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David Nightingale: Ernst Mach (1838 – 1916)

Ernst Mach, 1902
H. F. Jütte
Public Domain, Wikimedia.org

Everyone has heard of a fast plane having its speed described in terms of its Mach number. Mach 2, for example, means twice the speed of sound in air, Mach 3 is three times, and so on.

Mach has been described as philosopher, psychologist, physiologist and freethinker – as well as a fighter against fanatical nationalism and anti-Semitism [ref.1, pp.3-4].

Giving him his full name, Ernst Waldfried Josef Wenzel Mach was born in 1838 in a part of Austria that is now part of the Czech Republic, and attended the University of Vienna, earning a Ph.D. in physics.

Einstein said in his obituary for Mach in 1916, “I believe even those who consider themselves opponents of Mach are hardly aware of how much of Mach’s way of thinking they imbibed – so to speak, with their mother’s milk.” And Einstein later wrote that Mach’s book on mechanics had “exercised a profound influence” on him [ref.1, p.1].

So what did Mach do? He is probably best known for making the famous 1887 shadowgraph and photograph of the waves around a speeding bullet. Everyone has seen the V-shaped waves from a boat traveling faster than the actual speed of water waves, and the bullet example is similar except we are dealing with sound waves in air.

A shadowgraph, by the way, is what you see on a white screen behind, for example, the hot air rising from a cookout – the key point being that although one can’t see different air temperatures, the light is refracted differently, giving rise to patterns on the screen.

Mach wasn’t ‘just a physicist’. His book “The Analysis of Sensations” (the first of 5 editions) was published in 1885, and later in English in both England and America. In it, he discusses the difference between “appearance” and “reality” and discusses  how a pencil in water looks bent – obviously not reality, and how a sample of dark fabric separated from a slightly lighter sample thought to be the same actually looks darker when the two are brought close. These latter effects are called “Mach bands,” and he tried to explain it with reference to adjacent cells in our retinas.

Another example Mach is famous for is usually called “Mach’s Principle” – that many characteristics of the here-and-now come from the outside universe as a whole. Although this smacks of astrology he was not an astrologer, and, specifically, he put forth some famous “thought” examples concerning the universe. One of these occurred to him, it is said, while walking past a mill wheel in the country. What, he wondered, if a swinging pendulum were put inside a massive hollowed mill wheel – representing the universe – would the rotating mass slowly change the plane of the pendulum’s swing?  Experimenters have so far been unable to detect any of the predicted minuscule results. We say “predicted” because later, Einstein was able to put Mach’s principle onto a solid mathematical footing [ref.2].

Mach is also known for a bad mistake. In 1897, after attending a lecture by Boltzmann, he exclaimed “I don’t believe that atoms exist!”

But such an extraordinary error should not negate all the positive work that he did. Today, one can see “Mach diamonds,” which are bunched-up shock waves behind a jet fighter, particularly if there is an after-burner, and in astronomy it is believed that some quasars emit knots of these Machian shock diamonds.

Finally, Einstein was indeed one of Mach’s most fervent admirers – despite the fact that later the admiration was not really mutual. Mach, a thinker but not a mathematician, didn’t care for relativity. 


1.  “Science and Anti-Science”, by Gerald Holton; Harvard University Press, Cambridge Massachusetts, and London England.

2.  “Specific physical consequences of Mach’s Principle”, by J. David Nightingale; American J. of Physics, Vol45/4, April 1977.

David Nightinglale is an emeritus professor of physics at SUNY New Paltz where he taught for 31 years. His first novel, The Centauri Settlement, is produced by TheBookPatch.com .

The views expressed by commentators are solely those of the authors. They do not necessarily reflect the views of this station or its management.

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