Comments on Cotler, Penington, & Ranard

One way to think about the relevance of decoherence theory to measurement in quantum mechanics is that it reduces the preferred basis problem to the preferred subsystem problem; merely specifying the system of interest (by delineating it from its environment or measuring apparatus) is enough, in important special cases, to derive the measurement basis. But this immediately prompts the question: what are the preferred systems? I spent some time in grad school with my advisor trying to see if I could identify a preferred system just by looking at a large many-body Hamiltonian, but never got anything worth writing up.

I’m pleased to report that Cotler, Penington, and Ranard have tackled a closely related problem, and made a lot more progress:

Locality from the Spectrum
Jordan S. Cotler, Geoffrey R. Penington, Daniel H. Ranard
Essential to the description of a quantum system are its local degrees of freedom, which enable the interpretation of subsystems and dynamics in the Hilbert space. While a choice of local tensor factorization of the Hilbert space is often implicit in the writing of a Hamiltonian or Lagrangian, the identification of local tensor factors is not intrinsic to the Hilbert space itself. Instead, the only basis-invariant data of a Hamiltonian is its spectrum, which does not manifestly determine the local structure. This ambiguity is highlighted by the existence of dualities, in which the same energy spectrum may describe two systems with very different local degrees of freedom. We argue that in fact, the energy spectrum alone almost always encodes a unique description of local degrees of freedom when such a description exists, allowing one to explicitly identify local subsystems and how they interact.
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Links for March 2017

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Research debt

Chris Olah coins the term “research debt” to discuss a bundle of related destructive phenomena in research communities:

  • Poor Exposition – Often, there is no good explanation of important ideas and one has to struggle to understand them. This problem is so pervasive that we take it for granted and don’t appreciate how much better things could be.
  • Undigested Ideas – Most ideas start off rough and hard to understand. They become radically easier as we polish them, developing the right analogies, language, and ways of thinking.
  • Bad abstractions and notation – Abstractions and notation are the user interface of research, shaping how we think and communicate. Unfortunately, we often get stuck with the first formalisms to develop even when they’re bad. For example, an object with extra electrons is negative, and pi is wrong.
  • Noise – Being a researcher is like standing in the middle of a construction site. Countless papers scream for your attention and there’s no easy way to filter or summarize them. We think noise is the main way experts experience research debt.

Shout it from the rooftops (my emphasis):

It’s worth being clear that research debt isn’t just about ideas not being explained well. It’s a lack of digesting ideas – or, at least, a lack of the public version of ideas being digested. It’s a communal messiness of thought.

Developing good abstractions, notations, visualizations, and so forth, is improving the user interfaces for ideas. This helps both with understanding ideas for the first time and with thinking clearly about them. Conversely, if we can’t explain an idea well, that’s often a sign that we don’t understand it as well as we could…

Distillation is also hard.

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Abstracts for March 2017

  • Recent progress in synthetic chemistry and molecular quantum optics has enabled demonstrations of the quantum mechanical wave–particle duality for complex particles, with masses exceeding 10 kDa. Future experiments with even larger objects will require new optical preparation and manipulation methods that shall profit from the possibility to cleave a well-defined molecular tag from a larger parent molecule. Here we present the design and synthesis of two model compounds as well as evidence for the photoinduced beam depletion in high vacuum in one case.

    The technique of using “laser grating”, in place of physical grating (slits), for producing spatial interference of molecules relies on the laser’s ability to ionize the molecule. (Once ionized, standing electric fields can sweep it out of the way.) But for some molecules, especially large nanoparticles, this is ineffective. Solution: attach a molecular tag to the nanoparticle that reliably cleaves in the presence of a laser, allowing the nanoparticle to be vacuumed up. Rad.

  • This chapter discusses the asymptotics, singularities, and the reduction of theories. The reduction must involve the study of limits—asymptotics. The reduction is obstructed by the fact that the limit is highly singular. In addition, the type of singularity is important, and the singularities are directly connected to the existence of emergent phenomena and underlie some of the most difficult and intensively studied problems in physics today. The chapter provides six examples of singular limits and emergent phenomena such as special relativity and statistical mechanics. Reduction in its simplest form is well illustrated by special relativity.
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Links for February 2017

  • If you are a high school student, or know one, who would be interested in the SPARC summer camp, the deadline is March 1.

