Scott Aaronson's "The Ghost in the Quantum Turing Machine"

Scott Aaronson recently uploaded a mind-boggling paper, full of challenging ideas regarding free-will, quantum mechanics and computing, philosophical big questions, neuroscience, and many other hot topics. The title is The Ghost in the Quantum Turing Machine, and will be a chapter in the book The Once and Future Turing, edited by S. Barry Cooper and Andrew Hodges, 2013.

His paper is like a storm of puzzle pieces, which fit together perfectly in an amazing tapestry, centered around his idea of Knightian freedom.

Here is the abstract

In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will. I focus relatively narrowly on a notion that I call "Knightian freedom": a certain kind of in-principle physical unpredictability that goes beyond probabilistic unpredictability. Other, more metaphysical aspects of free will I regard as possibly outside the scope of science. I examine a viewpoint, suggested independently by Carl Hoefer, Cristi Stoica, and even Turing himself, that tries to find scope for "freedom" in the universe's boundary conditions rather than in the dynamical laws. Taking this viewpoint seriously leads to many interesting conceptual problems. I investigate how far one can go toward solving those problems, and along the way, encounter (among other things) the No-Cloning Theorem, the measurement problem, decoherence, chaos, the arrow of time, the holographic principle, Newcomb's paradox, Boltzmann brains, algorithmic information theory, and the Common Prior Assumption. I also compare the viewpoint explored here to the more radical speculations of Roger Penrose. The result of all this is an unusual perspective on time, quantum mechanics, and causation, of which I myself remain skeptical, but which has several appealing features. Among other things, it suggests interesting empirical questions in neuroscience, physics, and cosmology; and takes a millennia-old philosophical debate into some underexplored territory.

A local explanation of entanglement by using wormholes

Recently, a new paper by Maldacena and Susskind appears, named Cool horizons for entangled black holes (arxiv:1306.0533). In the paper, the two authors propose that two entangled particles are connected by an Einsten-Rosen bridge, a wormhole. Their stake is in fact related to the black hole information paradox, the Maldacena correspondence, and the recent idea of black hole firewalls. It was covered, among others, by Sean Carroll.

This article reminded me of an example I gave at FQXi's blog, under an article by Florin Moldoveanu, (whose blog, Elliptic composability, I highly recommend)
http://fqxi.org/community/forum/topic/976#post_40460


Here is my comment from two years ago:
Cristi Stoica wrote on Aug. 5, 2011 @ 13:32 GMT

AN EXPLICIT LOCAL VARIABLES TOPOLOGICAL MECHANISM FOR THE EPR CORRELATIONS

It is based on a non-trivial topology (wormholes).

Cut two spheres out of our space, and glue the two boundaries of the space together. This wormhole can be traversed by a source free electric field, and used to model a pair of electrically charged particles of opposite charges as its mouths (Einstein-Risen 1935, Misner-Wheeler's charge-without-charge 1957, Rainich 1925).

For EPR we need a wormhole which connects two electrons instead of an electron-positron pair. A wormhole having as mouths two equal charges can be obtained as follows: instead of just gluing together the two spherical boundaries, we first flip the orientation of one of them. Since the electric field is a bivector, the change in orientation changes the sign of the electric field, and the two topological charges have the same sign.

Now associate to the two electrons your favorite local classical description. The communication required to obtain the correlation can be done through the wormhole.

----------------

This may be the basis of a mathematically correct local hidden variable theory. Also, it seems to disprove, or rather circumvent, Bell's theorem. For Bohm's hidden variable theory, it provides a mechanism to get the correlation without faster than light signals. I proposed it here for theoretical purposes only, as an example. My favorite interpretation is another one.

Cristi

I did not want to spend more time on this, only to break my neck proposing local models of entanglement, especially since I did not find the idea of hidden variables relevant.

Pinball with disks and rays

Joseph O'Rourke proposed a beautiful problem on Math Overflow:

Let every point of $\mathbb Z^2$ be surrounded by a mirrored disk of radius $r\lt 1/2$, except leave the origin (0,0) unoccupied by a disk.
    Q. Is it the case that every disk can be hit by a lightray emanating from the origin and reflecting off the mirrored disks?

Here is an example

I liked the solution I gave, so I would like to share it here. It assumes the radius to be about $1/3$ or less. The idea is that, instead of light ray and reflection, to think in terms of rings and ropes connecting them. We assume the rings and the rope satisfying suitable idealizations. The following picture shows that any ring in the lattice $\mathbb Z^2$ is reachable.

Moreover, we can use this method to connect with the origin all rings in the plane, with a single rope.

Of course, if the radius gets close to $1$, the rope becomes overlapped with the rings, and this solution will no longer work. But we can still use it to find a correct solution. We start with a radius of $1/3$, then gradually increase it. At some point, the rope will become tangent to one or more rings. In this case, just wrap it more, using the moves in the following picture

Violation of Heisenberg's uncertainty principle, or evidence for Quantum Mechanics?

A recent paper entitled  Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements  appeared (see the arXiv link to the paper).

This paper was presented to the public in some articles which gave the wrong idea that quantum uncertainty is disproved  (see for example Heisenberg uncertainty principle stressed in new test, with the subtitle "Pioneering experiments have cast doubt on a founding idea of the branch of physics called quantum mechanics.").

I will argue that the experiment presented in the paper actually supports Quantum Mechanics. This may be not quite explicit in the paper, but also there is nothing against the standard view on quantum mechanics in it.

Heisenberg originally stated his principle in terms of measurement-disturbance relationship (MDR). This is how he understood it at that time. The uncertainty principle which was proven theoretically, either in the context of wave mechanics, or from the non-commutativity of the operators, is correct, and it's correctness is acknowledged by the paper. This is called Heisenberg's uncertainty principle (HUP), and is very different from MDR.

The paper refers to previous theoretical works which disprove MDR, and present experimental evidence purported to confirm the violation of the MDR.

Why do I claim that the violation of MDR supports Quantum Mechanics? Because, if MDR would be correct, it would be enough to explain quantum uncertainty. Recall that even Heisenberg originally thought that the uncertainty is due to disturbance caused by measurement. If the states would behave as they are due to the measurement disturbance, then we could consider them classical, and extract Born's probability rule as we calculate probabilities in statistical mechanics. But we know this is not true. Quantum states exhibit properties which can't be explained by classical mechanisms. Among these, HUP plays an important role, together with entanglement. The service made by this paper is that it shows that the wrong version of the uncertainty principle can be violated. The authors seem to me to support the HUP:

"These two readings of the uncertainty principle are typically taught side-by-side, although only the modern one [HUP] is given rigorous proof."

and

"Our work conclusively shows that, although correct for uncertainties in states [HUP], the form of Heisenberg's precision limit is incorrect if naively applied to measurement [MDR]."

[1] Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements

[2] arXiv link to the paper

[3] Heisenberg uncertainty principle stressed in new test

Analytic Reissner–Nordström singularity

This paper can be downloaded for the following 30 days from the Physica Scripta website.

Link to the arXiv version.

Abstract:

An analytic extension of the Reissner–Nordström solution at and beyond the singularity is presented. The extension is obtained by using new coordinates in which the metric becomes degenerate at r = 0. The metric is still singular in the new coordinates, but its components become finite and smooth. Using this extension it is shown that the charged and non-rotating black hole singularities are compatible with the global hyperbolicity and with the conservation of the initial value data. Geometric models for electrically charged particles are obtained.