Alexei Grinbaum

Reconstruction of quantum theory

What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently moved from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the work of Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction. 1. What is Wrong with Interpreting Quantum Mechanics2. Reconstruction of Physical Theory2.1. Schema2.2. Selection of the first principles2.3. Status of the first principles3. Examples of Reconstruction3.1. Early examples of reconstruction3.2. Hardys reconstruction3.3. Rovellis reconstruction3.4. The CBH reconstruction3.5. Intentionally incomplete reconstructions4. Conclusion What is Wrong with Interpreting Quantum Mechanics Reconstruction of Physical Theory2.1. Schema2.2. Selection of the first principles2.3. Status of the first principles Schema Selection of the first principles Status of the first principles Examples of Reconstruction3.1. Early examples of reconstruction3.2. Hardys reconstruction3.3. Rovellis reconstruction3.4. The CBH reconstruction3.5. Intentionally incomplete reconstructions Early examples of reconstruction Hardys reconstruction Rovellis reconstruction The CBH reconstruction Intentionally incomplete reconstructions Conclusion

ELEMENTS OF INFORMATION-THEORETIC DERIVATION OF THE FORMALISM OF QUANTUM THEORY

Information-theoretic derivations of the formalism of quantum theory have recently attracted much attention. We analyze the axioms underlying a few such derivations and propose a conceptual framework in which, by combining several approaches, one can retrieve more of the conventional quantum formalism.

Information-Theoretic Princple Entails Orthomodularity of a Lattice

No HeadingQuantum logical axiomatic systems for quantum theory usually include a postulate that a lattice under consideration is orthomodular. We propose a derivation of orthomodularity from an information-theoretic axiom. This provides conceptual clarity and removes a long-standing puzzle about the meaning of orthomodularity.

Which Fine-Tuning Arguments Are Fine?

Fine-tuning arguments are a frequent find in the literature on quantum field theory. They are based on naturalness—an aesthetic criterion that was given a precise definition in the debates on the Higgs mechanism. We follow the history of such definitions and of their application at the scale of electroweak symmetry breaking. They give rise to a special interpretation of probability, which we call Gedankenfrequency. Finally, we show that the argument from naturalness has been extended to comparing different models of the physics beyond the Standard Model and that naturalness in this case can at best be understood a socio-historic heuristic.

Reconstructing Instead of Interpreting Quantum Theory

A paradigmatic shift in the foundations of quantum mechanics is recorded, from interpreting to reconstructing quantum theory. Examples of reconstruction are analyzed, and conceptual foundations of the information‐theoretic reconstruction developed. A concept of intentionally incomplete reconstruction is introduced to mark the novel content of research in the foundation of quantum theory.

Quantum Theory as a Critical Regime of Language Dynamics

Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the continuity assumption as two pillars of quantum theory. Our approach sits on these pillars and combines new mathematics with a testable prediction. If the observer is defined by a limit on string complexity, information dynamics leads to an emergent continuous model in the critical regime. Restricting it to a family of binary codes describing ‘bipartite systems,’ we find strong evidence of an upper bound on bipartite correlations equal to 2.82537. This is measurably different from the Tsirelson bound. The Hilbert space formalism emerges from this mathematical investigation as an effective description of a fundamental discrete theory in the critical regime.

Cognitive Barriers in Perception of Nanotechnology

This article is concerned with predictions of future events, such as technological achievements and changes in the human condition that they will bring about. Cognitive barriers arise when human agents are either asked or forced to make judgments and decisions with respect to unknown singular events. This article argues that barriers such as an aversion to not knowing and the impossibility to believe trump expert and ordinary human reasoning. These barriers apply to nanotechnology. To avoid undesired societal effects arising from them, this essay proposes a set of steps designed to foster responsible public dialogue.

Information-theoretic constraints on correlations with indefinite causal order

Reconstructions of quantum theory usually implicitly assume that experimental events are ordered within a global causal structure. The process matrix framework accommodates quantum correlations that violate an inequality verified by all causally ordered correlations. Using a generalized probabilistic framework, we propose three principles constraining bipartite correlations to the quantum bound. Our approach highlights the role of a measure of dependence other than mutual information for an information-theoretic reconstruction of causal structures in quantum theory.

Renormalized entropy of entanglement in relativistic field theory

Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined unless an ultraviolet cutoff is introduced, but it still diverges in the continuum limit. This behavior is generic for arbitrary finite-energy states, hence a conceptual tension with the finite entanglement entropy typical of nonrelativistic quantum systems. We introduce a novel approach to explain the transition from infinite to finite entanglement, based on coarse graining the spatial resolution of the detectors measuring the field state. We show that states with a finite number of particles become localized, allowing an identification between a region of space and the nonrelativistic degrees of freedom of the particles therein contained, and that the renormalized entropy of finite-energy states reduces to the entanglement entropy of nonrelativistic quantum mechanics.

Quantum Observer, Information Theory and Kolmogorov Complexity

The theory itself does not tell us which properties are sufficient for a system to count as a quantum mechanical observer. Thus, it remains an open problem to find a suitable language for characterizing observation. We propose an information-theoretic definition of observer, leading to a mathematical criterion of objectivity using the formalism of Kolmogorov complexity. We also suggest an experimental test of the hypothesis that any system, even much smaller than a human being, can be a quantum mechanical observer.