Sep 292018

Enrico Fermi, the nuclear physicist was born in Rome on this date in 1901. The scientific school where I taught for 2 years in Mantua was named Enrico Fermi technical school and liceo (in Italian), so I feel the need to give him an extra nod even though I covered his supervision of the first sustained nuclear chain reaction here:  Now I can be a tad more general.

Fermi was the third child of Alberto Fermi, a division head (Capo Divisione) in the Ministry of Railways, and Ida de Gattis, a primary school teacher. One of Fermi’s first sources for his study of physics was a book he found at the local market at Campo de’ Fiori in Rome, the 900-page Elementorum physicae mathematicae(1840), which was written in Latin by Jesuit Father Andrea Caraffa, a professor at the Collegio Romano. It covered mathematics, classical mechanics, astronomy, optics, and acoustics, insofar as these disciplines were understood when the book was written. Fermi befriended another scientifically inclined student, Enrico Persico, and together the two worked on scientific projects such as building gyroscopes and trying to measure the acceleration of Earth’s gravity accurately (a young Galileo). Fermi’s interest in physics was further encouraged by his father’s colleague Adolfo Amidei, who gave him several books on physics and mathematics, which he read and assimilated quickly.

Fermi finished secondary school in July 1918 and, at Amidei’s urging, applied to the Scuola Normale Superiore in Pisa. The school provided free lodging for students, but candidates had to take a difficult entrance exam that included an essay. The given theme was “Specific characteristics of Sounds”. The 17-year-old Fermi chose to derive and solve the partial differential equation for a vibrating rod, applying Fourier analysis in the solution. The examiner, Professor Giulio Pittarelli from the Sapienza University of Rome, interviewed Fermi and praised him, saying that he would become an outstanding physicist in the future.

During his years at the Scuola Normale Superiore, Fermi teamed up with a fellow student, Franco Rasetti, with whom he would indulge in light-hearted pranks and who would later become Fermi’s close friend and collaborator. In Pisa, Fermi was supervised by the director of the physics laboratory, Luigi Puccianti, who acknowledged that there was little that he could teach Fermi, and frequently asked Fermi to teach him something instead. Fermi’s knowledge of quantum physics reached such a high level that Puccianti asked him to organize seminars on the topic. During this time Fermi learned tensor calculus, a mathematical technique invented by Gregorio Ricci and Tullio Levi-Civita that was needed to demonstrate the principles of general relativity. Fermi initially chose mathematics as his major field, but soon switched to physics. He remained largely self-taught, studying general relativity, quantum mechanics, and atomic physics.

In September 1920, Fermi was admitted formally as a teacher in the physics department even though he was still an undergraduate. Since there were only three students in the department—Fermi, Rasetti, and Nello Carrara—Puccianti let them freely use the laboratory for whatever purposes they chose. Fermi decided that they should research X-ray crystallography, and the three worked to produce a Laue photograph—an X-ray photograph of a crystal. During 1921, his third year at the university, Fermi published his first scientific works in the Italian journal Nuovo Cimento, “On the dynamics of a rigid system of electrical charges in translational motion” (Sulla dinamica di un sistema rigido di cariche elettriche in moto traslatorio). A sign of things to come was that the mass was expressed as a tensor—a mathematical construct commonly used to describe something moving and changing in three-dimensional space. In classical mechanics, mass is a scalar quantity, but within relativity mass changes with velocity. The second paper was “On the electrostatics of a uniform gravitational field of electromagnetic charges and on the weight of electromagnetic charges” (Sull’elettrostatica di un campo gravitazionale uniforme e sul peso delle masse elettromagnetiche). Using general relativity, Fermi showed that a charge has a weight equal to U/c2, where U was the electrostatic energy of the system, and c is the speed of light.

A Fermiac

The first paper seemed to point out a contradiction between the electrodynamic theory and the relativistic one concerning the calculation of the electromagnetic masses, as the former predicted a value of 4/3 U/c2. Fermi addressed this the next year in a paper “Concerning a contradiction between electrodynamic and the relativistic theory of electromagnetic mass” in which he showed that the apparent contradiction was a consequence of relativity. This paper was sufficiently well-regarded that it was translated into German and published in the German scientific journal Physikalische Zeitschrift in 1922. That year, Fermi submitted his article “On the phenomena occurring near a world line” (Sopra i fenomeni che avvengono in vicinanza di una linea oraria) to the Italian journal I Rendiconti dell’Accademia dei Lincei. In this article he examined the Principle of Equivalence, and introduced the so-called “Fermi coordinates”. He proved that on a world line close to the time line, space behaves as if it were a Euclidean space.

