Circularity and Reliabilityin Measurement

Hasok ChangUnio er sity Co II ege Lond o n

TIte direct use of a plLysical laut t'or the purpose of mensurement creates

n problen of circularity: the Intu needs ta be empirically lesfed in orderto ensure the reliability of neasuremenf , but the festing requircs that wenlready know the aalue of the quantitV to be nrcnsured. This problem is

discussed through some defqiled exnmples of energv tneasurements inquantum physics; tfuee major methods are anahlzed in thair interrelatlon, with a focus on fhe metlnd of "material rctnrdntion." It seens thnttlrc only reasonable solution is to estnblish the latt, neerled t'or tlrc rnea-

surement by relying on an alternite metltod of nreasurement. This soltL

tion is also circular, since it atnolLllts to letling dit'fercnt measurementmetlnds justit'y each lthet. Howeaer, this circula ty can be fntitftl forthe process of concept building; meaning can be ueLlted in a web of inter-con nc( t cd measu rtm en I mtl hods.

l. The Pro bl em of Nomic lv{easur€m€ntThe theoryladenness of observation is often seelr as a source of circu-larity for the empirical confirmation of theories. One aspect of theory-ladenness, however, creates circularity in observation itself, before weeven get to any explicit testing of theories. This problem is manifest inthe following situation. Often we measure a quantity by inferring itsvalue from the values of other quantities, on the basis of a physical lawthat specifies a relation between the quantities involved. In order to besure that this procedure is sound, we need to know that the physicallaw we employ is correct; in order to know that, we need to test it

I \^,oüid llke to thank Peter Galison, Nancy Cariwrighi, John Dupr6, Pairick Suppes,Olivier Darrigol, Allan Franklin, and two referees for helpful comments on va ous ear-lier versions of ihe ariicle- This r,ork lväs done partly under the sponsorship of GeraldHolton al Harvard University.

Pcrspectirß on Sciencc 1995, vol. 3, no.201995 bv Th€ University of Chlcaso. ALI rights resefl€d. 1063 61:15/95/0302-0001$01 00

't 5{ Cir(ulatity and Reliability in l "5ut'r"l

afnniricallvButihelawcaffrdbetes.edati6ci6ltrv''f:T^?j-]'..p*:ff:[::'il "ä;;;; 1"Y:.ffi'ffi tr#'T ffilfor this kind of measrsrclu ry".'--:*;" t,',i"u'vi situa-;:;;;il;""ri.'paramerers.andtrffi i"#;:uü'"1.",r."rion in which the me* *ä;i;;;; be guaranteed .

reliabiliwof the.me""'ryti;ä tu *6 of a measurementWe are caught in a crroe - *::" ll i=_;- ilc nr\-n results l

^"ää.;;T * ;*- -eg;'$"s-iä?il Ji'^"*.

wilt call this quanda4 * %;-;- edkit dependence onmeasurement_l.m€T*ff.:'j;;;;dcibesthemeasure-some physicat lan'1tt* l"TT'il:iJJ +ui.t it inf-eIed fromment interaction, thr$rgh rrtrn 5 T-

=:-'* oout of this a.-;ti:tffir#"ffi;;;

lpm of nonric measüemenL '

:WS!t*", ffiH*iili',{lof nomjc measurement' based orr *'-:i_"-...-i;ir,**

of nature. I

[r*:'r**#5ffiäffi:r;t'ments against the "tt"rr'Po.*;;;;"'üJü* ro. the purpose. ofguaran tÄes the truth

" .Pi:iä;ä;"C.r*ngh(s siron g. ihe;is th at

ih" oresent discussion' I do not reeu.* l'-Y-t t"."*, iiit sufficient

;ii",ä;"; ;s;, " ::' :* T::*THXffi"T.fä,#"',n "

*"io aclnowledge that there rs r'^-.

ü. pi*o-o,ological laws. Once

damental ldws are emPrncauy -trucr :-:f-'^:; t-'."".ases to be a

;ljl'l;;;; derivabÜry from tundanental laws ceases

method of iustification l . L^ 'L.+ -o,crrrernent laws can"'' o'ä.*',"",tuh,tri I'',

ilvrä'.e:l tr ffi,äffi ffi | ua y u""nbe trusied if they are d&b

rr.-,". The relev-ant distinchon,.tnen, is be-

shown to be more generany i:;", ä;; ;"O"aC a continuum).2 So

lweet Pßrficulor and getnat

I rr may be Possibre t:'::l,':fl: :'ät;\'J;J;ää*ffIää|:;HIi:?;:;rprq. For inilanre. Coulomb rnrhauy resls *

