Category Archives: Quantum mechanics

Bad Math, Quantum mechanics

An Item of Prime Importance

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I was busy with something or other, so I didn’t get to see the event Dennis Overbye describes in the New York Times, where the director and the star of the new film Jumper chatted with MIT professors Ed Farhi and Max Tegmark before a live audience in lecture hall 26-100. Not having been there, I don’t have very much to say, but I do feel the need to quote one paragraph of Overbye’s article and add just a tiny bit of emphasis:

The real lure, [Farhi] said, is not transportation, but secure communication. If anybody eavesdrops on the teleportation signal, the whole thing doesn’t work, Dr. Farhi said. Another use is in quantum computing, which would exploit the ability of quantum bits of information to have different values, both one and zero, at the same time to perform certain calculations, like factoring large prime numbers, much faster than ordinary computers.

Ahem.

In any other circumstance, I’d probably pontificate on how exponential parallelism is not the source of quantum computing’s calculation-fu, but I think we have a few other points to address first. . . .

Attentive readers will recall that Dr. Farhi was the guy who signed my paperwork when I was an undergraduate. For an amusing story from those days, see my post of last November, “Pay No Attention to the Man.”

(Tip o’ the fedora to Dave Bacon.)

Bibliophilia, Quantum mechanics

The Name is Planck, Max Planck

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The algorithm informs me that the title for the next James Bond movie, the sequel to the franchise reboot Casino Royale (2006), will be titled Quantum of Solace. This title comes from a short story in Ian Fleming’s collection For Your Eyes Only (1960); the movie of that name used elements from two stories in the book, a third story became part of Licence to Kill (1989), and the title of a fourth story was affixed to the film A View To A Kill (1985).

The title “Quantum of Solace” appears in the story as the smallest possible unit of human compassion. The following paragraph appears in both the Everything2 article on the story (dated 6 March 2001) and today’s Telegraph piece about the movie:

The crux of the story is the emotional phenomenon the Governor calls the Quantum of Solace, the smallest unit of human compassion that two people can have. As long as that compassion exists, people can survive, but when it is gone, when your partner no longer cares about your essential humanity, the relationship is over.

Well, OK, Lucy Cockcroft’s story in the Telegraph doesn’t have the words “of the story” following “crux.” Eit!

Popularizers of physics are going to have a field day with this one. Perhaps, just perhaps, we’ll finally have an example of quantum meaning small!

Quantum mechanics

SUSY QM 3: The Two-Body Problem

Our goal in this series is the solution of the hydrogen atom using the methods of supersymmetric quantum mechanics. Last time, we constructed the following picture of the procedure:

If the potential we wish to study satisfies a certain criterion, which we called “shape invariance,” we can construct a hierarchy of Hamiltonians, each missing the lowest-energy eigenstate of the last, and find the complete spectrum of the original Hamiltonian by “working leftward” in the state diagram. We shall see that with the hydrogen atom, each state in the diagram corresponds to a physical eigenstate of the system, but in order to get there, we have to turn the three-dimensional Coulomb potential of the hydrogen atom into the kind of problem we can study with the SUSY QM machinery we’ve built up so far. Two steps will be necessary to do this: first, moving to the center-of-mass reference frame, and second, separating the radial and angular dependencies. In this post, we’ll tackle the first of those two tasks.

While the SUSY part isn’t widely taught, these preliminary steps are more familiar. This brief note is based on Chapter VII of Cohen-Tannoudji, Diu and Laloë.
Continue reading SUSY QM 3: The Two-Body Problem →

Popularization, Quantum mechanics

Irony, Thy Name is Quantum

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I wonder how many instances of the phrase “quantum leap” Scott Bakula is personally responsible for? There is, as many others have observed before me, a hefty dose of irony in calling a major transition a “quantum leap” or “quantum jump,” as the original leaps to gain the name were the transitions of electrons between energy levels. We’re talking about an electron’s “orbit” changing its diameter from one zillionth of a centimeter to four zillionths of a centimeter. But science never stands in the way of evocative, quasi-scientific jargon!

It’s old irony, but it’s still worth a chuckle, as when India’s prime minister declares, “We need a quantum jump in science education and research.” Start at the top, my friend, start at the top. OK, points for effort:
Continue reading Irony, Thy Name is Quantum →

Quantum mechanics

SUSY QM 2: Shape Invariance

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Blogging on Peer-Reviewed ResearchAfter a while, you just get tired. An honest science blogger can only handle so much science jargon thrown around without meaning, only a limited amount of Choprawoo and quantum flapdoodle. How long can anyone with integrity, curiosity and a dose of genuine knowledge endure the trumpeting that, say, the brain’s limited ability to recover after injury is evidence for some quantum spirit? The brain is living flesh, made of living cells: by the same so-called logic, the scabbed knees of childhood are all evidence of quantum skin.