    SPARC helps talented high school students apply their quantitative thinking skills to their lives and the world.

    SPARC will be hosted in the San Francisco Bay Area from August 6 – 17, with students arriving the evening of the 6th and leaving the morning of the 17th. Room and board are provided free of charge.

    The curriculum covers topics from causal modeling and probability to game theory and cognitive science. But the focus of SPARC is on applying the same quantitative and rigorous spirit outside of the classroom. How can we understand our own reasoning and behavior? How can we think more clearly and better achieve our goals?

  • Indian Space Research Organisation’s Polar Satellite Launch Vehicle successfully launched 104 satellites into orbit on the same mission. Onboard video of the deployment:

    Pictures of some of the cubesats, including Planet‘s 88 imagining satellites for continuous Earth monitoring.
  • What is a ‘Shavers Only’ Electrical Outlet?
  • A possible rare shake-up of the GiveWell list: temporary subsidies for migrant workers in India.
  • How to think about cell walls:

    I most cells, the cell wall is flexible, meaning that it will bend rather than holding a fixed shape, but has considerable tensile strength. The apparent rigidity of primary plant tissues is enabled by cell walls, but is not due to the walls’ stiffness. Hydraulic turgor pressure creates this rigidity, along with the wall structure. The flexibility of the cell walls is seen when plants wilt, so that the stems and leaves begin to droop, or in seaweeds that bend in water currents.

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Links for January 2017

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Weinberg on the measurement problem

In his new article in the NY Review of Books, the titan Steven Weinberg expresses more sympathy for the importance of the measurement problem in quantum mechanics. The article has nothing new for folks well-versed in quantum foundations, but Weinberg demonstrates a command of the existing arguments and considerations. The lengthy excerpts below characterize what I think are the most important aspects of his view.

Many physicists came to think that the reaction of Einstein and Feynman and others to the unfamiliar aspects of quantum mechanics had been overblown. This used to be my view. After all, Newton’s theories too had been unpalatable to many of his contemporaries…Evidently it is a mistake to demand too strictly that new physical theories should fit some preconceived philosophical standard.

In quantum mechanics the state of a system is not described by giving the position and velocity of every particle and the values and rates of change of various fields, as in classical physics. Instead, the state of any system at any moment is described by a wave function, essentially a list of numbers, one number for every possible configuration of the system….What is so terrible about that? Certainly, it was a tragic mistake for Einstein and Schrödinger to step away from using quantum mechanics, isolating themselves in their later lives from the exciting progress made by others. Even so, I’m not as sure as I once was about the future of quantum mechanics. It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means. The dispute arises chiefly regarding the nature of measurement in quantum mechanics…

The introduction of probability into the principles of physics was disturbing to past physicists, but the trouble with quantum mechanics is not that it involves probabilities.

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Singular value decomposition in bra-ket notation

In linear algebra, and therefore quantum information, the singular value decomposition (SVD) is elementary, ubiquitous, and beautiful. However, I only recently realized that its expression in bra-ket notation is very elegant. The SVD is equivalent to the statement that any operator \hat{M} can be expressed as

(1)   \begin{align*} \hat{M} = \sum_i \vert A_i \rangle \lambda_i \langle B_i \vert \end{align*}

where \vert A_i \rangle and \vert B_i \rangle are orthonormal sets of vectors, possibly in Hilbert spaces with different dimensionality, and the \lambda_i \ge 0 are the singular values.

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Links for December 2016

Late, alas. Also: there have been a couple of complaints about the spam filter for comments on this blog, and I’m trying to track down the issue. The filter is supposed to tell you what’s wrong and help you successfully post the comment. If you’ve been unable to get past the filter, or if it’s just too much of a hassle even when you can get past it, please let me know so I can try to fix this.

  • Europe’s Galileo satellite navigation system recently went online, although without yet a complete constellation. In just a few years, there will be a full four independent navigations from great powers: the EU, the US (GPS), Russia (GLONASS), and China (BeiDou). Devices are already being built to use all four systems at once. Everyone wins through the increased redundancy and satellite count.
  • Design of the Solo cup.
  • I highly recommend this semi-technical talk on ARC fusion reactor design by Dennis Whyte.

    (Video DownloadHelper allows downloading video off YouTube.)

