Copenhagen, part 4

In the play Copenhagen, the quantum principles for which Bohr and Heisenberg are known become part of the story.

Scientific theories, at least in physics, are mathematical. It is a dangerous thing to try to say what the math really "means." And when we think we know what it "means," it is more dangerous still to extrapolate that "meaning" into other areas of life. But we do it all the time. This play extrapolates concepts from quantum mechanics onto the relationship between Bohr and Heisenberg. And it does so in a thought-provoking way.

If the uncertainty principle says that position and momentum are uncertain, what about history? Is it possible to know for certain what happened at that meeting in Copenhagen in September 1941?

What about uncertainty in our thoughts? "There is not one single thought or intention of any sort that can ever be precisely established...[T]his uncertainty in our thinking is also fundamental to the nature of the world." (postscript, p. 99)

If the complementarity principle says that an observation is required for something to be made "real," does that also apply to our thoughts?

Bohr [as Heisenberg is standing on the doorstep about to enter Bohr's house for the fateful dinner and conversation]: Until this instant his [Heisenberg's] thoughts have been everywhere and nowhere, like unobserved particles, through all the slits in the diffraction grating simultaneously. Now they have to be observed and specified. (p. 86)

I know that my own thoughts don't seem to coalesce until I either speak them or write them down. (It is one reason that I blog.) I have heard others say the same about their thoughts. In some sense our thoughts are not "real" until either spoken or written down, i.e. observed and specified.

A major theme of the play is what quantum mechanics says about humans. It may surprise you:

Bohr: We put man back at the centre of the universe. (p. 71)

Over the centuries, science has put humans farther and farther from the center of the universe. Science has made humans less and less special, as compared to the rest of nature. Bohr's point, at least in the playwright's words, is that since quantum mechanics (at least in the Copenhagen Interpretation) requires an observer to create reality, humans are pretty darn special.

Two pages after the above quote, we have this humorous exchange:

Bohr: Not to criticize, Margrethe, but you have a tendency to make everything personal.

Margrethe: Because everything is personal! You've just read us all a lecture about it!

As usual, I think it best to let the woman have the last word.

Copenhagen, part 3

Now for the contributions that Niels Bohr and Werner Heisenberg made to quantum mechanics.

Werner Heisenberg introduced the uncertainty principle in 1927: one cannot precisely know both the position and momentum of a subatomic particle at the same time. In fact, the more precisely one knows one quantity, the less precisely one knows the other.

This was a revolutionary idea. It is a basic premise of science that if one knows the present state of a system, one can use the laws of motion to predict future states. Scientists had previously assumed that any limitation in their ability to predict future states (think predicting the weather) was due to a combination of: a) the inexactness of their instruments in measuring the present state, and b) the sheer complexity of the calculations. What Heisenberg said was that in addition to those limitations, there are inherent limitations on what is knowable about the present state, at least at the subatomic level, even if we had perfect instruments.

Niels Bohr made many contributions to quantum mechanics. The contribution which figures prominently in the play is the principle of complementarity: any quantum object has both a wave nature and a particle nature, and there is a trade-off between them. Hence the wave-particle duality of subatomic particles described in the previous post. Furthermore it is the act of measurement, of observing, that determines what is manifested.

One aspect of both of these principles is that the world is not deterministic, as was thought by previous generations of scientists such as Sir Isaac Newton. The world is probabilistic, at least at the subatomic level. Quantum outcomes can be predicted only as probabilities.

This way of thinking about quantum mechanics became known as the Copenhagen Interpretation.

Heisenberg was mathematically gifted; he invented the matrix algebra used in one formulation of quantum mechanics. Bohr was more inclined to describe things in words. (According to the play, so that Margrethe could understand.) But as Heisenberg aptly noted, "Our words don't fit." (source, p. 150)

Copenhagen, part 2

To understand the play Copenhagen, it is necessary to have a basic understanding of the contributions that Niels Bohr and Werner Heisenberg made to quantum mechanics. But first, what is quantum mechanics?

It is the study of very small things, at atomic and subatomic scales. How do atoms behave? How do subatomic particles behave? The answer is that they behave strangely, unlike anything else we are familiar with.

The strangeness can be described by the "double slit experiment." Imagine a machine gun that sprays bullets at a thick metal plate with two parallel slits in it. Behind the metal plate is a brick wall. What will be the pattern of bullets striking the brick wall? There will be two concentrations: one behind slit #1 and one behind slit #2. Call this pattern A.

