Abstract
This chapter illustrates the path which led to the discovery that particles of extremely high energy, up to a few joule, come from extraterrestrial sources and collide with Earth’s atmosphere. The history of this discovery started in the beginning of the twentieth century, but many of the techniques then introduced are still in use. A relevant part of the progress happened in recent years and has a large impact on the physics of elementary particles and fundamental interactions.
This chapter illustrates the path which led to the discovery that particles of extremely high energy, up to a few joule, come from extraterrestrial sources and collide with Earth’s atmosphere. The history of this discovery started in the beginning of the twentieth century, but many of the techniques then introduced are still in use. A relevant part of the progress happened in recent years and has a large impact on the physics of elementary particles and fundamental interactions.
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Notes
- 1.
Charles Thomson Rees Wilson , (1869–1959), a Scottish physicist and meteorologist, received the Nobel Prize in Physics for his invention of the cloud chamber; see the next chapter.
- 2.
Hess was born in 1883 in Steiermark, Austria, and graduated at Graz University in 1906 where he became professor of Experimental Physics in 1919. In 1936 Hess was awarded the Nobel Prize in Physics for the discovery of cosmic rays. He moved to the USA in 1938 as professor at Fordham University. Hess became an American citizen in 1944 and lived in New York until his death in 1964.
- 3.
Robert A.Millikan (Morrison 1868—Pasadena 1953) was an American experimental physicist, Nobel Prize in Physics in 1923 for his measurements of the electron charge and his work on the photoelectric effect. A scholar of classical literature before turning physics, he was president of the California Institute of Technology (Caltech) from 1921 to 1945. He was not famous for his deontology: a common saying at Caltech was “Jesus saves, and Millikan takes the credit.”
- 4.
The Geiger-Müller counter is a cylinder filled with a gas, with a charged metal wire inside. When a charged particle enters the detector, it ionizes the gas, and the ions and the electrons can be collected by the wire and by the walls. The electrical signal of the wire can be amplified and read by means of an amperometer. The tension V of the wire is large (a few thousand volts), in such a way that the gas is completely ionized; the signal is then a short pulse of height independent of the energy of the particle. Geiger-Müller tubes can be also appropriate for detecting \(\gamma \) radiation, since a photoelectron or a Compton-scattered electron can generate an avalanche.
- 5.
Erwin Schrödinger was an Austrian physicist who obtained fundamental results in the fields of quantum theory, statistical mechanics and thermodynamics, physics of dielectrics, color theory, electrodynamics, cosmology, and cosmic-ray physics. He also paid great attention to the philosophical aspects of science, re-evaluating ancient and oriental philosophical concepts, and to biology and to the meaning of life. He formulated the famous paradox of the Schrödinger cat. He shared with P.A.M. Dirac the 1933 Nobel Prize for Physics “for the discovery of new productive forms of atomic theory.”
- 6.
Oskar Klein (1894–1977) was a Swedish theoretical physicist; Walter Gordon (1893–1939) was a German theoretical physicist, former student of Max Planck.
- 7.
Paul Adrien Maurice Dirac (Bristol, UK, 1902—Tallahassee, US, 1984) was one of the founders of quantum physics. After graduating in engineering and later studying physics, he became professor of mathematics in Cambridge. In 1933 he shared the Nobel Prize with Schrödinger. He assigned to the concept of “beauty in mathematics” a prominent role among the basic aspects intrinsic to the nature so far as to argue that “a mathematically beautiful theory is more likely to be right and proper to an unpleasant as it is confirmed by the data.”
- 8.
The term spinor indicates in general a vector which has definite transformation properties for a rotation in the proper angular momentum space—the spin space. The properties of rotation in spin space will be described in greater detail in Chap. 5 .
- 9.
The cloud chamber (see also next chapter), invented by C.T.R. Wilson at the beginning of the twentieth century, was an instrument for reconstructing the trajectories of charged particles. The instrument is a container with a glass window, filled with air and saturated water vapor; the volume could be suddenly expanded, bringing the vapor to a supersaturated (metastable) state. A charged cosmic ray crossing the chamber produces ions, which act as seeds for the generation of droplets along the trajectory. One can record the trajectory by taking a photographic picture. If the chamber is immersed in a magnetic field, momentum and charge can be measured by the curvature. The working principle of bubble chambers is similar to that of the cloud chamber, but here the fluid is a liquid. Along the tracks’ trajectories, a trail of gas bubbles condensates around the ions. Bubble and cloud chambers provide a complete information: the measurement of the bubble density and the range, i.e., the total track length before the particle eventually stops, provide an estimate for the energy and the mass; the angles of scattering provide an estimate for the momentum.
