Physics in a Mad World and Bohr's letter to Heisenberg

Werner Heisenberg's birthday is an excellent chance to promote a fantastic book on history of 20st century quantum physics by Misha Shifman.

Among other things, he quotes a letter Niels Bohr sent to Werner Heisenberg in 1957, here it is in full:

Dear Heisenberg, 

I have seen a book, “Stærkere end tusind sole” [“Brighter than a thousand suns”] by Robert Jungk, recently published in Danish, and I think that I owe it to you to tell you that I am greatly amazed to see how much your memory has deceived you in your letter to the author of the book, excerpts of which are printed in the Danish edition. Personally, I remember every word of our conversations, which took place on a background of extreme sorrow and tension for us here in Denmark. In particular, it made a strong impression both on Margrethe and me, and on everyone at the Institute that the two of you spoke to, that you and Weizsäcker expressed your definite conviction that Germany would win and that it was therefore quite foolish for us to maintain the hope of a different outcome of the war and to be reticent as regards all German offers of cooperation. I also remember quite clearly our conversation in my room at the Institute, where in vague terms you spoke in a manner that could only give me the firm impression that, under your leadership, everything was being done in Germany to develop atomic weapons and that you said that there was no need to talk about details since you were completely familiar with them and had spent the past two years working more or less exclusively on such preparations. I listened to this without speaking since [a] great matter for mankind was at issue in which, despite our personal friendship, we had to be regarded as representatives of two sides engaged in mortal combat. That my silence and gravity, as you write in the letter, could be taken as an expression of shock at your reports that it was possible to make an atomic bomb is a quite peculiar misunderstanding, which must be due to the great tension in your own mind. From the day three years earlier when I realized that slow neutrons could only cause fission in Uranium 235 and not, it was of course obvious to me that a bomb with certain effect could be produced by separating the uraniums. In June 1939 I had even given a public lecture in Birmingham about uranium fission, where I talked about the effects of such a bomb but of course added that the technical preparations would be so large that one did not know how soon they could be overcome. If anything in my behavior could be interpreted as shock, it did not derive from such reports but rather from the news, as I had to understand it, that Germany was participating vigorously in a race to be the first with atomic weapons. Besides, at the time I knew nothing about how far one had already come in England and America, which I learned only the following year when I was able to go to England after being informed that the German occupation force in Denmark had made preparations for my arrest. All this is of course just a rendition of what I remember clearly from our conversations, which subsequently were naturally the subject of thorough discussions at the Institute and with other trusted friends in Denmark. It is quite another matter that, at that time and ever since, I have always had the definite impression that you and Weizsäcker had arranged the symposium at the German Institute, in which I did not take part myself as a matter of principle, and the visit to us in order to assure yourselves that we suffered no harm and to try in every way to help us in our dangerous situation. This letter is essentially just between the two of us, but because of the stir the book has already caused in Danish newspapers, I have thought it appropriate to relate the contents of the letter in confidence to the head of the Danish Foreign Office and to Ambassador Duckwitz.

Before this letter was published in 2002, the version that Heisenberg's team was 'passively sabotaging' the German atomic bomb project was considered the most plausible one. It seems, however, that it doesn't have any solid justification.

It also seems that the idea of German superiority didn't work out quite right for them (quoting Shifman himself):

To have admitted that plutonium was used was to admit that the Allies had a vast reactor development and that everything the German scientists had worked on for so long and so hard had been insignificant. Heisenberg’s lecture, which represented the high water mark of the German understanding of nuclear weapons, shows that in the end they understood very little.

... 

Prior to Hiroshima the Germans were absolutely convinced on the basis of their own experience that a nuclear bomb could not be built in the immediate future. Their belief was based on the idea of their superiority: they were absolutely convinced that they were ahead of everyone else in their study of nuclear chain reaction. Because they had not been able to build a nuclear reactor, they were sure that no one else had done so.

...

From this letter it seems clear that Heisenberg’s team worked in earnest to make the bomb. They failed not because they sabotaged the project, but because they were not qualified to solve the problems that arose in the course of their work.

