BritJPhilSci1959-p48-50

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The British Society for the Philosophy of Science

The Falsifiability of the Lorentz-Fitzgerald Contraction HypothesisAuthor(s): Adolf GrnbaumSource: The British Journal for the Philosophy of Science, Vol. 10, No. 37 (May, 1959), pp. 48-50

Published by: Oxford University Press on behalf of The British Society for the Philosophy ofScienceStable URL: http://www.jstor.org/stable/685775

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ADOLF GRUNBAUMjust a verbal mistake, for the expression'metaphysical ontology' producesa kindof intellectualshudderwhich is not producedby the use of words like ' assumption'and ' presupposition'. R. HARR?LeicesterUniversity

THE FALSIFIABILITYOF THE LORENTZ-FITZGERALDCONTRACTIONHYPOTHESIS

IN his latest book TheLogic of ScientificDiscovery,K. R. Popper cites the Lorentz-Fitzgerald contraction hypothesis as 'an example of an unsatisfactory auxiliaryhypothesis', claiming that it 'had no falsifiableconsequencesbut merely served torestore the agreement between theory and experiment-mainly the findings ofMichelsonand Morley'.lThe chargeof being ad hoclevelledhereby ProfessorPopperagainstthe Lorentz-Fitzgeraldcontractionhypothesisis whollyincorrectbut has persistedin the literatureon the philosophyof science for the past half century. I thereforewish to give arefutationof the thesisof non-falsifiabilityon the basisof acomparisonof the reasoningunderlyingthe Kennedy-Thomdike experiment2with the design of the Michelson-Morley experiment.

Specifically,I shall show that, contraryto ProfessorPopper'scontention, (i) thecoupling of the Lorentz-Fitzgeraldcontractionhypothesiswith the classicalaethertheory entails a positive outcome of the Kennedy-Thomdike experiment differingquantitativelyfrom the positiveresultrequiredby theaethertheorywithouttheLorentz-Fitzgeraldauxiliaryhypothesis,and(ii) while entailingthe null outcome producedbythe Michelson-Morleyexperiment,the Lorentz-Fitzgeraldversionof the aethertheoryrulesout the negative result which was actually yielded by the Kennedy-Thorndikeexperiment.The essentialdifferencebetween the apparatusused in these two experimentsisthe following: as measuredby rods in the laboratory, the horizontal and verticalarms of the Michelson interferometer used in the Kennedy-Thorndikeexperimentare notequalbut aremadeasdiferentin length aspossible,so asto assurea considerabledifferencein the traveltimes of the two partialbeamsfrom the sourceto the point atwhich they recombine to produce interferencefringes. On the other hand, thehorizontalandverticalarmsof the apparatususedin the Michelson-Morleyexperimentare eachof the samelength I as measuredby the rods in the laboratory.

Accordingly, in the latterexperimentthe classically-expectedround-triptimes Tvand Thfor the verticaland horizontalarmsare given respectivelyby21 21 Iand Tv /(c2- v2)-- /(c 2- v 2)where ' c' representsthe velocity of light, ' v ' the velocity of the apparatusrelativelyto the aether,andf3= v/c. Now, without a Lorentz-Fitzgeraldcontractionhypothesis,the initial time difference Th - T between the two partiallight beams would be

expected to change in the courseof the rotation of the apparatusthrough go? in theMichelson-Morleyexperiment. And thus a shift in the interferencefringescorres-1K. R. Popper, TheLogicof ScientificDiscovery,London, I959, p. 832 Cf. R. J. Kennedyand E. M. Thorndike,PhysicalReview, I932, 42, 400, andW.PanofskyandM. Phillips,ClassicalElectricityandMagnetism,Cambridge,1955,p. 236

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ADOLF GRUNBAUMjust a verbal mistake, for the expression'metaphysical ontology' producesa kindof intellectualshudderwhich is not producedby the use of words like ' assumption'and ' presupposition'. R. HARR?LeicesterUniversity

THE FALSIFIABILITYOF THE LORENTZ-FITZGERALDCONTRACTIONHYPOTHESIS

IN his latest book TheLogic of ScientificDiscovery,K. R. Popper cites the Lorentz-Fitzgerald contraction hypothesis as 'an example of an unsatisfactory auxiliaryhypothesis', claiming that it 'had no falsifiableconsequencesbut merely served torestore the agreement between theory and experiment-mainly the findings ofMichelsonand Morley'.lThe chargeof being ad hoclevelledhereby ProfessorPopperagainstthe Lorentz-Fitzgeraldcontractionhypothesisis whollyincorrectbut has persistedin the literatureon the philosophyof science for the past half century. I thereforewish to give arefutationof the thesisof non-falsifiabilityon the basisof acomparisonof the reasoningunderlyingthe Kennedy-Thomdike experiment2with the design of the Michelson-Morley experiment.

