Author: Michael Nielsen

Top five conversation-stoppers when introduced to a physicist:

5. “Oh, really. My brother-in-law’s in medicine, too.”

4. “Um… Ahh… That must be…. interesting.”

3. “Physics was my worst subject in high school.”

2. “Physics was my best subject in high school.”

1. “You must be really smart.”

Number 1 is especially hard to respond to. What do you say? “Yes” is right out. “No” isn’t a whole lot more attractive. “Nah, I just cheated on all my exams” has the benefit of causing interest, but it’s not necessarily the kind of interest you want in those kinds of situations.

A substantial overhaul to the blogroll, for whatever it’s worth. I’ll give plugs to the new additions:

First, I’ve finally added some conservative blogs, Dan Drezner and the Volokh Conspiracy. Well worth reading, at least in this liberal reader’s opinion. I find most conservative blogs unreadable; these are welcome exceptions.

Second, I’ve added Sean Carroll’s new blog, which is the first blog I’ve seen with regular posts on astrophysics. (I’ve also made use of Sean’s online notes on general relativity, which I found quite useful. I understand he’s now the author of a text on a subject, which I plan to check out soon.)

Other additions include Jim Henley (libertarian politics, comics and fitness), Bill Tozier (complexity, personal stuff, weird stuff), and Jonathan Kleid (quantum computing). All worth checking out.

Let me follow up on the previous post with a few comments on the interpretation of quantum mechanics.

First of all, I do agree that there is a problem still to be solved in the foundations of quantum mechanics.

Not everybody agrees on this. Quantum mechanics works extremely well in all situations, so far as we know, which leads to people adopting the shut-up-and-calculate interpretation of quantum mechanics. In 99 percent of my professional work, I adopt that interpretation myself, sometimes quite explicitly – probably the single most frequent complaint I’ve heard about my book with Ike Chuang is that we take too pragmatic an approach to the foundations. (I suspect part of the problem is that we’re rather brazenly pragmatic, stating upfront that we’re not going to talk about foundations at all.)

However, it being a Saturday, I’ll let my hair down and admit that yes, I think there is a problem in the foundations.

Part of the difficulty is deciding what exactly is the nature of that problem. Is it an interpretational problem? Is the problem in the physics?

My own belief is that the problem is in the physics, and that if that problem can be solved, then there won’t be any interpretational problem.

So what is the physical problem?

Quantum mechanics as presented in many textbooks usually has postulates telling you that (a) a closed quantum system evolves according to unitary dynamics, i.e., Schroedinger’s equation, and (b) a quantum system that is measured evolves according to the so-called “projection postulate”, or something similar. Part (a) is completely deterministic, while part (b) is the part where probabilities enter quantum mechanics.

Now, of course, a measuring device is itself a quantum system. Furthermore, the quantum system being measured and the measuring device are both parts of larger closed systems (e.g., the Universe). That larger system should therefore be describable by a unitary evolution, if we believe the postulates of quantum mechanics.

Naively, then, one might think that it ought to be possible to derive the projection postulate from the postulate that closed systems evolve unitarily. Certainly, such a derivation ought to be possible if quantum mechanics is to be put on a single unified dynamical foundation.

The physical problem, in my opinion, is that no one has ever succeeded in carrying out such a deriviation.

There have, of course, been many attempts to put quantum mechanics on such a unified dynamical foundation. Perhaps the most fashionable in recent years has been the so-called “decoherence program”. Unfortunately, so far as I can determine, although the decoherence program has contributed substantially to our understanding of how classical physics arises from quantum, I still know of no convincing derivation of the projection postulate from unitary dynamics.

What are the prospects for carrying out such a derivation in the near future?

Not good, in my opinion, without the injection of some major new ideas, and quite possibly some experimental input. (Indeed, the possibility of experimental input into this issue is one reason for finding mesoscopic physics and quantum computing interesting.) This problem has simply been beating around for too long to be solved without some significant new ideas.

My own favourite crazy idea for resolution of the problem is that, in fact, the projection postulate will not be derived from unitary dynamics. Instead, unitary dynamics will be derived from the projection postulate. One of the insights to come out of quantuum computing in the past few years is that any unitary dynamics can be simulated by measurements alone. Perhaps, then, measurement is the underlying basis for all physical dynamics.

In a rather suspiciously dated post, Sean Caroll claims that:

As crazy as it sounds, most working physicists buy into the many-worlds theory (and, like approval for gay marriage, there is a significant demographic slant, in which younger people are more open).

Unfortunately, he doesn’t tell us what the basis for this comment is. Many physicists – myself included – spend a large fraction of our time moving within relatively small communities of people working on similar topics. It’s easy to become convinced that the impression one picks up from that community is true of physicists at large. That is not always the case.

To give an example at odds with Sean Carroll’s claim, at a quantum computing conference at Cambridge in 1998, a many-worlder surveyed the audience of approximately 200 people for opinions on the interpretation of quantum mechanics at the beginning of his talk.

Many-worlds did just fine, garnering support on a level comparable to, but somewhat below, Copenhagen and decoherence.

(The previous paragraph should be taken with rather a large grain of salt; it’s been almost six years. Anybody else who was at the conference, and cares to comment?)

My impression – admittedly, based in part on the irritated looks and comments of people around me as the poll was being conducted – was that the largest single group of people in the room was people who thought the poll was a waste of time.

Certainly, Asher Peres stole the show (and got a huge and sustained round of applause) when he got up at the end of the polling and asked “And who here believes the laws of physics are decided by a democratic vote?”

A mathematician whose work I have admired for years is Chandler Davis. I’ve only sampled a small selection of his ouvre, but it’s always interesting.

So I was extremely interested to find this page, describing how Davis went to jail for six months in 1960, for refusing, on principle, to testify before the House Unamerican Activities Committee.

(As a technical paranthetical aside, I was rather chuffed earlier this year when Chris Dawson and I found a way of using one of Davis’ best-known results in a paper. Specifically, we made use of the Davis-Kahan theorem to understand how quantum entanglement arises as the result of competition between local and interaction terms in many-body quantum systems. The Davis-Kahan theorem is a very nice theorem that gives detailed information about how the eigenspaces of an operator change under perturbation. )

Ike Chuang has just released a package enabling quantum circuits for quantum computers to be drawn easily (link.)

With standard tools, quantum circuits are a pain to draw. When writing our book on quantum information, I would sometimes email Ike a request for a circuit (usually a scanned hand-drawn image), and two minutes later a beautiful eps file would show up! I’ve never used the package Ike has created, but I’m pretty confident it will be extremely useful for that small group of people who regularly draw such circuits.

What’s the point of running an academic blog? I’ll come back to this at some point, but for now wanted to mention three of the betterposts I’ve seen on this: here, here and the entire comments thread here.

What do Omar Khayyam, Gore Vidal, Information Geometry, and Neural Coding have in common?

They all appear as the subject of entries in Cosma Shalizi’s Notebooks. Many of the notebooks are as informative and thought provoking as the total is eclectic. Highly recommended.

A nicely done Java demonstration. (Via Mark Fernee).