Abstract
Cosmology, astrophysics, and the physics of elementary particles and interactions are intimately connected. After reading this chapter, it will be clear that these subjects are part of the same field of investigation: this book will show you some of the connections, and maybe many more you will discover yourself in the future.
Cosmology, astrophysics, and the physics of elementary particles and interactions are intimately connected. After reading this chapter, it will be clear that these subjects are part of the same field of investigation: this book will show you some of the connections, and maybe many more you will discover yourself in the future.
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Notes
- 1.
Werner Heisenberg (1901–1976) was a German theoretical physicist and was awarded the 1932 Nobel Prize in Physics “for the creation of quantum mechanics.” He also contributed to the theories of hydrodynamics, ferromagnetism, cosmic rays, and subatomic physics. During World War II he worked on atomic research, and after the end of the war he was arrested, then rehabilitated. Finally he organized the Max Planck Institute for Physics, which is named after him.
- 2.
Max Planck (1858–1934) was the originator of quantum theory, and deeply influenced the human understanding of atomic and subatomic processes. Professor in Berlin, he was awarded the Nobel Prize in 1918 “in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta.” Politically aligned with the German nationalistic positions during World War I, Planck was later opposed to Nazism. Planck’s son, Erwin, was arrested after an assassination attempt of Hitler and died at the hands of the Gestapo.
- 3.
Sir Isaac Newton (1642–1727) was an English physicist, mathematician, astronomer, alchemist, and theologian, who deeply influenced science and culture down to the present days. His monograph Philosophiae Naturalis Principia Mathematica (1687) provided the foundations for classical mechanics. Newton built the first reflecting telescope and developed theories of color and sound. In mathematics, Newton developed differential and integral calculus (independently from Leibnitz). Newton was also deeply involved in occult studies and interpretations of religion.
- 4.
Albert Einstein (1879–1955) was a German-born physicist who deeply changed the human representation of the Universe, and our concepts of space and time. Although he is best known by the general public for his theories of relativity and for his mass-energy equivalence formula \(E = mc^2\) (the main articles on the special theory of relativity and the \(E=mc^2\) articles were published in 1905), he received the 1921 Nobel Prize in Physics “especially for his discovery of the law of the photoelectric effect” (also published in 1905), which was fundamental for establishing quantum theory. The young Einstein noticed that Newtonian mechanics could not reconcile the laws of dynamics with the laws of electromagnetism; this led to the development of his special theory of relativity. He realized, however, that the principle of relativity could also be extended to accelerated frames of reference when one was including gravitational fields, which led to his general theory of relativity (1916). A professor in Berlin, he moved to the USA when Adolf Hitler came to power in 1933, becoming a US citizen in 1940. During World War II, he cooperated with the Manhattan Project, which led to the atomic bomb. Later, however, he took a position against nuclear weapons. In the USA, Einstein was affiliated with the Institute for Advanced Study in Princeton.
- 5.
Arthur H. Compton (1892–1962) was awarded the Nobel Prize in Physics in 1927 for his 1923 discovery of the now-called Compton effect, which demonstrated the particle nature of electromagnetic radiation. During World War II, he was a key figure in the Manhattan Project. He championed the idea of human freedom based on quantum indeterminacy,
- 6.
Wolfgang Ernst (the famous physicist Ernst Mach was his godfather) Pauli (Vienna, Austria, 1900—Zurich, Switzerland, 1958) was awarded the 1945 Nobel prize in physics “for the discovery of the exclusion principle, also called the Pauli principle.” He also predicted the existence of neutrinos. Professor in ETH Zurich and in Princeton, he had a rich exchange of letters with psychologist Carl Gustav Jung. According to anecdotes, Pauli was a very bad experimentalist, and the ability to break experimental equipment simply by being in the vicinity was called the “Pauli effect.”
- 7.
This kind of interactionwas first conjectured and named by Isaac Newton at the end of the seventeenth century: “There are therefore agents in nature able to make the particles of bodies stick together by very strong attractions. And it is the business of experimental philosophy to find them out. Now the smallest particles of matter may cohere by the strongest attractions and compose bigger particles of weaker virtue; and many of these may cohere and compose bigger particles whose virtue is still weaker, and so on for diverse successions, until the progression ends in the biggest particles on which the operations in chemistry, and the colors of natural bodies depend.” (I. Newton, Opticks).
