Mar 042019

No, today’s post is not about the sitcom (which I detest), it is about George Gamow who was born on this date in 1904 and was an early advocate and developer of Lemaître’s Big Bang theory of the origins of the cosmos. So, buckle up for some real physics, not TV playacting (seasoned with perpetual mistakes).

Gamow was born Georgiy Antonovich Gamov in Odessa in the Russian empire. He was educated at the Institute of Physics and Mathematics in Odessa (1922–23) and at the University of Leningrad (1923–1929). Gamow studied under Alexander Friedmann for some time in Leningrad, until Friedmann’s early death in 1925. He aspired to do his doctoral thesis under Friedmann, but had to change dissertation advisors. At the University, Gamow made friends with three other students of theoretical physics, Lev Landau, Dmitri Ivanenko, and Matvey Bronshtein. The four formed a group known as the Three Musketeers, which met to discuss and analyze the ground-breaking papers on quantum mechanics published during those years. He later used the same phrase to describe the Alpher, Herman, and Gamow group.

On graduation, he worked on quantum theory in Göttingen, where his research into the atomic nucleus provided the basis for his doctorate. He then worked at the Theoretical Physics Institute of the University of Copenhagen from 1928 to 1931, with a break to work with Ernest Rutherford at the Cavendish Laboratory in Cambridge. He continued to study the atomic nucleus (proposing the “liquid drop” model), but also worked on stellar physics with Robert Atkinson and Fritz Houtermans.

In 1931, Gamow was elected a corresponding member of the Academy of Sciences of the USSR at age 28 – one of the youngest in the history of this organization. During the period 1931–1933, Gamow worked in the Physical Department of the Radium Institute (Leningrad) headed by Vitaly Khlopin. Europe’s first cyclotron was designed under the guidance and direct participation of Igor Kurchatov, Lev Mysovskii and Gamow. In 1932, Gamow and Mysovskii submitted a draft design for consideration by the Academic Council of the Radium Institute, which approved it. The cyclotron was not completed until 1937. In the early 20th century, radioactive materials were known to have characteristic exponential decay rates, or half-lives. At the same time, radiation emissions were known to have certain characteristic energies. By 1928, Gamow in Göttingen had solved the theory of the alpha decay of a nucleus via tunneling, with mathematical help from Nikolai Kochin. The problem was also solved independently by Ronald W. Gurney and Edward U. Condon, although Gurney and Condon did not achieve the quantitative results Gamow did.

Classically, the particle is confined to the nucleus because of the high energy requirement to escape the very strong nuclear potential. Also classically, it takes an enormous amount of energy to pull apart the nucleus, an event that would not occur spontaneously. In quantum mechanics, however, there is a probability the particle can “tunnel through” the wall of the potential well and escape. Gamow solved a model potential for the nucleus and derived from first principles a relationship between the half-life of the alpha-decay event process and the energy of the emission, which had been previously discovered empirically and was known as the Geiger–Nuttall law. Some years later, the name Gamow factor or Gamow–Sommerfeld factor was applied to the probability of incoming nuclear particles tunneling through the electrostatic Coulomb barrier and undergoing nuclear reactions.

Gamow worked at a number of Soviet establishments before deciding to flee the Soviet Union because of increased oppression. In 1931, he was officially denied permission to attend a scientific conference in Italy. Also in 1931, he married Lyubov Vokhmintseva (Любовь Вохминцева), another physicist in Soviet Union, whom he nicknamed “Rho” after the Greek letter. Gamow and his new wife spent much of the next two years trying to leave the Soviet Union, with or without official permission. Niels Bohr and other friends invited Gamow to visit during this period, but Gamow could not get permission to leave.

Gamow later said that his first two attempts to defect with his wife were in 1932 and involved trying to kayak: first a planned 250-kilometer paddle over the Black Sea to Turkey, and another attempt from Murmansk to Norway. Poor weather foiled both attempts, but they had not been noticed by the authorities. In 1933, Gamow was suddenly granted permission to attend the 7th Solvay Conference on physics, in Brussels. He insisted on having his wife accompany him, even saying that he would not go alone. Eventually the Soviet authorities relented and issued passports for the couple. The two attended and arranged to extend their stay, with the help of Marie Curie and other physicists. Over the next year, Gamow obtained temporary work at the Curie Institute, University of London, and the University of Michigan.

In 1934, Gamow and his wife moved to the United States. He became a professor at George Washington University (GWU) in 1934 and recruited physicist Edward Teller from London to join him at GWU. In 1936, Gamow and Teller published what became known as the “Gamow–Teller selection rule” for beta decay. During his time in Washington, Gamow published major scientific papers with Mário Schenberg and Ralph Alpher. By the late 1930s, Gamow’s interests had turned towards astrophysics and cosmology. George Gamow became a naturalized US citizen in 1940.

