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Author Archives: rojefferson
Information geometry (part 1/3)
Information geometry is a rather interesting fusion of statistics and differential geometry, in which a statistical model is endowed with the structure of a Riemannian manifold. Each point on the manifold corresponds to a probability distribution function, and the metric … Continue reading
Posted in Minds & Machines, Physics
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Disjoint representations and particle ontology
There is a beautiful paper by Clifton and Halvorson [1], which discusses the ontology of particles in quantum field theory using the famous example of Minkowski vs. Rindler quantizations of a free bosonic field. What is especially nice about this … Continue reading
Posted in Philosophy, Physics
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The ReehSchlieder Theorem
The ReehSchlieder theorem is perhaps the most notorious result in algebraic quantum field theory, simultaneously one of the least intuitive and most fundamental. Denote the vacuum sector of Hilbert space, which consists of all states that can be created from … Continue reading
Posted in Physics
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General covariance, diffeomorphism invariance, and background independence
My attempts to understand the significance of diffeomorphism invariance in general relativity have been hampered by the confusion surrounding active vs. passive transformations, invariance vs. (general) covariance, background independence, etc. This post comprises my ambitious attempt to settle the matter … Continue reading
Posted in Physics
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Decoherence with holography
I recently read an interesting paper [1] that uses holography to study decoherence in stronglycoupled systems. It relies on the fact that, in the case of a linear coupling between the subsystem and the environment, the FeynmanVernon influence functional — … Continue reading
Posted in Physics
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General relativity or gravitons?
Question: How is the existence of a graviton consistent with the GR paradigm of gravity as a purely geometrical effect? Answer: Ontologically, it’s not! Gravitons are predicated on a quantum fieldtheoretic formulation of gravity, while spacetime curvature is the corresponding … Continue reading
Posted in Physics
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Microcausality
Consider a scalar field in dimensions with the standard decomposition into creation and annihilation operators, Then the commutation relations between the creation/annihilation operators, where , imply exact commutativity of spacelike separated fields: where the last step follows from the fact … Continue reading
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A brief history of firewalls
Black hole thermodynamics In 1973, Jacob Bekenstein observed that black holes must be endowed with an entropy in order to preserve the second law of thermodynamics; otherwise, one could decrease the entropy of the universe by simply throwing subsystems with … Continue reading
The Renormalization Group
Why is the universe comprehensible? Wigner referred to this as the “unreasonable effectiveness of mathematics in the natural sciences”, and even Einstein is famous for writing, in 1936, that “[t]he eternal mystery of the world is its comprehensibility… The fact … Continue reading
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Measurement and evolution
In an earlier post, we sketched the basic mathematical description of quantum mechanics, culminating in the general description of quantum states as (reduced) density matrices. We also claimed that generic measurements are not orthogonal projections, and evolution is not unitary. … Continue reading
Posted in Physics
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