Radioactive beta decay

Radioactive alpha decay had been explained in 1928 by Russian physicist George Gamow, which he described as quantum tunneling of alpha-particles (i.e., He-4 nuclei, 2 protons and 2 neutrons) from inside the nucleus, through the strong force barrier (which usually keeps the nucleus together), and finally emerging free. In the case of U-238 transforming to Th-234, the alpha-particle is emitted with about 4.2 MeV of kinetic energy. (This means that they are traveling at about 9.5% of the speed of light, or about 64 million miles per hour. Even though they are traveling fast, they are very light, and therefore are easily stopped - and absorbed - by a thin sheet of paper. In fact, they only travel about 4 cm in air.) Here is one of Ernest Rutherford's early papers - 1899 - describing his experiments on radioactive decay.

Beta decay, on the other hand, was more confusing. The beta particles (now known to be electrons) were emitted with a variety of kinetic energies, prompting Niels Bohr to speculate that the long-held principle of the conservation of energy did not apply to radioactive decay. However, in 1930, Wolfgang Pauli proposed that another particle was emitted along with the electron, which he called a "neutrino," because it was (a) electrically neutral, like the neutron, and (b) very light, like a "little neutron." This particle had not been observed (and would not be directly observed until 1956), but it saved the principle of the conservation of energy.

Then, at Christmas 1933, Enrico Fermi developed a theory of beta decay, based on the quantum theory of the electron developed by Paul Dirac in 1928. As Robert Crease and Charles Mann put it, "The theory was his first and only work on beta decay and was so complete that its description of the phenomenon has remained essentially unchanged to this day. At a stroke, Fermi first accurately described beta decay, first identified the separate nature of its cause, and first predicted most of its essential features."

It wasn't until 1995 that Frederick Reines won the Nobel Prize for his neutrino discovery, and subsequently two other neutrinos were discovered (the mu and tau neutrinos), leading to the 2015 Nobel Prize for the discovery of "neutrino oscillations," in which the different types of neutrinos can change into each other.

Fascinating stuff.

The number 32

Sandy Koufax is arguably the best pitcher (ever) in baseball, although he has some competition in the current Dodger star Clayton Kershaw. Koufax wore number 32, and Magic Johnson and a whole host of sports superstars. I've been reading a great book about the Dodgers and I started thinking about player numbers.

The number 32 has some interesting properties, many of which are catalogued here.

One of the weirdest involves the so-called "totient" function φ(n) of 18th century mathematician, Leonhard Euler. It is defined as the number of integers less than or equal to n that are relatively prime to n. For example, φ(1) = 1, φ(2) = 1, and φ(5) = 4. The last is true because all the numbers 1, 2, 3, and 4, are relatively prime to 5. (In this definition, 1 is counted as prime.) There are 7 different numbers for which φ(n) is equal to 32. The first few are n = 51, 64, 68, 80, 96, ... and I'll let you find the other two.

One of the funniest is - Nobody ever says “32-skidoo.”

Rivers and Dams

Recently I picked up the book "The Emerald Mile" by Kevin Fedarko, about running the Colorado River, the dams on the river (Glen Canyon Dam particularly), and the great storm in 1983 that almost destroyed the Glen Canyon Dam. I highly recommend it.

The hook of the book is the attempt to run the 277 miles from Lee's Ferry, just below the Glen Canyon Dam, to Pierce Ferry at the Grand Wash Cliffs near Lake Mead in a wooden dory named Emerald Mile. This was attempted several times, but the focus was on the attempt during the 1983 flood. But to tell that story he backs up and covers John Wesley Powell's initial excursion, the outfitting community that has grown up on the river, the dams that block the river, and intimate portraits of some of the river guides.