During World War II, Gamow did not work directly on the Manhattan Project producing the atomic bomb, in spite of his knowledge of radioactivity and nuclear fusion. He continued to teach physics at GWU and consulted for the U.S. Navy. Gamow was interested in the processes of stellar evolution and the early history of the solar system. In 1945, he co-authored a paper supporting work by German theoretical physicist Carl Friedrich von Weizsäcker on planetary formation in the early solar system. Gamow published another paper in the British journal Nature in 1948, in which he developed equations for the mass and radius of a primordial galaxy (which typically contains about one hundred billion stars, each with a mass comparable with that of the Sun).

Gamow’s work led to developments in the hot big bang theory of the expanding universe. He was the first to employ Alexander Friedmann’s and Georges Lemaître’s non-static solutions of Einstein’s gravitational equations describing a universe of uniform matter density and constant spatial curvature. Gamow’s crucial advance provided a physical reification of Lemaître’s idea of a unique primordial quantum. Gamow did this by assuming that the early universe was dominated by radiation rather than by matter. Most of the later work in cosmology is rooted in Gamow’s theory. He applied his model to the question of the creation of the chemical elements and to the subsequent condensation of matter into galaxies, whose mass and diameter he was able to calculate in terms of the fundamental physical parameters, such as the speed of light c, Newton’s gravitational constant G, Sommerfeld’s fine-structure constant α, and Planck’s constant h.

Gamow’s interest in cosmology arose from his earlier interest in energy generation and element production and transformation in stars. This work, in turn, evolved from his fundamental discovery of quantum tunneling as the mechanism of nuclear alpha decay, and his application of this theory to the inverse process to calculate rates of thermonuclear reaction. At first, Gamow believed that all the elements might be produced in the very high temperature and density early stage of the universe. Later, he revised this opinion on the strength of compelling evidence advanced by Fred Hoyle et al. that elements heavier than lithium are largely produced in thermonuclear reactions in stars and in supernovae. Gamow formulated a set of coupled differential equations describing his proposed process and assigned, as a PhD. dissertation topic, his graduate student Ralph Alpher the task of solving the equations numerically. These results of Gamow and Alpher appeared in 1948 as the Alpher–Bethe–Gamow paper (read it out loud if you do not get the joke). Bethe later referred to this paper as being “wrong”. Before his interest turned to the question of the genetic code, Gamow published about twenty papers on cosmology. The earliest was in 1939 with Edward Teller on galaxy formation, followed in 1946 by the first description of cosmic nucleosynthesis. He also wrote many popular articles as well as academic textbooks on this and other subjects.

Gamow continued his teaching at the University of Colorado Boulder and focused increasingly on writing textbooks and books on science for the general public. After several months of ill health, surgeries on his circulatory system, diabetes and liver problems, Gamow was dying from liver failure, which he had called the “weak link” that could not withstand the other stresses. In a letter written to Ralph Alpher on August 18th, he had written, “The pain in the abdomen is unbearable and does not stop”. Prior to this, there had been a long exchange of letters with his former student, in which he was seeking a fresh understanding of some concepts used in his earlier work, with Paul Dirac. Gamow relied on Alpher for deeper understanding of mathematics.

On August 19th, 1968, Gamow died at age 64 in Boulder, Colorado, and was buried there in Green Mountain Cemetery. The physics department tower at the University of Colorado at Boulder is named for him.

I first came across Gamow by accident as a teen when I had swapped science and mathematics education for Classics, but I was still interested, and came across a copy of his One, Two, Three . . . Infinity, which considers a number of topics including Georg Cantor’s ( ) explorations of the types of infinity as well as his analysis of the nature of infinity (or infinities), plus his analysis of cosmological puzzles, genetics, topology, entropy, nuclear physics, and much more. The book kept my interest in the philosophical aspects of science and mathematics alive as my academic interests shifted. I still use his analogies to explain rudimentary number theory and the nature of infinity to students.

Odessa, Gamow’s birthplace, is a culinary joy with influences on the local cuisine from Russia, Greece, Turkey, Hungary, Moldova, and France. Here is a complex mushroom dish that shows off the influences on Odessa cooking. You should use whatever mix of mushrooms is available, especially wild ones. The ones in the ingredient list are for cooks with limited market choices. Branch out if you can.

Odessa Mushroom Zhulien


2 tbsp butter
1 onion, peeled and minced
1 ½ lb button mushrooms, chopped
1 lb porcini mushrooms, chopped
¼ cup dry white wine
½ cup cream
¼ cup Parmesan cheese
2 tbsp chopped chives
½ tbsp ground fennel seed
salt and freshly ground pepper
fresh nutmeg


Heat the butter in a large heavy skillet over medium heat. Add the onion and sauté until soft. Then add the mushrooms and continue to sauté until they release some juice. Add the wine and cream and bring to a simmer. Next add the cheese and stir until the cheese has melted and combined with the sauce. Season with the chives and fennel seed, and add salt pepper and freshly grated nutmeg to taste. Simmer for about 5 minutes, and serve hot.