Fermi submitted his thesis, “A theorem on probability and some of its applications” (Un teorema di calcolo delle probabilità ed alcune sue applicazioni), to the Scuola Normale Superiore in July 1922, and received his laurea at the unusually young age of 20. The thesis was on X-ray diffraction images. Theoretical physics was not yet considered a discipline in Italy, and the only thesis that would have been accepted was one on experimental physics. For this reason, Italian physicists were slow in embracing the new ideas like relativity coming from Germany. Since Fermi was quite at home in the lab doing experimental work, this did not pose insurmountable problems for him, and ended up making him something of a rara avis, a nuclear physicist equally at home with both theoretical and experimental physics.

While writing the appendix for the Italian edition of the book Fundamentals of Einstein Relativity by August Kopff in 1923, Fermi was the first to point out that hidden inside the famous Einstein equation (E = mc2) was an enormous amount of nuclear potential energy to be exploited. “It does not seem possible, at least in the near future”, he wrote, “to find a way to release these dreadful amounts of energy—which is all to the good because the first effect of an explosion of such a dreadful amount of energy would be to smash into smithereens the physicist who had the misfortune to find a way to do it.” Well, he did go on to find a way to do it, and was not smashed to smithereens. Unfortunately, many people were in Hiroshima and Nagasaki, and Fermi, after helping a team in Los Alamos develop the first atomic bombs in the US, became a staunch advocate for the limitation of nuclear weapons, especially after Russians invented a fusion bomb.

I could go on, but, combined with my post on Fermi’s CP-1 pile, you have a very good outline of his life’s work. I do wonder, more often than I would like, what goes into the making of geniuses such as Fermi. How can a teenager, barely starting as an undergraduate be more capable in his field than the head of the department?  A friend of mine who is a noted mathematician pointed out that mathematics and theoretical physics are often revolutionized by very young scholars, partly because their minds are agile and flexible, and partly because their lives are not cluttered with distractions. When they marry and have children their creativity begins to fade, although their work may still be very good.

One of the measures of Fermi’s greatness is the number of diverse things that are named after him: schools, roads, concepts in physics, devices, buildings, departments, and a trans-uranic element – fermium. This gives me an idea for creating a dessert in his honor: the Fermi Pile Tiramisu. Look at this photo for the general idea:

You need a package of ladyfinger biscuits, tiramisu custard, and high quality cocoa. Here is my recipe for the custard again:

Put 4 egg yolks and half a cup of sugar in the top of a double boiler. Bring the water in the bottom to a steady simmer, and make sure that the water does not touch the top part of the boiler. Whisk the sugar and egg yolk mixture vigorously for around 8 minutes. It will expand to a froth and cook. (Hint: you are not making scrambled eggs). Remove from the heat and fold in 1 pound (½ kg) of mascarpone. In a separate bowl whisk 1 cup of heavy cream to stiff peaks. Fold the mascarpone-egg mix into the cream. Chill in the refrigerator overnight.

Next day, make a base of custard and embed a layer of ladyfingers in it. Sprinkle some cocoa over the ladyfingers and then start layering custard and biscuits, finishing with custard and a generous shower of cocoa. Play with this concept to suit yourself.

Nov 212015


On this date in 1905 Albert Einstein’s paper, “Does the Inertia of a Body Depend Upon Its Energy Content?” was published in the journal Annalen der Physik. This paper explored the relationship between energy and mass via Special Relativity, and, thus, led to the mass–energy equivalence formula E = mc² — arguably the most famous formula in the world. I would also argue that it is the most misunderstood formula in the world, although I notice in researching this post that a lot of physicists in trying to help non-physicists understand it, seriously misrepresent its implications.

The problem frequently in trying to explain physics to the mathematically and scientifically challenged is that scientists and science teachers fall back on analogies – often involving cats for some inscrutable reason. The problem, as I have stated many times in many places before, is that analogies can help, but they can also be misleading.


