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Summary Article: Mach, Ernst (1838-1916)
From The Hutchinson Dictionary of Scientific Biography

Place: Austria

Subject: biography, physics

Austrian physicist whose name was given to the Mach number, the velocity of a body in a medium relative to the speed of sound in that medium. Mach also made an important contribution to science in a fundamental reappraisal of scientific thought. He sought to understand knowledge in the context of the physiological, sensory, and psychological processes that govern and limit its acquisition. This led him to question mechanical explanations of matter and the universe that could not be adequately observed, and to favour more conceptual or mathematical explanations. This approach to science had a profound influence on Albert Einstein in the formulation of the general theory of relativity.

Mach was born in Turas, then in Austria-Hungary but now in the Czech Republic, on 18 February 1838. His family moved to Unter Siebenbrunn near Vienna in 1840. He was almost entirely educated at home by his parents until the age of 15, when he entered the local Gymnasium. He was most impressed by the study of natural science and, in particular, enjoyed the lessons of his teacher of natural history, a man named F X Wessely. Mach began his studies at the University of Vienna in 1855 and was awarded his PhD in 1860 for a thesis on electricity. While in Vienna he was influenced by Gustav Fechner (1801-1887), who worked on ‘psychophysics’ or the physiology of perception.

Mach lectured at the university, and also earned extra money by giving popular lectures on a variety of scientific topics. He published two books in 1863, one on physics for medical students and the other on psychophysics. He moved to Graz in 1864 where he became professor of mathematics and, in 1866, professor of physics. He then went to the University of Prague in 1867, where he was appointed professor of experimental physics.

Mach remained in Prague for 28 years, conducting many research projects and publishing many books and lectures. He served as rector to the university 1882-84. In 1895 he became professor of history and theory of inductive sciences at the University of Vienna. He suffered a stroke in 1897, which paralysed his right side and from which he made only a slow recovery. He retired from the university in 1901, and was appointed to the upper chamber of the Austrian parliament, a post he held for 12 years. In 1913, Mach moved to his son's home in Vaterstetten, near Munich, Germany. He continued to write books and died there on 19 February 1916.

Mach's early work in Vienna was in the department of Andreas von Ettingshausen, who had succeeded Christian Doppler as professor of experimental physics. Accordingly, Mach's research was aimed at investigating Doppler's then controversial law describing the relationship between the perceived frequency of sound and light and the motion of the observer relative to that of the source. Mach also investigated vibration and resonance. His interest in subjects that his colleagues saw as being only of peripheral interest, such as perception, was active even in these early days. His book on psychophysics, published in 1863, examined the complex physiological problems associated with vision and Mach concluded that the reductionist mechanistic approach had not given satisfactory explanations of phenomena.

At Graz, Mach was forced to fund his research out of his own pocket and, lacking equipment for investigations into physics, he continued to study subjects such as vision, hearing, and our sense of time. He investigated stimulation of the retinal field with spatial patterns and discovered a strange visual effect called Mach bands. This was subsequently forgotten, and was rediscovered in the 1950s.

In Prague, Mach was able to turn to issues of a more physical nature. He made a long theoretical study of mechanics and thermodynamics. He did not, however, abandon his other interests. Among his projects were a study of the kinesthetic sense and how it responds to body movements, more work on Mach bands, investigations of hearing and vision, various aspects of optics, and wave phenomena of mechanical, electrical, and optical kinds. One of Mach's most important contributions arose from his work, published in 1887, on the photography of projectiles in flight, which showed the shock wave produced by the gas around the tip of the projectile. The Mach angle describes the angle between the direction of motion and the shock wave, and Mach found that it varies with the speed of the projectile, the flow of gas changing its character when the projectile reaches the speed of sound. This came to be very important in aerodynamics and particularly in supersonic flight, and in 1929 the term ‘Mach number’ came into use to describe the ratio of the velocity of an object to the speed of sound in the medium in which the object is moving. An aircraft flying at Mach 2 is therefore flying at twice the speed of sound in air at that particular height.

Mach's philosophy of science - although he would never have described it in those terms, feeling himself to be a scientist and not a philosopher - included an investigation of modern science based on an analysis of the sequence of previous developments. He felt that the very order in which discoveries had been made altered their content and that this was an important factor to bear in mind when assessing their value and meaning. Mach was very suspicious of any model that could not be tested in at least an indirect fashion. Because they could not be observed, he was forced to reject the theory of atoms (which was in his day quite inaccurate, but became less crude towards the end of his life) as being merely a hypothesis that had got out of hand. He was considered quite eccentric by many of his colleagues for whom atomism was an exciting development. However, it subsequently became increasingly difficult to explain atoms as concrete objects, and theoretical physicists turned to mathematical and statistical treatments of the energies and positions of atomic particles to obtain more valid descriptions of the atom; Mach can, therefore, be said to be vindicated in his approach and his views did in fact aid the development of quantum mechanics.

One of Mach's most important books was Die Mechanik (1863). This gave rise to an enduring debate on Mach's principle, which states that a body could have no inertia in a universe devoid of all other mass as inertia depends on the reciprocal interaction of bodies, however distant. This principle influenced Einstein who tried to find a mathematical formulation to describe it, and it played a role in Einstein's thinking that culminated in his explanation of gravity in the general theory of relativity.

Mach was greatly displeased to find that he was being hailed as a predecessor of relativity, a model he rejected. He intended to write a book criticizing Einstein's theory, but died before this was possible.

Mach postulated that all knowledge is mediated by perception, and believed that the greatest scientific advances would only arise through a deeper understanding of this process. His stubborn scepticism forced him into a somewhat isolated position, but he was subsequently respected by scientists as great as Einstein. Mach is remembered as a scientist skilled not only at experimental design, execution, and interpretation but also at thinking about the wider implications of his work - a rare quality.

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