In the last one, Shifman is talking about two problems:

(i) Using graphite as an absorbing medium for the nuclear reactor — the team of Walther Bothe declared it useless after giving it a try, and switched to heavy water instead. They didn't know that graphite they used was not sufficiently pure, and that graphite coming from other sources worked perfectly well for Americans.

(ii) The critical mass of uranium was miscalculated by Heisenberg, who did a rough estimate. His U.S. counterpart, Enrico Fermi, was both a brilliant theorist and experimentalist, and did a very thorough calculation.

Two more quotes:

The Farm Hall was bugged so that conversations of all detainees were recorded and transcribed. On August 6, 1945, the detained German physicists learned that a new weapon had been dropped on Hiroshima. They did not believe that it was nuclear. When they finally were persuaded that it was, they began trying to explain it. That evening, Otto Hahn and Heisenberg had a conversation. Heisenberg gave Hahn an estimate based on the data concerning the Hiroshima explosion published in newspapers. Heisenberg reasoned as follows. He knew that the Hiroshima explosion was about equivalent to 15,000 tons of TNT, and he knew that this amount corresponded to the fission of about 1 kg of uranium. Then he estimated that this would require about eighty generations of fissions assuming that two neutrons are emitted per fission. He then assumed that during this process the neutrons flow out to the boundary in a random walk of eighty steps with a step length equal to the mean free path for fission. This gave him a critical radius of 54 cm and a critical mass of several tons. (The correct estimate would give 15-20 kg.)

... 

There is one especially surreal aspect of this discussion that took place after the second bomb was dropped on Nagasaki. The mass of material for this bomb was given in news reports and it seemed too small. The Germans indulged in all sorts of wild speculations as to why this was so. It never occurred to them that the Nagasaki bomb was made of plutonium, despite the fact that von Weizsäcker, who had introduced the idea of transuranics into the German program, was in the audience.

Take care,

Misha

America runs on quarters

About two years ago, before leaving the United states, I've posted the following "study" friends-only on facebook. However, I feel that it might fit the format of this blog, so I'm reposting it here.

Everyone knows that the US monetary system is kind of screwed up. I you think America runs on Dunkin' Donuts – bullshit, America runs on quarters. Living in the US is a constant chase after the 25¢ coins: you need them for everything, whether it's parking, candy machines, or laundry.

The screwed up thing is that the rest of coins (1¢, 5¢, and 10¢) are absolutely useless. It's no Europe, in a store the cashier won't ever ask to look for ten cents, since she or he knows you don't have those. Instead, every American possesses a huge can at home where the coins are accumulated (you can cash them in a special machine later, to make sure that the worthless cycle continues).

And I was not an exception. This Mexican coffee tin filled up exactly by the end of my 3-year stay.

Recently, my old friend Valery Yundin was visiting and (after a couple of beers) we decided to estimate how much the coins were worth. Valery and I weighed the can (it was 3.5 kg) and looked up the mass of each coin on the Treasury Department website. Then we used two competing models to deduce the frequency with which 1¢, 5¢, and 10¢ occur:

(1) We assumed that the distribution of 1¢, 5¢, and 10¢ is uniform.

(2) We actually measured the coin distribution for a small sample of ~10 coins and assumed it is the same in the bulk.

Naively, one would expect (1) to be much less accurate than (2), since 1¢ is likely to occur 4 times more often than 5¢, for instance. However, this doesn't seem to be true: for the two cases we got very close estimates, of $57.33 and $57.48 respectively.*

Today I cashed the can and got $59.18 back.

You might be like: "Gosh, are you particle physicists or what?** Who else would get a 2.9% discrepancy and call it 'accurate' ?" Now watch my hands. Valery visited exactly 1 month ago, and I kept accumulating coins after he left. One month is 1/35th of my total stay in the US.

You know what I'm aiming at, alright. Linear extrapolation gives: $57.48 + $57.48/34 = $59.17

What do kids say these days? "Science works, bitches?" I guess that must be it.

