Monday, December 27, 2010

Black Swan - Mirror, Mirror

Black Swan movie poster,
courtesy of Fox Searchlight
This essay is taken from a note that I posted on FaceBook about Darren Aronofsky's recent film, Black Swan.  It does not contain spoilers.

The films that I have always found most compelling are those that present an intriguing character, one with whom identification is a difficult, but a rewarding, struggle, and send that character off on a journey of personal discovery. Their appeal, in part, has to do with the fact that the hero's quest for transcendence or, as is often the case, redemption suggests the possibility of our own transformation. They offer us a distorted but beguiling mirror in which the hero's hopes and fears and doubts become our own.

Darren Aonofsky's film, Black Swan, succeeds wonderfully as such a film.

The Aronofsky films I have seen - Pi, The Fountain, The Wrestler and now Swan - invite us to enter personally uncharted territory and there to step into the shoes - or slippers, as the case may be - of, respectively, an unhinged mathematician, a disillusioned conquistador, a dissipated professional wrestler and a psychologically scarred aspiring prima ballerina. It is a testimony to the director's skill and his uncanny selection of players, that we quickly begin to identify with these lost souls, in spite of the fact that their lives and their occupations are entirely foreign to us - an accomplishment all the more remarkable in a movie industry that relies on cookie-cutter characters and characterizations for commercial success.

In each of these works Aronofsky dispatches his reluctant hero on a quest, an attempt both to come to terms with a damaging personal history and to transcend the past by reconciling the demands of art or profession or craft with the reality of the world as it is.

For Swan, this journey of transcendence is rooted in a universal artistic challenge, how to move beyond the technical mastery of a medium and take the risk involved in opening oneself up to messy and often unwelcome psychic forces that are the heart of profound artistic expression.

On one level the film is the story of Nina Sayers (Natalie Portman), a beautiful and talented young ballerina who is poised to become the principal dancer of an unnamed New York company, and must overcome her slavish good-girl commitment to mechanical virtuosity and tap into dangerous emotional currents that emanate from her unexplored sexuality and a toxic relationship with a controlling, ever-watchful mother (played magnificently by Barbara Hershey).

On another level, Swan is a tale of the director's own struggle to put his mastery of the medium of film in service to the telling stories that are not only exquisitely crafted, but also emotionally compelling. Aronofsky's abundant skills are on display as he demonstrates a cinematic range that encompasses both the glossy presentation of lavishly staged ballet as well as the gritty exposition of the intimate details of Nina's personal ordeals. In doing this Aronofsky reminds us that for him the life of genius - and not only artistic genius - is a ongoing flirtation with insanity, a ceaseless effort to locate and occupy the razor's edge that is the wellspring of creativity.

Finally, Swan is a mirror of Natalie Portman's own trajectory as an actor. Poised, as her character Nina is, at a juncture in her career where accomplishment beyond mere technical excellence beckons, Portman has dared to take on a very different role, one that demands that she expose herself, both emotionally and sexually, in order to discover her true potential. This actress is determined to put away childish things - like so many stuffed animals tossed down a trash chute - and declare herself as a performer who can draw on both the light and the dark aspects of her nature.

So Black Swan is all of these, a story about a troubled young ballerina, a story about its director, Aronofsky, and a story about its star, Portman. It is a hall of mirrors, which teases and disorients us by confusing the real world with the imagined. Perhaps most importantly, it is a hall of mirrors in which we are invited - every now and then - to catch a glimpse of ourselves.  In this regard, in a small way, it is also a story about us.

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Black Swan - Mirror, Mirror by Marc Merlin is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
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Tuesday, December 14, 2010

A Conceptual Introduction to the Measurement Problem of Quantum Physics

This is the fourth and last in a series of essays to be used as background for the Atlanta Science Tavern discussion Quantum Physics and Consciousness. It began with this introductory post.

At the heart of the controversy concerning quantum physics and consciousness - raised by the What the Bleep Do We Know!? movie - is a conundrum that goes by the name the measurement problem.  My intention here is to introduce this problem to people not steeped in quantum physics.  I will try to do this while remaining faithful to the concepts that I believe are central to the discussion at hand..