    Proposed in 2014 by Whyte and collaborators, ARC is a newer but only under-development alternative to traditional Tokamak-style reactor, where rare earth barium copper oxide (ReBCo) superconductors play a crucial role. Whyte argues that the key hold-up on fusion reactors is their absolute size, which necessitate large-scale, lumbering international collaboration. ReBCo superconductors are the key technical advance allowing smaller magnetic confinement. The parameters of these designs scale extremely well with increased magnetic field. Significant downsides include increased vessel pressure and pulsed operation because of intrinsic limitations on neutrons shielding.The fusion fuel is deuterium and tritium, which is most amenable choice of reactant on the fusion slope of the nuclei binding energy curve.

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Comments on Bousso’s communication bound

Bousso has a recent paper bounding the maximum information that can be sent by a signal from first principles in QFT:

I derive a universal upper bound on the capacity of any communication channel between two distant systems. The Holevo quantity, and hence the mutual information, is at most of order E\Delta t/\hbar, where E the average energy of the signal, and \Delta t is the amount of time for which detectors operate. The bound does not depend on the size or mass of the emitting and receiving systems, nor on the nature of the signal. No restrictions on preparing and processing the signal are imposed. As an example, I consider the encoding of information in the transverse or angular position of a signal emitted and received by systems of arbitrarily large cross-section. In the limit of a large message space, quantum effects become important even if individual signals are classical, and the bound is upheld.

Here’s his first figure:

This all stems from vacuum entanglement, an oft-neglected aspect of QFT that Bousso doesn’t emphasize in the paper as the key ingredient.I thank Scott Aaronson for first pointing this out. a   The gradient term in the Hamiltonian for QFTs means that the value of the field at two nearby locations is always entangled. In particular, the value of \phi(x) and \phi(x+\Delta x) are sometimes considered independent degrees of freedom but, for a state with bounded energy, they can’t actually take arbitrarily different values as \Delta x becomes small, or else the gradient contribution to the Hamiltonian violates the energy bound. Technically this entanglement exists over arbitrary distances, but it is exponentially suppressed on scales larger than the Compton wavelength of the field.… [continue reading]

Links for November 2016

  • Somehow I had never heard of Georges Lemaître, Jesuit priest:

    [Lemaître] proposed the theory of the expansion of the universe, widely misattributed to Edwin Hubble. He was the first to derive what is now known as Hubble’s law and made the first estimation of what is now called the Hubble constant, which he published in 1927, two years before Hubble’s article. Lemaître also proposed what became known as the Big Bang theory of the origin of the universe, which he called his “hypothesis of the primeval atom” or the “Cosmic Egg”.

    (H/t Sean Carroll.)

  • Pangolins are weird.

    (H/t Will Riedel.)
  • An interview about the Merriam-Webster twitter account.
  • Jon Baez’s excellent coverage of Jarzynksi.
  • The presidential scandal out of South Korea is more bizarre than previously reported. (H/t Will Eden.)
  • An anonymous Physics.SE user, on the meaning of Haag’s theorem and attempts to make quantum field theory mathematically rigorous:

    This is a little bit like the development of calculus, which underlies Newtonian mechanics. It took a long time, and was clearly a very valuable exercise for both mathematics and physics. But, long before the subject was rigorously defined it was clear that Newtonian mechanics was correct, but the correct language for it does not exist yet. So, I think Haag’s theorem demonstrates that we are at the same stage of development of QFT.

  • Stimulating the vestibular system (inner ear balance) leads to neat fat-loss effects.
  • Steve Hsu links to and discusses the work of Ted Chiang (1, 2, 3), whose short work “Story of your life” has recently been made into the movie “Arrival”. (The PDF can be found with some light Googling.)
  • Inside the world of Australian opal miners who live underground“.
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How to think about Quantum Mechanics—Part 1: Measurements are about bases

[This post was originally “Part 0”, but it’s been moved. Other parts in this series: 1,2,3,4,5,6,7.]

In an ideal world, the formalism that you use to describe a physical system is in a one-to-one correspondence with the physically distinct configurations of the system. But sometimes it can be useful to introduce additional descriptions, in which case it is very important to understand the unphysical over-counting (e.g., gauge freedom). A scalar potential V(x) is a very convenient way of representing the vector force field, F(x) = \partial V(x), but any constant shift in the potential, V(x) \to V(x) + V_0, yields forces and dynamics that are indistinguishable, and hence the value of the potential on an absolute scale is unphysical.