Take care,

Misha

* Perhaps it's related to the way the prices are formed in the US – the xx.99¢ and xx.95¢ are too frequent, which biases the distribution. But I cannot prove that.

** Valery actually is.

The pressure to publish pushes down quality

An interesting read by Daniel Sarewitz in the recent Nature issue. It is a follow-up on the old discussion on the importance of the quality of the research papers as opposed to their quantity, and that the former should rather be taken into account to evaluate scientists for jobs, grants, and prizes.*

He gives an interesting example of poor quality, which is quite shocking from my naïve perspective:

"...The quality problem has been widely recognized in cancer science, in which many cell lines used for research turn out to be contaminated. For example, a breast-cancer cell line used in more than 1,000 published studies actually turned out to have been a melanoma cell line. The average biomedical research paper gets cited between 10 and 20 times in 5 years, and as many as one-third of all cell lines used in research are thought to be contaminated, so the arithmetic is easy enough to do: by one estimate, 10,000 published papers a year cite work based on contaminated cancer cell lines. Metastasis has spread to the cancer literature."

Take care,

Misha

* The main problem is, as usual, that the committee members rarely read the actual papers, and stick with the single-number estimates (such as journal impact-factors or h-index) instead.

More on bugs in Mathematica

In comments to my previous post, Rytis Jursenas pointed at an entire article in the Notices of AMS discussing several bugs in Mathematica. Since such problems are apparently quite common, I feel it deserves a separate post.

Here it comes:

"The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems. Can We Trust in Them?" by Antonio J. Durán, Mario Pérez, and Juan L. Varona

(just in case, here is the preprint)

"...We have been using Mathematica as a tool in our mathematical research. All our computations with Mathematica have been symbolic, involving only integers (large integers, about 10 thousand digits long) and polynomials (with degree 60 at most), so no numerical rounding or instability can arise in them, and we completely trusted the results generated by Mathematica. However, we have obtained completely erroneous results."

"...Software bugs should not prevent us from continuing this mutually beneficial 

relationship in the future. However, for the time being, when dealing with a problem whose answer cannot be easily verified without a computer, it is highly advisable to perform the computations with at least two computer algebra systems."

Well, I didn't expect such a conclusion to be drawn in 2014.

Take care,

Misha

A bug in Mathematica - 6 years later

In general, I'm a big fan of Wolfram Mathematica and their customer support. For instance, it happened that after my question "Do you guys have/plan to implement the X method to solve ordinary differential equations?" the support team would code and send me an implementation within a few days (although I obviously didn't ask for it).

Also, back to the day, when I found bugs in Mathematica routines I'd describe them in a blog post, and the support team would usually contact me very fast (sometimes within hours) and assist with solving the issue.

However, sometimes the bugs remain. One of the examples was a bug in evaluation of Clebsch-Gordan coefficients I've bumped into six years ago.

Today I mentioned it to a colleague ("...can you imagine how careful we had to be doing angular momentum algebra in grad school!"), and decided to check it, just for fun.

Here is my output from today:

Yep, after 6 years and 10 updates to Mathematica, it's still there...

Take care (especially using the Clebsch-Gordan routines),

Misha

Standing on the shoulders of giants

All of you have heard Newton's famous quote:

"If I have seen further, it is by standing on the shoulders of giants" *

It turns out that not only doesn't this quote originate from Newton, in fact, it was a very common saying at the time (such that Newton wouldn't even think there were people who hadn't heard it before).

That's how the "How to fly a horse" book describes it:

"Newton’s line was, in fact, close to a cliché at the time he wrote it. 

... Newton got it from George Herbert, who in 1651 wrote, "A dwarf on a giant’s shoulders sees farther of the two."

... Herbert got it from Robert Burton, who in 1621 wrote, "A dwarf standing on the shoulders of a giant may see farther than a giant himself."

