July 23, 2006

The Expansion of the Universe

Edwin Hubble, A Relation Between Distance and Radial Velocity Among Extra-galactic Nebulae, 1929

This discovery is quite simple to explain. During times when some astronomers were still arguing that there were no objects outside the Milky Way, Hubble used Cepheid variable stars and the biggest telescope in the world to discover that there are galaxies outside our own, and the farther away they are, the faster they are moving away from us. At the time, he wasn't sure just what this could mean, but by 1931 practically everybody had realized that the universe itself is expanding. The space between the galaxies is itself expanding, making the more distant galaxies appear to move even faster than the nearer ones.

That's it. There's a lot to be said about how several people came close to figuring this out before Hubble, either theoretically or observationally, but never had the precision afforded by the combination of the Hooker telescope and Cepheid variables to find the distance/velocity relation. There's also a lot to be said about the difference between static and dynamic models of the universe. However, I would like to take this opportunity to talk about the various scientists that have made these great discoveries.

Edwin Hubble completely breaks all the modern stereotypes about scientists. He wasn't nerdy. He wasn't a geek. He wasn't shy. To quote the book:

"By sixteen, Edwin was the star of the Central High School basketball team in Chicago. In a single track meet his senior year, he won the pole vault, the shot put, the standing high jump, the running high jump, the discus, and the hammer throw, and on May 6, 1906, he established the Illinois state record in the high jump. After compiling a superb academic record at the University of Chicago, he won a Rhodes Scholarship, which had been a personal obsession."

At Oxford, he studied Law, and also won track events and held an exhibition boxing match with a French champion. After returning to the US and spending a year as a lawyer, he went back to school as a graduate student in astronomy. When he got his Ph.D. in 1917, he joined the American Expiditionary Force in France, where he rose to the rank of Major before returning to begin work at Mount Wilson Observatory. He was, in short, handsome, athletic, and a good leader as well as smart.

Here are a few statistics about the scientists in The Discoveries: 25 papers covering 22 discoveries were written by 49 scientists (Einstein was sole author on two). 12 of the papers had a single author, 7 had two, 3 had three, 1 had five, and 1 had nine, with a definite trend towards more authors over time. 6 of the 49 were female, again with a definite increasing trend over time. At the time of publication, the ages of the 35 authors I could find biographical information on ranged from 26 (James Watson and Werner Heisenberg) to 60 (Otto Hahn and Lise Meitner), with a median age of 37. The distribution of ages appears to be flat from 26 to 49, then a gap until Hahn and Meitner. 18 of the papers were originally published in English, 7 in German (6 of those from before 1928). Of the individuals or groups publishing the papers, 9 were German, 9 American, 4 British, 1 Austrian/British (Perutz), 1 a New Zealander (Rutherford), and 1 Danish (Bohr). None of the papers were published during WWI, the Depression, or WWII. (Great science appears to be a fragile thing.) Many of the authors had their work interupted by WWII, including several who were forced to flee Germany because of their religion or politics.

There doesn't seem to be a stereotypical scientist. Some knew exactly what they were doing, while others stumbled upon their discoveries by accident. Some were theoretical and some observational, but most were a potent combination of the two. Some of the scientists understood the significance of their discoveries immediately, while others had to wait years until they realized what they had done. Some of them were total unknowns before their work, including some of the older scientists, such as Otto Loewi (47), while others had done good work already, including some of the youger scientists, such as Werner Heisenberg (26). Some worked well in a team, some were solitary geniuses, and some divided the theoretical and practical work between themselves (or assigned the practical work to assistants). Some were bold, some modest, some focused on details and some focused on generalities. And Hubble was also an athlete and a Major in the US Army.

Another interesting thing to note: the best way to make a great discovery seems to be to learn from someone who has already made a great discovery. For example, Cavendish Laboratory generated Nobel Prizes as if they were science fair medals. Its directors were, in order, James (electromagnetism) Maxwell, John (Argon) Strutt, Lord Rayleigh, J. J. (the electron) Thomson, Ernest Rutherford, and Lawrence (X-ray crystallography) Bragg, all of whom but Maxwell were Nobel laureates (and he only because the Nobels hadn't been established yet). Rutherford in particular taught a lot of students who also went on to win Nobel Prizes, including Neils Bohr, James (the neutron) Chadwick, Pyotr (superfluidity) Kapitza, John (nuclear physics) Cockcroft, and Patrick (cosmic ray particle collisions) Blackett. James Watson learned X-ray diffraction from Max Perutz at Cavendish. Watson and Crick won their Nobels at Cavendish. Perutz went on to establish his own laboratory at Cavendish and see it produce 9 more Nobels, including his own. Neils Bohr established his own institute which trained many more Nobel laureates, including Werner Heisenberg and Linus Pauling. Arno Penzias worked with Nobel Prize winners Isidor (magnetic resonance) Rabi (another of Neils Bohr's students) and Charles (the maser) Townes. Jerome Friedman's doctoral thesis advisor was Enrico (the nuclear reactor) Fermi, another student of Neils Bohr. Several other "grand old men of science" make appearances as the teachers of multiple Nobel laureates. Almroth (typhoid vaccine) Wright taught Alexander Fleming and many other great biologists. Otto (cellular respiration) Warburg, a former student of Nobel laureate Hermann (purines and sugars) Fischer, taught Hans Krebs and many more. Max Planck taught Max von Laue and Lise Meitner, among others. Most tellingly of all, Paul Berg had an inspiring high school teacher, one Miss Sophie Wolfe, who taught no less than three future Nobel Laureates: Berg, Arthur (DNA synthesis) Kornberg, and Jerome (direct X-ray crystallography) Karl!