One often hears that a quantum experiment measures an observable, but this is wrong, or very misleading, because it vastly over-counts the physically distinct sorts of measurements that are possible. It is much more precise to say that a given apparatus, with a given setting, simultaneously measures all observables with the same eigenvectors. More compactly, an apparatus measures an orthogonal basis – not an observable.We can also allow for the measured observable to be degenerate, in which case the apparatus simultaneously measures all observables with the same degenerate eigenspaces. To be abstract, you could say it measures a commuting subalgebra, with the nondegenerate case corresponding to the subalgebra having maximum dimensionality (i.e., the same number of dimensions as the Hilbert space). Commuting subalgebras with maximum dimension are in one-to-one correspondence with orthonormal bases, modulo multiplying the vectors by pure phases. a   You can probably start to see this by just noting that there’s no actual, physical difference between measuring X and X^3; the apparatus that would perform the two measurements are identical.… [continue reading]

PI accepting 2017 master’s student applications

The Perimeter Scholars International (PSI) program is now accepting applications for this Master’s program, to start next fall. The due date is Feb 1st. Me previously:

If you’re in your last year as an undergrad, I strongly advise you (seriously) to consider applying. Your choice of grad school is 80% of the selection power determining your thesis topic, and that topic places very strong constraints on your entire academic career. The more your choice is informed by actual physics knowledge (rather than the apparent impressiveness of professors and institutions), the better. An additional year at a new institution taking classes with new teachers can really help.

Here’s the poster and a brand new propaganda video:
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Sank argues for a SciRate issue tracker

SciRate is the best location I know of for public discussion and feedback on academic papers, and is an impressive open-source achievement by Adam Harrow and collaborators. Right now it has the most traction in the field of quantum informationQuantum info leading the way, as usual… a  , but it could stand to become more popular, and to expand into other fields.

My colleague and good friend Dan Sank proposes a small but important tweak for SciRate: issue tracking, à la GitHub.

Issues in Scirate?

Scirate enables us to express comments/opinions on published works. Another very useful kind of feedback for research papers is issues. By “issue” I mean exactly the kind of thing I’m writing right now: a description of

  1. a problem with the work which can be definitively fixed, or
  2. a possible improvement to that product.

This differs from comments which are just statements of opinion which don’t require any reaction from the author. We all know that issues are essential in developing software, and based on a recent experience where I used github to host development of a research paper with three coauthors and more than a dozen group members providing feedback, I think that issues should also be used for research papers.

It might be nice to attach an issue tracker to Scirate, or at least have Scirate give links to an external issue tracker attached to each paper.

Why not just use a public github repo and get the issue tracker for free?

Making a github repo public makes everything public, including any sensitive information including comments about particular works/people. Having written a paper using github, I can imagine the authors would not want to make that repo public before going through the entire issue history making sure nobody said anything embarrassing/demeaning/etc.

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Abstracts for October 2016

  • One of von Neumann's motivations for developing the theory of operator algebras and his and Murray's 1936 classification of factors was the question of possible decompositions of quantum systems into independent parts. For quantum systems with a finite number of degrees of freedom the simplest possibility, i.e. factors of type I in the terminology of Murray and von Neumann, are perfectly adequate. In relativistic quantum field theory (RQFT), on the other hand, factors of type III occur naturally. The same holds true in quantum statistical mechanics of infinite systems. In this brief review some physical consequences of the type III property of the von Neumann algebras corresponding to localized observables in RQFT and their difference from the type I case will be discussed. The cumulative effort of many people over more than 30 years has established a remarkable uniqueness result: The local algebras in RQFT are generically isomorphic to the unique, hyperfinite type III, factor in Connes' classification of 1973. Specific theories are characterized by the net structure of the collection of these isomorphic algebras for different space-time regions, i.e. the way they are embedded into each other.

    One of the key subtleties about trying to study quantum information in a field theory is that you can’t formally decompose the Hilbert space into a tensor product of spatially local subsystems. The reasons are technical, and rarely explained well. This paper is an exception, giving an excellent introduction to the key ideas, in a manner accessible to a quantum (non-field) information theorist. (See related work by Yngvason this blogpost by Tobias Osborne and my previous discussion re: Reeh-Schielder theorem.)

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