Einstein

Thomas Ryckman

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351707893
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

Albert Einstein (1879–1955) was the most influential physicist of the 20th century. Less well known is that fundamental philosophical problems, such as concept formation, the role of epistemology in developing and explaining the character of physical theories, and the debate between positivism and realism, played a central role in his thought as a whole.

Thomas Ryckman shows that already at the beginning of his career - at a time when the twin pillars of classical physics, Newtonian mechanics and Maxwell's electromagnetism were known to have but limited validity - Einstein sought to advance physical theory by positing certain physical principles as secure footholds. That philosophy produced his greatest triumph, the general theory of relativity, and his greatest failure, an unwillingness to accept quantum mechanics. This book shows that Einstein's philosophy grew from a lifelong aspiration for a unified theoretical representation encompassing all physical phenomena. It also considers how Einstein's theories of relativity and criticisms of quantum theory shaped the course of 20th-century philosophy of science.

Including a chronology, glossary, chapter summaries, and suggestions for further reading, Einstein is an ideal introduction to this iconic figure in 20th-century science and philosophy. It is essential reading for students of philosophy of science, and is also suitable for those working in related areas such as physics, history of science, or intellectual history.

Part I

Quantum theory

Two

On the road to Planck 1900

“We consider, however – this is the most essential point of the whole calculation – [the energy] E to be composed of a very definite number of equal parts and use thereto the constant of nature h = 6.55 × 10⁻²⁷ erg-sec. This constant multiplied by the frequency ν … gives us the energy element, ε”.

Max Planck, lecture of December 14, 1900¹

Introduction

At least by 1850, nearly all physicists had abandoned the theory of Lavoisier, Laplace, and Gay-Lussac that heat was a special type of substance caloric, an imponderable fluid passing from one body to another. In its place came a revival of the ancient atomist idea that heat is attributable to the motions of very small bodies. Though the doctrine that all matter is composed of tiny indivisible material (“ponderable”) particles remained controversial, in the late 1850s the concept of kinetic atom gained acceptance. These invisible “spheres of action” were regarded in various ways: as mental fictions or heuristic devices, as centers of repulsive forces or as physically real tiny indivisible particles. Possessing minimal material properties of size and motion, the kinetic atom became the central concept of the kinetic theory of heat, that a body’s temperature is a measure of the kinetic energy, or energy of motion, of its hypothetical microconstituents. Emil Wiechert’s and J.J. Thomson’s 1894–1897 discovery of electrons, “atoms of charge”, led by the turn of the century to the first models of an electrically neutral atom, a composite structure whose stability was explained by the attraction of oppositely charged constituent particles. Maxwell’s electromagnetic theory, spectacularly confirmed by Hertz’s wireless experiments in 1887, implied that charged moving bodies emit electromagnetic radiation. Lying at the intersection of the kinetic theory of heat and Maxwell’s theory are the phenomena of thermal radiation, electromagnetic radiation generated by the vibrational motions of charged particles in bulk matter. Investigations of thermal radiation in the last decades of the 19th century led to the quantum theory.

On the joint basis of Maxwell’s theory and the kinetic theory, in the autumn of 1900 Max Planck attempted to derive the recent empirically established frequency distribution law of thermal radiation for a so-called blackbody. In so doing, he found he was compelled to introduce the notion of a discrete minimal unit of energy. It is customary to say that Planck thereby “discovered” the quantum. Planck later on modestly described his brainchild as “an act of desperation”, a mathematical stratagem needed to obtain what he knew to be the correct answer. He proved a highly conservative revolutionary – so much so that Thomas Kuhn’s 1978 study of Planck’s reluctant embrace of the physical reality of energy quanta credits Einstein, not Planck, for the birth of the quantum theory. Kuhn argued that the quantum revolution really began with Einstein’s paper of March 1906, pointing out that Planck’s derivation, based on classical theory yet incorporating the above stratagem, was strictly speaking inconsistent. Nonetheless, Einstein observed, the derivation succeeded through implicit use of the non-classical light-quantum hypothesis he himself introduced in 1905. While historians of physics can disagree about the respective merits of Planck or Einstein as father of the quantum revolution (in no small measure due to genuine obscurity concerning what Planck actually believed), there is widespread recognition and general agreement that Einstein played a unique and revolutionary role in advancing and extending the quantum hypothesis, first in the theory of radiation and then pursuing it into the theory of matter.

