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.
    [arXiv:math-ph/0411058]

    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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Links for October 2016

I will start writing actual blog posts again soon, I promise. But until then, more nerdy space stuff…

  • ExoMars is approaching the Red Planet. The lander enters the atmosphere tomorrow.
  • The United States only operated continuous airborne alert — the maintenance of multiple nuclear-armed bomber aircraft continuously in flight to avoid the possibility of a sneak attack neutralizing the bomber force — during the ’60s, because the accident rate was too high. However, Operation Looking Glass kept at least one emergency command platform in the air around-the-clock for almost 30 years.

    At DEFCON 2 or higher, the Looking Glass pilot and co-pilot were both required to wear an eye patch, retrieved from their Emergency War Order (EWO) kit. In the event of a surprise blinding flash from a nuclear detonation, the eye patch would prevent blindness in the covered eye, thus enabling them to see in at least one eye and continue flying. Later, the eye patch was replaced by goggles that would instantaneously turn opaque when exposed to a nuclear flash, then rapidly clear for normal vision.

    They also continuously maintained airplanes flying over the ocean, dangling antenna into the water, to ensure constant communication with submarines. This stopped in 1991.

  • Very relatedly, former Secretary of Defense William Perry is teaching a MOOC about the continuing modern risk of nuclear weapons.
  • A history of the Project Orion. Abtract:

    The race to the Moon dominated manned space flight during the 1960’s. and culminated in Project Apollo. which placed 12 humans on the Moon. Unbeknownst to the public at that time, several U.S. government agencies sponsored a project that could have conceivably placed 150 people on the Moon, and eventually sent crewed expeditions to Mars and the outer planets.

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Executive branch reasonable on AI

President Obama was directly asked in a Wired interview about the dangers Bostrom raises regarding AI. From the transcript:

DADICH: I want to center our conversation on artificial intelligence, which has gone from science fiction to a reality that’s changing our lives. When was the moment you knew that the age of real AI was upon us?

OBAMA: My general observation is that it has been seeping into our lives in all sorts of ways, and we just don’t notice; and part of the reason is because the way we think about AI is colored by popular culture. There’s a distinction, which is probably familiar to a lot of your readers, between generalized AI and specialized AI. In science fiction, what you hear about is generalized AI, right? Computers start getting smarter than we are and eventually conclude that we’re not all that useful, and then either they’re drugging us to keep us fat and happy or we’re in the Matrix. My impression, based on talking to my top science advisers, is that we’re still a reasonably long way away from that. It’s worth thinking about because it stretches our imaginations and gets us thinking about the issues of choice and free will that actually do have some significant applications for specialized AI, which is about using algorithms and computers to figure out increasingly complex tasks. We’ve been seeing specialized AI in every aspect of our lives, from medicine and transportation to how electricity is distributed, and it promises to create a vastly more productive and efficient economy. If properly harnessed, it can generate enormous prosperity and opportunity. But it also has some downsides that we’re gonna have to figure out in terms of not eliminating jobs.

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Links for August-September 2016

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Abstracts for July-August 2016

  • Local dark matter searches with LISA
    Massimo Cerdonio, Roberto De Pietri, Philippe Jetzer and Mauro Sereno
    The drag-free satellites of LISA will maintain the test masses in geodesic motion over many years with residual accelerations at unprecedented small levels and time delay interferometry (TDI) will keep track of their differential positions at a level of picometers. This may allow investigations of fine details of the gravitational field in the solar system previously inaccessible. In this spirit, we present the concept of a method for measuring directly the gravitational effect of the density of diffuse local dark matter (LDM) with a constellation of a few drag-free satellites, by exploiting how peculiarly it would affect their relative motion. Using as a test-bed an idealized LISA with rigid arms, we find that the separation in time between the test masses is uniquely perturbed by the LDM, so that they acquire a differential breathing mode. Such an LDM signal is related to the LDM density within the orbits and has characteristic spectral components, with amplitudes increasing in time, at various frequencies of the dynamics of the constellation. This is the relevant result in that the LDM signal is brought to non-zero frequencies.
  • We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics.
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Three arguments on the measurement problem

When talking to folks about the quantum measurement problem, and its potential partial resolution by solving the set selection problem, I’ve recently been deploying three nonstandard arguments. To a large extent, these are dialectic strategies rather than unique arguments per se. That is, they are notable for me mostly because they avoid getting bogged down in some common conceptual dispute, not necessarily because they demonstrate something that doesn’t formally follow from traditional arguments. At least two of these seem new to me, in the sense that I don’t remember anyone else using them, but I strongly suspect that I’ve just appropriated them from elsewhere and forgotten. Citations to prior art are highly appreciated.

Passive quantum mechanics

There are good reasons to believe that, at the most abstract level, the practice of science doesn’t require a notion of active experiment. Rather, a completely passive observer could still in principle derive all fundamental physical theories simply by sitting around and watching. Science, at this level, is about explaining as many observations as possible starting from as minimal assumptions as possible. Abstractly we frame science as a compression algorithm that tries to find the programs with the smallest Kolmogorov complexity that reproduces observed data.

Active experiments are of course useful for at least two important reasons: (1) They gather strong evidence for causality by feeding a source of randomness into a system to test a causal model, and (2) they produce sources of data that are directly correlated with systems of interest rather than relying on highly indirect (and perhaps computationally intractable) correlations. But ultimately these are practical considerations, and an inert but extraordinarily intelligent observer could in principle derive general relativity, quantum mechanics, and field theoryOf course, there may be RG-reasons to think that scales decouple, and that to a good approximation the large-scale dynamics are compatible with lots of possible small-scale dynamics.[continue reading]