Mass and Mechanics

Mach took the opportunity of the footnotes to his lecture to reprint his discussion of the definition of mass, but also to set out an argument that Einstein later christened Mach’s principle. The central point Mach made was that Newton’s first law of inertia was undefined without specifying the actual bodies in relation to which a given body remained at rest or in uniform motion. This usually meant the laboratory, or the fixed stars, and Mach insisted that just because we can usually substitute another room or reference star didn’t mean we could abstract to an idea of motion in absolute space, independent of the particular material bodies through which we always actually form our understanding of coordinate systems. He made his point concrete by discussing rotation. Geometrically there is no difference between whether we consider the earth at rest and the stars spinning around it, or consider the stars to be fixed and describe the rotation of the earth, the relative motion is the same. But the second case is simpler astronomically, and in the ordinary conception of inertia it has a consequence that the first does not: a rotating body is subject to the inertial, centrifugal forces that lead the earth to bulge around the equator, and that explain the complex motions of Foucault’s pendulum. To solve this difficulty you could either consider all motion to be absolute, as Newton and others had done, or recognize that the law of inertia is wrongly expressed. Mach took the latter option, suggesting that what is required for the description of a phenomena should be regarded as part of the causal nexus, and arguing that we have to ask what share every mass has in the determination of direction and velocity in the law of inertia. He thought we forget this given the stability of our normal experience, but if an earthquake were to shake the earth, or the heavens were to swarm in confusion, we would be forced to ask what would become of the law of inertia, how would it be applied and expressed. Similarly, he said, a bankruptcy makes it clear that all money is important to the funding of a paper note (Mach 1911, 75-80).

The first thing I want to emphasize about Mach’s 1872 discussion is its cosmic scale, considering the masses of the universe in earthquake and star-storm and linking the behaviour of each body with the distant masses of the universe through the law of inertia. My second point concerns what Mach’s economic analogy reveals about his general philosophical perspective. His notes told Mach’s readers that since the beginning of his teaching he had stressed that science is chiefly concerned with the convenience and saving of thought; but a highly important corollary to this emphasis on economy was his view that the process of concept formation and abstraction was similar across all areas of thought (Mach 1911, 48, 55, 88). This is something that is often forgotten when historians and philosophers focus on Mach’s insistence on measurability for physical concepts, but it comes across very clearly in the classroom lectures he gave in this period. They illustrate the range of Mach’s thought and the centrality of psychophysics for his approach to physics.

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