To appreciate Einstein’s role in creating the “old quantum theory” in the next chapter, it will be useful to first sketch the situation of late-19th-century physical theory that Einstein inherited. This chapter briefly surveys the rise of thermodynamics, the kinetic theory, its application to gases and statistical generalization by Boltzmann, and the developments leading up to Planck’s radiation law. The next concerns how Einstein formulated then wielded what he termed “Boltzmann’s principle” in demonstrating the quantum hypothesis was here to stay. The story here begins with the rise of thermodynamics in the 19th century and subsequently its statistical foundation by Boltzmann.

Historical overview of the concept of energy

The concept of energy has a long history; precursors appear in Greek antiquity and again in the Middle Ages. But it was Leibniz who foreshadowed the modern concept of energy in 1686 with his notion of “living force” (vis viva). In the process he gave rise to a century-long dispute about whether vis viva (mν²) or linear momentum (mν) is the appropriate conserved quantity in mechanics.² The concept of energy is present in all but name in the 18th-century dynamics of d’Alembert and Lagrange, although to them it is not a generally conserved quantity. The general doctrine of energy conservation then emerged in the early 19th century from a combination of factors, among the most important being French engineers’ interest in the theory of machines, the idea that all physical phenomena might be reduced to conservative mechanical processes, and the discovery of the interconvertibility of various forms of energy.

The advent of steam engines in the Industrial Revolution brought a generalization of the energy concept from mechanics to the phenomena of heat and the definition of energy as “the capacity of a physical system to do work”. At the same time heat came to be regarded as a form of energy convertible into work. In a notable 1959 paper on simultaneous discovery in science, Thomas Kuhn pointed to the principle of energy conservation as a prime example.³ Between 1842–1847, a group of researchers, each working largely in ignorance of the others, proposed that within an isolated system different forms of energy might be transformed from one kind to another, but total energy is conserved by these processes. Synthesizing these results in 1847, Hermann von Helmholtz formulated a law of conservation of force (“Kraft”), a term not yet with a univocal meaning though soon to be understood as “energy”. Shortly afterwards, William Thomson, the future Lord Kelvin, coined the term “thermo-dynamics” in 1851 for the new science of the study of the effects of work, heat, and energy on a physical system.

The idea of transformational invariance appears central in establishing the concept of energy; that heat is a form of energy and that the internal energy of a system cannot be created or destroyed but only transformed from one form to another led to the first law of thermodynamics. On the other hand, Ernst Mach, in an influential 1872 monograph on the history of the principle of conservation of energy,⁴ argued that the actual root of the energy concept lay, as Helmholtz had maintained, in the historically attested record of failures to produce a perpetuum mobile, a machine that once started, would continue to run indefinitely without any external input. While this apparently restricts the concept of energy to mechanics, Mach insisted that the prohibition of perpetual motion arose in the course of human experience long antedating mechanics and hence logically distinct from it. Einstein followed Mach in similarly regarding the impossibility of perpetual motion as a “principle”, the indisputable empirical fact underlying thermodynamics.⁵

