Wednesday, February 25, 2009

A Path to Greater Wonderment

What is a violin made of? Bits of wood and bits of sheep’s intestine. Does its construction demean and banalize the music? On the contrary, it exalts the music further.

--Julian Barnes


The story is told that Hans Bethe, the man who finally unveiled the mystery of nuclear fusion in stars, was out with his girlfriend, sitting by a cliff and gazing at the night sky.

       “How beautiful they are,” said the girl at a loss for better words to describe the stars.

       “Yes,” Bethe replied, “and right now I am the only person in the world who knows why they shine.”

       You might be tempted to rebuke Bethe for spoiling a romantic moment, but before you do, allow me to plead his cause.

       Does scientific explanation spoil beauty? Consider what Bethe’s discovery led up to. We now know that all the atoms in the universe other than hydrogen --the simplest possible atom, with a proton for a nucleus and an orbiting electron-- were created in the interiors of stars that later exploded as supernovas. The stuff our planet is made of, and the stuff we ourselves are made of, was cooked in a stellar oven billions of years ago. So what Bethe and other astrophysicists have discovered is, in effect, a link between us and the cosmos. Those bright points of light that stud the night sky are even now brewing the substance of new life.

       As for poetry and romance, consider this: Where Bethe’s companion saw little pinpoints of faintly-colored brightness her physicist friend saw mighty suns, their incandescent atmospheres roiling with nuclear fury, their colors revealing their temperature, age and composition.

       In other words, it is with nature as it is with good books and good movies --you take more from it the more you bring to it. It is simply not true that the scientist is insensitive to the beauty of nature because he can understand part of that beauty. On the contrary, science is a path to greater wonderment. The play of forces and quantum effects that allows the stars to shine and later enrich the universe with heavy elements is so subtle it makes you dream. The deductive chain linking the Big Bang with the present-day structure of the universe --though still riddled with gaps-- is nothing less than awe-inspiring. But only, I’m afraid, to the trained eye and mind --as it is with good movies.

       Consider the movie Shakespeare in Love. At the screening I attended with my wife, Magali, several years ago, there were people from all walks of life, young, old, and even a few little kids. The plot plays on many levels. On the very surface, if the name Shakespeare doesn’t ring a bell (hard to imagine but not impossible), it is a love story with some vague comedy to it.

       On the next level, you can laugh at the idea of an uninspired Shakespeare intending to write a crowd-pleaser titled Romeo and Ethel, the Pirate’s Daughter. You know he eventually wrote a tragedy, Romeo and Juliet, which is widely considered a masterpiece.

       Going deeper still, you even catch a few snippets of actual Shakespeare diaglogue being uttered in the background as an oblivious Will goes by. Later he uses those very phrases in Romeo and Ethel. You may also appreciate the piquancy in the screenwriter’s ploy of having Christopher Marlowe, Shakespeare’s real-life rival, suggest a better plot for Romeo. This is as far as my Shakespearean experience (such as it is) will take me, but there are deeper layers to Shakespeare in Love. How much more delightful the film must be for the lucky ones who can understand it in full.

       On the opposite side of the spectrum, the little kids only laughed when a character said “boobies.”

       So don’t be too harsh on Hans Bethe, the physicist who helped explain the stars. His intent was not to spoil a moment of romance, but to share with his sweetheart the poetry of a great discovery.

Wednesday, February 18, 2009

Einstein Confesses his "Biggest Blunder"

In 1917 Albert Einstein began to explore the cosmological implications of his recently published general theory of relativiy. General relativity is a theory of gravitation, the only force acting between stars and galaxies, so it stood to reason that it should have something to say about the structure of the universe.

Einstein wrote his equations, gave them a nudge and watched them soar. To his astonishment, they revealed that under general relativity the universe could not be static, but must be either expanding or contracting. There was, at the time, no observational evidence for this, and Einstein was forced to conclude, much to his chagrin, that there must be something wrong with the theory. He did not discard it. Instead, he modified the equations adding an artificial term containing what he called the “cosmological constant.” The cosmological constant, he thought, would hold the universe in check.

He was wrong. The Russian mathematician Aleksandr Friedmann found that Einstein had made an algebraic error, upon correction of which the universe happily took wing again. Einstein was puzzled. The equations of general relativity were simple and elegant. They had the kind of mathematical beauty in which the insightful physicist discerns physical thruth even before the equations are tested experimentally. But the astronomers he consulted told him that the stars wander more or less randomly through space, showing no concerted motion. Nature, it appeared to Einstein, had spoken, and against nature´s last word no physicist in his right mind --least of all Einstein-- ought to rise.

