Ludwig Lange on the law of inertia

Abstract

Ludwig Lange (1863–1936) published in the years 1885–1886 (at the age of 22– 23 years!) three papers on the law of inertia which have to be judged as a stroke of genius because, nearly 200 years after Newton’s Principia, he succeeded in eliminating the concepts of absolute space and absolute time. A particular merit of Lange’s papers is that he clearly analyzed which parts of Newton’s first law are useful definitions and which parts are non-trivial experimental facts, if not wonders of nature, a distinction which is even missing in most modern textbooks on mechanics. (And it should be clear from the outset that any basic law of physics has to contain both definitions – here inertial system, in other cases electric field, temperature, entropy, quantum state, . . . – and new non-trivial facts about nature.) The papers [1] and [2] are quite extended works, containing, besides Lange’s innovative contributions, also historical and philosophical overviews of the law of inertia, the booklet [2] also containing Lange’s PhD-thesis of the year 1886 at the university of Leipzig. The shorter paper [3], translated here, concentrates on Lange’s own contributions and their mathematical foundations. In the year 1902 Lange published again a quite extended analysis [4] of the law of inertia, together with reactions of other authors on his work from 1885–1886; see below. Lange’s main new findings and his results of lasting significance are contained in part I of the paper [3]. In this part he also gives a clear motivation for his work by saying: “Newton’s absolute space is a phantom that should never be made the basis of an exact science”. “To find a fully valid substitute for it is the goal of the following”. The absolute highlight of Lange’s work are his Definitions I and II and his Theorems I and II, and these are also the parts which are later highly praised and often literally quoted by other authors. Lange’s papers obviously are the first place where the nowadays standard terms ‘inertial system’ and ‘inertial timescale’ are introduced into the literature. As Lange freely admits, his Definition II and Law II concerning the inertial timescale owe much to somewhat earlier work by Neumann [5] and Thomson, Tait [6]. Neumann’s work particularly was a decisive stimulus for Lange, as is clear from the quotation: “The question now arises whether it is possible to eliminate also absolute space by a similar procedure [as Neumann’s one]. Indeed this is possible”. Concerning Definition I we like to point to the fact that originally, in [1], Lange tried to base an inertial system on only two points left to themselves. After an objection