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CHAPTER 17

Did Mach Finally Acccpt Einstein s Theory of Rclatiińty?

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Ernst Mach not only admitted that one could postulatc a space of morc than thrcc dimensions, but as a young scicntist, hc had cven anticipatcd Ricmann in dcscribing such a geometry.¹ The point was that whilc one could mathcmatically construct multidimcnsions, the sensory world, or what Mach as a presentationalist considcrcd the cxtcrnal world, could ncvcr havc morc than the thrcc dimensions of simplc geometry. Machs book Space and Geometry, which was pub-lished in 1906, cxprcsscd this point in very elear language.

Seldom have thinkers becoinc so absorbed in rcvcry. or so far estranged from reality, as to imaginc for our space a number of dimensions exceeding the thrcc of the giycn space of sense, or 10 conccivc of rcprćscritTńg that space by any geometry that dcpartTapprcciably from the Euclidcan. Gauss, Lobachcvski, Bolyai, and Ricmann wcrc pcrfcctly elear on this point, and . cannot be hcld responsiblc for the grotcsquc fictions which were subsc ijucntly constructcd in this domain.²

Di (i Mach Finally Acccpt lii ns tętn's Theory oj Re lal i A ty?

Mach pubiished thrcc vcry brief rcfcrcnces to Minkowski (1909-1910). One linked Minkowski wirh Machs cpisremological theory of rclativity, one praiscd him for hclping to clarify Mach’s distinction betwccn "metric” and "physicar space, and one complimentcd him on approaching Mach's position that space and timc wcrc still probiems. There was no real mention of Minkowski’s four-dimensional theory at all.

In point of fact, howcver, Mach W3S wcll acquainted with four-dimensional theories and tendcd to havc a prejudicc against them.^ł Somc ycars earlier (1878-1881) the '‘scicntist," Johann Karl Friedrich Zollncr, had deposited four works in the local University of Lcipzig “Transactions.” Two titlcs wcrc: History of the Fourth Dimension (1879) and Nut unii Science and Christian Ret/elation: A Popular Con-tribution to the History of the Fourth Dimension (1881).⁵ Professor Edwin G. Boring wrotc on the scandal:

[Hclmholtz] . . . raised the qucstion as to what geometry would be dcveloped by bcings who livcd in another kind of space than ours. There might, for examplc, be “sphcrc dwcllers.” . . . Bcings who lived in an cgg-shaped surface. . . . Dwellcrs in a pseudosphere. . . . So cffcctivcly wcrc thcsc picturcs drawn that in ccrtain limited circles they bccamc the voguc of the timc. Zollncr, the astronoincr at Lcipzig, carne out with the theory that space must be curvcd and linitc (a theory that has a modern ring), or elsc, hc said, sińce timc is finite, all matter would alrcady havc bccn volatilizcd. This theory is intereSting, but thcrcaftcr Zollncr was drawn into a considcration of the pcrtormanccs of the great American medium, Slade. ... As has always bccn the casc when psychic research is in qucs-tion, the rcsult was a violcntly cmotional and personal controvcrsy. Heim holtz was criticizcd as having laid the ground for a gr*»at scicntihc scandal. One of IIclmhohz's accuscrs was even dismissed from Berlin on account of the naturę of the accusations.⁶

Mach nęver did publish an opinion spccifically on the soundness of Minkowskis theory, but his own writings of 1906 and his memorics of the Zbliner scandal lcavc no doubt that Mach no morc favorcd the positivc vicws of Minkowski than hc earlier had the opinions of any of his other negntive allies.⁷

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One of the great liopcs of science at the turn of the century was to relatc gravitation and clcctromagnctism. Since the work of Hem

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wo years latcr, on September 21, 1908, Hermann Minkowski chal-lenged Mach’s view by giving a well-publicizcd lecturc on his theory of four dimensions. Mach reactcd by sceking a copy of the lecture and making a determined effort to understand Minkowski’s argument.³ Hc soon decidcd to kcep silcnt about difTercnccs and treat Minkowski as a ncgativc ally as he had donc carlicr with Ostwald, Dricsch, and

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HacckcI, that is, as a man who opposcd much that Mach opposcd but 1 who hcld different positive vicws. In particular, Mach appreciated

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Minkowski’s implied attack on Newtonian "absolutc" space and time, two fundjrncnt.il pillars of "classical” mcchanics.