... Burton got it from a Spanish theologian, Diego de Estella, also known as Didacus Stella, who probably got it from John of Salisbury, 1159: "We are like dwarfs on the shoulders of giants, so that we can see more than they, and things at a greater distance, not by virtue of any sharpness of sight on our part, or any physical distinction, but because we are carried high and raised up by their giant size."

... John of Salisbury got it from Bernard of Chartres, 1130: "We are like dwarfs standing upon the shoulders of giants, and so able to see more and see farther than the ancients." 

We do not know from whom Bernard of Chartres got it." 

Take care,

Misha


* Some of you might have heard Murray Gell-Mann's interpretation:

"If I have seen further than others, it is because I am surrounded by dwarfs."

Superfluidity and Bose-Einstein Condensation

A few times I heard people from the outside of the atomic physics community wondering why was the discovery of Bose-Einstein Condensation (BEC) in alkali gases so special, since the existence of BEC in superfluid helium was considered to be an accepted fact.

Of course, very soon after a BEC of ultracold atoms was created, the implication of the employed technology (as well as of several related developments) became crystal clear. By now, the field of ultracold gases grew into one of the mainstream areas of physics; it already allowed to use our knowledge about atoms and molecules to understand solid state physics, photonics, and even chemistry better.

However, a direct experimental observation of the BEC, as a novel state of matter, was of crucial importance.

Almost immediately after the discovery of superfluidity by Kapitza and Allen and Misener,* Fritz London suggested that this phenomenon was closely related to Bose-Einstein condensation. László Tisza, who was together with London in Paris (no pun intended) at the time, got excited and quickly elaborated on these ideas. Tisza developed the basis for what is known as the "two-fluid model." He conjectured that one can understand the superfluid phase of helium as a mixture of two components. The first, superfluid component, represents a Bose condensate of the atoms occupying the same single-particle quantum state. This results in a macroscopic coherence allowing a flux without friction or viscosity. The second, normal component, whose fraction depends on temperature, behaves as a regular viscous fluid.

Three years later, Lev Landau derived his version of the two-fluid model, based on the quantization of classical hydrodynamics equations. His theory was phenomenological and didn't require the particles to obey Bose statistics. Moreover, he started the paper by bluntly opposing the ideas of Tisza:

...Tisza’s well-known attempt to consider helium II as a degenerate Bose gas cannot be accepted as satisfactory – even putting aside the fact that liquid helium is not an ideal gas, nothing could prevent the atoms in the normal state from colliding with the excited atoms; i.e., when moving through the liquid they would experience friction and there would be no superfluidity at all.

As a matter of fact, it took several decades to unify the ideas of Landau with the ones of London and Tisza. In the end of the 1950's and beginning of the 1960's, several hard-core many-body calculations allowed to theoretically prove that superfluidity is indeed accompanied by Bose-Einstein condensation of helium atoms.**

However, from the experimental side, establishing the existence of the BEC state in superfluid helium turned out to be extremely challenging. Namely, it was possible to obtain only indirect evidence that about 10% of the atoms form a condensate, based on high-energy neutron scattering and spectra of atoms evaporated from the helium surface.

Thus, it was the observation of a BEC in ultracold gases and later experiments on their superfluidity which allowed to establish a connection between the two concepts beyond all possible doubt.

Take care,

Misha

* While these two papers appeared back-to-back in Nature, only Kapitza was awarded a Nobel Prize for this discovery (and only 40 years later!). Quite unfortunately, even nowadays the contribution of Allen and Misener remains widely disregarded. There are several great articles discussing this peculiar story; there are even gossips that Kapitza refused to accept the prize together with Allen which made the Nobel committee postpone the decision for decades.

** Since the phenomenological theory of Landau happened to successfully reproduce the experimental data, the contributions of London and Tisza were not acknowledged as widely as they should have been. Among other things, it seems that Fritz London was the first person ever to recognize the effects of quantum mechanics at the macroscopic scale, and think about the emergence of quantum phenomena in many-particle systems. Phil Anderson wrote a nice essay about London's forgotten contributions, which resonates with his own "More is different"  very well.

