Sunday, July 01, 2007

The Broken Mirror: III

Building better Mirrors

The fall of Parity triggered the question: If our Universe does not obey simple mirror-symmetry, then what kind of symmetry does it obey? In other words, perhaps we were looking in the wrong mirror.

P-symmetry is a mirror of parity, reversing left and right. We can think of it also as a transformation: It is an exchange of every Left-handed interaction with a Right-handed interaction.

Let's consider other types of mirrors. Physicists also examined another mirror called C-symmetry, or Charge symmetry. C Symmetry is a mirror which exchanges every positively charged particle with a negatively charged particle. In the world of physics this essentially means that the C mirror transforms particles into anti-particles and vice-versa. A proton and electron become an anti-proton and a positron.

So, what happens when we use the C Mirror, when we swap particles for anti-particles? Do the anti-particles obey the same laws of physics? The answer is No. C-symmetry is not a property of this Universe.

Ok, let's consider another abstract mirror. What if we take all particles and interactions in the Universe and move them backwards? Shown a film of a particle interaction, can we tell whether the film had been reversed? (Note to all clever folks: This is not the same as the question addressed by the Second Law since that applies only to macroscopic systems.)

Is our Universe symmetric in Time? This question is known as that of T-symmetry. The answer is...mostly yes. That is, we cannot detect a reversed film unless it contains some particular time-asymmetric interactions. This all comes down to the interactions of one particle: The Kaon. I summarize here from a physics abstract:

Most fundamental physical processes are symmetric in time. The motion of the planets in the gravity field of the sun is reversable- a film of the motion of a planet around its sun can be shown backwards without anyone being able to tell. Similarly to gravity, the strong nuclear and electromagnetic forces are also time-symmetric. Only the weak nuclear force appears to violate this symmetry, and this so far only in the behavior of the neutral kaon.

We'll return to discuss the Kaon, later.

Combining symmetries
If I reflect a mirror image of a mirror image, I get the original. Mirrors can be combined to produce more mirrors.

The failure of P and C and T symmetry in our Universe is confounding. Recall that P symmetry is closest to what we consider a classic mirror, reversing left and right. What if we combine two mirrors (or more), combining the C mirror with the P mirror?

What this means in practice is that the mirror on the wall does show a valid Universe if we also exchange particles for anti-particles. The resulting symmetry is known as CP symmetry.

In 1980, James Cronin and Val Fitch earned the Nobel prize in physics for demonstrating that CP symmetry is not conserved. It was mostly conserved but violated in some interactions of the Kaon.

CPT: the Ultimate Mirror
The CP violation of the Kaon and the T violation of the Kaon are in fact related. They can be canceled out by throwing togther CP and T to make CPT: antiparticles in a mirror going backwards in time.

There is every reason to believe that CPT symmetry holds for our Universe. Even the Kaon (so far) obeys CPT symmetry. But what exactly does CPT symmetry imply? And what makes the Kaon such an anomaly?

Friday, May 11, 2007

The Broken Mirror: II

II Through the Looking-Glass

"One hopes that nature possesses an order that one may aspire to comprehend. When we arrive at an understanding, we shall marvel how neatly all the elementary particles fit into the great scheme."
-Madame Chien-Shiung Wu

If you look into a mirror, you look out into a reversed world. Left and Right are interchanged but otherwise the world in the mirror looks much like our own.

What about the Laws of Physics? Are they the same in the mirror-world? It appears so. If I throw a ball in the air, my double in the mirror also throws up a ball and both fall according the same law of gravity. I can play with magnets or tops or engines and again the actions of my double are also possible in this world.

Chemists work with the notion of Chirality. The left-right orientation of molecules has a profound impact on their properties. So a left-hand molecule in our world becomes its right-hand counterpart in the mirror world which, according to chemical precepts, is an entirely different molecule. But all of this is surprisingly irrelevant. Since every other molecule in the mirror-world has also changed its handedness, any chemical experiments our double performs are also possible in our world.

So it would seem that if we, like Alice, were unsure whether we were inside a mirror there would be no way for us to discover the truth. Or so it seemed, even to physicists, who refer to this mirror-symmetry property of the Universe as "Parity Conservation."

In 1956, an incredible (and vastly under-appreciated) experiment was performed whose purpose was in fact to determine on which side of the Looking-Glass we live in. The more prosaic intent was to determine the Question of Parity Conservation. The experimenter was a Chinese-born woman - Madame Chien-Shiung Wu.

Her fellow physicists, T.D. Lee and C.N. Yang, had predicted that there might be certain interactions among subatomic particles whose mirror was improbable or did not exist at all. Parity tests such as these had already been performed for a wide variety of interactions and so most physicists were dubious but intrigued.

It was Madame Wu, setting up a laboratory at the National Bureau of Standards in Washington, who set out to confirm or disprove their hunch. The key was in how one particular atom, cobalt-60, decayed. Unlike other atoms studied it decayed (ejecting pieces of itself in the form of beta particles) in an asymmetric manner. The mirror-image of this process was not one that was observed.

