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Ernst Mach (1838–1916)

Mach argued that science should confine itself to observable quantities and the relations among them — that atoms, forces, and other unobservable entities are useful fictions, not descriptions of reality. His positivism — the insistence that only sensory experience is real and that scientific theories are economical summaries of experience rather than pictures of a hidden world — shaped a generation of physicists and philosophers. Einstein credited Mach’s critique of absolute space and time as a direct influence on special and general relativity. The logical positivists of the Vienna Circle took Mach as their intellectual ancestor. But Mach’s rejection of the atomic hypothesis — his insistence that atoms were metaphysical constructs rather than physical realities — placed him on the wrong side of the most important empirical question of his era, and his opposition to Boltzmann’s statistical mechanics was the most visible expression of that error.

Life

Born 18 February 1838 in Chirlitz (Chrlice), Moravia (now Czech Republic). His father Johann was a schoolteacher. Educated at the University of Vienna (PhD in physics, 1860). Professor of mathematics at the University of Graz (1864–67), where he conducted early work on the physiology of sensation and on shock waves. Professor of experimental physics at the Charles-Ferdinand University in Prague (1867–95), a long and productive period during which he published on optics, acoustics, mechanics, and the philosophy of science.

In Prague, Mach conducted his best-known experimental work: high-speed photography of supersonic projectiles and shock waves. He demonstrated that a bullet travelling faster than the speed of sound produces a conical shock wave (the Mach cone), and he measured the ratio of the bullet’s speed to the speed of sound — now called the Mach number.

Appointed to the newly created chair of the philosophy of the inductive sciences at the University of Vienna (1895) — a chair created for him, in territory adjacent to Boltzmann’s professorship of theoretical physics, which Boltzmann had held at Vienna since 1894. A stroke (1898) left him partially paralysed; he retired from the chair in 1901. Boltzmann took over the chair in 1903, holding it until his death in 1906. Mach continued writing and corresponding after retirement. Appointed to the Austrian upper house of parliament (1901). Died 19 February 1916 in Vaterstetten, near Munich.

The critique of atomism

Mach’s opposition to the atomic hypothesis was not ignorance or stubbornness; it was a principled philosophical position consistently applied.

The economy of thought. Mach held that the purpose of science is to describe experience as economically as possible — to find the simplest relations among observable phenomena. A theory is a tool for organising experience, not a picture of unobservable reality. Atoms were not observable (in Mach’s time, no one had seen or directly measured an individual atom); therefore, claiming that atoms were real entities rather than convenient abbreviations for macroscopic regularities went beyond what the evidence warranted. The atomic hypothesis might be useful, but usefulness is not truth.

The energeticist programme. Mach was allied with Wilhelm Ostwald and Georg Helm in arguing that thermodynamics should be formulated in terms of energy and its transformations — observable, measurable quantities — without reference to the unobservable motions of hypothetical particles. The debate came to a head at the Lübeck meeting of the German Natural Scientists and Physicians (1895), where Boltzmann defended the kinetic theory against the energeticists. Boltzmann won the scientific argument (the kinetic theory made predictions the energeticist programme could not match), but the philosophical dispute persisted until the experimental confirmation of atoms in the early twentieth century — Jean Perrin’s Brownian-motion experiments (1908–09) and Einstein’s 1905 theoretical analysis of Brownian motion, which allowed the direct calculation of Avogadro’s number from observable phenomena.

Mach never accepted the reality of atoms. Even after the Brownian-motion evidence, he maintained that atoms were hypothetical constructs. He died in 1916, by which time the scientific community had moved decisively to the atomic view.

Mach’s principle and the critique of Newtonian mechanics

Mach’s other major contribution to physics was his critique of Newton’s concept of absolute space.

Newton’s bucket. Newton argued that the curvature of water in a spinning bucket demonstrates the reality of absolute rotation — rotation with respect to absolute space itself, not with respect to any material body. Mach objected: all we observe is the water’s motion relative to the distant stars. If the stars were removed, we would have no way to detect “absolute” rotation. The concept of absolute space is empirically empty — it does no work that relative motion with respect to the distribution of matter in the universe cannot do.