If you want to do great work, find a great teacher!

July 08, 2006

The Chemical Bond

Linus Pauling, The Shared-Electron Chemical Bond, 1928

Molecules are created by two basic kinds of bonds between atoms. In polar bonds, atoms with net positive charges attract atoms with net negative charges. This often occurs when a neutral atom loses an electron to another neutral atom. Although easily understood by early chemists (who already knew about electrical attraction and repulsion), polar bonds are weaker and have fewer interesting properties than non-polar bonds.

The discovery of the electron and Rutherford's discovery of the nucleus helped clarify what was going on in non-polar bonds: two atoms actually approach closely enough for electrons between the atoms to attract both nuclei. The electrons are effectively shared by both atoms. (Polar and non-polar bonds are actually the end-points of a scale. Real bonds are usually some mixture of sharing electrons and atom/atom attraction, as with H2O, where the Oxygen atom has a stronger grip on the shared electrons than the Hydrogen atoms, meaning that the O end has a slight negative charge and the H ends have a slight positive charge.)

Between 1913 and 1928, Bohr's quantum model of the atom aquired a lot more detail and complexity. In particular, it was discovered that only certain numbers of electrons can co-exist at each energy level: 2 at the lowest energy level, 8 on the 2nd and 3rd lowest energy levels, and 18 in the next few levels. This is, in fact, the reason that the periodic table's first five rows contain 2, 8, 8, 18, and 18 elements, respectively.

At each energy level, or shell, there are only a few stable orbits an electron can take. The quantum model of the atom describes these as wave functions (another example of jargon with distracting and incorrect connotations), which give the probability that an electron will be at a particular place at a particular time. These wave functions take many interesting shapes, ranging from spheres and dumbbells through cloverleaves and beyond. However, strictly speaking, the model only describe the orbits of single electrons around a single nucleus. As soon as additional electrons (which repel each other) are added to an atom, or worse, another atom comes close enough to form a non-polar bond, all the wave functions become approximations at best, and complete fictions at worst.

Linus Pauling, arguably the greatest chemist of all time, published a series of papers beginning in 1928 that detailed how to calculate the wave functions of electrons participating in a non-polar bond. Pauling knew that hybridizations of wave functions were possible, that is, that the actual wave function of an electron could take some of its properties from two or more of the basic wave functions. He realized that the most likely wave functions for electrons being shared between atoms would be those that were as asymetric as possible, so that the electron would spend most of its time between the atoms participating in the bond, as opposed to spending half its time between the atoms and half on the far side of one. Pauling figured out how to identify the most asymetrical hybridization possible.

One of the first practical results of this theory explained the structure of methane, CH4. Without hybridization, CH4 is predicted to have 3 bonds on the same plane, and a fourth in an arbitrary direction. With hybridization, CH4 is predicted to have 4 bonds pointing to the corners of a tetrahedron, which matches real observations of the molecule.

My own thoughts on this:

Hybrid orbitals are effectively a hack. A useful hack, since they work well in predicting the structure of molecules composed of relatively light atoms like carbon, nitrogen, and oxygen, but still approximations of the real situation. In particular, hybrid orbitals don't work well to explain bonds involving transition metals or other heavy atoms. Hybridization theory is, in fact, part of a whole series of increasingly sophisticated hacks that describe approximately how electrons behave in molecules. This is not meant to trivialize Pauling's work: hybridization theory is an effective way to predict the structure of organic molecules.

Figuring out how the electrons and nuclei in a molecule behave seems a lot like trying to solve the n-body problem. It looks to me like the whole thing is leading towards simply simulating all the attractive and repulsive forces between the electrons and nuclei involved in a molecule, much like a gravity simulation involving dozens of particles. If you were to do that, you could run the simulation for a while, and come up with some very accurate wave functions for the electrons. (Or rather, probability maps, since at this point they are neither waves nor functions.)