Ig;*".I;a ,"t'"t ,hI *:,.::lT*.::wirhout knowins the vd::" :l tt",;;,';;;;t; my disclrssion, sLnce a law

equdl . härgecr.I hi< q*,*."ton ouo'-'* it ir i, rr,o*r, .oolpt"tely so that numeri-

fo'r measurement in the sPec*ied.n

.ul ,e"'tt" tun b" o"d'.t"l frtTll.n". .t .uld not be conlldted wiLh the frrndamentdl-

. The eenerdl-pdrticuldr d i5hn' tLv"h" '"" - menologl.al läws tend to be parlicular

phenomenälogical distinclion Altrru"b" :.;;;", For exampte, cartesianb accepted

l"J t""a''"'''t lav!5 seneral' '"ü;;:;:'.äil;i;tused torreatrtacf''ndamental'rhät NewLons gravitational law w;

Perspectives on 5cienc€

\r'e \rould sav that measurement laws are particular laws that can bejustitied through derivation from some general laws whose trulh has

been demonstrated in wide-ranging sets of circumstances. But even

such general laws may not apply to certain particular situations inß hich they have not been tested. It is not my purpose here to tacklethe problem of induction and make arguments about how generaliza-tions can be justified. Rather, I simply want to note that there are clear

cases of failed generalizations.lvhai can a practicing scientist do in designing measurernent meth-

.rds, if it happens that no useful general laws are known? One ready:esponse is to establish particular laws for use in measurement case by;ase, through experimentation. With this move we come right back to

:he problem of nomic measurement: how can a particular measure-nent law be discoverecl or tested, when the value of the quantity thatr. ihe subject of measurement is not knownl Scientists often get:round this problem by using an alternate method of measurenent to.leiermine the value of the quantity in question, making it Possible:.-. lind or test the measruement lan'within the relevani domain ofrhenomena. But how is the alternate measurement method justified?ihere is an obvious problem of circularitv in this straiegy; the burden.ri justification is merely pushed around among different measurementnethods. I want to argue, however, that there is something fruitfrrl in:his circularity.

ln Section tl, I will describe the strategv of establishing'a measure-:nent law by relying on another neasurement meihod. For that Pur-:ose, I cannot find a better means of exposition than the detailed dis-

--ussion of an example. The example I have chosen is the measurement

-.f energy in early quanhrm physics; ihis study should also hold some

historicai interest in its own right, apart from the illustration of the

ehilosophical point. In Section III, I will discuss some wider philo-

'ophical implications of adopting the strategy described in Section II.ir is hoped that this discussion l\'ill throw some new light on the notionot reliabilityl and the process of concept building.

irr them ihe gra\'ltational law was ä generai phenomenological law thai had to be cx-

:Laine.l bv thc more furdamental lah.s of coniact action lt is difficult to find examples

,,4 Fnrtrcular fundamental laws, but some singulnr causal statements could be regarded

i I use thc term "establishment" to refer b either ihe Process of drsco\€ry or the

:r..ejs of testing, or both.

- \\'hat I ß'ill be discussing is the reliabilitv of measurement' which bears only indi-1,.:lr on thc reliabilitv of theori€s.

't 55

156 Circularity and Reliability in Measurem€nt

ll. Mutual Grounding: lhe Ca se of Energy in eüa n tum physicsIn early quantum phvsics, there were three major methods of measur-ing energy.5 In magnetic def-lection, a charged particle's energy is mea-sured bv passage through a uniform magnetic field, in which the parti-cle curves around in a circular arc. The measurement law here specifiesa relationship betl'een the radius of curvature and the energy of theparticle, so that the energy can be inferred from the shape of the trajec-torv In electrosiafic retardation, an electrostatic field is applied againsta particle's motion; the measurement law here states that the initialkinetic energv of the particle is equal to the amount of electrostaticpoientral it tra|erses before coming to a stop, multiplied by its electriccharge. The measurement laws for magnetic deflection and electro-stalic retardation l'ere derived from Newtonian dynamics and classi-cal elecirodvnarnics (.it'ith relativistic corrections when necessary).Since phr,sicists initially had a firm belief in the classical laws, thesemeasurement methods appeared largely unproblematic.6

The ihird method of energy measurement, material retardation, ismuch more interesting for the purpose of this article, and it deservesa detailed description. For material retardation, there were no widelybelier,,ed general theories available. Accordingly a multitude of partic-ular measuremeni lar.r's were discovered, tested, and used. The experi-mental $'ork in|oh'ed here reveals the process of mutual groundingverv clearh: In this section I will first discuss the character of the mea-surement larls for maierial retardation and then show how they reliedon other methods of energv measurement.