After a while, a deep reserve of psyche cries out, “Enough! If my freedom means aught, I must stop responding to these charlatans and move beyond. I must send a message of my own, a message which is not a reaction but an expression unto itself. I must sing the quantum genuine!”

In my case, this means another post on supersymmetric quantum mechanics.

RECAP

Last time, we deduced some interesting properties of Hamiltonians which can be factored into operators and adjoints:

[tex]H_1 = A^\dag A,\ H_2 = AA^\dag.[/tex]

We observed that [tex]H_1[/tex] and [tex]H_2[/tex] are isospectral. That is, while the forms of their eigenfunctions may be different, the eigenvalues associated with those functions are the same; or, in physical terms, the wavefunctions have different shapes, but the energies match. The only exception is the ground state: if [tex]H_1[/tex] has a zero-energy ground state, then [tex]H_2[/tex] will not. Furthermore, the operator [tex]A[/tex] maps eigenstates of [tex]H_1[/tex] into those of [tex]H_2[/tex], and the operator [tex]A^\dag[/tex] maps eigenstates in the reverse direction:


Continue reading SUSY QM 2: Shape Invariance →

BPSDB, Pseudoscience, Quantum mechanics

Shorter Sal Cordova

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BPSDBSal Cordova, famous for calling Charles Darwin a puppy-killer, has attempted to reply to Tyler DiPietro’s demonstration that he, Cordova, is blitheringly ignorant of quantum physics. (Such ignorance would not be a crime, of course, except that Cordova is hell-bent on using quantum physics to prop up his “Advanced Creation Science.” See here, here, here, here and here if you’re morbidly curious.) Cordova’s latest reply compresses down rather nicely; once you do him the favor of cutting out the prevarications and the contradictions, the result resembles the following.

Stringing words I don’t understand together in a row is just as good as a logical argument, thank you very much, and if the laws of physics impose any limits on the “Ultimate Observer”, well then Jesus will come down and make everything better.

Click away if you want the gory details. . . .

Neuroscience, Pseudoscience, Quantum mechanics

The Unbinding Problem

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We human folk are pretty good at taking information from different sensory channels and combining it into unified impressions. When I watch a video recording of Richard Feynman, for example, my optic nerves carry a flood of data pulses, signals which somehow arrive in my brain and sync up with the voice which sounds like a Brooklyn gangster (but which actually came from Far Rockaway, of course). A unified whole then emerges, without my conscious effort.

Like they’ve done with all the other odd aspects of brain function, people have invoked quantum mechanics to “explain” this: the mind is mysterious, quantum physics is mysterious, and so the two must be related. Only your blind devotion to linear, Western, patriarchal science prevents you from seeing the Truth! (Oddly enough, the Oprah–Chopra-woo crowd never seem to remark on how the original developers of quantum physics were, almost all of them, White Males who are now Dead.) The “binding problem” is no exception.

However, as both Max Tegmark and Ray F. Streater have pointed out, the proponents of what we might call “quantum binding” — Henry Stapp in particular — fail to consider that correlations are perfectly possible in classical physics. The invocation of quantum physics is only a maladroit solution to a non-problem. In Tegmark’s words,

For instance, oscillations in a guitar string are local in Fourier space, not in real space, so in this case the “binding problem” can be solved by a simple change of variables. As Eddington remarked [77], when observing the ocean we perceive the moving waves as objects in their own right because they display a certain permanence, even though the water itself is only bobbing up and down. Similarly, thoughts are presumably highly non-local excitation patterns in the neural network of our brain, except of a non-linear and much more complex nature.

Now, a patient has turned up in whose brain binding does not occur. G. Lee and H. B. Coslett write of the patient “K.E.,”

He was unable to report more than one attribute of a single object. For example, he was unable to name the color of the ink in which words were written despite naming the word correctly. Several experiments demonstrated, however, that perceptual attributes that he was unable to report influenced his performance.

K.E. had suffered stroke damage to his parietal lobes on both sides of his brain, or in technical terms, “bilateral posterior parietal infarcts.” In addition to his binding difficulties, he experienced simultanagnosia, an inability to see more than one object out of several presented to his view at once.

It may be a “dog bites man” report by now, but I think it’s worth noting that finding patients with neural dysfunctions is still a more productive way of gaining new neuroscientific knowledge than woolly-headed speculation about quantum mechanics, speculation which incidentally ignores big facts about physics.

