Abstract
The evolution of physics from the Renaissance until today could be the subject of a book thousands of pages long. But if a book is intended to help the readers in the “organization” of physics they already know into a “logical” structure, it should be limited to the major branches of this discipline. Furthermore, if this knowledge is of high school level, then necessarily the selection of these important branches should start with “classical” physics, namely that which was known until the late 19th century. As such we have included in this book the mechanics of particles and solids, optics, electromagnetism, heat, thermodynamics, and the theory of perfect gases, because these branches constitute the backbone of classical physics. If some readers are further interested, they can use this knowledge as a “frame” to integrate easily the remaining branches of classical physics, such as acoustics, elasticity, and fluid mechanics. Finally, for completeness, we briefly present the three branches of physics, developed in the 20th century, that constitute the so called “modern” physics, i.e., the theory of relativity, quantum mechanics and the theory of chaos.
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Notes
- 1.
It is worth noting that the assumption that the Sun is the center of the Solar System was originally proposed by Aristarchus of Samos in the 3rd century BC and, much later, pulled from obscurity by Nicolaus Copernicus (1473–1543) and supported by Johannes Kepler (1571–1630), who used Tycho Brahe’s planetary observations (1546–1601). A, somehow, “incomplete” heliocentric theory had been proposed, before Aristarchus, by the Greek natural philosopher Heraclides Ponticus (ca. 390 BC–ca. 310) in the 4th century BC. According to this theory, Sun is orbiting the Earth as the other planets do, except for Mercury and Venus, which are orbiting the Sun.
- 2.
This idea came to him for the first time when observing the oscillations of a chandelier in Pisa’s Cathedral. An interesting point is that Galileo believed that oscillations of any amplitude are isochronous (accurate clocks had not been invented yet). The fact that this is true only for oscillations of small amplitude was realized later, through the use of differential calculus introduced by Newton.
- 3.
The next Pope, Gregory the 15th, remained on the throne for only 2 years.
- 4.
It is worth mentioning that in this book, a discussion is described between a philosopher who supports the heliocentric theory and an Aristotelian philosopher, whose name is Simplicius, a further indication that Galileo was aware of the Philoponus–Simplicius debate.
- 5.
Functions that are locally given by a convergent power series.
- 6.
The complete reference is “I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses”. From Isaac Newton (1726): Philosophiae Naturalis Principia Mathematica, General Scholium, third edition, page 943 of I. Bernard Cohen and Anne Whitman's 1999 translation, University of California Press.
- 7.
It is worth noting that what is varying in the above integral is not the variables x and \( \dot{x} \) but the functions \( \dot{x}(t) \) and \( \dot{x}(t) \). As a result, the integral is not a function but a different kind of mathematical object, called functional.
- 8.
Birefringence is the optical property of a material having a refractive index that depends on the propagation direction of light. Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split into two rays taking slightly different paths.
- 9.
Fraunhofer had invented a new instrument, the spectroscope, which made the recording of spectral lines far more effective.
- 10.
Kirchhoff is best known to high school students from Kirchhoff’s circuit laws (rules), which are used in the calculation of currents in a node of an electrical circuit as well as voltage drops in the elementary loops of a circuit.
- 11.
The dependence of the degree of ionization from temperature and density is given by the famous Saha’s law, which can be found in any standard astrophysics book.
- 12.
It is not consistent with the third law in its strong form, which requires the two forces to be collinear. However, it is consistent with the third law in its weak form, which requires the two forces to be just opposite.
- 13.
Note that heat was not recognized as a form of energy until 1850.
- 14.
It should be noted that one of the equations of this set, known as Ampère’s law, does not refer to the force law between currents, proposed by the great French mathematician, but rather to a theorem he proved in vector calculus.
- 15.
It is important to note that the existence of wave solutions to Maxwell’s equations is due to a term that Maxwell added to Ampère’s law, partly for reasons of symmetry, i.e. on “philosophical” grounds.
- 16.
In science, phenomenology is the organization of scientific research on the basis of classification of observations according to the phenomena and not according to the mechanisms that cause them. A classic example is the phenomenon of supernovae in astronomy, which initially were considered as a single type of celestial objects. Then, it was discovered that there are two, quite different, mechanisms through which a massive star can end up as a supernova—both mechanisms producing the same observed phenomenon, namely, an extremely brilliant “new” star (a “nova”) in the sky.
- 17.
A perfect gas is a gas considered to consist of “hard” point masses that interact only through elastic collisions. Sometimes the term ideal gas is used interchangeably, but usually a perfect gas is a simplified model of an ideal gas. The main difference is that the specific heat at constant V, C V , may be temperature or pressure dependent in an ideal gas, but not in a perfect gas.
- 18.
It should be noted that work and energy are relatively new concepts. Clausius was using the concept of work systematically only since 1850 (see next paragraph); as far as the concept of energy is concerned, although it had been introduced by Young, it was routinely used by Rankin (William John Macquorn Rankine, 1820–1872) at about the same time.
- 19.
Definition of perpetual motion machine: A device that produces work in violation of the thermodynamic principles. More specifically, a perpetual motion machine of the first kind is a machine that produces work without consuming energy (thus, violating the first principle of thermodynamics), while a perpetual motion machine of the second kind is a machine that converts thermal energy to mechanical work with 100 % efficiency (thus, violating the second principle of thermodynamics, see also Sect. 4.5.4).
- 20.
From the Greek word τομή (cut) and the negation “α-” in front of it, i.e. something that cannot be divided (cut) in smaller parts.
- 21.
In a new mathematical model of theoretical physics, named string theory, the “elementary particles” are strings, i.e., one-dimensional objects with a length of the order of 10−35 m, or twenty orders of magnitude (i.e., a hundred billion, billion times) smaller than a proton. This leaves ample room for quarks to have a “structure”.
- 22.
It is worth noting that this pioneering—for that time—result was received with skepticism. Many physicists, including Clausius, thought that all molecules in a gas are moving with the same speed. As we mention in the next paragraph, the correct mathematical form of this function was proved shortly after by Boltzmann, and from then on the function f(v) is known as Maxwell–Boltzmann distribution function.
- 23.
In this case, the cross section is the area of the section of a sphere defined by a plane passing through the center of the sphere.
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Varvoglis, H. (2014). The Major Branches of Physics. In: History and Evolution of Concepts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-04292-3_4
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DOI: https://doi.org/10.1007/978-3-319-04292-3_4
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