# Quantum Bayesian Networks

## September 14, 2012

### Dull Measurements (aka Weak Measurements)

Filed under: Uncategorized — rrtucci @ 5:53 am

Let me start by warning the reader that the terms  “weak measurements” and “weak values” are both misnomers. It’s difficult to understand how the adjective “weak” can apply to the noun “measurement”. And the values involved can be very large (even infinite), which is not very weak.

Instead, I like to call them dull measurements (dull Ms), because they have a very large variance (The name dull M also fits well because, once one understands what dull Ms are, talking further about them makes any honest physicist incredibly bored.)

Besides Dull Measurements, other useful names for them are dumb measurements, BS measurements, almost fake measurements, fuzzy-wuzzy measurements, …

Dull Ms consist of a weak INTERACTION (not weak measurement) between two systems, call them S and M, followed by a measurement of M. S is usually called the system and M the meter or pointer or ancilla. S can be taken to be microscopic and M macroscopic, but that’s not necessary. It’s common to use the symbol $\langle A \rangle_W$ to denote the so called weak value of an operator $A$ for the initial state $|\psi_i\rangle$ and final state $|\psi_f\rangle$

$\langle A \rangle_W = \frac{\langle\psi_f |A| \psi_i\rangle} {\langle\psi_f |\psi_i\rangle}$

If you are interested in a short, more mathematical discussion of dull Ms, I’ve written one which you can find here. It’s just 2 pages long.

• Do dull Ms constitute new or fundamental physics?  Absolutely not. Dull M proponents try to extend, in a dubious way, some theory that was first proposed eons ago, by von Neumann and others. The physics and math necessary to understand dull Ms is standard, VERY BASIC, quantum mechanics, the stuff taught in a beginning quantum mechanics course. It’s that trivial.

It’s really important to face the truth: the effects called “weak measurements” can all be explained by standard quantum mechanics. No modifications of standard quantum mechanics are required to explain them.

• Will the study of dull Ms lead to new, useful technological applications, like, for instance, improvements in precision metrology? Very unlikely. Dull Ms are very noisy measurements. Usually, improvements in precision metrology arise from discoveries of new ways of reducing noise, not of increasing it.
• Do dull Ms violate Heisenberg’s uncertainty principle, as claimed by people like Aephraim Steinberg? Absolutely not. Heisenberg’s uncertainty principle for momentum and position (or any other conjugate pair of variables) is a simple application of the Cauchy-Schwarz inequality. So according to Aephraim Steinberg, he has found a way of violating the Cauchy-Schwarz inequality. Don’t laugh.

The familiar Heisenberg uncertainty principle refers to measuring $p$ on one particle and $x$ separately on a second particle that is prepared identically to the first. Steinberg, following a theoretical calculation by Ozawa, is measuring $p$ and $x$, one after the other, on the same particle. The fact that these two situations obey different uncertainty principles has been known since the early days of quantum mechanics.

As evinced by many quotes of him that have appeared in news articles, Mr. Steinberg is in the habit of telling the press that his work is super revolutionary, that it will rewrite the physics books, that most physicists did not expect this or thought it to be outright false, that he has found a violation of a cherished principle of physics. Then you go to his papers. There he chooses his words a bit more carefully. There he only claims to have checked a fairly standard prediction of standard quantum mechanics. One is reminded of the bait and switch sales scheme, and of the Roman god Janus, guardian of doorways, two-faced.

• Are dull Ms always well defined? Sometimes they aren’t, as has been pointed out by Stephen Parrott and others. Let me try to explain this.

(1)Dull M theory is ONLY VALID TO FIRST ORDER in an expansion parameter (also called a coupling constant) $g$. That’s why it’s called a weak measurement. Hence, dull M theory is invalid for large $g$.

(2)Dull M proponents always find equations that give $\langle A \rangle_W$ in terms of actual lab measurements. The problem is that in those equations, $\langle A \rangle_W$ and $g$ always appear together, as a product $g\langle A \rangle_W$. So when $g=0$, all information about $\langle A \rangle_W$ goes away. $\langle A \rangle_W$ is a random variable whose variance is infinite when $g=0$. That variance is finite but still very large when $g\in (0,\epsilon]$ for some $\epsilon \neq 0$.

(1) and (2) imply that dull M theory is vacuous for small $g$ and invalid for large $g$. It ONLY WORKS FOR INTERMEDIATE VALUES OF $g$. This poorly defined region of intermediate $g$ values may be the empty set.

• But aren’t there alternative definitions of $\langle A \rangle_W$ which are not based on an ill defined approximation? Some people like Johansen have given “interpretations” of  $\langle A \rangle_W$ based on Bayesian estimation.

It’s easy to explain what Johansen is saying. Suppose you are given a Hermitian matrix $A$ and a fixed orthonormal basis $|b\rangle$ for all $b$. Then suppose you want to find a Hermitian matrix $\theta$, called an estimate of $A$, which is diagonal in the $|b\rangle$ basis. Thus, it can be expressed as $\theta = \sum_b \theta_b |b\rangle\langle b|$. $\theta$ should be as close as possible to $A$. Close as possible is defined as minimizing $L=\langle \psi|(\theta-A)^2|\psi\rangle$ for some state $|\psi\rangle$. Then some math shows that the best estimate is $\theta_b = Re\left(\frac{\langle \psi|A|b\rangle}{\langle \psi|b\rangle}\right)$.

