Redundant consistency

I’m happy to announce the recent publication of a paper by Mike, Wojciech, and myself.

[ArXiv version.]

Consistent histories is the (essentially unique) formalism for describing the past in a fully quantum universe, and this paper shows how to talk about realistic, localized, and above all redundant records about that past. The paper is longer than usual, but that’s mostly pedagogy; the new content is very compact.

The introduction contains a summary of the set selection problem, with a historical overview and many references. If my ranting about the importance of this problem has got you curious enough to dive into the literature, this is where I recommend you start (even if you don’t care about redundant information and Darwinism).

The second and third sections of the paper contain condensed summaries of decoherence & quantum Darwinism, and the consistent histories framework, respectively. We’re trying to tie together two pretty different topics, so we figured many readers would be familiar with only one or the other. But if you’ve seen that stuff before, then skip it.

The meat is in the fourth section, where we extend an old and underappreciated idea due to Finkelstein that links decoherence with consistent histories. Sections five and six are examples and discussion.

This paper will eventually be followed up by a sequel that fleshes out the connection with prior work on quantum Darwinism, but it may have to wait until I’ve got a permanent job…… [continue reading]

KS entropy generated by entanglement-breaking quantum Brownian motion

A new paper of mine (PRA 93, 012107 (2016), arXiv:1507.04083) just came out. The main theorem of the paper is not deep, but I think it’s a clarifying result within a formalism that is deep: ideal quantum Brownian motion (QBM) in symplectic generality. In this blog post, I’ll refresh you on ideal QBM, quote my abstract, explain the main result, and then — going beyond the paper — show how it’s related to the Kolmogorov-Sinai entropy and the speed at which macroscopic wavefunctions branch.

Ideal QBM

If you Google around for “quantum Brownian motion”, you’ll come across a bunch of definitions that have quirky features, and aren’t obviously related to each other. This is a shame. As I explained in an earlier blog post, ideal QBM is the generalization of the harmonic oscillator to open quantum systems. If you think harmonic oscillator are important, and you think decoherence is important, then you should understand ideal QBM.

Harmonic oscillators are ubiquitous in the world because all smooth potentials look quadratic locally. Exhaustively understanding harmonic oscillators is very valuable because they are exactly solvable in addition to being ubiquitous. In an almost identical way, all quantum Markovian degrees of freedom look locally like ideal QBM, and their completely positive (CP) dynamics can be solved exactly.

To get true generality, both harmonic oscillators and ideal QBM should be expressed in manifestly symplectic covariant form. Just like for Lorentz covariance, a dynamical equation that exhibits manifest symplectic covariance takes the same form under linear symplectic transformations on phase space. At a microscopic level, all physics is symplectic covariant (and Lorentz covariant), so this better hold.… [continue reading]

My talk on dark matter decoherence detection

I gave a talk recently on Itay’s and my latests results for detecting dark matter through the decoherence it induces in matter interferometers.

[Download MP4]If you ever have problems finding the direct download link for videos on PI’s website (they are sometimes missing), this Firefox extension seems to do the trick.a  

Relevant paper on the diffusion SQL is here: . The main dark matter paper is still a work in progress.

Footnotes

(↵ returns to text)

  1. If you ever have problems finding the direct download link for videos on PI’s website (they are sometimes missing), this Firefox extension seems to do the trick.
[continue reading]

Comments on Myrvold’s Taj Mahal

Last week I saw an excellent talk by philosopher Wayne Myrvold.

(Download MP4 video here.)

The topic was well-defined, and of reasonable scope. The theorem is easily and commonly misunderstood. And Wayne’s talk served to dissolve the confusion around it, by unpacking the theorem into a handful of pieces so that you could quickly see where the rub was. I would that all philosophy of physics were so well done.

Here are the key points as I saw them:

  • The vacuum state in QFTs, even non-interacting ones, is entangled over arbitrary distances (albeit by exponentially small amounts). You can think of this as every two space-like separated regions of spacetime sharing extremely diluted Bell pairs.
  • Likewise, by virtue of its non-local nature, the vacuum contains non-zero (but stupendously tiny) overlap with all localized states. If you were able to perform a “Taj-Mahal measurement” on a region R, which ask the Yes-or-No question “Is there a Taj Mahal in R?”, you always have a non-zero (but stupendously tiny) chance of getting “Yes” and finding a Taj Mahal.
  • This non-locality arises directly from requiring the exact spectral condition, i.e., that the Hamiltonian is bounded from below. This is because the spectral condition is a global statement about modes in spacetime. It asserts that allowed states have overlap only with the positive part of the mass shell.
  • This is very analogous to the way that analytic functions are determined by their behavior in an arbitrarily small open patch of the complex plane.
  • This theorem says that some local operator, when acting on the vacuum, can produce the Taj-Mahal in a distant, space-like separated region of space-time.
[continue reading]

How fast do macroscopic wavefunctions branch?

Over at PhysicsOverflow, Daniel Ranard asked a question that’s near and dear to my heart:

How deterministic are large open quantum systems (e.g. with humans)?