Now imagine a light source that shines onto a metal plate with two parallel slits. Behind the plate is a screen. What will we see on the screen? We will see an interference pattern of alternating light and dark bands. Call this pattern B.

So far so good. Nothing unusual yet. Light behaves like waves (pattern B) and bullets behave like particles (pattern A).

But we also know that light consists of subatomic particles called photons, like little bullets. Suppose we slow our experiment down until the light source emits just one photon at a time. Over time, we get the same interference pattern mentioned above: pattern B, the wave pattern. How does each photon "know" where to go to produce the interference pattern? Why don't the photons go straight through one slit or the other to produce pattern A? No one knows. It is as if each photon goes through both slits simultaneously, interfering with itself, to produce pattern B. This is strange behaviour for a "particle."

It gets even more strange. We know that each photon had to go through either slit #1 or slit #2. Suppose we want to know: which slit did each photon go through? As soon as we introduce any mechanism to answer that question, we destroy the interference pattern. Instead of pattern B we get pattern A. Why? No one knows. It is as if each photon goes through both slits simultaneously until it is observed, and then it goes through only one of the two slits.

The experiment can be done with electrons instead of photons. The result is the same.

The essence is that subatomic particles can behave either as waves or particles. And what the observer is doing (i.e., watching the slits or not) affects which aspect is observed. This is bizarre.

That was a dry explanation, with no pictures. For a better explanation, with pictures and cool simulations that you can play with, click here (total of 3 screens).

Copenhagen, part 1

Parents Weekend at Colorado College this year is Oct. 10-12. One of the events is a discussion of the play Copenhagen, by Michael Frayn. This promises to be most interesting.

The play is about a meeting between three people: physicists Niels Bohr and Werner Heisenberg, and Bohr's wife Margrethe. This meeting did in fact take place, in Copenhagen in September 1941.

In 1924-27 Heisenberg worked for Bohr at the University of Copenhagen and the two scientists made major contributions to the development of quantum mechanics. But in 1941 Heisenberg was in charge of Germany's atomic program and Bohr, his former mentor, was in German-occupied Denmark. The two friends were also enemies.

The meeting must have been difficult. There is much controversy about what was said at the meeting, and that forms the basis for the play. On one level the play is about morality (friendship, loyalty, developing atomic weapons). On another level the play is about the contributions that these two scientists made to quantum mechanics, and how this meeting can be interpreted in light of those contributions.

That last sentence probably doesn't make any sense to you. I'll try to explain it in the next three posts (this one being long enough already).

More info about the play Copenhagen: Wikipedia entry, Amazon entry. The play was first performed on stage in 1998. The book, with a lengthy Postscript, was published in 2000.

Almost Fall

Emily posted recently about spring in New Zealand, so here is a post about fall in Vermont. It isn't officially fall until Monday 9/22, but it felt like a beautiful fall day today.

This year's firewood is all stacked in the basement. Today Nancy and I finished stacking next year's firewood outside to dry over the winter:

After visiting Pager, we went for a walk in the Mills Riverside Park in Underhill and Jericho. This park was established about 8 years ago. It is 20 minutes from home and I drive by it on my way to work, but we have never been there until today. It is very nice!

Jericho was the home of Snowflake Bentley, and the pavilion in the park is named for him. (Pager remembers going to a talk by Snowflake Bentley as a youth.)


There are several nice trails. One of the trails in the woods came out on a meadow where a farmer was baling hay with Mt. Mansfield in the background:

Another meadow was devoted to monarch butterflies:

This was an Eagle Scout project last year by Brian Kennedy:

Nancy took some great photos of monarch butterflies feeding on the wild asters:


There was also plenty of milkweed, which they eat in the caterpillar stage:


In a couple of weeks we should have some good foliage pictures to post. Happy fall to everyone in the northern hemisphere, and happy spring to everyone in the southern hemisphere!

Robert Diamond

It was a tumultuous week on Wall Street. Two weeks ago the Federal government took over Fannie Mae and Freddie Mac. That contributed to dramatic events last weekend: Lehman Brothers filed for bankruptcy and Bank of America bought Merrill Lynch in a rushed transaction. The Dow Jones Industrial Average started the week at 11,422. A brief recap of the week:

9/15 Monday - DJIA down 504 (4.4%), reacting to the Lehman Brothers and Merrill Lynch events over the weekend. Concern mounting over AIG. (AIG owns Stowe Mountain Resort. One of its minor holdings.)

9/16 Tuesday - DJIA up 142 (1.3%) on news that the Federal government planned to bail out AIG. Volume on the New York Stock Exchange set a record. The AIG takeover, akin to the takeover of Fannie and Freddie, was completed Tuesday evening after markets closed.