In material retardation one measures tl.re kinetic energy of particlesby obsen'ing hol'much matter they can penetrate, on the basis of aprer.iouslv known functional relation between the energy and therange (penetration length).: This method played an important role inthe early t\.ventieth cenlury especially when circumstances made theother t\a'o methods inconvenient. For example, H. Geiger and E. Mars-

5. In ihe rest of the.rrticle "energ','' rr'ill mean kinetic enerfl\i rlt1less other$'is€ speci6ed.

6. Even after the fundamental lah's of classical mechanics fell out of favor these andsome other measurement mcthods based on classical reasoning continucd to be usedand, moreover, produced results that suppofted the ne$ cluanium mechanics. For adeiailed discussion of this peculiar situation, see Chang (1995).

7. R. Whiddington (1912ü, p. 371) explained the mechanism as follows, for a paricular casc: "It is known ihat the distance d which a cathodc particl€ can iravel through agas depends on its initial \,'elocity r., so that if the exact form of lhe relation il = l(.,.)r €r€ knoh'n, it would be possible to calculate ai once the velocitv of a cathode pariiclewhose range was knon'n." This is the basic idea behind all material retardation techniques.

PerspectiY€s on Science

.len 11913) used material retardation for an ernpirical test of ErnestRuiheriord's theory of o-particle scattering. Both C. T. R. Wilson (1923)

and R. lVhiddington (1912ü) used it to rneasure the energy ofphotoelectrons ejected by x-rays. Material retardation was also commonh'used in measuring the energies of cr- and B-rays from variousradioactive substances.s Perhaps the most famous instance was theCermpton-Simon experiment (Cornpton and Simon 1925), commonlyreqarcled as a decisive result against the Bohr-Kramers-Slater conjec-.-rre (Bohr, Kramers, and Slater 1924) that energy was conscrved only.iatisticallv and not in every individual interaction.e

I l'ill start with that case in describing the character of material::rarc-lation lart's. In the Compton Simon experiment, strong beams ofr rar s produced B-rays in a cloud chamber; some of ihe B-rays were

-;entitied as recoil electrons "kicked off" from atorns in collision with::.e r ravs. The energies of these particles rn"ere measured by means ofC. T. R. Wilson's result that the range of a ß-particte in air is V'?/44

::- i.n, rr-here y is the potential in kilovolts reqriired to give the particle::. initial velocity" (Compton and Simon 1925, p.311). Wilson (1923,

: q) had establisl.red the range-energy relation experimentallv and

:,.ted that his result was "in approximate accordance with Whidding-:..r'. fourth-power law" That refers to Whiddingion's (1912n) work.:...rving that the range of a B-parlicie $'as proportional to the folrrth:..',r'er of its initial velocity. So we can identify Whidclington's forrrth-r!r\\ er 1aw as the measurement law for the material retardation method:. emploved in the Compton-Simon expedment.

\\ hiddington'.s fourth-power law is a particular law Both Whidding-:..:. and Wilson experimented only with electrons, only in limited en

:::\ ranges, and only with a few retarding substances. What n'oulc1

... ihe range-energy relaiions in other situations? Others did investi-:-1:e the range-energy relations under differing circumstances. E. J.'. ,:-,iams (1931, p. 322) studied B-rays wiih a cloucl chamber and found:.'.::iions from Whiddington's law, reporting that ihe range vaied as

::.. 1.. ith po\'!.er of velocity rather than the fourth power. It is not

=::::ell clear n'hat the source of this discrepancy was; possibly the:e:-:rding n.raterial made a difference, as Williams rn'orked rvith gases

-:r..i \\ hiclclington's rnost reliable tesults were obtalned in metal. M. A.',::.ler r1915), B. F J. Schonland (i925), E. Madgwick (1927), and C. E.

E;;ir 1919) all studied the absorption of electrons in metals. Their

: a.rr .r nlore deiaile.l historical ireatmcnl of ihe matcrial retarLlation nethod, see

: -...: 1991, rh.1p. 3).: Frr a briei dcscription of the Bohr-Krameß-Slatcr PäPer and its e\Perinental test-

rr: ...Inmmer (1989, pp. 188-90).