Consider some large system modeled as an open quantum system — say, a person in a room, where the walls of the room interact in a boring way with some environment. Begin with a pure initial state describing some comprehensible configuration. (Maybe the person is sitting down.) Generically, the system will be in a highly mixed state after some time. Both normal human experience and the study of decoherence suggest that this state will be a mixture of orthogonal pure states that describe classical-like configurations. Call these configurations branches.

How much does a pure state of the system branch over human time scales? There will soon be many (many) orthogonal branches with distinct microscopic details. But to what extent will probabilities be spread over macroscopically (and noticeably) different branches?

I answered the question over there as best I could. Below, I’ll reproduce my answer and indulge in slightly more detail and speculation.

This question is central to my research interests, in the sense that completing that research would necessarily let me give a precise, unambiguous answer. So I can only give an imprecise, hand-wavy one. I’ll write down the punchline, then work backwards.

Punchline

The instantaneous rate of branching, as measured in entropy/time (e.g., bits/s), is given by the sum of all positive Lyapunov exponents for all non-thermalized degrees of freedom.

Most of the vagueness in this claim comes from defining/identifying degree of freedom that have thermalized, and dealing with cases of partial/incomplete thermalization; these problems exists classically.

Elaboration

The original question postulates that the macroscopic system starts in a quantum state corresponding to some comprehensible classical configuration, i.e., the system is initially in a quantum state whose Wigner function is localized around some classical point in phase space.… [continue reading]

Loophole-free Bell violations

The most profound discovery of science appears to be confirmed with essentially no wiggle room. The group led by Ronald Hanson at the Delft University of Technology in the Netherlands claim to have reported a loophole-free observation of Bell violations. Links:

I hope Matt Leifer is right and they give a Nobel Prize for this work.

EDIT Nov 12: Two other groups, who were clearly in a very close race, have just posted their loophole-free experiments: and . (H/t Peter Morgan. Also, note the sequential numbers.) Delft’s group published as soon as they had sufficient statistics to reasonably exclude local realism, but the two runner-ups have collected gratifyingly larger samples, so their p-values are more like 1 in 10 million.… [continue reading]

How to think about Quantum Mechanics—Part 6: Energy conservation and wavefunction branches

[Other parts in this series: .]

In discussions of the many-worlds interpretation (MWI) and the process of wavefunction branching, folks sometimes ask whether the branching process conflicts with conservations laws like the conservation of energy.Here are some related questions from around the web, not addressing branching or MWI. None of them get answered particularly well.a   There are actually two completely different objections that people sometimes make, which have to be addressed separately.

First possible objection: “If the universe splits into two branches, doesn’t the total amount of energy have to double?” This is the question Frank Wilczek appears to be addressing at the end of these notes.

I think this question can only be asked by someone who believes that many worlds is an interpretation that is just like Copenhagen (including, in particular, the idea that measurement events are different than normal unitary evolution) except that it simply declares that new worlds are created following measurements. But this is a misunderstanding of many worlds. MWI dispenses with collapse or any sort of departure from unitary evolution. The wavefunction just evolves along, maintaining its energy distributions, and energy doesn’t double when you mathematically identify a decomposition of the wavefunction into two orthogonal components.

Second possible objection: “If the universe starts out with some finite spread in energy, what happens if it then ‘branches’ into multiple worlds, some of which overlap with energy eigenstates outside that energy spread?” Or, another phrasing: “What happens if the basis in which the universe decoheres doesn’t commute with energy basis? Is it then possible to create energy, at least in some branches?” The answer is “no”, but it’s not obvious.… [continue reading]

Integrating with functional derivatives

I saw a neat talk at Perimeter a couple weeks ago on new integration techniques:

Speaker: Achim Kempf from University of Waterloo.
Title: “How to integrate by differentiating: new methods for QFTs and gravity”.

Abstract: I present a simple new all-purpose integration technique. It is quick to use, applies to functions as well as distributions and it is often easier than contour integration. (And it is not Feynman’s method). It also yields new quick ways to evaluate Fourier and Laplace transforms. The new methods express integration in terms of differentiation. Applied to QFT, the new methods can be used to express functional integration, i.e., path integrals, in terms of functional differentiation. This naturally yields the weak and strong coupling expansions as well as a host of other expansions that may be of use in quantum field theory, e.g., in the context of heat traces.

(Many talks hosted on PIRSA have a link to the mp4 file so you can directly download it. This talk does not, but you can right-click here and select “save as” to get the f4v file.This file format can be watched with VLC player. You can find it for any talk hosted by PIRSA by viewing the page source and searching the text for “.f4v”. There are many nice things about learning physics from videos, one of which is the ability to easily speed up the playback speed and skip around. In VLC player, playback speed can be incremented in 10% steps by pressing the left and right square brackets, ‘[‘ and ‘]’.a  )

The technique is based on the familiar trick of extracting a functional derivate inside a path integral and using integration by parts.… [continue reading]