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

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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

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The Reeh-Schlieder Theorem

The Reeh-Schlieder 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

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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

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Decoherence with holography

I recently read an interesting paper [1] that uses holography to study decoherence in strongly-coupled systems. It relies on the fact that, in the case of a linear coupling between the subsystem and the environment, the Feynman-Vernon influence functional — … Continue reading

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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 field-theoretic formulation of gravity, while spacetime curvature is the corresponding … Continue reading

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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

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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

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