Nov 202017

Today is the birthday (1889) of Edwin Powell Hubble an amazingly influential U.S. astronomer who is probably known chiefly these days outside of astrophysics for the telescope named after him. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology and is regarded in scientific circles as one of the most important astronomers of all time. Hubble discovered that many objects previously thought to be clouds of dust and gas and classified as “nebulae” were actually galaxies beyond the Milky Way. Before Hubble astronomers thought that the Milky Way was the universe. After Hubble the universe was an awful lot bigger and more complex than ever conjectured. Not only that, his calculations directly implied that the universe is expanding.

Hubble was born in Marshfield, Missouri, and moved to Wheaton, Illinois, in 1900. In his youth he was noted more for his athletic prowess than his intellectual abilities, although he did earn good grades in every subject except for spelling. Hubble was skilled in baseball, American football, and basketball, and he ran track in both high school and college. He played a variety of positions on the basketball court from center to shooting guard. In fact, Hubble even led the University of Chicago’s basketball team to their first conference title in 1907. He won seven first places and a third place in a single high school track and field meeting in 1906.

His studies at the University of Chicago were concentrated on law with some science leading to a bachelor of science degree in 1910. Subsequently he spent three years at Queen’s College, Oxford as one of the university’s first Rhodes Scholars, initially studying jurisprudence instead of science (as a promise to his dying father), and later added literature and Spanish. His father died in the winter of 1913, while Edwin was still in England, and in the summer of 1913, Edwin returned to care for his mother, two sisters, and younger brother, as did his brother William.

Hubble did not have the motivation to practice law. Instead, he got a job teaching Spanish, physics and mathematics at New Albany High School in New Albany, Indiana, where he also coached the boys’ basketball team. After a year of high-school teaching, which he did not like very much but where he was liked by all the students, he entered graduate school with the help of his former professor from the University of Chicago to study astronomy at the university’s Yerkes Observatory. He received his PhD in 1917 with a dissertation, “Photographic Investigations of Faint Nebulae.” He was on track. Note to fathers: don’t hobble your sons with your own desires for them.  Let them choose their own paths.

After the United States declared war on Germany in 1917, Hubble rushed to complete his PhD dissertation so he could join the military. Hubble volunteered for the United States Army and was assigned to the newly created 86th Division, where he served in 2nd Battalion, 343 Infantry Regiment. He rose to the rank of lieutenant colonel, and was found fit for overseas duty on July 9, 1918, but the 86th Division never saw combat. After the end of the war, Hubble spent a year in Cambridge University, where he renewed his studies of astronomy. In 1919, Hubble was offered a staff position at the Carnegie Institution for Science’s Mount Wilson Observatory, near Pasadena, California, by George Ellery Hale, the founder and director of the observatory. Hubble remained on staff at Mount Wilson until his death in 1953.

Edwin Hubble’s arrival at Mount Wilson Observatory, California in 1919 coincided with the completion of the 100-inch (2.5 m) Hooker Telescope, then the world’s largest. At that time, the prevailing view of the cosmos was that the universe consisted entirely of the Milky Way Galaxy. Using the Hooker Telescope at Mt. Wilson, Hubble identified Cepheid variables (a kind of star used to calculate stellar distances) in several spiral nebulae, including the Andromeda Nebula and Triangulum. His observations, made in 1922–1923, proved conclusively that these nebulae were much too distant to be part of the Milky Way and were, in fact, entire galaxies outside our own, suspected by researchers at least as early as 1755 when Immanuel Kant published General History of Nature and Theory of the Heavens. This idea had been opposed by many in the astronomy establishment of the time, in particular by Harvard University-based Harlow Shapley. Despite the opposition, Hubble, then only 35, had his findings first published in the New York Times on November 23, 1924, and then more formally presented in the form of an academic paper at the January 1, 1925 meeting of the American Astronomical Society.

Hubble’s findings fundamentally changed the scientific view of the universe. Let me repeat that: Hubble’s findings fundamentally changed the scientific view of the universe. Although some of his more renowned colleagues simply scoffed at his results, Hubble ended up publishing his findings on nebulae. Hubble also devised the most commonly used system for classifying galaxies, grouping them according to their appearance in photographic images. He arranged the different groups of galaxies in what became known as the Hubble sequence.

In 1929, Hubble examined the relation between distance and redshift of galaxies. Combining his measurements of galaxy distances with measurements of the redshifts of the galaxies by Vesto Slipher, and by his assistant Milton L. Humason, he found a roughly linear relation between the distances of the galaxies and their redshifts, a discovery that later became known as Hubble’s law (v = Ho d where: v = velocity of a galaxy, in km/s. Ho = Hubble Constant, measured in km/s/Mpc).