There is a second problem in that E = mc² does not represent the whole story. That’s the part about theory that non-scientists rarely get. Einstein’s theories of relativity, Darwin’s theory of natural selection, etc. are not complete, hence they are called “theories.” No one is seeking radically new alternatives (although some day they might); scientists are just trying to explain messy bits in the theories that cannot be explained now. That’s how Einstein came to unravel Newton. Newton was not totally wrong; it’s just that his “laws” of motion, for example, are incomplete – as stated by Newton they apply only to mass, force, acceleration, etc. as we encounter them in the everyday world. When physicists started looking at interstellar, and subatomic worlds at the turn of the 20th century, Newton’s physics did not work very well for them. That’s when Einstein came along and added bits to Newton to make his equations more encompassing.

Here’s a couple of provisos before I get into things more. First, for the non-mathematically inclined I am going to have to be simplistic and in doing so I will have to be a little misleading, or, you might say, downright wrong. The only way to understand physics deeply is to understand the underlying mathematics deeply (which, incidentally, I don’t, although I am better at it than most non-scientists). Second, my usual caveat, I don’t find physics per se very interesting. My son switched from being a physics major to an anthropology major a few years ago for precisely the same reason. Physics does very well in helping us build computers, cell phones, and what not, and I use them all the time. Thanks physics. It is useless when it comes to issues that I really care about such as the existence of God, how to mend a broken heart, and so forth. To be sure, philosophers and theologians can sometimes gain insight into problems they are working on by learning some physics, and vice versa. But the one realm cannot explain the other. Their methods and goals are radically different. When it comes to understanding the formation of the universe as we now know it, I’ll study physics; when it comes to understanding God, I’ll read the Bible and other spiritual texts. Both areas still have a long way to go.


The formula E = mc² is incomplete, but let’s stick with it for now. In the formula, E is energy, m is mass, and c is the velocity of light (here it is squared). Most people know that. Where they go drastically wrong is in thinking that mass = matter. That is false. Mass is mass, matter is matter, and energy is energy. E = mc² does not talk about matter directly, but about the relationship between energy and mass. It’s not about the conversion of matter into energy, as most people think the atom bomb or atomic energy are all about (as in the TIME cover photo). Einstein was not involved in the Manhattan project because he lacked the proper security clearance. But even if he had been, E = mc² has very little application in making a bomb. Atomic bombs and atomic energy concern releasing energy within the atom, not converting matter into energy as such. This is a bit of a semantic quibble, but at least you can get the general idea that matter is made up of particles and energy. Under certain conditions it is possible to set the energy free – and a little goes a long way.

In a nuclear bomb or energy plant, you are not converting the particles into energy; you are setting energy free that keeps the atoms together. It requires an incredible amount of energy to keep the particles of the atomic nucleus together, so, if you can tear them apart, you can release that energy. That’s why it’s called nuclear energy. You are not converting the particles into energy, you are simply setting it free. The particles remain as particles, just much less organized since nothing is holding them together.


So, then, what is it about E = mc²? It’s simply telling you that energy has mass, but it’s very, very small. Nonetheless, if you add energy to something, you increase its mass. For example, if you accelerate something it gains energy, therefore mass. At usual speeds the increase in mass is minute. But when you start approaching the speed of light you have to increase the energy input enormously, and in so doing, what you are pushing gets enormously massive. That fact is an important component of Special Relativity.

Explaining all of this will help you understand why I generally find physics dull. I’ll leave professional physics up to people who care about mathematical puzzles. I am not especially interested in how atomic bombs or cell phones work at a deep level. I’m much more interested in how and why people use (or don’t use) them, and for that kind of question physics is no help.

Physics burst on the scene a few years ago in the form of so-called “molecular” gastronomy. I’ve mentioned this fad before as a trend that I feel is more trickery than artistry – a way to amuse the eyes once in a while, but not much of an enhancement on classic cooking techniques. I expect it will vanish ere long. So . . . you can make spherical stuff, and foams, and “instant” frozen things. Big whoop. The equipment to do this is expensive, especially If you are only going to use it occasionally for a flashy dinner party. I will admit that I bought a rechargeable soda siphon once, about 40 years ago, which allowed me to make carbonated liquids – usually water. But it’s a whole lot cheaper to buy carbonated water than to have a machine. If I want something fizzy these days I’ll turn to chemistry and put a little sodium bicarbonate in an acidulated liquid. But I usually only do that when I have an upset stomach.

For the sake of completeness, though, here’s a video on making mock fried eggs with mango “yolks” and coconut milk “whites.” I expect they are delicious, but I’ll content myself with the video, and settle for mango balls in coconut milk for my next dessert.