Specifically,I shall show that, contraryto ProfessorPopper'scontention, (i) thecoupling of the Lorentz-Fitzgeraldcontractionhypothesiswith the classicalaethertheory entails a positive outcome of the Kennedy-Thomdike experiment differingquantitativelyfrom the positiveresultrequiredby theaethertheorywithouttheLorentz-Fitzgeraldauxiliaryhypothesis,and(ii) while entailingthe null outcome producedbythe Michelson-Morleyexperiment,the Lorentz-Fitzgeraldversionof the aethertheoryrulesout the negative result which was actually yielded by the Kennedy-Thorndikeexperiment.The essentialdifferencebetween the apparatusused in these two experimentsisthe following: as measuredby rods in the laboratory, the horizontal and verticalarms of the Michelson interferometer used in the Kennedy-Thorndikeexperimentare notequalbut aremadeasdiferentin length aspossible,so asto assurea considerabledifferencein the traveltimes of the two partialbeamsfrom the sourceto the point atwhich they recombine to produce interferencefringes. On the other hand, thehorizontalandverticalarmsof the apparatususedin the Michelson-Morleyexperimentare eachof the samelength I as measuredby the rods in the laboratory.

Accordingly, in the latterexperimentthe classically-expectedround-triptimes Tvand Thfor the verticaland horizontalarmsare given respectivelyby21 21 Iand Tv /(c2- v2)-- /(c 2- v 2)where ' c' representsthe velocity of light, ' v ' the velocity of the apparatusrelativelyto the aether,andf3= v/c. Now, without a Lorentz-Fitzgeraldcontractionhypothesis,the initial time difference Th - T between the two partiallight beams would be

expected to change in the courseof the rotation of the apparatusthrough go? in theMichelson-Morleyexperiment. And thus a shift in the interferencefringescorres-1K. R. Popper, TheLogicof ScientificDiscovery,London, I959, p. 832 Cf. R. J. Kennedyand E. M. Thorndike,PhysicalReview, I932, 42, 400, andW.PanofskyandM. Phillips,ClassicalElectricityandMagnetism,Cambridge,1955,p. 236

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LORENTZ-FITZGERALD CONTRACTION HYPOTHESISponding to this changewas anticipated. But, once the aethertheory is amendedbythe introductionof the Lorentz-Fitzgeraldcontraction,the length I in the expressionfor Thmust be replacedby the length IV/(I-_f2). As a consequenceof the introduc-tion of this auxiliary hypothesis, Th becomes equalto T,, and the differencebetweenthe round trip times of the two partialbeams is zero throughout the Michelson-Morley experiment,in conformity with its null result.It will be noted that the equality of the terrestrially-measuredlengths of the twoarmsis a necessaryconditionfor the vanishingof the differencebetween the two roundtrip times in the Lorentz-Fitzgeraldaccount of the Michelson-Morley experiment.But precisely this necessary condition is not fulfilled in the Kennedy-Thordikeexperiment in which the terrestrially-measuredlengths of the vertical and horizontalarmshave the unequalvalues L and I respectively. Thus, uponassumingthe Lorentz-Fitzgeraldcontraction,the differencebetween the travel times of the two light beamsof the Kennedy-Thorndikeexperimentis given by

2L 21 2T- Th V(c2 -v2) /(C - v2) = (c_ - 2)( ).Insteadof vanishing throughout the experiment, this time differencevarieswith the

diurally and annually changing velocity v of the apparatusrelatively to the fixedaether. Moreover,if we do notassumeaLorentz-Fitzgeraldcontraction,the differencebetween the two travel times of the Kennedy-Thornmdikeexperimenthas the differentvalue given by2L 21 I 2 /

rT.v Th ( - ) (2C- 2- ) v(I - )= V( - v2) \ -V( 2)And this differenceis likewise a function of the diurnally and annually varyingvelocity v of the apparatus. It is apparent that the Lorentz-Fitzgeraldcontractionhypothesishas a falsifiablebearingon the outcomeof the Kennedy-Thorndikeexperimentand that thisexperimentcouldhave detectedanyexistingvelocityof theapparatusrelativelyto theaethereven on theassumptionof a Lorentz-Fitzgeraldcontraction:if the period ofthe light source does not itself depend upon this velocity, the appropriateannuallyand diurally changing time differencegiven above would have given rise to cor-respondingobservableshifts in the interferencefringe pattern. Contrary to boththe original and the Lorentz-Fitzgeraldversion of the aethertheory, Kennedy andThorndike found that such shifts did not materialise.