His writing is good, but sometimes a bit over the top. For example, "His face, which was ovular, was dominated by a hook-boned nose, at the top of which floated a pair of deeply skeptical brown eyeballs." I'm not quite sure how eyeballs can be skeptical. But its enjoyable, and for the most part he gets the technical parts correct. When discussing the river flow and the dam, there's a lot of technical parts, and it's especially interesting to read his discussion of cavitation - the effect of tiny bubbles on the flow of the water through the spillways at Glen Canyon Dam that ended up tearing them apart, and eating through the concrete liner and into the pink sandstone. However, he does make some mistakes. For example, when discussing the blocking of the river by a debris flow, he says, "The flood and the debris fan had narrowed the river to one-quarter its former width, doubled the drop, and increased the speed by a factor impossible to quantify." Of course, it's fairly simple to quantify, using fluid dynamics principles. But I guess the sentence sounds nice.

That book led me to watch the Patagonia documentary, DamNation. Another high recommendation.

This is a beautifully shot look at the history of dams in the US, mostly in the West, and it focuses on the removal of several dams in Washington state. I learned two important facts. First, how many dams there are in the US - over 60,000! And second, how many dams have already been removed. It makes sense that dams have a finite lifetime - for many reasons, not least of which is that the silt that usually flows downstream builds up in the reservoir behind the dam, lowering its utility - and that removal is a logical option. I had just never thought about removing a dam before. As David Montgomery, a geologist at U Washington said, 50 years ago, removing a dam was unthinkable.

One of the most powerful scenes was the description of Celilo Falls on the Columbia River, where native Americans have fished for salmon for (probably) the last 10,000 years [it's one of the oldest settlements in North America]. Those falls were submerged by the reservoir behind The Dalles Dam in 1957.

Addendum: My own river running experience is rather limited. I took a two-day trip down the Stanislaus River in the Sierras when I was a teenager. And I've done three day trips down the Chatooga River in NE Georgia in the past few years. I love the Chatooga because I can camp at Talulah Falls Park, and it's a short drive to the outfitters (SEE) headquarters.

Why "Big Bang" is a bad word

In John Mather's talk last Saturday at Embry-Riddle's Elston Memorial Lecture, he covered all the standard cosmology topics (but focused on his Nobel-prize winning work with COBE, the Cosmic Background Explorer), but also showed some neat videos of how the James Webb Space Telescope will unfold once it gets to the L1 point. You can see one here.

As with all popular talks on the expanding universe, he had to contend with the perennial problem of explaining the current "standard model" of cosmology (the study of the universe and how it came to be the way it is today), known as the ΛCDM model, or the "Lambda Cold Dark Matter" model. It consists of Einstein's equations of general relativity applied to the entire universe, which, in addition to the visible matter (stars, galaxies, dust, etc) is comprised of dark matter (represented essentially by a cold gas) and dark energy (embodied in Einstein's cosmological constant Λ).

Because in every direction we look in the night sky, we see galaxies moving away from us, it is tempting to deduce that we are at the center of the universe. However, it is easy to show that an observer anywhere in the universe would see the same thing, and to draw the conclusion that there is no center. In fact, the so-called Big Bang occurred everywhere simultaneously, and the universe has always been infinite in extent. For this reason, the term "big bang" is really a misnomer, and gives non-astrophysicists the incorrect view that the "explosion" occurred at a single point and moved "outward".

It would be great to rid our lexicon of this term, but unfortunately we are stuck with it (and it clearly shows the weakness of language when describing subjects that are inherently mathematical in nature), and so every popular exposition has to set aside at least some space to explain why this we don't like it. At its core, the standard model of cosmology is based on the expanding space paradigm, in which rather than stuff expanding into already existing space, it is space itself that is expanding.  I can do no better than to quote Edward Harrison from his 1993 paper

From purist point of view one cannot but deplore the expression big bang, "loaded with inappropriate connotations" (McVittie 1974), which conjures up a false picture of a bounded universe exploding from a center in space. In modern cosmology, the universe does not expand in space, but consists of expanding space... 

And he quotes Willem de Sitter (1931), one of the founders of modern cosmology

The theory of [general] relativity brought the insight that space and time are not merely the stage on which the piece is produced, but are themselves actors playing an essential part in the plot.

For those of you who want a more technical explanation, see here, a page from the Physics FAQ, hosted by John Baez.