9/17 Wednesday - DJIA down 449 (4.1%). The AIG takeover did not calm investors. An institutional money market fund, the Reserve Primary Fund, failed to maintain a $1 share price on Tuesday, sending tremors through the market. Another institutional money market fund, the Putnam Prime Money Market Fund, did not reopen after the close of business Wednesday. Volume on the New York Stock Exchange was the second highest in history, second only to Tuesday.

9/18 Thursday - DJIA up 410 (3.9%) on reports that the Federal government is planning a mechanism to take bad assets off the balance sheets of financial institutions.

9/19 Friday - DJIA up 369 (3.4%), helped by moves announced by the U.S. Treasury and the Fed to bolster money market funds and by the SEC to restrict short-selling. For the week, the DJIA was down just 34 (0.3%) to 11,388.

Click here for more info about the week.

The government's efforts to stanch the crisis and investors' euphoria at those actions capped a wild week which has permanently resculpted the landscape of Wall Street. (source)

Today's Wall Street Journal has an article about the handful of men who are the major players in these history-making events: Street Scenes: The Players Remaking Financial World. One of the men discussed in the article is Robert Diamond, president of Barclays Bank in England, which this week purchased a large portion of Lehman Brothers.

Robert Diamond is a graduate of Colby College and gave the commencement address at Brian's graduation last May.

Ozone Depletion

Ozone is a form of oxygen—three atoms to a molecule instead of the usual two. When ozone exists in the atmosphere at ground level, it contributes to smog. But ozone in the stratosphere, from 5 to 30 miles above the Earth's surface, protects life by absorbing harmful ultraviolet (UV) radiation from the sun.

In the 1970s scientists began to suspect that certain human-produced chemicals were damaging the ozone layer in the stratosphere. In the 1980s scientists discovered that the ozone layer above Antarctica was greatly reduced each spring. This became known as the Antarctic ozone hole. Chlorofluorocarbons (compounds containing chlorine, fluorine and carbon) were among the chemicals that were found to cause ozone depletion. Chlorofluorocarbons, or CFCs, were commonly used at the time as refrigerants (e.g., freon) and as propellants in aerosol cans.

Under the auspices of the United Nations Environment Programme (UNEP), the Vienna Convention for the Protection of the Ozone Layer was negotiated in 1985. The Vienna Convention obligated signatory countries to study the problem of ozone depletion. In 1987 the Montreal Protocol on Substances That Deplete the Ozone Layer was negotiated. The Montreal Protocol obligated signatory countries to actually reduce the production of CFCs and other ozone-depleting chemicals.

World-wide production and use of CFCs and other ozone-depleting chemicals have fallen dramatically, and the ozone layer in the stratosphere is starting to recover.

The United States has ratified both the Vienna Convention and the Montreal Protocol. The U.S.—along with Canada, Sweden and Norway—banned the use of CFCs in consumer aerosols in 1978, before either treaty was negotiated. Many people are surprised to learn that CFCs were banned in consumer aerosols that long ago.

If you are interested in additional information, you may find the following web sites helpful:

Wikipedia article on ozone depletion
UNEP Ozone Secretariat
U.S. EPA web site on ozone depletion

Brian's Birthday

Brian is a big fan of Monty Python and the Holy Grail. For his birthday this year we took him to see Spamalot on stage at the Bushnell Theater in Hartford on Sept. 6, just a few days before his birthday. Several roommates and friends joined us, too. It was great fun!

Spamalot is a spoof not only on Monty Python and the Holy Grail, but also on Broadway. One of my favorite lines was after King Arthur and Patsy brought a shrubbery to the Knights Who Say Ni, they were given a new task: to make a Broadway musical, but not an Andrew Lloyd Webber musical! I wrote about an Andrew Lloyd Webber musical on this blog earlier this year. Brian and I saw that musical in Milwaukee in 2000. That may have been the last musical Brian saw before Spamalot.

Spamalot was scheduled to run through Sunday, Sept. 7 at The Bushnell. Matinee and evening shows were scheduled for both Saturday and Sunday. We saw the matinee show on Saturday. That was a good thing. In the early hours of Sunday morning, Hurricane Hanna swept through southern New England. I found this on the web site for The Bushnell as I was writing this post: "Due to last evening's storm, which has left The Bushnell with little electricity, the matinee and evening performances of Monty Python's SPAMALOT for today, Sunday, September 7, have been cancelled."