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CHAPTER 7

CHAPTER 7

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Theoretical Physics

We often use the terms ‘‘mathcmatical physics” and ‘‘theoretical phy_S-ics” intcrchangcably, but Mach did not, and in terms of his under-standing of the distinction thcrc was a sense in which hc did not believe in theoretical physics at ąlj. If the purposc of science (the “irT ternal” purposc) was merely to describc and relate the appcaranccs in the simplest way possiblc, which for Mach was by mcans of mathe-matical functions, then “theories” would sccm to have at best merely “provisional value.” ¹ EvcntuaIIy, the discovcry of the most suitablc mathcmatical functions would make all theories superfluous and pre-sumably theoretical physics as wcll. Mach was an expciimcntal physi-cist who wished to rcdircct mathcmatical physics from the description of theories to the direct description of naturę, but in order to show the inadcquacies of theoretical physics, he found it ncceessary to rcad through the subject in detail. Out of this effort camc a number of books on the history of different branches of physics and a number of contributions to theoretical physics. But we should not mislcad oursclves with rcspect to his primary motivation. Hc aimed to make all physics expcrimental in method and mathematical (sans theory) in end rcsult.*

Robert Mayer formulatcd his vcrsion of the law of the conscrvation of cnergy in 1842. James Joulc, Von Helmholtz, and Lord Kclvin each cont/ibuted an csscntial part to the generał acceptancc of this major addition to theoretical physics. Rudolf Clausius put forward the second law of thermodynamies in 1850 and latcr refined it with the notion

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Theoretical Physics

that the amount of "entropy" in the univcrse (the amount of heat dividcd by its absolutc temperaturę) incrcased in irrcvcrsible trans-formations. Mach did not so much oppose thcsc laws, providcd that they could be put in strict mathcmatical form, as rcjcct the attempt of Mclmholtz and Clausius to understand them as mechanical theories ^: or as mathematical formulas rccjuiring mcchanistic cxplanation in terms of atoms and moleeules.

Mach argucd in his Consereation of Energy (ij^a) that the first law of thermodynamies had two forrm: a mathcmatical form and the vcrbal notion that "It is impossiblc to crcate work out of nothing, or to construct a perpetuum mobile.'' I Ic further argucd that this second or nonmathcmatical vcrsion of the "law of the conservation of work," as hc preferred to cali it, first, had bccn known from the carlicst times; sccond, was merely a form of the law of causality (i.c., when under-stood in terms of "functional rclations"); third, had bccn known be-fore the devclopmcnt of mcchanics; and fourth, was logically morę fundamcntal than mcchanics. Mach belicved that mechanics was no morę basie to physics than optics, acoustics, elcctricity, magnetism, or heat theory, that its historical priority was only accidcntal, and that bccausc the atomie theory sccmed to havc somc transient value in mcchanics was no cvidenrc that cither mcchanics or the atomie theory had necessary relevance or value in the other branches of physics, par-licularly in thermodynamies.

Mach endcd his book with a finał rather poctical attack on theoretical physics. "The object of natural science is the connexion of phenomena, but theories are likc dry leaves which fali away when they havc ccascd to be the lungs of the tree of science.” ³

But while Machs division of physics resembled that of the nature-philosopher Friedrich Schclling in his attempt to have each branch study a difTerent typc of sensory object, noneiheless, there wcrc am-biguitics that mirrored the influence of practical considerations. When Mach was philosophically consistent he denied that "elcctricity” was a separate field, and argued that it was a merc inclusive label that cov-crcd quite diverse "thermal,” “optical,” and “chcmical” phenomena But in other morę practical moments hc allowed that it was a separate field. Also, hc sometimes treated “mechanics” merely as "the study of motion," as if other branches of physics were not conccrned with mo-tion, but needless to say, he found it hard to follow consistcntly such a point of vicw. Also, when in this particular phenomenalistie or

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