At the time many astronomers still believed that the stars in the Milky Way galaxy were more or less the whole universe. The spiral nebulae had not yet been recognized as galaxies in their own right. Many scientists thought they were solar systems in the process of formation, so when the astronomer Vesto Slipher of Lowell Observatory discovered that several spiral nebulae seemed to be receding from the earth at speeds much greater than the typical velocities of stars, nobody knew what to make of his data. He had in fact found the first observational indication that the universe is expanding.

But Slipher did not know that his spiral nebulae were faraway galaxies. Only after Edwin Hubble discovered Cepheid variable stars in the spiral nebulae were they identified as such. Moreover, the presence of Cepheid variables in the spirals allowed astronomers to determine their distances. In 1929 Hubble plotted the distances of 25 galaxies against their velocities of recession from the earth as measured by the “redshift” in their spectra. If the velocities were random, if the observation that most spirals seemed to be receding from the earth were just a coincidence, the graph would show a swarm of points scattered every which way. Instead, Hubble found a straight line.

Hubble was no theorist, and he was completely innocent of general relativity. He was wary of this “redshift-distance relation,” as he cautiously called it, and did not draw conlcusions from his discovery. But his graph was a message in the handwriting of the powers that be. To all who had eyes it read: “Behold, the universe is expanding.”

Einstein later called the cosmological constant his "biggest blunder". However, watch this for later developments in the fate of  this strange antigravity force:

Monday, February 16, 2009

Sticks and Shadows to Measure the Earth

The size of the Earth was determined for the first time some 2,200 years ago. At the time it was already known that our world is a sphere, but nobody had as yet come up with a way of accurately measuring its circumference.

That the earth is round was clear from several easily observable facts: when ships put out to sea their hulls always sink below the horizon before their masts; during a lunar eclipse the Earth’s shadow on the moon is always round. And so on.

One day the mathematician Erathostenes, head of the famed Alexandria library, learned about a curious fact while “leafing through” a papyrus book (presumably part of the library’s huge collection). Every year at noon on June 21 the columns of the temples in the distant city of Syene (present day Aswan), in Egypt, ceased to cast a shadow. As Erathostenes later verified, this was not the case in Alexandria, where vertical columns cast definite shadows at noon on the summer solstice.

Erathostenes knew that on a round Earth columns in Alexandria and columns in Syene do not point in the same direction. He reasoned that at noon on June 21 the sun came directly overhead in Syene so that temple columns were parallel to its rays, while at the same time vertical columns in Alexandria (or vertical sticks, or vertical whatever) were at an angle to the sun’s rays. Erathostenes saw how he could use this fact to determine the Earth’s circumference.

He planted a vertical stick on the ground in Alexandria and waited for the summer solstice. He then computed the angle formed by his stick and the sun’s rays by measuring the length of the stick’s shadow and comparing it to its height, a method involving math taught in highschool today. Erathostenes hired someone to walk all the way from Alexandria to Syene (located exactly due south from Alexandria, near the first cataract of the Nile) and measure the distance between the two cities. It is not too hard to see that the angle formed by the sun’s rays and the stick in Alexandria must be the same as the angle that the vertical of Syene and the vertical of Alexandria would form if extended to the center of the earth. So the clever mathematician now had an angle and the length of arc it traced on the surface of the earth. The angle turned out to be one fifitieth of 360 degrees, so the distance between Alexandria and Syene must equal one fiftieth of the Earth’s circumference. The figure Erathostenes came up with is equivalent to some 40,000 kilometers --remarkably close to present-day measurements.

Many centuries later a Genoese seaman by the name of Cristoforo Colombo was trying to prove that the Earth was small enough for him to reach China by sailing westward from Europe in a reasonably short time. His critics, who were probably aware of Erathostenes’s figure, claimed that the ocean separating Europe from Asia to the west was too vast, that Columbus’s proposed voyage could not be done. And they were on to something. In his eagerness to prove himself right the studious future Admiral of the Ocean Sea had rejected all ancient measurements which were incompatible with his claim, including Erathostenes’s. Had our continent not been in the way, Columbus would have sailed from Palos into oblivion.