Fun in the snow

After Kathy, Megan, and Sarah left, Caitlin stayed for a couple more days. We went to the two main palaces in Munich, the Schloss Nymphenburg on the last day of the year, when the building was closed, but the grounds were open. In addition to a huge building, the grounds are extensive, with many walking paths and gardens. On summer days its a popular place to go for Münchner.

Panorama of the 'summer' palace for the Bavarian royalty, Schloss Nymphenburg. On this day, however, it was covered in snow.

And on the previous day we went to the "Munich Residenz," the main palace of the Bavarian royalty, which is now a museum. Also, a portion of the museum houses the treasury - all the crowns and precious jewels that they had collected over the years.

Crown of Queen Kunigunde (975-1040). It is assumed that she actually wore this crown, but it is not known for sure. The crown was on a "head reliquary" and therefore might have been placed there after her death. It's one of the oldest items in the treasury.

St George slaying the dragon. With lots of jewels.  St George is the patron saint of the House of Wittelsbach, which ruled Bavaria from the 1100s until 1918, when they were deposed. He is also the patron saint of the Munich Residenz, and this valuable item is not allowed to leave the Residenz.

Really cool pocket watch from 1620. Unfortunately there was no detailed description, even in the self-guided audio, so I don't know anything about its history. However, if you look closely, on a high resolution image below, the dials denote the following. Top: Lunar cycle and phases of the moon. Right: Standard 12 hour clock. Bottom: Calendar with the day of the month and month of the year. Left: Day of the week. Center: I-II-III-IIII, but I'm not sure what this represents. Anybody?

It's good to be home

After a month of this

I came back to this

The autumn in Munich was very mild, lots of warm days, and only a couple of brief snowfalls that immediately melted. Then, the day after Christmas, we got four days of solid snow, which was good for the family, who wanted to see snow. We also were able to visit Neuschwanstein in snow, and also Salzburg - and, of course, Munich. Most of January, and the beginning of February, it was snowing. Not an overwhelming amount, though, just a few inches every few days. In fact, I enjoyed the snow; there wasn't too much of it, and it looked very nice. A change of pace from Florida. The temperature was pretty steady, right around freezing, but not brutally cold, so my jackets that I had brought with me served their purpose admirably.

The best part was that I met a lot of great people and I'd like to thank them for making my time in Germany worthwhile:

Karl, Philip, Alec, Connor, Sophie, Billy, Will, Timo, Astrid, Luis, Tessa, Sebastian, Helmut, Lukas, Guido, Alexander, Wolfram, Gerald, Dirk, Ruslan, Sandro, Nicole, Aino, Christian, Thomas, Annette, Veronica, Michael, Jack, Klemens, Peter, Carolyn, Merit, Maria, Alexandra, Shyam, Eno, Kevin, Ralph, Steffie, all my students, and last, but not least, Coco.

I can't wait to return!

Chinese in Berlin?

My airbnb host in Berlin told me an interesting story that I have not had time to confirm. He said that there were four countries that were to divvy up Berlin after WWII: Russia, US, Britain,  and China! For some reason, France was not included since they had already "lost." Since China was so far away and didn't want to have to administer an area on another continent, they said Russia could have their region, just give them money. This was why Russia had half of Berlin, and the Allies had the other half. I said that I hadn't heard of that, and he said "if you dig deeply enough on the internet, you'll find it." I took that to mean that he was into conspiracies, you could probably find some whacko espousing this view, but it wasn't true. So far, I haven't been able to find out anything about this.

But the map of Berlin is interesting. It shows the city divided almost exactly in half along a north-south line, except for the city center, the Mitte, cut out and given to the Soviets. This was where my airbnb apartment was, just off of Alexanderplatz, along Alexandrestraße. The BrandenburgerTor is at the west end of this cutout, just inside the Soviet zone.

Map of Berlin from the Berlin Wall Memorial, showing the Berlin Wall in red.

Map of the German occupations zones. From Wikipedia.

As can be seen from the entire map of postwar Germany, the US occupation zone included Bavaria. And if you look closely at the photos of the town of Garmisch here, you can barely see barracks that are part of a US installation, one of the few remaining in Germany.