Kinetic theory

Thermodynamics, a science of the macroscopic properties of matter, developed rapidly in the first half of the 19th century. Its results are largely independent of hypotheses about underlying dynamics and microstructural composition, among which the most influential was physical atomism, a speculative hypothesis pertaining to invisible, indivisible corpuscles.⁶ But from the early 19th-century atomism of another type, the “chemical atomism” (1808–1810) of John Dalton (1766–1844), was quickly accepted as it proved successful in explaining the respective weights of chemical elements in compounds. If chemistry suggested the existence of atoms of the chemical elements, the experimental data represented in the gas laws due to Boyle (1627–1684) and Mariotte (1620–1684) showing that the pressure of air is proportional to its density, suggested that the elasticity (“spring”) of air is due to the motions of tiny bodies, although Boyle himself was critical of Greek atomism and Mariotte disliked atomism altogether. Molecules of air were assumed in the prototype kinetic theory of Daniel Bernoulli (1700–1782) in 1738. Bernoulli correctly understood that air pressure within a closed cylinder supporting a weighted piston is due to the repeated impacts of vast numbers of rapidly moving “very minute corpuscles”. However, despite Bernoulli’s derivation of Boyle’s law relating the pressure and volume of a gas, there were competing theories of gas pressure and for a considerable time, no agreement on the nature of heat and temperature. Only in 1854 did Kelvin propose a generally accepted absolute temperature scale.⁷ The kinetic-molecular theory remained incomplete. For almost a century, further progress in developing the concept of heat as molecular motion was delayed.

Bonn physicist Rudolf Clausius (1822–1888) formulated the two initial laws of thermodynamics. The first is the principle of conservation of energy that Clausius applied to heat and thermodynamic processes. Expressed in the form of a prohibition, the first law of thermodynamics states the impossibility of a machine that can perform work without modifying the environment, a so-called perpetuum mobile of the first kind. Clausius’s initial version of the second law affirmed that heat cannot pass from a colder to a warmer body without compensation in the environment, as for example by a refrigerator’s compressor. Another formulation, deriving from Sadi Carnot’s 1824 theory of the limits of efficiency of heat engines, is that there is a fixed upper limit to the amount of work obtainable from a given amount of heat. This effectively states the impossibility of a perpetuum mobile of the second kind; namely, the impossibility of building a machine that produces work in a cycle of operation by borrowing heat from a single source (in Kelvin’s formulation). Clausius subsequently gave the second law quantitative expression, in the process introducing the notion of entropy, the most characteristically thermodynamic concept, a more abstract notion lying further away from sense experience than volume or pressure or temperature. Designating entropy by the letter S, Clausius’s quantitative statement of the second law is an inequality holding that the incremental change in entropy in a closed system cannot be negative.⁸

The development of the concept of energy in the 1830s and 1840s and the new thermodynamics around 1850 set the stage for the kinetic theory of gases by the end of the 1850s. In the famous characterization of Clausius, molecular motion is “the kind of motion that we call heat”. Between 1855–1865, Clausius and Maxwell were able to derive the law of perfect gases, assuming molecules freely flying around within a containing vessel except for occasional elastic collisions among themselves and with the walls of the container. Temperature was thereby interpreted as the average or mean kinetic energy (or velocity) of the particles of the gas. In this way the kinetic theory explained the established empirical regularities between the macroscopic thermodynamic quantities in terms of the random motions of molecules.

The next step was to similarly account in kinetic terms for the two laws of thermodynamics, both regarded as exceptionless absolute laws by Clausius. Kinetically, entropy is a measure of the state of molecular disorder in a macroscopic system: e.g., the molecules of a gas within a container may be mostly bunched in one corner (low entropy) or distributed more or less uniformly throughout the container’s volume (high entropy). But the statement that entropy never decreases posed a difficult philosophical problem for the kinetic theory according to which matter is composed of atoms in continual motion and subject to the laws of Newtonian mechanics. The basic equations of mechanics are both exceptionless and time-reversible; they do not change their form in the least if the sign of the time variable is reversed (making the substitution t → − t). As Newton’s second law,

$\overrightarrow{F}=m\overrightarrow{a}=m{d}^{2}x/d{t}^2$

contains the second derivative of the time variable, any solution of Newtonian equations can be transformed into another solution with the time variable reversed and the system re...

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Contents
• Acknowledgements
• Chronology
• Introduction
• One Life and works
• Part I Quantum theory
• Part II Relativity
• Part III Geometry and philosophy
• Glossary
• Index