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 Nobel Prize in Physics for 1932 “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 presently in Munich is entitled to 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 opposing nazism. Planck’s son, Erwin, was arrested attempting assassination 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.
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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). Professor in Berlin, he moved to the United States 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 US, Einstein was affiliated to the Institute for Advanced Study in Princeton.
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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”.
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This kind of interaction was 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 divers 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)
- 7.
Galileo Galilei (1564–1642) was an Italian physicist, mathematician, astronomer, and philosopher who deeply influenced scientific thoughts 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. In 1616 Galilei argued that tides were an additional evidence for the motion of the Earth. In 1933 the Roman Inquisition found Galilei suspect of heresy, sentencing him to indefinite imprisonment; he was kept under house arrest in Arcetri near Firenze until his death.
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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.
- 9.
Note that frequently astrophysicist use as a unit of energy the old “cgs” (centimeter-gram-second) unit called erg; 1 erg = 10\(^{-7}\) J.
- 10.
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 \(\Delta \): \(p+\gamma \rightarrow \Delta \rightarrow N+\pi \). 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.
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Usually the planar representations of maps of the Universe are done in galactic coordinates. 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) projection preserving areas. This projection transforms latitude and longitude to plane coordinates x and y via the equations (angles are expressed in radiants):
$$\begin{aligned} x= & {} R \frac{2 \sqrt{2}}{\pi } \cos \theta \\ y= & {} R \sqrt{2} \sin \theta \, , \end{aligned}$$where \(\theta \) is defined by the equation
$$\begin{aligned} 2 \theta + \sin \left( 2 \theta \right) = \pi \sin \phi \end{aligned}$$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).
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Appendices
Further Reading
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[F1.1]
A. Einstein and L. Infeld, “The Evolution of Physics,” Touchstone. This inspiring book is about the main ideas in physics. With simplicity and a limited amount of formulas it gives an exciting account for the advancement of science down to the early quantum theory.
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[F1.2]
L. Lederman and D. Teresi, “The God Particle: If the Universe Is the Answer, What Is the Question?”, Dell. This book provides a history of particle physics starting from Greek philosophers down to modern quantum physics.
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[F1.3]
G. Smoot and K. Davidson, “Wrinkles in time,” Harper. This book discusses modern cosmology in a simple way.
Exercises
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1.
The Universe. Find a dark place close to where you live, and go there in the night. Try to locate the Milky Way and the Galactic center. Comment on your success (or insuccess).
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2.
Telescopes. Make a research on the differences between Newtonian and Galileian telescopes; discuss such a difference.
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3.
Size of an atom. Explain how you will be able to find the order of magnitude of an atom size using a drop of oil. Make the experiment and check the result.
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4.
Thomson atom. Consider the Thomson atom model applied to a helium atom (the two electrons are in equilibrium inside a homogeneous positive charged sphere of radius \(r \sim 10^{-10}\) m).
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(a)
Determine the distance of the electrons to the center of the sphere.
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(b)
Determine the vibration frequency of the electrons in this model and compare it to the first line of the spectrum of hydrogen.
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(a)
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5.
Atom as a box. Consider a simplified model where the hydrogen atom is described by a one dimensional box of length r with the proton at its center and where the electron is free to move around. Compute, taking into account the Heisenberg uncertainty principle, the total energy of the electron as a function of r and determine the value of r for which this energy is minimized.
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6.
Cosmic ray fluxes and wavelength. The most energetic particles ever observed at Earth are cosmic rays. Make an estimation of the number of such events with an energy between 3 \(\times 10^{18}\) and \(10^{19}\) eV that may be detected in one year by an experiment with a footprint of 1000 km\(^2\). Evaluate the structure scale that can be probed by such particles.
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7.
Energy from cosmic rays: Nikola Tesla’s “free” energy generator. “This new power for the driving of the world’s machinery will be derived from the energy which operates the universe, the cosmic energy, whose central source for the Earth is the Sun and which is everywhere present in unlimited quantities.” Immediately after the discovery of natural radioactivity, in 1901, Nikola Tesla patented an engine using the energy involved (and expressed a conjecture about the origin of such radioactivity). As below, we show a drawing (made by Tesla himself) of Tesla’s first radiant energy receiver. If an antenna (the higher the better: why?) is wired to one side of a capacitor (the other going to ground,) the potential difference will charge the capacitor. Suppose you can intercept all high-energy cosmic radiation (assume 1 particle per square centimeter per second with an average energy of 3 GeV); what is the power you could collect with a 1 m\(^2\) antenna, and how does it compare with solar energy?
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De Angelis, A., Pimenta, M.J.M. (2015). Understanding the Universe: Cosmology, Astrophysics, Particles, and Their Interactions. In: Introduction to Particle and Astroparticle Physics. Undergraduate Lecture Notes in Physics. Springer, Milano. https://doi.org/10.1007/978-88-470-2688-9_1
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