157

158 Circularity and Rcliability ;n Measurem€nt

res ts indicated that Whiddington's law held roughlv in low energiesbut began to break down seriously around the initial electron veloiityof 0.4c (where c is the speed of light). Whiddington had obtained hisresults with electrons of lower energy, only up to the speed ot about0.3c.10 Wilson's (1923, p.9) above-mentioned result was also obtainedwith electrons whose velocities were at most in the neighborhood of0.3c. Norman Feather (1930, p. 1560) examined the high-energy resultsobtained bv Varder and by Madgwick and concluded that the rangew-as proportional to the square of the initial electron speed.

The range-energy relations looked quite different again for cr-rays.In cr-ray research the most commonly recognized range-energy rela-iion was Ceiger's law, which was usually expressed as o. : kR, wherel is the particle's initial velocity R is its range, and k is a constant.Geiger (1910ü, esp. p. 508) initially established this law from his experi-ments on the retardation of o-particles in mica. E. Marsclen and T. S.Taylor (1913, p.453) investigated ct-ray retardation in rarious materialsand found that Geiger's law held rather well in air, though not insome other materials. P M. S. Blackett (1922, p. 316) made furthermeäsurements and concluded that even in air Geiger,s law brokedown {or short ranges, the range-velocitv relationship being approxi-mately R : kz3l2 when R was less than 1 cm. Blackett noted thatMarsden and Taylor's confirmation of Geiger! law was based ondata with range greater than 2 cm and did not conflict with hisown results. At the long-range end, G. H. Briggs (1928, p. 555) noteddepartures from Geiger's law for n-ravs from radium C, though theywere slight. (Blackett [1923] also studied the range-energv relationsfor atoms set in motion by collision with cr-particles, obtainingcurves that were smooth but not easil)' represented bv simple mathe-matical formulas.)

A passage from J. S. Marshall (1939, pp. 394 95) gives a nice sum-m.try illu.irdtion ol the "p.itchlne5- ot m,rlerial rr,iardalion law,:

For the derivätion of energies from ranges, thcre is the relationestablished by Nuttal and Williams (1926),

R = 0.0284ErlN,

where R is the range (cm.), E is the energy (keV), and N is theaverage number of electrons per molecule; for a mixture of hy-

10. See Whiddington (1912d, p. 365, rabte t). Williarns'.s abo\€-rnenrioned results,rvhich differed slightly from Whictdington's, were obtaincd ai the range ofl) = o.ic tc)0.3c; see Williams (1931, p.314).

Persp€<live' on Science

::.rgen and alcohol vapour the value of N was 3. Williams (1931)

:-.und that R increases less rapidly with E, and suggested the:r.ler 1 82 in ihe case of oxvgen. In neither case were measure-rents made for energies greater than 27 kev At greater energies,r-honland's (1925) ranges in foil are all that are available. The foil:ange tends to be appreciably less than the average length of-ack lin a cloud chamber] (Williams 1931).

. -läLrus range-energy relations were established and used for energy::.easurement. The factors affecting the form of the range-energy rela::!rn \rere many the most important ones being the t,vpe of particle that.!.is being retarded, the initial energy of the particle, and the iype of:riarding substance.

\laterial retardation laws give a clear illustration of the possible dif-:.-ultv of knowing which factors are relevant to the limits of general--z.ltion. It proved difficult to obtain a general theory ihat would give:..e range-energy relation for arbitrary values of the mass and charge---- the retarded pariicle. Even for a given type of particle ihere were:riierent functional relations for low and high energies, as I'e saw in::.e breakdown of Whiddington's and Ceiger's larvs; on the other hand,r: i. undeniable that these Lrws held quite u'ell in somc resiricted en::ql ranges. The nature of the reiarding material affected the form of1:.e range-energ)r relation, but in a somewhat manageable r,\.ay so that:i:e range-energy relation obtained for one kind of material could often:.. used for ar.rother, if put in terms of "effective range."rl

Civen all of this unpredictability, the experimenters proceeded withiieat caution in establishing the measurement laws for material retar-;ntion. The range-energy relations u'ere obtained tl.uough direct exper-:rentation, as there was no useful theoretical treatment of material::;arclation available. Although there were some serious attempts at:..rmulating a general theory of penetration phenomena, initiated by:..ne other than Niels Bohr (1913, 1915),r']the experimenters felt a clear:eed to establish the range-energy relaiions case by case through er-

11 For hsiance, Sargeni (1929, p.520) observeLl, in iis papcr on the ß-raJ' specka-.4 a.tinium B and C": "Schonlandls 119231 uork sho!\,s that for cathode ravs lvith cner-:re: irom 18,500 to 2E,500 volts the effecti\,e [rass range for a gi,,'en l-elocitv is inclepen-:.:r: of the sübstancc. Evcn if this.loes not hold accuraielv for fasi p rays the mass.:-:.qes in paper and in alüminum rvould not diffcr much, and for thc present pu+)ose:r:r be taken to be equal-" The effective range was expressed in terms of nass per cross-..:nonal area, or sometimes ihe equivaleni length in air

I l. For an exposition of Bohr's theory and further theoretical developments, see Cajii --:r 19E7, pp.97-102).