If you had placed a large mirror against one wall of Madame Wu's laboratory, her double in the mirror was performing a similar experiment but obtaining results which do not appear in our Universe. The mirror world is not our world merely reconfigured, it is a distinct and alternate reality. Deep within the subtle textures of the Universe there is indeed a small asymmetry, a telltale, a crack, which can be used to distinguish ourselves from the mirror world.

The result was completely unexpected. Mirror-symmetry appeared to be true and appeared to continue to hold true across thousands of other experiments. Looking upon this event, the fall of Parity, the physicist I. Rabi remarked "A rather complete theoretical structure has been shattered at the base and we are not sure how the pieces will be put together"

Wednesday, May 09, 2007

The Broken Mirror: I

The Broken Mirror
I. The Shape of Space

I don't recall the name of the professor who taught the course on Cosmology. I do recall he wore stiff suits and large spectacles and that he was British. Also, he kept his upper body completely fixed when he moved about. Scratching out equations on the chalkboard, for example, he would raise one hand and then bend his knees up and down to write. The effect, as seen from behind, was as if a large frog was anxiously stretching its legs against the front wall of the classroom. Meanwhile the professor/frog was also sagely informing us about the nature of stars and galaxies.

We were discussing the shape of space. Space can be negatively curved, positively curved or it can be flat. The verdict relies on understanding how much matter is in our Universe and whether it exceeds a theoretical critical number. This grand ratio is known as Omega. If Omega is greater than 1, then space is positively curved and the Universe is headed toward collapse. If Omega is less than 1, space is negatively curved and will expand forever.

The discussion turned philosophical. Astronomers had tried to measure Omega and values ranged from 0.001 to 1.2. Surely, our professor argued, this meant that the value was likely to be exactly 1. His argument was an aesthetic argument. An Omega of 1 was perfectly symmetrical. And if it were not 1, why would it be so tantalizingly close to 1? Omega could have been measured to be in the billions or a mere tiny billionth. But it was not.

The argument is alluring but it also recalls the struggle between idealizations of the natural world and the true natural world, that is bare reality, which obeys symmetry from a rough distance but, when magnified, obeys its own impenetrable logic. Planets do not move in perfect circles in a Ptolemaic harmonic symphony. They move in wobbly ellipses, tugged constantly in their orbits. The Earth is not a perfect sphere but an oblate spheroid, tilted sideways, drawn off-center by a heavily cratered moon.

Symmetry as an ordering principle is a rough guide. Inspected more closely, the Universe is riddled with tiny asymmetries. This seems obviously true on the larger scale; we all know there is no perfect circle or straightedge.

But it is also true in the idealized world of natural laws. Just when we believe we have fully understood some force or interaction or particle, just at the moment we are ready to formulate a Universal Law or Rule, we find one or two exceptions. Not thousands or millions of exceptions, but just a couple, a few... sometimes only one. But only one exception is needed to invalidate the rule altogether. It is a confounding feature of our world that every symmetry is broken, but only barely broken, it is like an otherwise perfect mirror with a hairline crack. A broken mirror, nonetheless.

With what I know now, it is obvious, contrary to what the professor was saying, that Omega may be slightly less than 1 or slightly greater than 1 but it is certainly not 1. That would make the Universe perfectly symmetrical in that respect. Such symmetry, as far as I know, is forbidden in this world.

Monday, April 30, 2007

Paintings of Paintings: Teniers and the Archduke's cabinet

I first discovered Teniers because I had a fondness for his paintings of alchemists. Teniers (the Younger, not the older or Teniers III) paintings are of daily life, peasants in the field and in the kitchen, 17th century snapshots.

His paintings of alchemical laboratories depict the alchemist at work. Rooms cluttered with books, creatures - stuffed on hooks, perched on tables, jars with murky and mysterious contents. The painting The Alchemist from 1645 is typical. He returned to this theme several times: The Alchemist, Teniers as an Alchemist, The Alchemist, An Alchemist in his Workshop and many more.

One of Teniers' patrons was the Archduke Leopold William, an aristocrat and art collector. His collection of over a thousand paintings included Titian, Breugel, Van Eyck, Raphael, Veronese and Giorgione. In the series of paintings Archduke Leopold William in his Gallery, Teniers set out to document this collection - or at least its greatest stars.

The painting above shows not only these paintings but also Teniers (on the far left) and the Archduke, prominent with his hat and cape. Another version of this painting appears here along with clickable identifications of many of the paintings.

The painting can be considered a catalog of sorts. The intention of the work is to showcase the Archduke's treasures. The collection is oriented on one wall and toward the viewer. The Archduke stands regally in the middle with Teniers, his humble curator and assistant off to the side.

