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Category Archives: Physics
What is entropy?
You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really … Continue reading
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Information geometry (part 3/3)
Insofar as quantum mechanics can be regarded as an extension of (classical) probability theory, most of the concepts developed in the previous two parts of this sequence can be extended to quantum information theory as well, thus giving rise to … Continue reading
Posted in Minds & Machines, Physics
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Boundary conditions in AdS/CFT
The issue of boundary conditions in AdS/CFT has confused me for years; not because it’s intrinsically complicated, but because most of the literature simply regurgitates a superficial explanation for the standard prescription which collapses at the first inquiry. Typically, the … Continue reading
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TomitaTakesaki in Rindler space
Rindler space provides a convenient example to elucidate some basic properties of AQFT — specifically TomitaTakesaki theory — in what is arguably the case of greatest interest to highenergy theorists. We shall begin by introducing a few fundamental objects in … Continue reading
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Information geometry (part 2/3)
In the previous post, we introduced the connection, and alluded to a dualistic structure between and . In particular, the cases are intimately related to two important families of statistical models, the exponential or efamily with affine connection , and … Continue reading
Posted in Minds & Machines, Physics
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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
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
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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 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
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