1. What the Mach Number Is and Who It Is Named After
The "Mach number" is a value calculated by dividing an object’s speed by the speed of sound at that specific location. If an object moves at twice the speed of sound, it is traveling at Mach 2 [4]. According to records, this term was named after Ernst Mach by the Swiss aviation engineer Jakob Ackeret in 1929 [3]. Since Mach passed away in 1916, the naming happened thirteen years after his death [3].
Ernst Mach was born in 1838 in a region that is now part of the Czech Republic. He served as a professor of experimental physics at Charles University in Prague from 1867 to 1895, during which time he also served as rector twice [1]. Japanese encyclopedias introduce him as a physicist and philosopher who introduced the concept of the Mach number through his research on waves and supersonic speeds [6]. The root of this naming lies in a specific photograph he took.
2. How Schlieren Photography Captured Invisible Air Waves Around Bullets
Bullets fly by in an instant, and air is transparent. A standard photograph cannot capture the waves in the air. To solve this, the Schlieren method was used. This technique was developed by August Toepler between 1859 and 1864. It visualizes differences in air density by converting them into differences in brightness and darkness. Mach used this method to record the shadows of shock waves in photographs [7].
Mach, along with his collaborator Peter Salcher, presented the first photographs of shock waves formed around supersonic bullets to the Vienna Academy of Sciences in 1887 [2]. The experiments were not conducted in Prague, but in Fiume (now Rijeka), with the cooperation of the Austrian Navy [2]. Depending on the source, Salcher is described as either a student or a co-researcher. The photographs showed lines spreading in a V-shape from the tip of the bullet. These lines hold the key to understanding speed.
3. How the V-Shaped Wave Angle Shows a Bullet's Speed
When a bullet travels faster than sound, the angle α between the wave front and the direction of travel is determined by the relationship: sine of α equals the speed of sound divided by the speed of the bullet [2]. Since the result of this division is less than 1, a specific angle is formed. For example, if a bullet flies at twice the speed of sound, sine α equals 1/2, making α 30 degrees. If it flies at three times the speed of sound, sine α equals 1/3, and the V-shape becomes narrower. This angle later became known as the "Mach angle" [2].
It is important to note that "Mach 1" does not always mean the same speed in kilometers per hour. The speed of sound changes depending on the type of gas and the temperature [4]. In Japanese explanations, Mach 1 is listed as approximately 1,225 km/h (about 761 mph) in standard air near sea level, but about 1,060 km/h (about 659 mph) in the stratosphere [4]. This is because sound travels more slowly in the colder air of high altitudes. Therefore, when converting Mach numbers to km/h, one must check the location and temperature.
4. How Mach Also Discovered an Eye Illusion with Gray Shades
In 1865, twenty-two years before the bullet photographs, Mach reported a visual phenomenon. At the boundary where gray shades of different brightness touch, the area near the boundary appears emphasized: the lighter side looks lighter, and the darker side looks darker [5]. Mach speculated that this happens because nerve cells in the retina inhibit each other, a process called lateral inhibition [5]. The gray paint on the paper does not change; rather, the way our eyes process light creates this effect.
Both of Mach’s major works—photographing invisible air waves and documenting the illusion of Mach bands—investigated what it means to "see." One made the invisible visible, while the other revealed that what is visible is not always what is real.
5. How Mach's Questioning of Newtonian Ideas Influenced Einstein
In Newtonian mechanics, time and space were considered fixed, separate from the motion of objects. Japanese encyclopedias note that Mach critically examined these ideas [6]. From this examination came the idea that the inertia of matter has meaning only in relation to other matter in the universe. This concept was later called "Mach’s principle" [1]. The World Encyclopedia states that this idea opened the path to the general theory of relativity [6].
Albert Einstein regarded Mach as a philosophical forerunner to relativity theory. However, there is debate about how Mach viewed relativity theory in his later years [1]. Einstein did not fully adopt Mach’s principle exactly as it was. From 1895, Mach became a professor of "History and Philosophy of Inductive Science" at the University of Vienna. In 1898, he suffered a stroke that paralyzed his right side, and he retired from the university in 1901 [1]. He also opposed the atomic theory prevalent in Vienna at the time, considering atoms to be "thought constructs" that should not be used in physical descriptions unless necessary [1].
6. How to Test the Gray Shade Illusion with Paper and Pencil
You can try this experiment at home. Draw three squares side by side. Shade them with a pencil, layering the graphite one, three, and six times respectively, ensuring the shading is even. Look closely at the boundaries where the three squares touch. Do you see the areas near the boundaries appearing slightly lighter or darker? Next, cover the boundary with your finger. Does the appearance change?
Perception varies from person to person and depends on the paper, so it is not strange if you do not see the effect clearly. If you wish to read more, you can look up the entry for "Mach" in the Japanese Kotobank encyclopedia [6].