The Physics Book

DK

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First annotation on Jul 20th, 2025. Last on Jul 25th, 2025.

Chapter 10

Notions of time, distance, and acceleration are fundamental to an understanding of motion. Newton argued that space and time are entities in their own right, existing independently of matter. In 1715–1716, Leibniz argued in favor of a relationist alternative: in other words, that space and time are systems of relations between objects.

Chapter 11

"Nonsense will fall of its own weight, by a sort of intellectual law of gravitation. And a new truth will go into orbit." Cecilia Payne-Gaposchkin British–American astronomer

Chapter 15

Between 1827 and 1833, Irish mathematician William Rowan Hamilton expanded on Lagrange's work and took mechanics to a new level. Drawing on the "principle of least time" in optics, first proposed by French mathematician Pierre de Fermat in the 17th century, Hamilton developed a method to calculate the equations of motion for any system based on a principle of least (or stationary) action. This is the idea that objects, just like light rays, will tend to move along the path that requires the least energy. Using this principle, he proved that any mechanical system could be described by solving it with a mathematical method similar to identifying the turning points on a graph.

Chapter 17

The variables of temperature, volume, pressure, and entropy seem to only be averages of microscopic processes involving innumerable particles. The transition from microscopic huge numbers to a singular macroscopic number was achieved through kinetic theory. Physicists were then able to model complex systems in a simplified way and link the kinetic energy of particles in a gas to its temperature. Understanding matter in all its states has helped physicists solve some of the deepest mysteries of the universe.

Chapter 25

In 1865, Clausius introduced the word "entropy" (coined from the Greek for "intrinsic" and "direction") to sum up the one-way flow of heat.
His definition contained the first mathematical formulation of entropy, though at the time he called it "equivalence value," with one equation for S (entropy) for open energy systems and another for closed systems. An energy system is a region where energy flows—it could be a car engine or the entire atmosphere. An open system can exchange both energy and matter with its surroundings; a closed system can only exchange energy (as heat or work).

Chapter 45

In effect, the string produces a wave with a wavelength that is twice its own length and a frequency determined by the wavelength and the tension in the string. This is known as the fundamental tone or "first harmonic"
Standing waves of shorter wavelengths, known as "higher harmonics," can be created by "stopping" a string (holding or limiting its movement at another point on its length)
The "second harmonic" is produced by stopping the string precisely halfway along its length. This results in a wave whose entire wavelength matches the string length—in other words, the wavelength is half and the frequency double that of the fundamental tone.
Even if two notes have the same pitch, their sound depends on the shape of their waves. A tuning fork produces a pure sound with just one pitch. A violin has a jagged waveform with pitches called overtones on top of its fundamental pitch
The difference between the second and third harmonics was important. Equivalent to a 3:2 ratio between the frequencies of vibrating waves, it separated pitches (musical notes) that blended together pleasingly, but were also musically more distinct from each other than harmonic notes separated by a whole octave.
The 3:2 ratio defined the fifth of these steps, and became known as the "perfect fifth."
For Pythagorean philosophers, the realization that music was shaped by mathematics revealed a profound truth about the universe as a whole. It inspired them to look for mathematical patterns elsewhere, including in the heavens. Studies of the cyclic patterns in which the planets and stars moved across the sky led to a theory of cosmic harmony that later became known as the "music of the spheres."
Another long-standing musical misunderstanding passed down from the Pythagoreans was their claim that the pitch of a string had a proportional relationship to both its length and to the tension at which it was strung. When Italian lute-player and musical theorist Vincenzo Galilei (father of Galileo) investigated these supposed laws in the mid-16th century, he found that while the claimed relationship between length and pitch was correct, the law of tension was more complex—the pitch varied in proportion to the square root of the tension applied.