In particular, he sketched the essential equivalence between matrix product states (MPS) and restricted Boltzmann machinesThis is discussed in detail by Chen et al. See also good intuition and a helpful physicist-statistician dictionary from Lin and Tegmark.b (RBM) before showing how he and collaborators could train an efficient RBM representations of the states of the transverse-field Ising and XXZ models with a small number of local measurements from the true state.
“There are now five different lines of observational evidence pointing to the existence of Planet Nine,” Konstantin Batygin, a planetary astrophysicist at the California Institute of Technology (Caltech) in Pasadena, said….
…a study that examined the elliptical orbits of six known objects in the Kuiper Belt…all of those Kuiper Belt objects have elliptical orbits that point in the same direction and are tilted about 30 degrees “downward” compared to the plane in which the eight official planets circle the sun…
Using computer simulations of the solar system with a Planet Nine…there should be even more objects tilted a whopping 90 degrees with respect to the solar plane.
[This is akin to a living review, which will hopefully improve from time to time. Last edited 2017-11-26.]
This post will collect some models of decoherence and branching. We don’t have a rigorous definition of branches yet but I crudely define models of branching to be models of decoherenceI take decoherence to mean a model with dynamics taking the form for some tensor decomposition , where is an (approximately) stable orthonormal basis independent of initial state, and where for times and , where is the initial state of and is some characteristic time scale.a which additionally feature some combination of amplification, irreversibility, redundant records, and/or outcomes with an intuitive macroscopic interpretation. I have the following desiderata for models, which tend to be in tension with computational tractability:
Regarding that last one: we would like to recover “classical behavior” in the sense of classical Hamiltonian flow, which (presumably) means continuous degrees of freedom.In principle you could have discrete degrees of freedom that limit, as , to some sort of discrete classical systems, but most people find this unsatisfying.b Branching only becomes unambiguous in some large-N limit, so it seems satisfying models are necessarily messy and difficult to numerically simulate.… [continue reading]
A senior colleague asked me for thoughts on this paper describing a single-preferred-branch flavor of quantum mechanics, and I thought I’d copy them here. Tl;dr: I did not find an important new idea in it, but this paper nicely illustrates the appeal of Finkelstein’s partial-trace decoherence and the ambiguity inherent in connecting a many-worlds wavefunction to our direct observations.
We propose a method for finding an initial state vector which by ordinary Hamiltonian time evolution follows a single branch of many-worlds quantum mechanics. The resulting deterministic system appears to exhibit random behavior as a result of the successive emergence over time of information present in the initial state but not previously observed.
We start by assuming that a precise wavefunction branch structure has been specified. The idea, basically, is to randomly draw a branch at late times according to the Born probability, then to evolve it backwards in time to the beginning of the universe and take that as your initial condition. The main motivating observation is that, if we assume that all branch splittings are defined by a projective decomposition of some subsystem (‘the system’) which is recorded faithfully elsewhere (‘the environment’), then the lone preferred branch — time-evolving by itself — is an eigenstate of each of the projectors defining the splits. In a sense, Weingarten lays claim to ordered consistency [arxiv:gr-qc/9607073] by assuming partial-trace decoherenceNote on terminology: What Finkelstein called “partial-trace decoherence” is really a specialized form of consistency (i.e., a mathematical criterion for sets of consistent histories) that captures some, but not all, of the properties of the physical and dynamical process of decoherence.… [continue reading]
Here is an underemphasized way to frame the relationship between trajectories and symmetries (in the sense of Noether’s theorem)You can find this presentation in “A short review on Noether’s theorems, gauge symmetries and boundary terms” by Máximo Bañados and Ignacio A. Reyes (H/t Godfrey Miller).a . Consider the space of all possible trajectories for a system, a real-valued Lagrangian functional on that space, the “directions” at each point, and the corresponding functional gradient in each direction. Classical solutions are exactly those trajectories such that the Lagrangian is stationary for perturbations in any direction , and continuous symmetries are exactly those directions such that the Lagrangian is stationary for any trajectory . That is,
There are many subtleties obscured in this cartoon presentation, like the fact that a symmetry , being a tangent direction on the manifold of trajectories, can vary with the tangent point it is attached to (as for rotational symmetries). If you’ve never spent a long afternoon with a good book on the calculus of variations, I recommend it.
For nuclear power plants governed by the United States Nuclear Regulatory Commission, SAFSTOR (SAFe STORage) is one of the options for nuclear decommissioning of a shut down plant. During SAFSTOR the de-fuelled plant is monitored for up to sixty years before complete decontamination and dismantling of the site, to a condition where nuclear licensing is no longer required. During the storage interval, some of the radioactive contaminants of the reactor and power plant will decay, which will reduce the quantity of radioactive material to be removed during the final decontamination phase.
The other options set by the NRC are nuclear decommissioning which is immediate dismantling of the plant and remediation of the site, and nuclear entombment which is the enclosure of contaminated parts of the plant in a permanent layer of concrete.Mixtures of options may be used, for example, immediate removal of steam turbine components and condensors, and SAFSTOR for the more heavily radioactive containment vessel. Since NRC requires decommissioning to be completed within 60 years, ENTOMB is not usually chosen since not all activity will have decayed to an unregulated background level in that time.
You’re taking a vacation to Granada to enjoy a Spanish ski resort in the Sierra Nevada mountains. But as your plane is coming in for a landing, you look out the window and realize the airport is on a small tropical island. Confused, you ask the flight attendant what’s wrong. “Oh”, she says, looking at your ticket, “you’re trying to get to Granada, but you’re on the plane to Grenada in the Caribbean Sea.” A wave of distress comes over your face, but she reassures you: “Don’t worry, Granada isn’t that far from here. The Hamming distance is only 1!”.
After you’ve recovered from that side-splitting humor, let’s dissect the frog. What’s the basis of the joke? The flight attendant is conflating two different metrics: the geographic distance and the Hamming distance. The distances are completely distinct, as two named locations can be very nearby in one and very far apart in the other.
Now let’s hear another joke from renowned physicist Chris Jarzynski:
The linear Schrödinger equation, however, does not give rise to the sort of nonlinear, chaotic dynamics responsible for ergodicity and mixing in classical many-body systems. This suggests that new concepts are needed to understand thermalization in isolated quantum systems. – C. Jarzynski, “Diverse phenomena, common themes” [PDF]
Ha! Get it? This joke is so good it’s been told by S. Wimberger“Since quantum mechanics is the more fundamental theory we can ask ourselves if there is chaotic motion in quantum systems as well.… [continue reading]
Crux was known to the Ancient Greeks due to the fact that it can be seen from southern Egypt; Ptolemy regarded it as part of the constellation Centaurus. It was entirely visible as far north as Britain in the fourth millennium BC. However, the precession of the equinoxes gradually lowered its stars below the European horizon, and they were eventually forgotten by the inhabitants of northern latitudes. By AD 400, most of the constellation never rose above the horizon for Athenians.
Zotero 5.0 has significant changes and is out now.
Sentience Institute: “In discussions of effective animal advocacy (EAA) — the field of study for how we can most effectively help animals, also known as effective altruism for animals — there are several important, challenging, and sometimes controversial foundational questions that come up over and over. This post attempts to summarize and catalog the key evidence cited by EAA supporters on each side of these debates for easy reference.”