This meant that the greater the distance between any two galaxies, the greater their relative speed of separation. If interpreted that way, Hubble’s measurements on 46 galaxies lead to a value for the Hubble Constant of 500 km/s/Mpc, which is much higher than the currently accepted value of 70 km/s/Mpc due to errors in their distance calibrations.

Yet the reason for the redshift remained unclear. In reality, Georges Lemaître, a Belgian Catholic priest and physicist, predicted, on theoretical grounds based on Einstein’s equations for General Relativity, the redshift-distance relation two years before the proposal of Hubble’s law. However, many cosmologists and astronomers (including Hubble himself) failed to recognize the work of Lemaître. Hubble remained doubtful about Lemaître’s interpretation for his entire life. In 1931 he wrote a letter to the Dutch cosmologist Willem de Sitter expressing his opinion on the theoretical interpretation of the redshift-distance relation:

Mr. Humason and I are both deeply sensible of your gracious appreciation of the papers on velocities and distances of nebulae. We use the term ‘apparent’ velocities to emphasize the empirical features of the correlation. The interpretation, we feel, should be left to you and the very few others who are competent to discuss the matter with authority.

Today, the “apparent velocities” in question are understood as an increase in proper distance that occurs due to the expansion of spacetime. Light traveling through stretching space will experience a Hubble-type redshift, a mechanism different from the Doppler effect (although the two mechanisms become equivalent descriptions related by a coordinate transformation for nearby galaxies). Basically, objects traveling away from an observer at high speed will be redshifted, that is, the spectrum of light from those objects will be shifted towards the red end of the spectrum. Objects traveling towards the observer will appear violet shifted. ALL stars in the universe appear red shifted to observers on earth, leading to the conclusion that the universe is expanding, as demonstrated in the raisin bread analogy.

In the 1930s, Hubble was involved in determining the distribution of galaxies and spatial curvature. These data seemed to indicate that the universe was flat and homogeneous, but there was a deviation from flatness at large redshifts. There were methodological problems with Hubble’s survey technique that showed a deviation from flatness at large redshifts, however. In particular, the technique did not account for changes in luminosity of galaxies due to galaxy evolution. Earlier, in 1917, Albert Einstein had found that his newly developed theory of General Relativity indicated that the universe must be either expanding or contracting. Unable to believe what his own equations were telling him, Einstein introduced a cosmological constant (a fudge factor) to the equations to avoid this “problem.” When Einstein learned of Hubble’s redshifts, he immediately realized that the expansion predicted by General Relativity must be real, and in later life he said that changing his equations was “the biggest blunder of [his] life.” In fact, Einstein apparently once visited Hubble and tried to convince him that the universe was expanding. In December 1941, Hubble reported to the American Association for the Advancement of Science that results from a six-year survey with the Mt. Wilson telescope did not support the expanding universe theory. Even great scientists make mistakes. These were the days well before the Big Bang theory although Hubble’s observations led in that direction. Until 1964, when the cosmic background radiation was discovered, astrophysicists were split between the Big Bang and the Steady State theories. Now the Big Bang is the prevailing model.

In Hubble’s day the Nobel Prize committee did not recognize work done in astronomy as part of physics and so did not award prizes to astronomers. Hubble spent much of the later part of his career attempting to have astronomy considered an area of physics, instead of being its own science, not least so that astronomers could be recognized by the Nobel committee. This campaign was unsuccessful in Hubble’s lifetime, but shortly after his death, the Nobel Prize Committee decided that astronomical work would be eligible for the physics prize. Sadly, the prize cannot be awarded posthumously.

Given that the raisin bread analogy is the common one for explaining the redshifts of galaxies in an expanding universe, we have to bake raisin bread today. It’s normally baked as a yeast bread, but can be made using baking powder, which I find more convenient. For my money, raisin bread is best served in toasted slices with lashings of butter.

Raisin Bread


3 cups all-purpose flour
½ cup white sugar
3 tsp baking powder
½ tsp baking soda
1 tsp salt
¾ tsp ground cinnamon
1 cup raisins
1 egg
¼ cup melted butter
1 cup milk


Preheat oven to 350˚F/175˚C.

Grease a 9x5x3” loaf pan.

Sieve the flour, sugar, baking powder, baking soda, salt, and cinnamon into a mixing bowl. Add the raisins and stir thoroughly. Make a well in center.

In small bowl beat the egg until frothy. Mix in the melted butter and milk.

Pour the wet ingredients into the well in the dry ingredients. Stir the ingredients gently so they are just combined, but do not overmix. Scrape the dough into the greased loaf pan.

Bake for 1 hour.