Sextans A, member of the
Local Group
One of the pervasive concepts in physics is that of a system.  It is an abstraction that is used to refer to something as small as an electron orbiting the nucleus of a hydrogen atom or something as large as our own Milky Way orbiting the gravitational center of the Local Group of more than 30 galaxies.  It can represent something as simple as a pair of photons, particles of light, entangled in a quantum pas de deux, or as complex as a human brain, a wet, warm, messy computational engine, sporting over 1,000 trillion synaptic connections.  Even (Austrian) cats have been recruited in the service of constructing such hypothetical systems.

There is an important assumption regarding a system and that is that it can be regarded as independent or free-standing.  In other words, it is meaningful to discuss a system, at least for limited purposes, as though it exisits in isolation from the rest of the world.  Without this idealization the scientific enterprise as we know it would be doomed, mired in complexity.  Nonetheless, we should keep in mind that it is an approximation.

A gyroscope as a
demonstration of angular
Properties and States of a System
Ultimately the goal of a physical theory is to offer an accurate description of the behavior of a system over a period of time.  Such a description emphasizes what are considered to be significant properties, features either of the system as a whole or of its constituent parts.

Most notable among these properties of a system (or its parts) are its position and its velocity.  Less concrete, but no less significant, is the property of a system which we call as its energy.  Other properties include mass and electrical charge and quantities having to do with a system's rotational motion, namely its angular momentum or spin.  Modern physics has added a large number of much less familiar properties to this list of quantities used to describe systems.

For our purposes, it is not so much important to know what each of these properties means individually, as it is to understand that they can be used collectively to create a "snapshot" of a system, which defines what is called its state.  One can think of the state of a system as way to designate an enumeration of its properties and their corresponding values at a particular instant in time.

Measurement in General
Measurement can be seen as the process by which the properties, and hence the state, of a system are discovered.  We typically imagine this as involving some sort of measuring device or apparatus, a ruler, a telescope, a radar gun, or a thermometer, for example, but in a very austere sense measurement may involve any kind and any size of physical "probe", used to determine a value for a property of a system.

Measurement in Classical Physics
In classical physics the measurement of the properties of a system, although perhaps technologically challenging, is philosophically straightforward.  A measuring device can, in theory, be refined to obtain an arbitrarily precise value for a property, while at the same time inducing an arbitrarily small amount of disruption to the system as a whole.

Collectively these measured properties, drawn from a continuously-varying range of values, define the state of the system, which is, in principle, indifferent to the effect to the act of measurement.

Bohr atom with
energy levels
Measurement in Quantum Physics - First Twist
Quantum physics adds some unexpected twists to the classical theory of measurement.

For purposes of concreteness, but without loss of generality, we will use the example of a hydrogen atom consisting of a lone electron in orbit around a single proton.

It turns out that when we measure the energy of the orbiting electron we obtain not a continuous range of values, but a discrete set of values, the so-called energy levels of the system.  These fixed amounts, or quanta, of energy - from which the theory derives its name - represent a departure from the classical view of the world in which quantities like energy were assumed to vary continuously

Interestingly enough, and consistent with classical theory, repeated measurements of the energy of the electron yield the very same answer.  Furthermore, measurements of certain "compatible" properties, such as its angular momentum, leave the system undisrupted, and subsequent  measurements of the electron's energy are unaffected.

All hell breaks out, though, when you go to measure something else.

Measurement in Quantum Physics - Second Twist
For example, if you start with a hydrogen atom in a known energy state and measure, say, the position of its electron, then the result of a subsequent measurement of its energy is no longer determined, but may take on any value from the range of allowed energy levels.

In fact the measurement of an "incompatible" property, no matter how carefully made, disrupts the system.  Contrary to classical expectations, the disrupted electron is described as then occupying not one but a multiplicity of energy states, and its amount of "participation" in each of these states determines the probability that the corresponding energy level will be measured the next time around.