In addition to the Kennedy-Thorndikeexperiment, the following experimentsuggestedby C. M/ller and others qualifiesas a test of the Lorentz-Fitzgeraldcon-traction within the framework of pre-relativisticconceptions: although a terrestrialobserver could not detect a Lorentz-Fitzgeraldcontractionin a Michelson-Morleyexperiment, 'an observerat rest in the aether outside the earthwould, however, inprinciplebe ableto observethe shorteningandhe would find the earthandall objectson the earth contractedin the direction of motion of the earth '.

1C. Mt(ller,The Theoryof Relativity,Oxford, I952, p. 29. For a discussionof theimportantdifferencesbetween the pre-relativisticand the relativisticconceptionsof thestatusof any contractiondisclosedby the extra-terrestrialexperimentsuggestedherebyMiller, cf. H. Reichenbach,ThePhilosophyof SpaceandTime,New York, I958, ?3I,and A. Griinbaum,'Logical and PhilosophicalFoundationsof the Special Theory ofRelativity', AmericanJournalofPhysics,I955, 23, 460-464.D 49


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MAGOROH MARUYAMALorentz himself was quite clearthat the contractionhypothesiswould not sufficeto make the body of experimentalfindings known at the time conform to the ex-pectationsof the aethertheory. He thereforeinvoked thefurtherauxiliaryhypothesisknown as the Lorentz-Larmor-Poincaretime dilation, construed as issuing in a

spurious' local' time in all systems moving relativelyto the aether.1 Only a versionof the aether theory incorporatingboththe Lorentz-Fitzgeraldcontractionand theLorentz-Larmor-Poincaretime dilation is vulnerable to the ad hoc charge, whichtraditionand ProfessorPopper have unjustlylevelled againstthe first of these twoauxiliaryhypothesesalone. ADOLFGRiNBAUMLehigh UniversityBethlehem,Pennsylvania,U.S.A.

TESTABILITY AND (AD-HOCNESS' OF THE CONTRACTIONHYPOTHESIS

PROFESSORGRUNBAUM'S most lucid explanationof the Kennedy-Thomdike experi-ment (I932) is a very welcome contribution to the discussionof the problemwhetheror not the introductionof a new hypothesisis to be regardedas a potentialadvance.In the passage of my book referredto by Professor GriinbaumI said that thegoodness of an auxiliary hypothesiswould depend on whether it is independentlytestable,or perhapsmerelyrescuinga refutedtheory. ProfessorGriinbaumpointsout,rightly, that I have been guilty of uncriticallyaccepting (or possiblyeven spreading)the myth that the Lorentz-Fitzgeraldcontraction hypothesis was not testable.ProfessorGriinbaum'scorrection shows that this hypothesis was testable and thusnot ad hocto the degree I believed. Accordingly it was an advance. But it was, ofcourse,more adhocthanspecialrelativity. In otherwords,we have herean excellentexample of' degreesof ad-hocness' and of one of the main theses of my book--thatdegreesof ad-hocnessare related(inversely)to degreesof testabilityand significance.K. R. POPPER

COMMUNICABLE AND INCOMMUNICABLE REALITIES

THEpurposeof this note is not to resume the worn-out discussionof the incompara-bility of the 'subjective' quality of perceptionand feeling in different individuals.Our point is ratherthat even if one should assume the identity of sensoryand per-ceptualqualitiesin organismsequippedwith identicalsensoryandperceptualmechan-isms and nervous systems, the incommunicabilityof certain realitiesemerges evenon the basisof logical considerations.

GabrielMarcel,in hisL'HommeProbltmatique,presentsa man who has lost every-thing in the war and askshimself, 'Who am I ? ', 'What does all this mean ?'.' Qui suis-je? Quel sens a tout cela ? Est-ce qu'un autrehomme, un individului aussi,sera en mesure de l'clairer ? II pourrafaire tous ses effortspour intro-duire notre homme dans sa proprevie, dans son universa lui, il pourrameme1 Cf. Moller, op. cit. p. 30

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BritJPhilSci1959-p48-50