This piece is in fact a direct precursor to the first Art catalog - Teniers' Theatrum Pictorium. Teniers employed engravers to reproduce the greatest works of the ArchDuke in miniature. These engravings were used to print the Theatrum Pictorium, a book of reproductions, the antecedent of photographic plates. The engravers worked off of small oil reproductions produced by Teniers himself. That is, the images in the catalog are copies of copies, an engravers take on a Teniers oil copy of a painting by Giorgione for example. In a few cases, the original paintings have either been lost or altered, making the Theatrum Pictorium illustration more real than the painting itself.

Saturday, April 21, 2007

Flight and Pursuit

When I was at the MFA in Boston last month, I was traveling idly through rooms content to let paintings catch my gaze rather than hunting for specific works. The MFA is oddly organized, a patchy quilt of rooms where it is easy to walk from 19th Century Continental European into Egyptian relics without the benefit of any transitive space.

It was walking through one of these rooms that I noticed and was drawn to William Rimmer's Flight and Pursuit. Unlike the surrounding paintings, it is not immediately clear what is going on here. A man is running through the scene, about to exit on the left. Behind him, not directly behind him but parallel, is a robed and transparent figure also running in the same direction. They appear to be inside a palace. The running man casts a shadow and a shadow appears to be directly behind him as well, cast, presumably, by something outside the painting to the right.

After my visit, I decided to learn more about the painting and the man who painted it. I assumed that I was ignorant of some crucial element of mythology or history upon which the painting was based. However, it appears that this particular painting is puzzling for many more reasons and, so far, has resisted attempts at decipherment.

The painter, William Rimmer, was a well-known mid-19th century English-born American painter. He practiced Medicine. He taught Art classes. He was mainly a sculptor, creating a statue of Alexander Hamilton for the city of Boston, but also produced lithographs and paintings.

But this abbreviated biography leaves out some of the more interesting aspects of Rimmer. Rimmer's father was an emigrant from France and believed that his son William was the lost Dauphin. It appears that William Rimmer believed this too, that he had been usurped of his royal role.

Also, Rimmer not only taught Art but specialized in Art and the human anatomy, and became a professor of Anatomy and Sculpture. He even published several well-received books on Art and Anatomy.

In Flight and Pursuit, we have an anatomical puzzle. The running man is in an unbalanced position. His left arm and left foot are thrust forward. This is not how someone appears in the act of running. It is also not a mistake a professor of Art Anatomy would make.

The title of the painting, Flight and Pursuit, is the painting's second title. The original title was On the Horns of the Altar. This has led several scholars to surmise that this painting is about a Biblical tale of usurpment.

In Kings 1, we find the tale of Adonijah:

1 Then Nathan asked Bathsheba, Solomon's mother, "Have you not heard that Adonijah, the son of Haggith, has become king without our lord David's knowing it?

But Solomon soon regains his throne from Adonijah and Adonijah is left fearing for his life:

49 At this, all Adonijah's guests rose in alarm and dispersed. 50 But Adonijah, in fear of Solomon, went and took hold of the horns of the altar. 51 Then Solomon was told, "Adonijah is afraid of King Solomon and is clinging to the horns of the altar. He says, 'Let King Solomon swear to me today that he will not put his servant to death with the sword.' "

Here, the "horns of the altar" is synonymous with sanctuary. The usurper fears for his life. This does very little to clear up the painting's mysteries for me. Is this a painting of the usurper running from his assassins? Is this Rimmer and his ghost, a Boston painter and the Dauphin? I was initially drawn to the urgency and motion in this painting. It is impossible to look at this painting and not believe that the painter drew with intent and purpose. This is why I at first felt that this was an illustration of a common myth that had eluded me. The painters purpose may have been clear, but the painting, it appears, will continue to mystify.

Thursday, April 19, 2007

The Obscene Bird

A new project, one which allows me to revisit my favorite works and make some small attempt at unraveling them.

The initial novel is one of my old favorites, Jose Donoso's El Obsceno Pajaro de la Noche (The Obscene Bird of Night), a little known masterpiece of Spanish literature.

The trail begins here.

Sunday, January 14, 2007

Writers of the No

Writers of the No

The haunting words of von Hofmannsthal's Lord Chandos: "I have completely lost the ability to think or speak in a connected manner about anything.", this rejection of expression, this acceptance of the futility of mere words, is adopted by Enrique Vila-Matas as the theme of his book/novel/fiction Bartleby & co.

Bartleby of course is Melville's Bartleby, a copy clerk whose passivity becomes the means by which he unshackles from the world, retreating into nothingness, into inexpression. As Vila-Matas writes:

"...for some time now I have studied the illness, the disease...the negative impulse or attraction towards nothingness that means that certain creators...never manage to day they become literally paralysed for good."

Paradoxically, Vila-Matas believes that the impulses which belies this sudden silence is the highest form of expression itself, the writing of the No - an unwritten creation by unwilling creators. He continues:

"Only from the negative impulse, from the labyrinth of the No, can the writing of the future appear."