Troubling as this is finding may be for measurements of energy, it is even more unsettling to consider that this inevitable mixing of states also applies to measurements of position, the implication being that the electron can find itself, to a greater or lesser degree, at a multiplicity of locations!

DVD cover for Tom
Stoppard's "Rosencrantz
& Guildenstern" Are Dead
Measurement in Quantum Physics - Bottom Line
Unlike measurement in classical physics which can be consigned to a secondary - and diminishing - role, measurement in quantum physics insists on playing a leading one.  The choice of which properties to measure and the order in which these measurements are conducted unavoidably effect the system under observation.

It turns out that the act of measuring specific properties, most significantly energy, places a system in a stable state, referred to as a stationary state or eigenstate, in which values of those properties and compatible ones persist indefinitely.  Intervening measurements of incompatible properties, though, force the system into a configuration that is a mixture of these stationary states, called a superposition.  Although the outcome of individual measurements on a system described by a superposition is unpredictable, their statistical distribution is entirely determined.

A digital multimeter
The Measurement Problem
Since measurement is not a particularly important process in classical physics, it hardly commands a lot of attention.  But in quantum mechanics, measurement is a first class feature of the theory and so this activity has to be much more carefully considered.

First and foremost, what does it mean to say that a measurement has occurred?  Does this happen when a measuring device interacts with the system being investigated?  What distinguishes these "measurement" interactions from other  routine interactions between the system and its environment?

To the extent that the act of measurement is, itself, a causal chain of events described, ultimately, by quantum theory, when, if ever, can we say that it concludes?  Does a measurement end, for example, when photons of light refelected off an LCD display strike the the retina of the experimenter working in her lab?   What if the experimental data is collected autonomously and stored on-line?  Does the measurement finally occur when the data is downloaded and viewed by the experimenter on a remote computer?

Furthermore, what is the detailed mechanism involved in transforming the quantum mechanical superposition of states into a single eigenstate state, which is characterized by the measured value of a property such as energy?  How does this collapse of the wave function (an alternative name for this superposition of states), take place?

Enter Consciousness
These are some of the puzzling questions that have given rise to the variety of interpretations of quantum physics in circulation.  Consciousness enters the picture because some people believe that it may be the critical feature that distinguishes measurement from other physical processes.

So consciousness is, to some extent, reasonably offered as a potential "solution" to the measurement problem of quantum mechanics.  Be that as it may, it is one thing to suggest that consciousness is implicated in the collapse of the wave function, and quite another to insist it is a mechanism that allows us to project our will and desires on the physical world.  This is the leap that the movie What the Bleep takes and this is why its claims are so controversial.

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A Conceptual Introduction to the Measurement Problem in Quantum Physics by Marc Merlin is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
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Sunday, December 5, 2010

Adventures in Quantum Tourism

This is the third in a series of informal posts to be used as background for the Atlanta Science Tavern discussion Quantum Physics and Consciousness.

Cover of Anne Tyler's
"The Accidental Tourist"
Imagine yourself a young person - or an unworldly adult - about to embark on a first-ever trip abroad. You arrive by plane at your destination and are immediately overwhelmed by the strangeness of the place.

For example, the language you hear at the gate sounds less like human speech than like dogs barking. How could anyone understand what's being said?

The signs you see posted as you make your way down the concourse are inscrutable. It's not clear whether the symbols are letters or words, or whether the script is intended to be read right-to-left or top-to-bottom. It all looks so unnecessarily complicated.

Somehow you find your way to a shuttle bus and, as it departs for your hotel, you are alarmed to discover that everyone is driving on the wrong side of the road! Whose crazy idea was this dangerous scheme?

At the hotel, weary from your travel but wanting a bite to eat before you go settle down for a well-deserved nap, you decide to visit the restaurant off the lobby which, mercifully, has photos to accompany the utterly unintelligible text on its menu. Little consolation that, since not one of the items depicted is a dish recognizable to you. To make matters worse, when your meal is served, what appears to be the entrée is unexpectedly sweet and what appears to be the dessert is not sweet at all, but unexpectedly spicy. This is a gratuitously cruel reversal of the correct culinary order of things, as far as you are concerned.