't59

160 Circulärity and Reliäbilrty in Meäsur€m€nt

perimentation. hr all of the cases T have erarnined. when a range-

energy relation was rscd, it r'r'as never derived theoretically.rrThe experimental establishment of range-energy relations reqlrired

an independent way of determining the energies of the particles in-volved in the expedments. Most commonlv magnetic det-lection was

used for this purpose. Whiddington's work provides a good illustra-tion. The following is Whiddington's description (1912n, pp. 360 61)

of his experimental arrangement, shown in figure 1:

Heterogeneous cathode ravs from the cathode E suffer magnetic

dispersion in the solenoid B; [a ray ofl a definite velocity corre-

sponding to deflection through a right angle is allowed io enter

D and to traverse a thin metal sheet contained therein. The trans-

miited r.rv- ettter the sccond -olcnoid C .lnd ;g;in 'uller rnäA-

neiic dispersion, and so have their velocity n.reasuted. In this way

relations can be obtained connectillg the velocities of the incidentancl emergent rays and the thickness of the absorbing materiai

Once a functional relation was established between the initial speed,

the final speed, and the thickness of the material tra\-ersed, ihe range-

speed relationship could be derived bv setiing the final speed at zero

in the forrnula. Under the classical conception, the range-speed rela-

tion r'r'as freely converted into a range energv relation Many other ex-

pedmenters also used rnagnetic del1ection in establishing range-

energy relaiions. Geiger! law n'as basecl on magnetic deflection, bothin its orillinal determination (Ceiger 1910&, pp 505-7) and in its con-

firmation by Marsden and Tavlor (1913, p.'l'+-1). W. Wilson (1910, p

142), Varder (1915, p. 725), Schonland (1925, pp 189 90), Madgwick(7927, p. 973), and Feather (1930. pp. 1560-61) all relied on magnetic

deflection in their $'ork \\.ith electrons (p-ravs and cathode rays).

13. It ma)' bc objecied that mnterial retitrLlation is a peculiar nnd uninshrcli\c e\an1ple, srnce it makes use oi a lerv compler phenomenon; in contrast, magnetic deflec'

tio; and clectrosiaiic rftardaiion nake use of rclaii|eh simPle Phenomena li should

cone as no surprisc that a lalL :iovcrning a more comFlet Phenomenon is more di[ti'u]tto generalize. This argument comcs !lol\'n tcr a taut()log\l Playing on the meaning Lrf ihe

noicl "simple." lVhen ll,e call, sav magncuc det-leciion "simPlc," wt'are alreacll' making

the assumption that its rneasuremeni larv holds gcncrallr' for a vadetv oi def-le'ied

particles, for nll ranges of energv values, for all ranges of n]agneiic llcld strength, ilnd

;o forih. It is even assu ed ihai it aPPlies in clorLd chanlbers (not just in vacuum), in

which the cietl€cted Particle! Passage shoüld inl()h e just ihe snnlc kinct of compli'aiionsas in maiedal rctardaiioll. In or.ler tu) sav ihat ihc jnieraciions iakinllPllce in lnafinetic

deflecii(nl or electrostauc retardation are sirnpler ihan those taking Place n1 maierial

retar.:lation, $,e need ridr knor^'ledge of the cäse of generalization for each t]'pe of i t'raction. Thai is prt'ciselv r!hat we cannoi clairn io have, r\'ithout Lloing ihc detailed tnrPir

P€rspcctiYes or Scien.e 161

Figure 1. Diagram of Whicldington,.s experiment to measure the range of cath_:- r,rvs in metais. (This is a reproduciion of fig. 1 in Wliaaingt'on fvtza,::r1.)

. \lthough magnetic deflection was the dominant stanclard bv .ivhich:. . range-energy relations were established, it was not the oilv c,ne.

