How to think about Quantum Mechanics—Part 4: Quantum indeterminism as an anomaly

[Other parts in this series: 1,2,3,4,5,6,7,8.]

I am firmly of the view…that all the sciences are compatible and that detailed links can be, and are being, forged between them. But of course the links are subtle… a mathematical aspect of theory reduction that I regard as central, but which cannot be captured by the purely verbal arguments commonly employed in philosophical discussions of reduction. My contention here will be that many difficulties associated with reduction arise because they involve singular limits….What nonclassical phenomena emerge as h 0? This sounds like nonsense, and indeed if the limit were not singular the answer would be: no such phenomena.Michael Berry

One of the great crimes against humanity occurs each year in introductory quantum mechanics courses when students are introduced to an \hbar \to 0 limit, sometimes decorated with words involving “the correspondence principle”. The problem isn’t with the content per se, but with the suggestion that this somehow gives a satisfying answer to why quantum mechanics looks like classical mechanics on large scales.

Sometimes this limit takes the form of a path integral, where the transition probability for a particle to move from position x_1 to x_2 in a time T is

(1)   \begin{align*} P_{x_1 \to x_2} &= \langle x_1 \vert e^{-i H T} \vert x_2 \rangle \\ &\propto \int_{x_1,x_2} \mathcal{D}[x(t)] e^{-i S[x(t),x'(t)]/\hbar} = \int_{x_1,x_2} \mathcal{D}[x(t)] e^{-i \int_0^T \mathrm{d}t L(x(t),x'(t))/\hbar} \end{align*}

where \int_{x_1,x_2} \mathcal{D}[x(t)] is the integral over all paths from x_1 to x_2, and S[x(t),x'(t)]= \int_0^T \mathrm{d}t L(x(t),x'(t)) is the action for that path (L being the Lagrangian corresponding to the Hamiltonian H). As \hbar \to 0, the exponent containing the action spins wildly and averages to zero for all paths not in the immediate vicinity of the classical path that make the action stationary.

Other times this takes the form of Ehrenfest’s theorem, which shows that the expectation values of functions of position and momentum follow the classical equations of motion.… [continue reading]

Links for February 2015

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Decoherence detection and micromechanical resonators

In this post I want to lay out why I am a bit pessimistic about using quantum micromechanical resonators, usually of the optomechanical variety, for decoherence detection. I will need to rely on some simple ideas from 3-4 papers I have “in the pipeline” (read: partially written TeX files) that seek to make precise the sense in which decoherence detection allows us to detect classical undetectable phenomena, and to figure out exactly what sort of phenomena we should apply it to. So this post will sound vague without that supporting material. Hopefully it will still be useful, at least for the author.

The overarching idea is that decoherence detection is only particularly useful when the experimental probe can be placed in a superposition with respect to a probe’s natural pointer basis. Recall that the pointer basis is the basis in which the density matrix of the probe is normally restricted to be approximately diagonal by the interaction with the natural environment. Classically detectable phenomena are those which cause transitions within the pointer basis, i.e. driving the system from one pointer state to another. Classically undetectable phenomena are those which cause pure decoherence with respect to this basis, i.e. they add a decoherence factor to off-diagonal terms in this basis, but preserve on-diagonal terms.

The thing that makes this tricky to think about is that the pointer basis is overcomplete for most physically interesting situations, in particular for any continuous degree of freedom like the position of a molecule or a silicon nanoparticle. It’s impossible to perfectly localize a particle, and the part of the Hamiltonian that fights you on this, p^2/2m, causes a smearing effect that leads to the overcompleteness.… [continue reading]

Bateman et al. dark matter model in the news

As previously reported, Bateman, McHardy, Merle, Morris, and Ulbricht ran with the idea of detecting dark matter with large quantum superpositions and have proposed an explicit dark matter model that could be tested by the proposed MAQRO satellite . That paper is now in print , and it has gotten a bit of press!


Top: What space looks like right now. Pretty boring. Bottom left: The innards of the LPF science spacecraft, on which the MAQRO experiment would be built. Bottom right: MAQRO in space. Cf. top image. Notice the change in awesomeness.

All aboard the hype train! If this satellite gets built, it WILL discover dark matter, and probably extra dimensions, a solution to the is-ought problem, and the secret to true happiness.

EDIT 2015-2-16: Here is a copy of the proposal recently submitted by the MAQRO consortium, led by Rainer Kaltenbaek, for the M4 satellite mission slot with the European Space Agency.

EDIT 2015-3-10: I was bummed to find out that MAQRO did not make the short list for the M4 slot. The updated version of the proposal is now available on the arXiv. Hats off to Rainer for the excellent submission. Here’s looking to M5, just 36 months down the road!