- 8.
Richard Feynman (New York 1918–Los Angeles 1988), longtime professor at Caltech, is known for his work in quantum mechanics, in the theory of quantum electrodynamics, as well as in particle physics; he participated in the Manhattan project. In addition, he proposed quantum computing. He received the Nobel Prize in Physics in 1965 for his “fundamental work in quantum electrodynamics, with deep-plowing consequences for the physics of elementary particles.” His life was quite adventurous, and full of anecdotes. In the divorce file related to his second marriage, his wife complained that “He begins working calculus problems in his head as soon as he awakens. He did calculus while driving in his car, while sitting in the living room, and while lying in bed at night.” He wrote several popular physics books, and an excellent general physics textbook now freely available at http://www.feynmanlectures.caltech.edu/.
- 9.
Galileo Galilei (1564–1642) was an Italian physicist, mathematician, astronomer, and philosopher who deeply influenced the scientific thought down to the present days. He first formulated some of the fundamental laws of mechanics, like the principle of inertia and the law of accelerated motion; he formally proposed, with some influence from previous works by Giordano Bruno, the principle of relativity. Galilei was professor in Padua, nominated by the Republic of Venezia, and astronomer in Firenze. He built the first practical telescope (using lenses) and using this instrument he could perform astronomical observations which supported Copernicanism; in particular he discovered the phases of Venus, the four largest satellites of Jupiter (named the Galilean moons in his honor), and he observed and analyzed sunspots. Galilei also made major discoveries in military science and technology. He came into conflict with the Catholic Church, for his support of Copernican theories. In 1616 the Inquisition declared heliocentrism to be heretical, and Galilei was ordered to refrain from teaching heliocentric ideas. Galilei argued that tides were an additional evidence for the motion of the Earth. In 1633 the Roman Inquisition found Galilei suspect of heresy, sentencing him to indefinite imprisonment; he was kept under house arrest in Arcetri, near Florence, until his death.
- 10.
The parsec (symbol: pc, and meaning “parallax of one arcsecond”) is often used in astronomy to measure distances to objects outside the solar system. It is defined as the length of the longer leg of a right triangle, whose shorter leg corresponds to one astronomical unit, and the subtended angle of the vertex opposite to that leg is one arcsecond. It corresponds to approximately 3 \(\times 10^{16}\) m, or about 3.26 light-years. Proxima Centauri, the nearest star, is about 1.3 pc from the Sun.
- 11.
The brightness of a star at an effective wavelength \(\lambda \) as seen by an observer on Earth is given by its apparent magnitude. This scale originates in the Hellenistic practice of dividing stars into six magnitudes: the brightest stars were said to be of first magnitude (m \(=\) 1), while the faintest were of sixth magnitude (m \(=\) 6), the limit of naked eye human visibility. The system is today formalized by defining a first magnitude star as a star that is 100 times as bright as a sixth magnitude star; thus, a first magnitude star is \(\root 5 \of {100}\) (about 2.512) times as bright as a second magnitude star (obviously the brighter an object appears, the lower the value of its magnitude). The stars Arcturus and Vega have an apparent magnitude approximately equal to 0. The absolute magnitude M\(_{V}\) is defined to be the visual (\(\lambda \sim 550\) nm) apparent magnitude that the object would have if it were viewed from a distance of 10 parsec, in the absence of light extinction; it is thus a measure of the luminosity of an object. The problem of the relation between apparent magnitude, absolute magnitude, and distance is related also to cosmology, as discussed in Chap. 8. The absolute magnitude is nontrivially related to the bolometric luminosity, i.e., to the total electromagnetic power emitted by a source; the relation is complicated by the fact that only part of the emission spectrum is observed in a photometric band. The absolute magnitude of the Sun is M\(_{V,\,\odot } \simeq 4.86\), and its absolute bolometric magnitude is M\(_{\mathrm{bol},\,\odot } \simeq 4.76\); the difference M\(_{V}\)-M\(_{\mathrm{bol}}\) (for the Sun, M\(_{V,\,\odot }\)- M\(_{\mathrm{bol},\,\odot } \simeq 0.1\)) is called the bolometric correction BC, which is a function of the temperature. It can be approximated as BC\((T) \simeq 29500/T + 10\log _{10}T- 42.62.\)
- 12.