Fine. But such an interpretation has nothing to do with an experiment that yields $\langle A \rangle_W$ from a weak interaction. In fact, such an interpretation totally avoids a coupling constant $g$ because it doesn’t consider any sort of interaction, whether a weak one or a strong one. Such an interpretation is quite different to what most people call a “weak measurement” experiment.

• Are weak measurement skeptics rare? No. It seems that there are quite a few, including some famous people. For example, I already mentioned Stephen Parrott. Anthony Leggett has also expressed some misgivings about weak measurements in a lecture which can be found on You Tube. Lubos Motl, who knows a lot of physics, thinks they are total rubbish.

Wikipedia entry for weak measurements here. Notice flag questioning neutrality of article.

Lies, Damn Lies and Hilariously Dishonest Hype about dull Ms.

• Check out

“Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?” by M V Berry, N Brunner, S Popescu and P Shukla.
J. Phys. A: Math. Theor. 44, 492001 (2011)
Published 11 November 2011
(arxiv 1110.2832)

If you skim this paper, you will find that it was not intended as a joke. It has a very serious tone, except maybe for the abstract. Notice that the journal “Journal of Physics A: Mathematical and Theoretical” published this embarrassing nonsense just one month after it was submitted. According to Wikipedia, the Journal of Physics A is run by IOP, which is a UK institution whose current president is the unsavory character, Peter Knight. (I once had a very unpleasant experience with this guy. I suspect I’m not the only one that dislikes him.)

• Check out

“Heisenberg uncertainty principle stressed in new test” Pioneering experiments have cast doubt on a founding idea of the branch of physics called quantum mechanics. , by Jason Palmer, BBC news, September 7, 2012

which extolls the virtues of the paper

“Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements.” by Lee A. Rozema, Ardavan Darabi, Dylan H. Mahler, Alex Hayat, Yasaman Soudagar, and Aephraim M. Steinberg (arxiv 1208.0034)

• (for adults only) Lubos Motl’s reaction to Steinberg’s paper “Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements.”

Pseudoscience hiding behind “weak measurements”

• The magazine PhysicsWorld, also published by IOP, recently published a hilariously biased “contest”. Check it out

Physics World reveals its top 10 breakthroughs for 2011

The “Physics World editorial team” awarded 10 prizes. First and second prizes were awarded to weak measurement experiments. The output of such crap experiments is just a very noisy, washed-out interference pattern. Real useful and novel, for a caveman, that is. On the other hand, Cleland’s and Martinis’ quantum computer with RAM, which I think is truly revolutionary, only rated ninth prize. Sigh…the English.

The article says about Steinberg’s team, which won the first prize:

“…the team is the first to track the average paths of single photons passing through a Young’s double-slit experiment – something that Steinberg says physicists had been “brainwashed” into thinking is impossible.”

What BS! Mr. Steinberg. Stop lying. Physicists are taught that one can only “estimate” those paths with very high variance. What are the variances in your crap experiment? They’re huge.

• Dull Ms were originally promoted by Yakir Aharonov, David Albert and Lev Vaidman. AAV used dull Ms in their crackpot interpretation of quantum mechanics called 2 state-vector formalism (2S). According to AAV, particles have two parts: one part lives in the present and another in the future; these 2 parts send encrypted messages to each other. LOL. The 2S interpretation generated a lot of heated debate in PhysicsToday in 2011. More recently, one finds the following priceless blog post

Physics World gets high on Tel Aviv catnip
by Charles Bennett

in which Charles Bennett comments on an over-exuberant article (in the magazine IOP-PhysicsWorld) about the 2S interpretation.

Update: A more recent post of mine on dull Ms:

Weak Measurements Remind Me of…

1. Strong words on dull measurements for the weak minded. I had high hope for Aephraim Steinberg. Really thought he was doing neat stuff on quantum erasers in the nineties. He lost me with the revisited double slit experiment. My reaction to that one was similar as described here. Haven’t even looked at the Heisenberg Uncertainty papers as the whole premise seems absurd (the Fourier transformation won’t care about dull measurements).

Comment by Henning Dekant — September 15, 2012 @ 3:24 am

2. Reblogged this on wavewatching.

Comment by Henning Dekant — September 15, 2012 @ 3:26 am

3. […] Yes, Heisenberg did at some time speculate that the uncertainty relationship may be due to the measurements disturbing the system that is probed, but this idea has long been relegated to the dust bin of science history and Robert R. Tucci deservedly demolishes this. […]

Pingback by Strong words on Dull Measurements | Wavewatching — September 15, 2012 @ 3:57 am

4. Apparently the reblog button doesn’t work for me, so I published a little piece to point here.

Comment by Henning Dekant — September 15, 2012 @ 4:00 am

5. Hi Henning, thanks for mentioning me in your blog.

Comment by rrtucci — September 15, 2012 @ 4:49 am

6. Thank You very much! This certainly answers clearly clarifying the confusions about weak measurements that have been dancing on the internet:)
Dunno why reblog button is not working. Will write a post linking here.

Comment by Sankalp Ghatpande — September 15, 2012 @ 11:55 am

7. […] an excellent post here pretty much clears all the confusion by systematically explaining everything. The post also has […]

Pingback by Clearing the confusions of Weak Measurements « kryptomusing — September 15, 2012 @ 7:51 pm

8. What might be a fine mathematical argument is weakened by unrelated ad hominem attacks.

Comment by Geoff Robbins (@_TheGeoff) — September 16, 2012 @ 12:32 am

Blog at WordPress.com.