Ernst Mach

Ernst Mach (February 18, 1838 to February 19, 1916) was an Austrian physicist and philosopher of science. As an experimenter he worked on sound, on the sense of motion, on the perception of light and, with Peter Salcher, on the shock waves of supersonic bullets. The ratio of a speed to the speed of sound is called the Mach number in his honor; so are the bands of exaggerated brightness at the edges of gray steps, and a loosely worded principle about inertia. As a philosopher he held that science should be an economical summary of observations and that any concept it could do without was suspect. He applied the test to Newton's absolute space and to atoms. Among the scientists who doubted atoms he is the best known, which is why he appears in the account of how Jean Perrin and others settled the question in Molecular reality (history of science).^[1]

Mach was born in Chirlitz, now a district in the south of Brno, and his family moved in 1840 to a farm in Untersiebenbrunn, northeast of Vienna. He went to the Benedictine gymnasium at Seitenstetten and then to the University of Vienna. His doctoral dissertation (1859), written with two colleagues, was on electrical discharge and induction.^[1]

He was professor of mathematics at Graz from 1864 and of physics from 1866. In 1867 he was appointed to the chair of experimental physics at Prague, where he stayed until 1895 and served twice as rector, in 1879 to 1880 of the undivided university and in 1883 to 1884 of the German one. His son Heinrich, a chemist with a new doctorate, killed himself in September 1894. In 1895 Mach took a chair in Vienna, in the history and theory of the inductive sciences, a philosophy post. In July 1898 he had a stroke on a train that paralyzed the right side of his body for good. He retired in 1901, and his son Ludwig helped him with his daily needs and his experiments. In 1913 he moved to Vaterstetten, near Munich, and he died there on February 19, 1916, the day after his seventy-eighth birthday.^[1]

Mach entered sensory physiology, by his own later account, because experiments there needed no costly equipment.^[1] In 1873 he and the physician Josef Breuer, working separately, concluded that the semicircular canals of the inner ear detect rotation through the movement of the fluid inside them.^[2]

His best-known result in vision came from a spinning disc. Between 1865 and 1868 he published a four-part study of how the spatial distribution of light on the retina shapes what is seen. It began, in his words, with "rotating discs endowed with black and white sectors": he "casually noted a phenomenon which, as I pursued it, led me to a more general law of physiological optics."^[1] Where a gradual ramp of brightness meets a flat region, a bright band appears at the lighter end of the ramp and a dark band at the darker end, although the measured light has no such feature. Optical illusions were usually explained as errors of judgment. Mach concluded that this one was rooted in the physiology of the retina.^[1]

Physiologists found the mechanism in the 1950s. Haldan Keffer Hartline and Floyd Ratliff recorded from the eye of the horseshoe crab Limulus and showed that each receptor is inhibited by its neighbors, so that a receptor at a bright edge fires more than one in the middle of a bright field and a receptor at a dark edge fires less. Ratliff, who wrote a book on Mach bands (1965), also studied Mach's work as history.^[3] Hartline shared the 1967 Nobel Prize in Physiology or Medicine with Ragnar Granit and George Wald "for their discoveries concerning the primary physiological and chemical visual processes in the eye".^[4] That put the mechanism in the retina, as Mach had argued.

In the 1870s Mach analyzed the blast produced by electric sparks. He and his students found that the soot patterns that showed the motion of air were produced by any explosion, and that the waves traveled at about the speed of sound or faster. In the 1880s he and Peter Salcher combined a schlieren apparatus of the type devised by August Toepler with photography and captured the cone of compressed air at the nose of a projectile in flight. They called it the head wave, and related the shape of the cone to the ratio of the speed of the bullet to the speed of sound.^[1] Their paper appeared in 1887.^[5] For a bullet at a speed of Mach 2 the half-angle of the cone is 30 degrees, since its sine is the reciprocal of the Mach number. His son Ludwig modified an interferometer in the early 1890s, and the arrangement is now called the Mach-Zehnder interferometer, after Ludwig Mach and Ludwig Zehnder.

Mach never heard the term. The Swiss engineer Jakob Ackeret proposed the name "Mach number" in a lecture in 1929, thirteen years after Mach's death.^[6]

Die Mechanik in ihrer Entwickelung (1883), translated as The Science of Mechanics, was a history of physics written to expose concepts that had hardened into dogma. Mach defined mass without asking what a body is made of: two bodies have equal mass if, acting on one another, they produce equal and opposite accelerations. Of that definition he wrote that it had "simply designated, or named, an actual relation of things".^[1] He was equally unwilling to accept Newton's absolute space, the fixed frame against which a rotating bucket of water is supposed to show its rotation by the curve of its surface.

Albert Einstein, who read Mach as a young man, called one idea drawn from this critique "Mach's principle" in a paper of 1918: that inertia is a product of interaction with other matter in the universe.^[7] Mach did not state it in that form, and physicists have not agreed on one since. Hermann Bondi and Joseph Samuel listed eleven versions in 1997, numbered Mach₀ to Mach₁₀. Two of them, they found, give "diametrically opposite predictions" when applied to a simple physical situation. "By popular usage Mach's principle has acquired a range of meanings, some of which are in conflict with each other."^[8]

Mach's objection to atoms began in the early 1870s and was a form of Occam's razor. A description that can do without unobservable entities should not credit them with the properties of visible bodies, and until it does, atoms are "pure things of thought", like absolute space.^[1] The story that Ludwig Boltzmann told of the disagreement, and what Boltzmann made of it, is in the article on molecular reality, as is what he purportedly told Einstein in 1910, that atoms might be allowed as a way to organize appearances. The question "Have you ever seen one?" is attached to him in popular retellings. The statement that is documented is the one Boltzmann reported from a meeting of academicians: "I do not believe that atoms exist."^[a]

Recent scholarship reads the position as less simple. Erik Banks has argued that Mach sometimes called atoms by definition things in themselves, inaccessible to any experiment, and that his skepticism came from preferring his own theory of "elements" as the fundamental constituents of the world.^[1] A study of Mach's last notebook suggests that soon after Max Planck's attack on his philosophy in 1909 he threatened to leave physics if belief in atoms were required.^[9]

A preface to Mach's Principles of Physical Optics, dated July 1913 and published by Ludwig in 1921, five years after his father's death, rejects the theory of relativity and says that Mach is not its forerunner. It was long read as Mach's repudiation of Einstein's use of him. In a book of 1987 the philosopher Gereon Wolters argued that Ludwig Mach wrote the preface himself, and cited a letter of May 1914 to Joseph Petzoldt in which Mach speaks well of Einstein's work.^[10][11]

Einstein credited Mach as a forerunner of relativity for his criticism of absolute space and time.^[1] Lenin attacked "Machism" in Materialism and Empirio-Criticism (1909). The Vienna Circle published its manifesto in 1929 under the auspices of the Verein Ernst Mach, an association founded shortly before.^[1] The version of Mach as a phenomenalist who reduced physics to sensations spread through these readers, and the Stanford Encyclopedia of Philosophy describes recent work as correcting it.^[1]

Erwin Müller's field ion microscope resolved individual atoms at the tip of a tungsten needle in 1955, thirty-nine years after Mach's death.^[12]

• Molecular reality (history of science)
• Ludwig Boltzmann
• Jean Perrin
• Brownian motion
• The Seeing Eye
• Evolution of the eye
• History of the microscope