IMG81

Ernst Mach

thc assignmcni of the number of degrecs of frccdom is detcrmined by thc succcssful rcprcscntation or correct dcscription of thc cxperimental materiał. This proceduro is also charactcristic of Schrddinger's quantum mcchanics. . . .

For both thc moderns and Mach, thc mathcmatical postulatcs of thc cal-culus and of the multiplicity of dimensions, ultimately scrvc to dcscribe what is actually obscrvcd in expcrimcnt, namcly, thc complcxity of linrs in thc spectra of clcmcnts. Therc is no doubt whatsocvcr in my mind, that had Mach livcd to sec the risc of Schródingcr’s theory and thc associatcd non-commutative mathematies, hc would havc elaimed (and with con-siderable justificatton) that thc cjuantum mcchanics of thc atom was mcrely a further substantiation of his doctrinc that mathcmatical physics is an economic ordering of obscrvablc things (c.g. spcctral lines), and that thc w-dimcn$ional space (c.g. six dimensions or degrecs of frccdom for two intcracting clcctrons.) within thc atom has prccisely thc same significancc as his n-dimcnsional space or n-degrecs of frccdom betwccn thc atoms. In both cascs, therc is providcd an cconomical hypothesis capable of embody-ing, in convenient mcchano-mathcmatical form, thc cquations or functions neccssary for providing a satisfactory or correct dcscription of thc obscrvcd spectrum. . . .

If thc present discussion has dcmonstratcd anything at all, it has clcarly shown that we would lxr quite justified in regarding Mach as the father of thc modern quantum mcchanics o: thc atom, so far as thc generał methodology of atomie physics is conccrned.³¹

Mr. Weinberg also added, howcvcr, that Mach himsclf failed to explain linc spectra by mcans of “thc atomie hypothesis” and rejectcd the nccessity of introducing multidimcnsional geometries into physics.³² Indeed, shortly after Mach’s spcculatipn during thc i86os on thc usc of ■'n-dimensions" hc abandoncd and discouraged all further atomie theorizing.

VIII

But if Mach failed whcrc Bohr and his colleagucs succccdcd in rclat-ing linc spectra and the behavior of atoms and moleeules, we still shonld not forget that scveral of Maęh’s ideas, particularly on thc methodology and philesophy of science, havc wormed their way, though admittcdly often in distorted form, into thc vcry cntrails of quantum theory, indeed, to such an extcnt as oncc again to provoke thc wrath of Max Planck.

Mach significantly influenccd all quantum theorists through his

crilicisms of Nc\vton’s definitions of mass and forcc and his rcjcction of “absolute” morion, space, and time. but as with Mach’s impact on Albert Einstein therc was a confusion of physical and epistcmological considcrations. Einstein finally separated somc of thcsc factors out and at least tried to rcject Mach’s phenomenalistie point of vicw. Many quantum theorists, howcvcr, continucd to cmploy an ambiguous con-ceptual mixturc in both their mcthodological theorizing and in the “physical mcaning” which they attached to their incrcasingly abstruse and complicated mathcmatical formalism. Opponents of this approach, and they havc bccn very numerous among both philosophers and physicists, havc labclcd it "thc Copenhagen interpretation of quantum physics.” ³³ Its chief advocatcs havc bccn Nicls Bohr, Werner Heisen-berg, and Wolfgang Pauli, and its principal opponents Albert Einstein, Max Planck, Erwin Schródingcr, and Louis dc Broglic.³¹

The Copenhagen interpretation, formulated by Nicls Bohr and his institutc frlchćTs and allies in 1926/1927, insisted that all micronature was ncccssaiily buth particie and wavc in charactcr, that this vicw would not be overthrown in thc futurę, and that quantum physics was ncccssarily statistical and noncausal sińce it was impossible to under-stand thc charactcristics of particular particle-wavcs which of ncccssity were significantly altcrcd by all observational or cxperimental attempts to mcasurc them.³⁵

This interpretation madc use of a number of phenomenalistie ideas but not in thc way that Mach intended them. There was talk, for example, about “describing and relating sensory appcarances," but what was mcant was thc dcscription and relation of highly mediated photographs and instrument data. Similarly, thc Mach-sounding Copenhagen restriction on “meaningful” rcfcrcncc to observablcs was compromised in a varicty of ways: by the particle-wave ambiguity of observables, by thc un-Machian appcal to “theories,'' and by the act rather than content naturę of thc phenomenalism.

Mach belicved that all sensations could be known with ccrtainty and that ambiguitics and paradoxcs (such as thc partidc-wavc naturę of microsensatioris) rcflcćtcT a vcrbal, conccptual, or mcthodological confusion. Heisenbergs “unccrtainty principlc," on thc other hand, whilc ; admittedly phenomenalistie, was not compatible with this approach.

Mach opposed theories in “cnd-scicncc” but madę occasional use of them in “bccóming-s'ciencc” as transitional or mcthodological aids. All Copenhagen theorists and many of their opponents rejcctcd Mach's