(Tip o’ the fedora to Mind Hacks, and to Warren Ellis, whose “4am” provides my current background score.)

Cosmology, Electromagnetism, Pseudoscience, Quantum mechanics, Relativity

Teh Burning Stupid: Relativity Edition

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To put the “moral” at the beginning, let’s summarize. If you want to raise my blood pressure, one good way to do it is to write a completely wrong, back-to-front absurd tirade against all of twentieth-century physics. Anyone can slip a few errors into an essay, or even a few “fundamental” errors, but if you want the brass ring, you need at the very least to misrepresent the special theory of relativity, the general theory of relativity, quantum mechanics, the use of mathematics in physics and the scientific method. Bonus points if you confuse general relativity with quantum physics; a woop-woop-woop special prize for taking a non-true assertion and calling it a “fundamental premise” of quantum mechanics; and an extra cherry on top if you take three famous observations which support general relativity, lie about two of them and forget the third.

The story so far:

I might write an actual, non-linkfesty post about this. . . but then again, other corners of the Network are calling to me and reminding me of overdue obligations, so I might leave it to my colleagues.

UPDATE (6 December): gg now has Part 2 out on the blogonets.

UPDATE (16:47 o’clock): Tyler DiPietro dons the asbestos and joins the fun, followed quickly by Mark Chu-Carroll.

UPDATE (9 December): Flavin of the St. Louis Skeptical Society offers an essay.

Network theory, Neuroscience, Popularization, Quantum mechanics

Yawn: More Abuse of the Quantum

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Binocular rivalry is a phenomenon which occurs when conflicting information is presented to each of our two eyes, and the brain has to cope with the contradiction. Instead of seeing a superimposition or “average” of the two, our perceptual machinery entertains both possibilities in turn, randomly flickering from one to the other. This presents an interesting way to stress-test our visual system and see how vision works. Unfortunately, talk of “perception” leads to talk of “consciousness,” and once “consciousness” has been raised, an invocation of quantum mechanics can’t be too far behind.

I’m late to join the critical party surrounding E. Manousakis’ paper, “Quantum theory, consciousness and temporal perception: Binocular rivalry,” recently uploaded to the arXiv and noticed by Mo at Neurophilosophy. Manousakis applies “quantum theory” (there’s a reason for those scare quotes) to the problem of binocular rivalry and from this hat pulls a grandiose claim that quantum physics is relevant for human consciousness.

A NOTE ON WIRES AND SLINKYS

First, we observe that there is a healthy literature on this phenomenon, work done by computational neuroscience people who aren’t invoking quantum mechanics in their explanations.

Second, one must carefully distinguish a model of a phenomenon which actually uses quantum physics from a model in which certain mathematical tools are applicable. Linear algebra is a mathematical tool used in quantum physics, but describing a system with linear algebra does not make it quantum-mechanical. Long division and the extraction of square roots can also appear in the solution of a quantum problem, but this does not make dividing 420 lollipops among 25 children a correlate of quantum physics.

Just because the same equation applies doesn’t mean the same physics is at work. An electrical circuit containing a capacitor, an inductor and a resistor obeys the same differential equation as a mass on a spring: capacitance corresponds to “springiness,” inductance to inertia and resistance to friction. This does not mean that an electrical circuit is the same thing as a rock glued to a slinky.

MIXING THE QUANTUM AND THE CLASSICAL

One interesting thing about this paper is that the hypothesis is really only half quantum, at best. In fact, three of the four numbers fed into Manousakis’ hypothesis pertain to a classical phenomenon, and here’s why:

Manousakis invokes the formalism of the quantum two-state system, saying that the perception of (say) the image seen by the left eye is one state and that from the right eye is the other. The upshot of this is that the probability of seeing the illusion one way — say, the left-eye version — oscillates over time as

[tex]P(t) = \cos^2(\omega t),[/tex]

where [tex]\omega[/tex] is some characteristic frequency of the perceptual machinery. The oscillation is always going, swaying back and forth, but every once in a while, it gets “observed,” which forces the brain into either the clockwise or the counter-clockwise state, from which the oscillation starts again.

The quantum two-state system just provides an oscillating probability of favoring one perception, one which goes as the square of [tex]\cos(\omega t)[/tex]. Three of the four parameters fed into the Monte Carlo simulation actually pertain to how often this two-state system is “observed” and “collapsed”. These parameters describe a completely classical pulse train — click, click, click, pause, click click click click, etc.

