Links for April 2017

  • Why does a processor need billions of transistors if it’s only ever executing a few dozen instructions per clock cycle?
  • Nuclear submarines as refuges from global catastrophes.
  • Elite Law Firms Cash in on Market Knowledge“:

    …corporate transactions such as mergers and acquisitions or financings are characterized by several salient facts that lack a complete theoretical account. First, they are almost universally negotiated through agents. Transactional lawyers do not simply translate the parties’ bargain into legally enforceable language; rather, they are actively involved in proposing and bargaining over the transaction terms. Second, they are negotiated in stages, often with the price terms set first by the parties, followed by negotiations primarily among lawyers over the remaining non-price terms. Third, while the transaction terms tend to be tailored to the individual parties, in negotiations the parties frequently resort to claims that specific terms are (or are not) “market.” Fourth, the legal advisory market for such transactions is highly concentrated, with a half-dozen firms holding a majority of the market share.

    [Our] claim is that, for complex transactions experiencing either sustained innovation in terms or rapidly changing market conditions, (1) the parties will maximize their expected surplus by investing in market information about transaction terms, even under relatively competitive conditions, and (2) such market information can effectively be purchased by hiring law firms that hold a significant market share for a particular type of transaction.

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Branches and matrix-product states

I’m happy to use this bully pulpit to advertise that the following paper has been deemed “probably not terrible”, i.e., published.

When the wave function of a large quantum system unitarily evolves away from a low-entropy initial state, there is strong circumstantial evidence it develops “branches”: a decomposition into orthogonal components that is indistinguishable from the corresponding incoherent mixture with feasible observations. Is this decomposition unique? Must the number of branches increase with time? These questions are hard to answer because there is no formal definition of branches, and most intuition is based on toy models with arbitrarily preferred degrees of freedom. Here, assuming only the tensor structure associated with spatial locality, I show that branch decompositions are highly constrained just by the requirement that they exhibit redundant local records. The set of all redundantly recorded observables induces a preferred decomposition into simultaneous eigenstates unless their records are highly extended and delicately overlapping, as exemplified by the Shor error-correcting code. A maximum length scale for records is enough to guarantee uniqueness. Speculatively, objective branch decompositions may speed up numerical simulations of nonstationary many-body states, illuminate the thermalization of closed systems, and demote measurement from fundamental primitive in the quantum formalism.
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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.
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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.

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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.
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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.

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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.

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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 bases, 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.

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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.… [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.

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How to think about Quantum Mechanics—Part 0: Measurements are about bases

[Other parts in this series: 0,1,2,3,4,5,6.]

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.[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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