- \1. Terrill (1923, p. 101) modified Whidclington,s apparatus;o that: .-initial v€locity of the cathode ral was Llown nor fhÄugh magnetic--::lection but through preparatioir by accelerafion o.rnaa o k!,.,*l,:,e.trostatic pofential. His tcchr.riqrre \\,as based on the same principle.-: electrostatic retardation, except il.r this case the electrost;tjc field:..rs used to accelerate rather than retard the particles. Terrill,s experr_::'.ert is the only case I have discovered in r,r,hicJr the range_energy work::.1ed explicitlv on electrostatic retarclation, bui there räre othir cases:: rrhich it \,\.as used more subtly. C. T. R. Wilson (1923, p.9), !.M.\'.rital and E. J. Williams ,1926, pp.1110 11),and E.J. Willilms (.1931,

161 Cir.ularity and Reliability in ^,lea5ur€Incltt

p. 314) made use of Einstein's photoelectric equation in gaining an rn-dependent knowledge of the energies involved.'r Since Einstein's equa-tion received its most important confirmation from Robert A. Milli-kan's (19i6) work employing the electrosiatic retardation method ofenergy measurement, it would be fair to say that any experiment mak-ing use of Einstein's equation in this period made an implicit use ofelectrostatic retardation.

A more subtle approach is exemplified by the work of Blackett, whoestablished range-energy relations without any direct means of de-termining energy. He managed to deduce the velocities as well as theranges from examining the photographs of scattering tracks, by assum-ing energy and momentum conservation and Rutherford's theory ofscaiiering.rs Blackett's analysis amounted to a sophisticaied method ofenergy measurement. l will not discuss this n'ork in detail, but I men-tion it as a reminder that there were other, less cornmon methods ofenergy measurements in addition to the three major ones that are ex-tensivelv discussed here.

In every case examined, the range-energ1, relation was establishedby relying on an independent method of energy rneasurement; I willsay that the matedal retardation method was grctunded in other meth-ods of measurernent. For that reason, most experimenters who usedmaterial retardation regarded it as a secondary method whose validityhad to be established through grounding in other methods that them-selves had independent validityr{' But if material retardation wasgrounded in magnetic deflection and electrostatic retardaiion, where$€re ihe laiter t$'o methods grounded? These methods did not haveindependent jusiification, since their deril,ability from the fundamen-tal laws of classical physics do not guarantee their truth. It would seemthat the phvsicists rvere grounding material retardation in other mea-sluement nethods that u.ere just as groundless.

The fruitfulness of ihis procedure can be recognized only if we lookaway from foundational justification. The grounding of material retar-dation in another measurement method can be reconceptualized as themulrral grounding of the two methods. Then the various methods exist

14. These i{orks also assumed Bohr'.s atomic theoiy, in calcrilating the amount ofenergv that each electron needs to free itself from the atom.

15. See the theoretical ireahnents in Blackett (1922, pp.303 8;1923, PP.62-63).16. Some expedmenters were quite cxplicii aboui this point. J. A. Chalmers (1q2q, P

331) called rnaie al retardation an "approximate method"; B. W Sartent (1929, P. 5il4;

1933, p.66,1) called magnetic deflection "direct" and material r€tardation "indirect";Briggs (1928, p. 554, iable ll) labeled results obtajncd by rnagnetic deflection "observed,"

and results obtajned by material retardation "calcu1ated."

Per5peclives on scienc€

. :l-.. :äme level, none more direct or fundamental than any other,:r: i:.i., Lrne grounded in some other(s). Historically physicists did: :..:jer rnagnetic deflection to be more fundamental than material:::::Jniion, and the magnetic deflection law had a simPle form Blrt in:.-,:;r:le one could postulate some simple material retardation law:.:.: :ren end up discovering various magnetic deflection laws for v.lri-. ji .itu.rtions. Either rvay, the desired effect is convergence-to have

::..:-.ro methods produce approximately the same results when ap

:-:..i tcr ihe same phenomena.'7-:. ensuring the convergence betrveen two measurement methods,

.--::e phlsicists did not consider it to be enough to have the measure-- ::.: lal's for one method initiallv determined in reference to the other:-.:herd. Some efforts were made to double-check the converflence un-:=: ., arioLrs circumstances, and these effofts constituted a process of:. - :nding that was more explicitly mutual. Metaphoricallv speaking,. . , :s as if tt'o broad sheets had been stapled together in a few places,

-::..ne siill felt the need to put in more staples, trying to make sure

: -:: the sheets iouched each other throughout.i:s kind of double-checking was commonlv done on the conver-

t=:.:e betl'een rnaterial retardation and magnetic deflection. Briggs:1i. p. 554), for instance, studied d-ravs from thorium C and thorium

-- ,:rC concluded that the values obtained bv magnetic deflection and

- -:::rial retardation were in close agreement; the material retardation: .'. :.ere (Geigert law) had originally been specified through magnetic:.r-..tion on cr-rays from radium C (Briggs 1928, p. 5a9) J. A. Chal-

