Special Relativity

The revolution of Albert Einstein

 The main postulate of classical mechanics developed by Galileo and Newton is that the existence of space and time is absolute: the way in which spatial distances and temporal intervals are measured gives the same results independent of the state of motion of the observer. Measuring the length of a board inside or outside a moving train gives the same result. Thus, in any system moving at a constant speed, called the “inertial reference system”, the same laws of physics apply. This implies that no experiment can determine whether the inertial system in which it’s conducted is in motion or not: the oscillation of a spring or pendulum, the fall of a weight along an inclined plane, two marbles hitting each other and so on follow the same laws of physics in all inertial systems. The experimenter considering themself at rest will come up with the same results as the experimenter passing by in a vehicle moving at a constant velocity. One can define only the relative speed between inertial reference systems but cannot identify an absolute speed. This is the principle of galileian relativity: in this view the pace of time is absolute, independent of the state of motion of the observer.

In 1864, Maxwell unified electricity and magnetism in his famous equations, demonstrating that light is nothing more than an electromagnetic wave. This allowed optics and electromagnetism to be unified into a single theory. Nonetheless, according to the knowledge of the time, a wave couldn’t be anything but a mechanical vibration of a medium, like sound waves that propagate in the atmosphere. The hypothesis of the wave-like nature of light made it necessary to introduce a medium, ether, that pervades the entire universe and through which light could propagate.

With the introduction of ether, all mechanical, electric and magnetic phenomena could be interpreted through Newtonian mechanics and Maxwell’s equations. However, Maxwell’s equations appeared to be in contrast with the postulates of classical Galileian physics. If, in fact, we assume that the composition of the speed predicted by Galileian mechanics is also valid for electromagnetic waves, then the speed of light should differ if observed in two inertial systems with different velocities. On the other hand, the Maxwell equations show that light travels at a fixed velocity, experimentally estimated to be around 300,000 kilometers per second: but then in which reference system can we observe light traveling at that velocity? At the time it was suggested that it would be that system of reference in which the ether is at rest.

In 1887, with an experiment that would become famous and replicated over the years, physicists Michelson and Morley tried to measure the variations of the speed of light in various reference systems. They used an instrument called an interferometer that would prove the existence of ether, hypothesized as being integral to fixed stars. The experiment, however, gave negative results and so ether could not exist. If ether doesn’t exist, electromagnetic waves propagate at the speed of light…through what??

Various attempts were to preserve the concept of ether until, in 1905, an examiner in the patent office of Bern, Switzerland, by the name of Albert Einstein published an article entitled “On the Electrodynamics of Moving Bodies”. The article was based on two fundamental principles; these allowed the principle of relativity, originally assumed valid for the laws of of Newtonian mechanics, to extend to all physical phenomena including electromagnetics. The first is the new Principle of Relativity according to which all physical laws remain the same passing from one initial reference system to another in a uniform straight line. The second is the Principle of constant speed of light in a vacuum; in other words, the speed of light in a vacuum has the same value in all inertial reference systems. The principles of relativity introduced by Einstein allows us to abandon the idea of the existence of an absolute system of reference.  In fact, since the speed of light is the same in every inertial system it’s no longer possible to use the measure of its speed to determine if a system is in absolute movement or at rest.

Einstein’s two principles lead to certain unexpected and counter-intuitive consequences. The fact that the speed of light is constant in Einstein’s relativity implies that we need to give up the concept of absolute time and space: the measure of time, understood as the rhythm of a clock, changes with the variance of the state of motion relative to the observer and to the clock itself. The most famous manifestation of this aspect is the Twin Paradox: a twin that travels at a speed near that of light ages much more slowly compared to the twin who remains at home. Just as famous is the phenomenon of Length Contraction: an object seems shorter to an observer in movement in respect to the object. Both these effects have been measured with extremely high precision.

Einstein’s theory, which completely redefines the structure of space-time and the relationship between mass and energy, has many different consequences; one of the most fascinating is the intuition that mass and energy are two aspects of the same entity and that it’s possible to convert one into the other and vice versa. Everyone knows the famous equation E=mc2, energy is equal to mass multiplied by the speed of light squared: an extraordinary concept that, it’s said, ruined Einstein’s sleep because of the possible military implications. The equation essentially implies the equivalence of mass and energy. It’s precisely this principle that is used in nuclear reactors where, for example, a mass of 10 grams of uranium is transformed into 900,000 billion joules of energy: 10 kilograms of uranium can satisfy the national energy needs for a  year.

In one of his first scientific articles, it was Enrico Fermi who expressed a certain enthusiasm for Einstein and his pioneering theories on space-time: “For example, if we were to liberate the energy contained in a gram of material we could obtain more energy than that created in three years of continuous work by a 1,000HP engine (comments are useless!). We can rightly say that, at least for the next few years, finding the means of liberating this fearsome quantity of energy doesn’t seem possible—and let’s hope we don’t—because the explosion of energy of such proportions would have as an initial effect the reduction in smithereens of the physicist who had the bad luck to figure out how to do it.” As we’ll see, that physicist would be Fermi himself.

The life of Enrico Fermi: phase one

Enrico Fermi was born in Rome on September 29, 1901, to Alberto Fermi and Ida De Gattis. He showed extraordinary abilities even as a young boy in his ability to deepen his self-taught scientific knowledge, during his school years and in his ability to create friendships that would last his whole life with other talented students like Enrico Persico who also became a physics professor:

“When I met him for the first time he was 14 years old, I was amazed to find I had a classmate gifted with an intelligence that was different from what the other kids considered smart and studious. In mathematics and physics he showed his knowledge on many subjects, not just scholastically but in a way that could be the most useful and knowledgable; even back then, knowing a theorem or scientific law meant for him above all knowing how to put it to use.”

In 1918 Fermi was accepted to the prestigious university “Normal High School of Pisa” where some of the brightest mathematicians and physicists of the time were teaching. In Pisa, he became friends with classmate Franco Rasetti who in the future would work with him in Rome. Outside university studies the two shared the same interest in mountain climbing and revelling in the undergrad lifestyle. In fact, they organized a group of students into an association whose only objective was to play practical jokes and bother people. Physics, however, was always at the center of Fermi’s thoughts. After graduating “cum laude” in July of 1922 he decided to dedicate himself to university research. Back in Rome, he introduced himself to Orso Mario Corbino, director of the physics institute on Via Panisperna and influential political personality, who brought Fermi into the international scientific milieu also thanks to some grants to study abroad.

In autumn of 1926, thanks to Corbino, the first national competition for the post of professor of theoretical physics was announced. It was the first step in the transformation of the institute at Via Panisperna into a center comparable to the finest foreign schools. Fermi won the competition and eventually became the leader of a brilliant research group that included his old friends Rasetti and Persico, to whom were soon added Edoardo Amaldi, Emilio Segrè, Ettore Majorana, Oscar D’Agostino and Bruno Pontecorvo.