November 2022

The study of indefinite causal order has seen rapid development, both theoretically and experimentally, in recent years. While classically the causal order of two timelike separated events A and B is fixed – either A before B or B before A – this is no longer true in quantum theory. There, it is possible to encounter superpositions of causal orders. In light of recent work on quantum reference frames, which reveals that the superposition of locations, momenta, and other properties can depend on the choice of reference frame or coordinate system, the question arises whether this also holds true for superpositions of causal orders. Here, we provide a negative answer to this question for quantum diffeomorphisms. First, we provide an unambiguous definition of causal order between two events in terms of worldline coincidences and the proper time of a third particle. Then, we show that superpositions of causal order defined as such cannot be rendered definite even through the most general class of coordinate transformations – quantum-controlled, independent diffeomorphisms in each branch. Finally, based on our results, we connect the information theoretic and gravitational perspectives on indefinite causal order.

Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual structure appropriate to make sense of the quantum aspects of space and time. In the course of the last decades, an extensive discussion on this problem has led to a clear conceptual picture, that provides a coherent conceptual foundation of today’s Loop Quantum Gravity. We review this foundation, addressing issues such as the sense in which space and time are emergent, the notion of locality, the role of truncation that enables physical computations on finite graphs, the problem of time, and the characterization of the observable quantities in quantum gravity.

A discrete space-time structure lying at about the Planck scale may become manifest in the form of very small violations of the conservation of the matter energy-momentum tensor. In order to include such kind of violations, forbidden within the General Relativity framework, the theory of unimodular gravity seems as the simplest option to describe the gravitational interaction. In the cosmological context, a direct consequence of such violation of energy conservation might be heuristically viewed a “diffusion process of matter (both dark and ordinary)” into an effective dark energy term in Einstein’s equations, which leads under natural assumptions to an adequate estimate for the value of the cosmological constant. Previous works have also indicated that these kind of models might offer a natural scenario to alleviate the Hubble tension. In this work, we consider a simple model for thecosmological history including a late time occurrence of such energy violation and study the modifications of the predictions for the anisotropy and polarization of the Cosmic Microwave Background (CMB). We compare the model’s predictions with recent data from the CMB, Supernovae Type Ia, cosmic chronometers and Baryon Acoustic Oscillations. The results show the potential of this type of model to alleviate the Hubble tension.

Local flatness is a property shared by all the spin foam models. It ensures that the theory’s fundamental building blocks are flat by requiring locally trivial parallel transport. In the context of simplicial Lorentzian spin foam theory, we show that local flatness is the main responsible for the emergence of geometry independently of the details of the spin foam model. We discuss the asymptotic analysis of the EPRL spin foam amplitudes in the large quantum number regime, highlighting the interplay with local flatness.

The Ehlers-Pirani-Schild (EPS) constructive axiomatisation of general relativity, published in 1972, purports to build up the kinematical structure of that theory from only axioms which have indubitable empirical content. It is, therefore, of profound significance both to the epistemology and to the metaphysics of spacetime theories. In this article, we set the EPS approach in its proper context, by (a) discussing the history of constructive approaches to spacetime theories in the lead-up to EPS; (b) addressing some of the major concerns raised against EPS; (c) considering how EPS compares with ‘chronometric’ approaches to affording the metric field of general relativity its operational significance; (d) distinguishing quite generally between different kinds of constructive approach, and fitting EPS into this classification; (e) discussing how constructivism bears on a number of other issues in the foundations of physics; and (f) assessing the merits of constructivism qua local foundationalist project. There are two companion papers, in which we provide a pedagogical walkthrough to the EPS axiomatisation (Part I), and discuss/develop versions of EPS with quantum mechanical inputs (Part III).