Quantum Foundations

Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The challenge is to specify how those constraints are themselves updated.

The important ingredients are two: the cotangent bundle associated to the probability simplex inherits (1) a natural symplectic structure from ED, and (2) a natural metric structure from information geometry.

The requirement that the dynamics preserves both the symplectic structure (a Hamilton flow) and the metric structure (a Killing flow) leads to a Hamiltonian dynamics of probabilities in which the linearity of the Schrödinger equation, the emergence of a complex structure, Hilbert spaces, and the Born rule, are derived rather than postulated.

While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through theories. While most theories of physics are based on real numbers, quantum theory was the first to be formulated in terms of operators acting on complex Hilbert spaces. This has puzzled countless physicists, including the fathers of the theory, for whom a real version of quantum theory, in terms of real operators, seemed much more natural. Are complex numbers really needed in the quantum formalism? Here, we show this to be case by proving that real and complex quantum theory, understood in terms of operators in Hilbert spaces and tensor products to represent independent systems, make different predictions in network scenarios comprising independent states and measurements.  This allows us to devise a Bell-like experiment whose successful realization would disprove real quantum theory, in the same way as standard Bell experiments disproved local physics.

In absence of both experimental evidence for and a fully understood  theory of quantum gravity, the possibility that gravity might be  fundamentally classical presents an option to be considered. Such a  semiclassical theory also bears the potential to be part of an  objective explanation for the emergence of classical measurement outcomes. Nonetheless, the possibility is mostly disregarded based on the grounds of arguments of consistency. I will discuss these arguments, attempting to present the broader picture of the constraints that need to be dealt with in order to formulate consistent semiclassical models of gravity, and the implications this  has with regard to concrete proposals for theoretical models and 
experimental tests of semiclassical versus quantized gravity.

Zoom Link: https://pitp.zoom.us/j/99590707415?pwd=MHFMZlhSMUdMbFFoMEFmQTIxSUhBQT09

This talk is about how to think about probabilistic reasoning and its use in physics.  It has become commonplace, in the literature on the foundations of probability, to note that the word “probability” has been used in at least two distinct senses: an objective, physical sense (often called “objective chance”), thought to be characteristic of physical situations, independent of considerations of knowledge and ignorance, and an epistemic sense, having to do with gradations of belief of agents with limited information about the world.  I will argue that in order to do justice to the use of probabilistic concepts in physics, we should go beyond this familiar dichotomy, and make use of a third concept, which I call “epistemic chance,” which combines epistemic and physical considerations.

There are many different interpretations of quantum mechanics. Among them, QBism and Rovelli's Relational Quantum Mechanics (RQM) are special because they both propose that reality itself is produced relative to "observers". For QBism, observers are defined as rational decision-making "agents", while in RQM any physical system can be an observer. But both interpretations agree that reality is shaped by what happens when observers encounter the world external to themselves. In this talk I will try to understand what these interpretations imply for the ongoing problem of defining an ontological model of quantum mechanics.

A toy model due to Spekkens is constructed by applying an epistemic restriction to a classical theory but reproduces a host of phenomena that appear in quantum theory. The model advances the position that the quantum state may be interpreted as a reflection of an agent’s knowledge. However, the model fails to capture all quantum phenomena because it is non-contextual. Here we show how a theory similar to the one Spekkens proposes requires only a single augmentation to give quantum theory for certain systems. Specifically, one must combine all possible epistemically restricted classical accounts of a quantum experiment. The rule for combination is simple: sum the nonrandom parts of all classical predictions to arrive at the nonrandom part of the quantum prediction.