Foundations of Quantum Mechanics and Quantum Information Theory: A Workshop with Jeffrey Bub (20 June 2018)
The foundations of quantum mechanics have long been a focus of philosophical interest, from both philosophers of science and physicists: what is the best resolution of the so-called “measurement problem”? What is the nature and status of the quantum correlations? And how best do we understand the differences between quantum and classical mechanics? With Jeffrey Bub, whose recent book Bananaworld explores quantum foundations from an information-theoretic perspective, this workshop will examine such conceptual and philosophical issues.
- Jeffrey Bub (University of Maryland)
- Omid Charrakh (MCMP/LMU Munich)
- Erik Curiel (MCMP/LMU Munich)
- Benjamin Eva (University of Konstanz/MCMP)
- Stephan Hartmann (MCMP/LMU Munich)
- F.A. Muller (Erasmus University Rotterdam)
|09:30 - 10:00||Registration and coffee|
|10:00 - 10:45||Erik Curiel: Interaction and Evolution in Quantum Mechanics|
|10:45 - 11:00||Break|
|11:00 - 11:45||Benjamin Eva: A Bridge Between Q-Worlds|
|11:45 - 12:00||Break|
|12:00 - 12:45||Stephan Hartmann: The Open Systems View as Fundamental (with Michael Cuffaro)|
|12:45 - 14:00||Lunch break|
|14:00 - 14:45||F.A. Muller: Ranting and Raving About Locality in Quantum Mechanics (with Gijs Leegwater)|
|14:45 - 15:00||Break|
|15:00 - 15:45||Omid Charrakh: On the Reality of the Wavefunction|
|15:45 - 16:00||Break|
|16:00 - 17:00||Jeffrey Bub: In Defense of a "Single-World" Interpretation of Quantum Mechanics|
In a recent “no go” result, Frauchiger and Renner argue that no “single-world” interpretation of quantum mechanics can be self-consistent, where a single-world interpretation is any interpretation that asserts, for a measurement with multiple possible outcomes, that just one outcome actually occurs. They conclude that if quantum theory accurately describes complex systems like observers who perform measurements, then “we are forced to give up the view that there is one single reality.” I’ll review the Frauchiger-Renner argument and argue that quantum mechanics should be understood probabilistically, as a new sort of non-Boolean probability theory, rather than representationally, as a theory about the elementary constituents of the physical world. I show that this way of understanding quantum mechanics is not in conflict with a consistent “single-world” interpretation of the theory.top
Within the Ontological Models Framework (OMF), Pusey, Barrett, and Rudolph (PBR) proved a theorem according to which the realist epistemic view on the wavefunction must be ruled out. This study suggests that PBR's finding is neither due to the nature of the wavefunction nor to the realist epistemic view, but rather because of a traditional formulation of OMF. To be precise, while OMF considers an ontic description of prepared systems, it does not model the ontology of measurement devices. Such an asymmetric treatment becomes problematic, in scenarios in which measurement devices have a quantum nature. Consequently, to make valid assertions about the ontological status of the wavefunction, it might be necessary to consider the ontic states of both systems (i.e., the prepared system and the measurement device). Extending OMF's definition such that the ontology of the measurement device becomes included, I will propose a Psi-epistemic ontological model which can reproduce the statistics of PBR's scenario. In light of this analysis, I will argue that PBR's finding should not be construed as an argument for/against any philosophical stand toward the ontology of the wavefunction.top
I think there is no satisfactory resolution of the Measurement Problem in quantum mechanics. My feeling is that there is something about the idea of "interaction" we do not understand that is blocking us, in the way that the lack of understanding of "simultaneity" at the end of the 19th Century stood in the way of a proper understanding of electromagnetism, light, and motion. In this vein, I explore the following idea. In classical mechanics, the vector fields on the space of states that represent possible dynamical evolutions of system and those that represent possible interactions the system can have with its environment ("externally imposed forces") are different families of vector fields. In other words, evolutions and interactions are conceptually, physically and mathematically distinct things in classical physics. In quantum mechanics, to the contrary, the vector fields on a Hilbert space that represent possible evolutions and those that represent possible interactions with the environment are exactly the same vector fields. There is no distinction between "evolution" and "interaction" in quantum mechanics. I attempt to draw out and discuss some of the consequences of this fact, as this is one aspect of "interaction" I think we do not understand in quantum mechanics.top
Quantum set theory (QST) and topos quantum theory (TQT) are two long running projects in the mathematical foundations of quantum mechanics that share a great deal of conceptual and technical affinity. Most pertinently, both approaches attempt to resolve some of the conceptual difficulties surrounding quantum mechanics by reformulating parts of the theory inside of non-classical mathematical universes, albeit with very different internal logics. We call such mathematical universes, together with those mathematical and logical structures within them that are pertinent to the physical interpretation, 'Q-worlds'. Here, we provide a unifying framework that allows us to (i) better understand the relationship between different Q-worlds, (ii) define a general method for transferring concepts and results between TQT and QST, thereby significantly increasing the expressive power of both approaches, and (iii) obtain a powerful new approach to formalising state dependent operator inequalities.top
Open systems features such as dissipation and pumping play a crucial role in many standard quantum optical applications (for instance in lasers and resonance fluorescence) and a proper quantum theoretical account of these (and other) applications requires that one models the environment, and not just the system of interest, quantum mechanically. To do so, one typically employs a Markovian quantum master equation which is of the 'Lindblad form'. Note that, importantly, the Schr\"odinger equation governing the unitary evolution of closed systems is a special case of the Lindblad equation.
To derive the master equation, there are two possible routes. The first is a microscopic and specific derivation that must be carried out for the particular system under consideration in a given application. The second is a general and abstract derivation which does not relate to a particular system, but rather begins from general constraints on the dynamical evolution of quantum systems. These include, in particular, the requirement that the dynamical map governing the state transitions of a quantum system be 'completely positive', i.e. such that it will never evolve (i.e. no matter what the system's initial state) a valid state description for a particular quantum system to an invalid state description.
We consider both the general and the more specific derivation in some detail and argue that in both cases one can discern clear and strong physical motivations for considering the open-systems view of quantum systems (rather than the traditional closed-systems view) as the fundamental one from which to consider the metaphysics of quantum systems, and discuss the consequences of so doing.top
Discussions about the locality or non-locality of quantum mechanics persist. In other words, different people assign different meanings to the word 'locality’. Familiar situation. We rehearse a few meanings. Then we home in on the celebrated Bell experiment in more detail than is usually done, by involving the concept of localisability, the kinematics of the singlet state, and the position degree-of-freedom in addition to that of spin. We resolve a puzzle about what is the appropriate anti-symmetric state, by introducing the concept of a snapshot Hilbert-space and a Hilbert-space movie. Bearings on the incompleteness argument of Einstein, Podolsky and Rosen enter the stage, e.g. blocking the argument altogether while adhering to their sufficient conditions for an epr and for the incompleteness of quantum mechanics, as well as to their locality condition in terms of epr.top
There is no fee to attend this workshop.
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