References

Bateman, James, Ian McHardy, Alexander Merle, Tim R. Morris, and Hendrik Ulbricht. 2015. “On the Existence of Low-Mass Dark Matter and Its Direct Detection.” Scientific Reports 5 (January): 8058. https://doi.org/10.1038/srep08058.
Riedel, C. Jess. 2013. “Direct Detection of Classically Undetectable Dark Matter through Quantum Decoherence.” Physical Review D 88 (11): 116005. https://doi.org/10.1103/PhysRevD.88.116005.
Kaltenbaek, Rainer, Gerald Hechenblaikner, Nikolai Kiesel, Oriol Romero-Isart, Keith C.
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Links for January 2015

  • There’s been some coverage of using etching to produce superhydrophobic metals. Unfortunately, it probably suffers from the same durability issues (no resistance to being destroyed through normal wear) as previous techniques that used special chemical coatings.
  • A funnel plot is a quick graphical way to check for publication bias on a topic.
  • Apparently, the best way to avoid a fight with a confrontational Red Kangaroo (the largest kangaroo species) is to give a deep cough. This is a signal of submission by subdominant males, and can assure the dominant male that you aren’t challenging him. Otherwise…

  • Daniel Dennett, synthesizing Anatol Rapoport, on how to compose a successful critical commentary:

    • You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says, “Thanks, I wish I’d thought of putting it that way.
    • You should list any points of agreement (especially if they are not matters of general or widespread agreement).
    • You should mention anything you have learned from your target.
    • Only then are you permitted to say so much as a word of rebuttal or criticism.

    If only the same code of conduct could be applied to critical commentary online, particularly to the indelible inferno of comments.

    But rather than a naively utopian, Pollyannaish approach to debate, Dennett points out this is actually a sound psychological strategy that accomplishes one key thing: It transforms your opponent into a more receptive audience for your criticism or dissent, which in turn helps advance the discussion.

    (H/t Rob Wiblin.) Although most folks have heard and approve of many of these tips, it’s common for people to get lazy about implementing them because, frankly, it’s kind of a lot of work.

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Records decomposition talk

Last month Scott Aaronson was kind enough to invite me out to MIT to give a seminar to the quantum information group. I presented a small uniqueness theorem which I think is an important intermediary result on the way to solving the set selection problem (or, equivalently, to obtaining an algorithm for breaking the wavefunction of the universe up into branches). I’m not sure when I’ll have a chance to write this up formally, so for now I’m just making the slides available here.

Screen Shot 2015-01-26 at 7.42.02 AM

Scott’s a fantastic, thoughtful host, and I got a lot of great questions from the audience. Thanks to everyone there for having me.… [continue reading]

Musk donates $10M to Future of Life Institute

The Future of Life Institute (FLI) is a group of folks, mostly academics with a few notable celebrities, who are jointly concerned about existential risk, especially risks from technologies that are expected to emerge in the coming decades. In particular, prominent physicists Anthony Aguirre, Alan Guth, Stephen Hawking, Saul Perlmutter, Max Tegmark, and Frank Wilczek are on the advisory board. I attended their public launch event at MIT in May (a panel discussion), and I am lucky to be acquainted with a few of the members and supporters. Although not a self-described Effective Altruist (EA) organization, FLI has significant overlap in philosophy, methods, and personnel with other EA groups.

One of the chief risks that FLI is concerned with is the safe development of artificial intelligence in the long term. Oxford Philosopher Nick Bostrom has a new book out on this topic, which seems to have convinced nerd hero Elon Musk that AI risk is a valid concern. Yesterday, Musk made a $10 million donation to FLI to fund grants for researchers in this area.

This is a big deal for those who think that there is a huge underinvestment in this sort of work. It’s also good fodder for journalists who like to write about killer robots. I expect the quality of the public discussion about this to be…low.

EDIT: The grant application process is now open. … [continue reading]

Links for December 2014

  • Steve Hsu notes that BGI has applied preimplantation genetic diagnosis (PGD) using next-generation sequencing techniques. Previous uses of PGD have only used simple screening methods, like searching for single-nucleotide polymorphisms, to avoid implanting embryos with a handful of well-understood genetic defects (which are then destroyed). Next generation methods have the potential to sequence most/all of the genome, allowing for traits influences by many genes to be selected for, like height and intelligence.
  • Crab housing exchange.
  • That the National Reconnaissance Office publicly releases the mission patches for their highly classified satellites is well-known on the internet, but I hadn’t realized that there was reason to think that classified details had been accidentally leaked through them in the past.
  • If correct, this is a surprisingly comprehensive and intuitive answer to many aspects of human bilateral (a)symmetry:

    Most of our asymmetry is due to just two organ systems: the GI tract and the heart. The concept that best explains the shape of both of these systems is the idea that a long organ that has to fit in a small body does so by being wound up.

    The heart could be composed of a linear arrangement of a pump, the lungs, and then a second pump. In some organisms like the worm, the heart is a linear pump. However the human body cannot accommodate a linear arrangement and thus we have what is effectively a tube curled up on itself.

    The GI tract is the same story. It would be hugely long if a linear, thus it has to be wound up inside of us. There is no symmetrical way to wind it up. Many organs like the pancreas and the liver actually bud off of the GI tract during development so the asymmetry of the GI tract explains the asymmetry of many of the other abdominal organs.

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