Exhausted from dealing with this onslaught of the unfamiliar, you retire to your room, where, although sleep beckons, you lie awake struggling to come up with explanations for the disconcerting experiences of your day. You are convinced that if only you had the intellectual chops to think long enough and hard enough about the strange things you had seen and heard and read and tasted, then the reasons why they are the way they are would become clear. But struggle as you might, no realization emerges and you finally succumb to sleep, your last thought being, "I'll never understand this place, it makes no sense at all."

The Twice-Told Allegory of the Bewildered Traveler
The above tale is an allegory for the frustration - and sometimes despair - everyone feels when first introduced to the mysterious world of quantum physics. The story continues, of course, taking one of two divergent paths.

In the first variation, the traveler wakes and beats a hasty retreat back to the airport, where she catches the first flight home. There she regales friends, family and colleagues of the bizarre details of her misadventure and the absolute impossibility of living abroad.

With the second telling, the traveler, refreshed by her nap, pauses and then decides to explore a bit before considering whether to cut her trip short. (It seems like the prudent thing to do, since she has come so far.) Fortunately she makes the acquaintance of an expatriate, a fellow from her home country no less, who helps her to understand a useful phrase or two in the local language and to appreciate a couple of tasty offerings of the local cuisine.

Intrigued, she vows to extend her stay, even going so far as to purchase a bicycle which she, with some trepidation, learns to ride on the "wrong" side of the road. Feeling increasingly comfortable in her new environment, she contemplates the possibility of establishing a second home here, and laughs when she reminds herself that she still has no answer as to why this place is so strange, a once pressing question that no longer seems relevant at all.

The Fallacy of Extrapolation
Terra Incognita (BBC Archive)
There's a category of misguided reasoning that goes by the name "the fallacy of extrapolation". Typically it is used to describe the mistake that people make when they assume that a current trend will continue, unchanged, into the future. But it also is a good way to characterize an error that results from imagining that the rules that govern our everyday lives should be the same as those that apply to a novel situation, one for which we have no first-hand experience.

This is exactly the kind of mistake late-19th century physics made when initially confronted with the uncharted territories of the "very fast" (speeds close to that of light) and of the "very small" (distances on the scale of atoms and molecules). And it is the mistake that we all repeat when we are first exposed to the ideas of special relativity or of quantum mechanics, the theories used to describe those two unfamiliar realms.

But, like seasoned travelers, we can benefit from knowing that, if we are open-minded and patient, then the confusion and dissonance that we feel with the first encounter a strange new world will slowly dissipate, and that through acceptance and immersion we can come to enjoy a new home away from home.

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Adventures in Quantum Tourism by Marc Merlin is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
Based on a work at

Saturday, December 4, 2010

Does Anyone Understand Quantum Mechanics?

This is the second in a series of informal posts to be used as background for the Atlanta Science Tavern discussion Quantum Physics and Human Consciousness.

Richard Feynman, Los
Alamos ID badge
Richard Feynman, one of the great physicists of the 20th century, offered this somewhat discouraging claim in his book, The Character of Physical Law, "I think I can safely say that no one understands quantum mechanics."  Given that Feynman was not only a technical but also an intuitive master of the subject - the likes of which will seldom be seen again, I might add - it would be pointless for me to try to contradict him.  But I think it is reasonable to suggest that this oft-quoted statement might benefit from some clarification.

Certainly, as a practical endeavor, many, many thousands of scientists and engineers around the world today understand quantum mechanics.  They use it routinely in their work, whether designing computer circuits or predicting the outcome of the collisions of the protons that hurtle toward each other at near light speed at the intersections of the beam lines of the Large Hadron Collider outside of Geneva, Switzerland.  Indeed, the related theory of Quantum Electrodynamics, of which Feynman was a pioneer, is, hands down, the most successful physical theory ever devised as far as the precision of its predictions is concerned.  It would be hard to beat.