Mach’s principle (the name was given by Einstein): the inertia of a body is determined by the distribution of all other matter in the universe, not by its relation to an absolute space. The principle is not precisely formulated (Mach stated it in philosophical terms, not in equations), and whether general relativity fully incorporates it is debated — Einstein was inspired by Mach but general relativity admits solutions (such as the rotating Gödel universe) that appear to violate the principle. The precise content of “Mach’s principle” remains a topic in the foundations of general relativity.

Perception and psychophysics

Mach was as much a psychologist of perception as a physicist, and several of his contributions in this area still carry his name.

Mach bands. In the 1860s, Mach identified and explained a visual phenomenon: at the boundary between a lighter and a darker region, the eye perceives an exaggerated bright band on the light side and an exaggerated dark band on the dark side — bands that do not correspond to any physical change in luminance. Mach attributed the effect to lateral inhibition in the retina: neighbouring receptors suppress each other’s response, enhancing the contrast at edges. The explanation anticipated the neural mechanisms of edge detection that neurophysiology later confirmed. Mach bands remain a standard topic in vision science and a foundational example of how the nervous system processes sensory information.

The vestibular system. Working in parallel with Josef Breuer, Mach identified the semicircular canals of the inner ear as the organs responsible for detecting rotational motion. His experiments on human subjects in rotating chairs established the relationship between the canals’ geometry and the perception of angular acceleration — work that connected anatomy, physics, and the phenomenology of sensation in a way that exemplified his broader programme.

The Analysis of Sensations (Beiträge zur Analyse der Empfindungen, 1886; expanded editions through 1906) is the synthesis: a sustained argument that the elements of experience — colours, sounds, pressures, spaces, times — are the ultimate data of science, and that the distinction between the physical and the psychological is a matter of the arrangement of these elements, not a difference in their nature. The book made Mach a central figure in the philosophy of mind as well as the philosophy of physics, and it was a direct influence on the Vienna Circle’s phenomenalism and on later sense-data theories in analytic philosophy.

Where Mach stops

The rejection of atoms was principled but wrong. Mach’s epistemological criterion — only the observable is real — was too restrictive: it excluded entities that turned out to be real and measurable by instruments Mach could not have anticipated. The philosophical position was internally consistent (and his insistence on empirical grounding was salutary), but it produced a specific empirical error that he refused to correct even when the evidence shifted. Whether the error discredits the philosophical method or merely shows that the method was applied too rigidly is debated: the logical positivists who claimed Mach as their ancestor refined his criterion (verificationism) and then abandoned it when it proved unworkable; Popper built his falsificationism in explicit opposition to Mach’s positivism.

Mach’s influence on Einstein was real but limited. Einstein credited Mach’s critique of absolute space as a formative influence and attempted to incorporate Mach’s principle into general relativity. But Einstein also rejected Mach’s positivism — the insistence that science should avoid unobservable entities — as too restrictive. The atoms Mach denied were real; the spacetime curvature that general relativity describes is not directly observable in Mach’s sense. Mach’s philosophical framework could not accommodate the physics that his own critique of Newton helped to inspire.

The economy-of-thought view of scientific theories — that theories are tools for organising experience, not descriptions of a reality behind experience — influenced not only the Vienna Circle but also the instrumentalist tradition in the philosophy of science. Whether scientific theories are descriptions of reality (realism) or instruments for prediction (instrumentalism) is a question that Mach sharpened but did not settle, and it remains alive in the philosophy of science.

Mach’s positivism also drew a major attack from outside the Western philosophical tradition. Lenin’s Materialism and Empirio-Criticism (1909) attacked Mach’s philosophy as bourgeois idealism incompatible with dialectical materialism — arguing that Mach’s denial of an objective reality independent of sensation was politically as well as philosophically dangerous. The book made Mach a contested figure in Soviet philosophy for decades, and it established the orthodoxy that Marxist-Leninist epistemology was realist in a way that Machian positivism was not. The episode is a reminder that Mach’s philosophy had political as well as scientific stakes — his insistence that science deals only in sensations, not in an objective material world, was read as a threat by materialisms that required objectivity as a philosophical foundation.

Key works

See also: Boltzmann · Einstein · Carnap · Popper