- 10.
Bruno Rossi (Venice 1905—Cambridge, MA, 1993) graduated in Bologna, and then moved to Arcetri near Florence before becoming full professor of physics at the University of Padua in 1932. In Padua he was charged of overseeing the design and construction of the new Physics Institute, which was inaugurated in 1937. He was exiled in 1938, as a consequence the Italian racial laws, and he moved to Chicago and then to Cornell. In 1943 he joined the Manhattan project in Los Alamos, working to the development of the atomic bomb, and after the end of the second World War moved to MIT. At MIT Rossi started working on space missions as a scientfic consultant for the newborn NASA, and proposed the rocket experiment that discovered the first extra-solar source of X-rays. Many fundamental contributions to modern physics, for example the electronic coincidence circuit, the discovery and study of extensive air showers, the East–West effect, and the use of satellites for the exploration of the high-energy Universe, are due to Bruno Rossi.
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Appendices
Further Reading
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[F3.1]
P. Carlson, A. de Angelis, “Nationalism and internationalism in science: the case of the discovery of cosmic rays”, The European Physical Journal H 35 (2010) 309.
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[F3.2]
A. de Angelis, “Atmospheric ionization and cosmic rays: studies and measurements before 1912”, Astroparticle Physics 53 (2014) 19.
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[F3.3]
J.W. Cronin, “The 1953 Cosmic Ray Conference at Bagneres de Bigorre”, The European Physical Journal H 36 (2011) 183.
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[F3.4]
D.H. Griffiths, “Introduction to Quantum Mechanics, 2nd edition”, Addison-Wesley, Reading, MA, 2004.
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[F3.5]
J. Björken and S. Drell, “Relativistic Quantum Fields” McGraw-Hill, New York, 1969.
Exercises
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1.
The measurement by Hess. Discuss why radioactivity decreases with elevation up to some 1000 m, and then increases. Can you make a model? This was the subject of the thesis by Schrödinger in Wien in the beginning of twentieth century.
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2.
Klein-Gordon equation. Show that in the nonrelativistic limit \(E\simeq mc^2\) the positive energy solutions \(\Psi \) of the Klein-Gordon equation can be written in the form
$$\begin{aligned} \Psi (\vec {r},t) \simeq \Phi (\vec {r},t) e^{-\frac{mc^2}{\hbar }} \, , \end{aligned}$$where \(\Phi \) satisfies the Schrödinger equation.
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3.
Uncertainty relations. Starting from Eq. (3.5), demonstrate the uncertainty principle.
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4.
Antimatter. The total number of nucleons minus the total number of anti nucleons is believed to be constant in a reaction—you can create nucleon–antinucleon pairs. What is the minimum energy of a proton hitting a proton at rest to generate an antiproton?
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5.
Fermi maximum accelerator. According to Enrico Fermi, the ultimate human accelerator, the “Globatron,” would be built around 1994 encircling the entire Earth and attaining an energy of around 5000 TeV (with an estimated cost of 170 million US1954 dollars...). Discuss the parameters of such accelerator.
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6.
Cosmic pions and muons. Pions and muons are produced in the high atmosphere, at a height of some 10 km above sea level, as a result of hadronic interactions from the collisions of cosmic rays with atmospheric nuclei. Compute the energy at which charged pions and muons respectively must be produced to reach in average the Earth’s surface. You can find the masses of the lifetimes of pions and muons in your Particle Data Booklet.
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7.
Very-high-energy cosmic rays. Justify the sentence “About once per minute, a single subatomic particle enters the Earth’s atmosphere with an energy larger than 10 J” in Chap. 1.
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8.
Very-high-energy neutrinos. The IceCube experiment in the South pole can detect neutrinos crossing the Earth from the North pole. If the cross section for neutrino interaction on a nucleon is \((6.7 \times 10^{-39} E)\) cm\(^2\) with E expressed in GeV (note the linear increase with the neutrino energy E), what is the energy at which half of the neutrinos interact before reaching the the detector? Comment on the result.
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De Angelis, A., Pimenta, M.J.M. (2015). Cosmic Rays and the Development of Particle Physics. In: Introduction to Particle and Astroparticle Physics. Undergraduate Lecture Notes in Physics. Springer, Milano. https://doi.org/10.1007/978-88-470-2688-9_3
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