Note that frequently astrophysicist use as a unit of energy the old “cgs” (centimeter–gram–second) unit called erg; 1 erg \(=\) 10\(^{-7}\) J.
- 13.
The Chandrasekhar limitis the maximum mass theoretically possible for a star to end its lifecycle into a dwarf star: Chandrasekhar in 1930 demonstrated that it is impossible for a collapsed star to be stable if its mass is greater than \(\sim \)1.44 times the mass of the Sun. Above 1.5–3 solar masses (the limit is not known, depending on the initial conditions) a star ends its nuclear-burning lifetime into a black hole. In the intermediate range it will become a neutron star.
- 14.
In this textbook we define as cosmic rays all particles of extraterrestrial origin. It should be noted that other textbooks instead define as cosmic rays only nuclei, or only protons and ions—i.e., they separate gamma rays and neutrinos from cosmic rays.
- 15.
A theoretical upper limit on the energy of cosmic rays from distant sources was computed in 1966 by Greisen, Kuzmin, and Zatsepin, and it is called today the GZK cutoff. Protons with energies above a threshold of about 10\(^{20}\) eV suffer a resonant interaction with the cosmic microwave background photons to produce pions through the formation of a short-lived particle (resonance) called \(\varDelta \): \(p+\gamma \rightarrow \varDelta \rightarrow N+\pi \). This continues until their energy falls below the production threshold. Because of the mean path associated with the interaction, extragalactic cosmic rays from distances larger than 50 Mpc from the Earth and with energies greater than this threshold energy should be strongly suppressed on Earth, and there are no known sources within this distance that could produce them. A similar effect (nuclear photodisintegration) limits the mean free path for the propagation of nuclei heavier than the proton.
- 16.
Usually the planar representations of maps of the Universe are done in galactic coordinates. To understand what this means, let us start from a celestial coordinate system in spherical coordinates, in which the Sun is at the center, the primary direction is the one joining the Sun with the center of the Milky Way, and the galactic plane is the fundamental plane. Coordinates are positive toward North and East in the fundamental plane.
We define as galactic longitude (l or \(\lambda \)) the angle between the projection of the object in the galactic plane and the primary direction. Latitude (symbol b or \(\phi \)) is the angular distance between the object and the galactic plane. For example, the North galactic pole has a latitude of \(+\)90\(^\circ \).
Plots in galactic coordinates are then projected onto a plane, typically using an elliptical (Mollweide or Hammer; we shall describe the Mollweide projection here) projection preserving areas. The Mollweide projection transforms latitude and longitude to plane coordinates x and y via the equations (angles are expressed in radians):
$$\begin{aligned} x= & {} R \frac{2 \sqrt{2}}{\pi } \cos \theta \\ y= & {} R \sqrt{2} \sin \theta \, , \end{aligned}$$where \(\theta \) is defined by the equation
$$ 2 \theta + \sin \left( 2 \theta \right) = \pi \sin \phi $$and R is the radius of the sphere to be projected. The map has area \(4\pi R^2\), obviously equal to the surface area of the generating globe. The x-coordinate has a range \([-2R\sqrt{2}, 2R\sqrt{2}],\) and the y-coordinate has a range \([-R\sqrt{2}, R\sqrt{2}].\) The galactic center is located at (0, 0).
Less frequently, a projection using equatorial coordinates is used. In this case, the origin is at the center of Earth; the fundamental plane is the projection of Earth’s equator onto the celestial sphere, and the primary direction is toward the March equinox; the projection of the galactic plane is a curve in the ellipse.
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De Angelis, A., Pimenta, M. (2018). Understanding the Universe: Cosmology, Astrophysics, Particles, and Their Interactions. In: Introduction to Particle and Astroparticle Physics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-78181-5_1
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