'. :.. i 1929, p. 334) studied the high-velocity limits of the g-ray sPectra

r:-.me radioactive elements by material retardation and noted fhat::, result on thodum C was in good agreement with R. W. Gurney's

- :1., resuli obtained by magnelic deflection; B. W Sargent (1929, p

: : noted that Chalmers's result on thorium B was also in good:::renent with Gurnev's result. In a later work Sargent (1933, p. 670,

:,::-e \'I) compiled previous measurement results on the high-velocity:r'-:. ol the B-ray spectra of various radioactive elements and noted

::,:: Eenerallv there was good agreement bet\^'een magnetic deflection-'-:.i material retardation. Sit.rce the range-energy relations under dis-

--;ssion had been established by reference to magnetic deflection in::..- iirst place,': the check on convergence amounted to an examination

: Irx\'sicisis often speak of "calibraiior" in referring to the process of bringlng:: -: :rrn\ergence, and some PhilosoPhers havc follon ecl suit See, e.g, Franklin et al

-r: ! lltl) dnd Frdnklin (1986, chap. 6).

: >ee Ceiger 11910&), Varder (1915), Schonland (I923, 1925), Madgwick (1927)'

163

164 Cir<ularity and Rcliability in Measuremcnt

of whether those relations could be generalized and applied in variousother circumstances.

Although the historical material I have examined shows most workin the mutual grounding between material retardation and magneticdeflection, there were also cases of mutual grounding between mate-rial retardation and electrostatic retardation, as mentioned earlier. Ihave not seen instances of direct mutual grounding between magneticdeflection änd electrostatic retardation, but photoelectricity was stud-ied by both of those methods with no apparent divergence in the re-sults. So history shows some amount of mutual grounding among allof the three major methods of kinetic energy measurements that I havediscussed so far. The convergence shown was not perfect, but it wasmostly good enough for practical purposes.re In my view more explicitand more extensive efforts at rnutual grounding would have beenuseful.

lll. Meaning, Definition, and the Reliäbility of MeasurelnentThe mutual grounding of measurement methods provides a solutionto the problem of nomic measurement, because it allows the discoveryand testing of measurement laws in particular dornains. But it is notan immediately attractive solution when we consider the issue of justi-fication. Whai is achieved by mutual grounding of measurement meth-ods, other than circularity? Is it not possible that a/l of the methods arebad, even if they are perfectly consistent with each other? Perhaps onecan argue that such a coincidence would be very unlikely, but thatwould be a difficult argument to sustain in this context, since mutualgrounding molds the measurement methods just so that they agreewith each other.ro In any case, I believe there is a more interestinganswer.

If we ask whether a given measurement method is a good one whileassuming that there must be some absolute criterion of goodness, themutual grounding of measuremeni methods can only seem viciously

i9. Franklin (1990, pp. 16 17) noies ihai ihere h'ere discrcpancies in the ll ra]' energ,ies measured bv various melhodsi by 19i10 "a consensus seems to havc been achieved,"but this was in large part due to the "almost universal use of the magnetic spectrometer"in measurements canied oui in ihe late 1930s.

20. In a different conlext ihe coincidence ar[iument may have more force. For insiance, consi.ler Ian Hacking's (i983, p.202) famous argument for the reality of smallstructures obseNed with differeni types of microscopesi "It would be a preposterouscoincidencc if two iotally different kinds of physical systems here to produce exactlvthe same arrangements of dots on micrographs," iI the dois werc ärtifacts. T})e mutualgmundint beth€en the different t)'pes of microscopes probably had not played a crucialrole in the designing of eäch.

Persp€ctivca on Scicnce .t 65

circular. But we can also dispense with absolute criteria, at least provi-sionally and regard the mutual grounding as a process of conceptbuilding. When two nomic measurement methods are brought to-gether by mutual grounding, a pattern is revealed between two distinctsets of phenomena. For example, Whiddington's grounding of materialret.rrd.rtion in mag,nelic deflection {or vice versd) would have been im-possible had there not been a stable correlation between how muchmetal electrons can penetrate and how much they are curved in a mag-netic field. The success of the grounding shows the existence of thecorrelation, for otherwise the result of the attempted grounding wouldhave been incoherent. The abstract concept serves as a means of or-ganizing such correlations, as a rubric under which they can be under-stood or at least collected. Every time one measurement method isgrounded in another, a new correlation is established between twopreviously unrelated sets of phenomena. Such a new correlation addscoherently to the meaning of the abstract organizing concept.