Compact Muon Solenoid at
the LHC at CERN
Yet it comes as a surprise to lay people, who find themselves beguiled by the mystery of quantum physics, to learn only a fraction of physicists are troubled, at least professionally, with the philosophical questions that it raises.  The dictum. "shut up and calculate!" holds sway in laboratories and universities, with the meaning of the theory being no more and no less than its thoroughly demonstrated correctness and utility.

And this is where, to a certain extent, they part company with Feynman, whose discouraging words might more accurately - and perhaps more hopefully - be expressed as, "no one understands yet what quantum mechanics means."  The fact of the matter is that, after almost nine decades of earnest striving, there is no agreed upon interpretation of what quantum physics says about the very nature of the world it so successfully models.  Some have more currency than others, but none has proven so superior that it has vanquished its competitors.

In my opinion it is our failure to formulate a convincing interpretation that fuels the controversy that surrounds the question of quantum physics and consciousness which has motivated the discussion at hand.  The absence of a conclusive answer to the stubborn question of meaning has been an invitation for all contending interpretations of quantum mechanics, of whatever stripe, to enter the fray.

That said, I do think that the central concepts of quantum physics are in fact understandable by "ordinary" people, that is if they are willing to let go of preconceptions and to imagine themselves, instead, as inquisitive travelers to an unexplored country.  This will be the topic of the next post in this series.

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Does Anyone Understand Quantum Mechanics? by Marc Merlin is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
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Thursday, December 2, 2010

Quantum Physics and Consciousness - Why this Discussion?

This is the first in a series of informal posts to be used as background for the Atlanta Science Tavern discussion Quantum Physics and Human Consciousness.

Why this Discussion?
When a handful of science enthusiasts get together to share their thoughts on the "big" questions, the conversation often turns to the mysterious world of quantum physics. Indeed, in a cursory survey of the interests of members of the Science Tavern meetup, the subject ranks near the top of the list of stated science interests.

We are drawn to quantum physics for many reasons, but primarily because it tells us a fascinating and unexpected story, that the world as we experience it is an illusion, and that a deeper reality exists, full of marvels and wonders, accessible to those with the determination to look beyond mere appearance.

The Cave: An Adaption of
Plato's ;Allegory in Clay
In this regard quantum physics arrives as a concrete realization of Plato's Allegory of the Cave and the alluring prospect that knowledge can truly set us free. It also represents the last best hope for the existence of any kind of magic, a possibility that had been all but banished from consideration by the thoroughly deterministic program of classical physics that began with Newton and reached its apogee at the end of the 19th century. Likewise, the overthrow of determinism by quantum physics offers hope to some for a theory of free will compatible with our scientific understanding of the world.

"What the Bleep" movie
It is not surprising that these intriguing ideas have found there way into popular culture. The treatment that motivated the discussion at hand is a movie from 2004, What the Bleep Do We Know?, which sparked a brief, but heated exchange, on our meetup website recently. As a result of the way it interprets the relationship between quantum mechanics and human consciousness, the film has become both a manifesto for adherents of so-called quantum mysticism and a target for derision by the scientific community at large.

Our purpose is to probe the origins of this controversy and to try to come to a common understanding about the physics that is at its core.

Two Questions in One
I should note in closing this introduction that the question of quantum physics and consciousness - I will refrain from using the somewhat parochial qualification "human" consciousness from here on - divides itself, not so neatly, into two.

The first has to do with metaphysics - in the strict sense of that word. Does a comprehensive theory of physics require consciousness as a fundamental feature? This is the quandary at the center of the What the Bleep dispute.

The second question has to do with the origin of consciousness and the role that quantum physics plays in the emergence of it as a physical phenomenon. In this case the question, on its face, is not so controversial; brains, at least from a materialistic perspective, are physical entities describable, ultimately, in quantum mechanical terms. There is, though, much active discussion and disagreement about the variety of schemes that have been proposed as possible answers.

The two questions are not entirely independent, but for the time being, I will focus on the first as this series continues.

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Quantum Physics and Consciousness - Why this Discussion? by Marc Merlin is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
Based on a work at