Talks

In classical mechanics, the representations of dynamical evolutions of a system and those of interactions the system can have with its environment are different vector fields on the space of states: evolutions and interactions are conceptually, physically and mathematically different in classical physics, and those differences arise from the generic structure of the very dynamics of classical systems ("Newton's Second Law"). Correlatively, there is a clean separation of the system's degrees of freedom from those of its environment, in a sense one can make precise. I present a theorem showing that these features allow one to reconstruct the entire flat affine 4-dimensional geometry of Newtonian spacetime---the dynamics is inextricably tied to the underlying spacetime structure. In quantum theory (QT), contrarily, the representations of possible evolutions and interactions with the environment are exactly the same vector fields on the space of states ("add another self-adjoint operator to the Hamiltonian and exponentiate"): there is no difference between "evolution" and "interaction" in QT, at least none imposed by the structure of the dynamics itself. Correlatively, in a sense one can make precise, there is no clean separation of the system's degrees of freedom from those of the environment. Finally, there is no intrinsic connection between the dynamics and the underlying spacetime structure: one has to reach in and attach the dynamics to the spacetime geometry by hand, a la Wigner (e.g.). How we distinguish interaction from evolution in QT and how we attach the dynamics to a fixed underlying spacetime structure come from imposing classical concepts foreign to the theory. Trying to hold on to such a distinction is based on classical preconceptions, which we must jettison if we are to finally come to a satisfying understanding of QT. These observatons offer a way to motivate and make sense of, inter alia, the idea of indefinite causal structures.

"The Causaloid framework [1] is useful to study Theories with Indefinite Causality; since Quantum Gravity is expected to marry the radical aspects of General Relativity (dynamic causality) and Quantum Theory (probabilistic-ness). To operationally study physical theories one finds the minimum set of quantities required to perform any calculation through physical compression. In this framework, there are three levels of compression: 1) Tomographic Compression, 2) Compositional Compression and 3) Meta Compression. We present a diagrammatic representation of the Causaloid framework to facilitate exposition and study Meta compression. We show that there is a hierarchy of theories with respect to Meta compression and characterise its general form. Next, we populate the hierarchy. The theory of circuits forms the simplest case, which we express diagrammatically through Duotensors, following which we construct Triotensors using hyper3wires (hyperedges connecting three operations) for the next rung in the hierarchy. Finally, we discuss the implications for the field of Indefinite Causality. [1] Journal of Physics A: Mathematical and Theoretical, 40(12), 3081"

It has been previously discussed how events (interactions) in quantum mechanics are time-symmetric and an arrow of time is only due to the arrow of inference in the paper “Quantum information and the arrow of time”, arXiv:2010.05734 by Andrea Di Biagio, Pietro Dona, and Carlo Rovelli. In the relational interpretation of Quantum Mechanics, these interactions are relative facts. Stable facts result from relative facts through the process of decoherence as shown in the paper "Di Biagio, A., Rovelli, C., Foundations of Physics 51, 30 (2021)". They are separate from observed facts in laboratories due to the reason that they do not depend on a decision-making agent for their creation. In my talk, I will discuss my work with Carlo Rovelli and Andrea Di Biagio where we show that the process of decoherence and the notion of stability of facts is indeed time-symmetric. This is in contrast to the observed facts of our everyday world where an arrow of time emerges due to the presence of agents and traces.

"Making progress in quantum gravity requires resolving possible tensions between quantum mechanics and relativity.  One such tension is revealed by Bell's Theorem, but this relies on relativistic Local Causality, not merely the time-reversal symmetric aspects of relativity.  Specifically, it depends on an arrow-of-time condition, taken for granted by Bell, which we call No Future-Input Dependence.  One may replace this condition by the weaker Signal Causality arrow-of-time requirement -- only the latter is necessary, both for empirical viability and in order to avoid paradoxical causal loops.  There is then no longer any ground to require Local Causality, and Bell's tension disappears.  The locality condition which is pertinent in this context instead is called Continuous Action, in analogy with Einstein's ""no action at a distance,"" and the corresponding ""local beables"" are ""spacetime-local"" rather than ""local in space and causal in time.""    That such locally mediated mathematical descriptions of quantum entanglement are possible not only in principle but also in practice is demonstrated by a simple toy-model -- a ""local"" description of Bell correlations.  Describing general physical phenomena in this manner, including both quantum systems and gravitation, is a grand challenge for the future. [K.B. Wharton and N. Argaman, ""Colloquium: Bell's Theorem and Locally-Mediated Reformulations of Quantum Mechanics,"" Rev. Mod. Phys. 92, 21002 (2020).]"