What’s more, the classical part is the higher-level one, the one which intrudes on the low-level processing. Crudely speaking, it’s like saying there’s a quantum two-state system back in the visual cortex, but all the processing up in the prefrontal lobes is purely classical.
Continue reading Yawn: More Abuse of the Quantum →

Information Theory, Network theory, Plectics, Quantum mechanics, Statistical mechanics, Topology

Currently Reading

Oliver Johnson, Christophe Vignat (2006). Some results concerning maximum Renyi entropy distributions.

We consider the Student-t and Student-r distributions, which maximise Renyi entropy under a covariance condition. We show that they have information-theoretic properties which mirror those of the Gaussian distributions, which maximise Shannon entropy under the same condition. We introduce a convolution which preserves the Renyi maximising family, and show that the Renyi maximisers are the case of equality in a version of the Entropy Power Inequality. Further, we show that the Renyi maximisers satisfy a version of the heat equation, motivating the definition of a generalized Fisher information.

Luciano da F. Costa, Francisco A. Rodrigues, Gonzalo Travieso, P. R. Villas Boas (2006). Characterization of complex networks: A survey of measurements.
Continue reading Currently Reading →

Bibliophilia, BPSDB, Electromagnetism, Favorites, Pseudoscience, Quantum mechanics

I Get E-Mail

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BPSDBBelow the fold is an e-mail I received this morning from Victor Senchenko, human space navigator, and his “Media Team.” According to his website, Senchenko can explain why homosexual humans exist (OK), why God doesn’t exist (not clear whether this is the Abrahamic tantrum-tosser or something more sophisticated) and why time also does not exist (and right there, we hear the fuses blow).

Greetings Blake,

Considering your involvement with science, the following Press Release may be of interest to you.

As an astute person, you probably would agree that for a long while humans – especially the scientists – had been claiming that they wanted to solve all the mysteries of physical existence. They have also repeatedly indicated that they wanted to understand the causes of human behavior.

I don’t know many scientists who’ve claimed they want to solve all the “mysteries of physical existence.” We’ll settle for solving one mystery big enough to get us tenure; the others are left as an exercise to the interested reader.
Continue reading I Get E-Mail →

Bibliophilia, ICCS, Plectics, Quantum mechanics, Seminar Summaries

ICCS: Monday Evening

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The parts between talks are the best parts of conferences. Sure, it’s great to hear Greg Chaitin deliver his sermon about the ideal realm of pure mathematics being an infinite ocean of complexity, out of which we can only seize finite buckets — but Chaitin writes about that kind of thing, and you can read it for free online. It’s an altogether different experience to discuss during the coffee break Mike Stay and Cristian Calude’s paper, “From Heisenberg to Gödel via Chaitin,” with one of the three men in the title.

Question-and-answer sessions after the presentations can also be quite good. Last night, for example, Barbara Jasny of Science Magazine explained how that publication is adapting to the whizbang modern world. It’s reassuring to hear that at least one person in the publishing community has a common-sense understanding of what cheap, open digital access means: journals can only justify charging prices if those prices reflect the actual value which those journals add. More interesting than that, however, was Jasny’s reaction to the question from Frannie Leautier, former Vice-President of the World Bank and currently head of the World Bank Institute. Leautier asked if Science would publish articles which used cartoons as illustrations (instantly endearing herself to all the Larry Gonick and Sid Harris fans in the audience).
Continue reading ICCS: Monday Evening →

Cosmology, Favorites, Popularization, Quantum mechanics, String Theory

Sunday Egan

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Greg Egan writes,

I wish we had a good word in English that meant only “the shattering majesty of reality”, so atheists could make it abundantly clear that they’re aware of this majesty, but don’t imagine that it’s due to anything that resembles a person in any way. But what atheists absolutely should not do is say “Well, I’m going to use the word ‘God’ to mean ‘the awesomeness of the universe’”. This is helpful for selling lots of tenth-rate pop-science books with “God” in their titles, and for winning the Templeton prize, but even when it’s not plain venal and dishonest it’s linguistically sloppy.

This is why I describe quantum mechanics as Loki playing dice with the Universe. Come on, Loki may be subtle, but he’s not malicious, right?

We can take this one step further. There is a model of the early Universe called string gas cosmology, in which the reason why the Cosmos has three dimensions is essentially the same as the reason why knots can exist in three dimensions but not more or less. (In 2D, there’s not enough “room” for a string to overlap itself, and in 4D or higher, there’s too much room, and a knotted loop can always “slip free”, returning to a simple circle.) I wonder if the Templeton Foundation will pay me for declaring that the Cosmos is the way it is because Aphrodite likes to get tied up in knots?

(Hah! And you thought I was going to quote a passage from Quarantine, didn’t you?)