I will explore how different types of singularities play a role in the search for quantum gravity, and how different `attitudes' towards singularities can lead to different scenarios for the new theory. [Based on joint work with Sebastian DeHaro].

String theory has not come close to a complete formulation after half a century of intense research. On the other hand, a number of features of the theory suggest that the theory in its complete form may be a final theory. The combination of conceptual incompleteness and allusions to finality seems difficult to grasp. Two main points are made in this talk. First, it is pointed out that finality claims in the context of string theory are motivated in a fundamentally different way than traditional claims of finality one finds in earlier physics. Second, it is argued that finality and chronic conceptual incompleteness may be related to each other in a string theory context in an interesting way. The talk ends with discussing possible implications of this situation for the long-term prospects of theory building in fundamental physics.

Effective field theory analysis are inadequate to describe the evolution of the very early universe. I will describe an approach to obtain emergent time, emergent space, an emergent metric and an emergent early universe cosmology starting from the BFSS matrix model, a proposed non-perturbative definition of superstring theory. In this approach there is no cosmological constant problem.