"Ambulance chasing" in particle physics

The progress in particle physics crucially depends on a few large experiments, releasing new data to the entire community of theorists several times a year.

Such a format of theory-experiment interaction leads to what is called the "ambulance chasing" phenomenon. Namely, every time after an announcement of a preliminary experimental result (i.e. one with less than 6 sigma deviation), the arxiv.org preprint server explodes from the amount of theory submissions explaining it. Widely-known examples would be the detection of superluminal neutrinos five years ago, or the recent ATLAS observation of a two-photon peak at 750 GeV.

Quite often, it turns out that the result happened to be within an experimental error bar and is not confirmed by future measurements. However, whether right or wrong, the theory papers receive a fair amount of citations - the more the earlier the preprint appeared.

The race for priority is so intense that dozens of theory preprints are submitted within hours (!) after the official announcement, which means that they were written in advance based on some insider information from the experimentalists.

In any case, in a recent preprint Mihailo Backović (Catholic University of Louvain, Belgium) developed a theory describing the ambulance chasing phenomenon both qualitatively and quantitatively.

The analysis is based on the assumptions that the number of papers on a particular topic can be described using Poisson statistics, and that the interest in the topic as well as the number of available ideas decrease in time (he considers power-law and exponential decays). This resulted in a two-parameter model, which provided a perfect fit to 9 cases of ambulance chasing, considered by the author.

Thus, even if all these theory papers were wrong in explaining the measurements, they at least can be used to study universality in complex systems. :-)

Take care,

Misha

Surprisingly elegant expressions for fundamental constants and other applied numerology

A few years ago, when I was still at Harvard, Ariel Amir knocked on my door. Somehow, he bumped into my old blog post on the (probably) shortest physics article ever, and was wondering whether such a numerological coincidence is truly random or not.

I've seen this paper by Friedrich Lenz for the first time in the Fall of 2006, visiting the Fritz Haber Institute to interview for a PhD position (I cannot believe it was almost ten years ago). There was a talk by an experimentalist who was aiming to measure the change in the proton-to-electron mass ratio using a molecular fountain (I think that was someone from the Rick Bethlem's, but I'm not absolutely sure). There, the "shortest paper ever" was shown as a joke to spice up the introduction.

Since then I was somewhat puzzled whether Lenz actually meant what he wrote, or was basically trolling the scientific community.

Thus, Ariel and I chatted and decided that the only way to answer this was to do an actual calculation. It turned out that Tadashi Tokieda was on sabbatical at the Radcliffe Institute – basically around the corner – and we decided to discuss the idea with him first.

To prove the point, we considered all possible combinations of the 0-9 digits and standard mathematical constants (such as pi or e) and calculated the probability that a combination of three of them would reproduce a 5-digit number of the form xxxx.x.

The probability turned out to be as low as 1.2%!

In other words, the Lenz observation was indeed quite intriguing, in the sense that such an elegant expression for the proton-to-electron mass ratio might have signaled for some underlying physical theory. While, as far as I know, this theory has not ever been revealed (and later measurements actually deviate from 6pi^5), paying attention to such surprises might pay off and deepen our understanding of physics.

Tadashi, Ariel, and I wrote a little popular piece about such surprising coincidences, which will appear in the June issue of the American Mathematical Monthly.

I hope you will enjoy reading it!

Take care,

Misha

Blogging While Untenured and Other Extreme Sports

Hello there,

In the good old times I used to be a blogger. Moreover, this blog still appears on the first page of the Google output if one searches for my name.

Long story short, I decided to follow the classic piece by Christine Hurt and Tung Yin (or did I misunderstand their advice?) and give blogging another try after several years of silence.

As a faculty, I do not really have more time as I used to have being a postdoc, when blogging became a luxury that I could not afford. I feel, however, that now I might have more stories to tell, and those will be lost if I don't put them out somewhere.

Not much has changed concerning the things that excite me - it's still mostly funny stories from science and its history, although we'll see how it goes (and how long I will last as a blogger this time :-)

Take care,

Misha