From this perspective, the problem of nomic measurernent indicatesa useful starting point for concept building, rather than a hindrance toreliable measurement. Potentially, every empirical regularity gives anomic measurement method. But no empirical regularity involving theconcept can be established without an independent means of measur-ing it, so every regularity requires a connection between two (or more)measurement methods and a correlation between sets of phenomena.The necessity for grounding becomes the opportunity for establishingnew correlations. In this manner the concept grows more enriched asthe web of interconnected measurement methods grows more in-tricate.I

Initially I treated measurement methods as ways of getting at someconcept whose meaning was preset. but it is also possible thai the con-cept itself arises from the web of interconnected measurement meth-ods. That is to say, we do not have to start with measurement methodsas such and then try to connect them with each other. We can start byobserving correlations among sets of phenomena and then obtain aunified view of those correlations by postulating a more abstract con-cept. If we look at the web of measurement methods as the sorl'ce ofihe concept, the connection between the various methods takes on a|erv different meaning. The concept does not exist apart frorn the in-

11. Concepts ihai are built up in this way would have much durability. sinc€ ihey::e based on empirically well-established laws. These laws arc not easily affected byrer\' discoveries made in other domains of phenonena, because they are particular laws;:her are also not easily affected by changes in fundamentat theories, because they are:henomenological laws.

166 Circul.rity dnd Reliabitity in Measur€menr

terconnections, and each method cannot even be considered a rnea_surement method in the usual sense u,hen it stancls alone. This is notto deny that there are measurements that are attempts to get at thevalues of well-established concepts; however, there are othei cases inr,r'hich measurement methods are essential in the process of conceptbuilding.

This perspective has some affinity to Percy Bridgrnant (1927) view.Recognizing that a given concept might be nreasureä bv many possiblemethods with no intrinsic connections to each other, Bridgman (1927,pp. 10 25) maintained that each measurement method defined a separate concept, in principle. For practical purposes, Bridgman allowed,we may regard the different methods as me.rsuring the same conceptif they give convergent results in overlapping domains of application.rlBridgman's convergence is not so different frorn r,r,hat I call mutualgrounding. The significant difference between Bridgrnans view anclmine is that Bridgman came close to suggesting that the method ofmeasurement c-rlrolsfs the meaning of a concept, rr hile I do not wantto make any such suggestion. This difference has signilicant bearingson the question of reliability; to handle the question of reliability prop_erly we need to operate with a more comple\ notron of meaning thinBridgman's. I will not offer or even discuss anv full-fledged theoiies ofmeaning, but I will make one small suggesfion that slrould be compati-ble witli a broad range of theories of meaning.

What is the sense in which a measurement method is ,,reliable,, ornot? Comnonsensically a measureneni method is reliable if it revealsthe true value of a quantiq/. What is this "true" r,alue, and how is itdetermined? If we are to speak of the true value of a quantiq, thequantity must have a definition. Here I want to make a distinctionbetween meaning and definition. One does not have to be an avid Witt-gensteinian to grant that the meaning of a concept is based on its vari-ous uses, which typically change in time and may even contradict eachother at a given time. The meaning ot any sign icant physical conceptis likely to be fluid and ambiguous. In order to regulate the meaning,we can impose a definition, which demands that all uses of the conceptconform to it.

A definition may be operational or theoretical. A concept has anoperational definition if its other uses are regulated by some methodsof measurement. Concepts such as length and time irave had opera-tional definitions, as there have been clear material standards of mea-

22. Ernst Mach (19E6, pp. 65 66) had made a similar point in his discussion of py

167

surement against which we attempt to judge all statements aboui those.oncepts in physics-be they the meterstick, the rotation of the earth,Lrr the oscillation and radiation of atoms. A theoretical definition, onihe other hand, is an abstract description to which the uses of the con-.ept are expected to conform. Most often, a theoretical definition con-itructs a concept from other concepts that already have definitionstuhich in themselves may be operational or theoretical) or whosemeanings are commonly understood wiihout explicit definitions. Forinstance, in classical mechanics velocity is defined as the timederivative of position, and acceleration as the time-derivative of veloc-iir lt would be possible to give direct operational definitions of veloc-itt and acceleration, but that was not the historical practice. It turnedout to be more appealing to maintain the theoretical definitions andtudge tl.re reliability of measurernent methods according to them.

lVhen we have a definition, we can distinguish correct and incorrectuses of the concept; for a quantitative concept, a definition fixes its.orrect value (or distributior.r of values) in any given situation. Hence,rn the presence of a clear definition, it makes sense to say whether a:reasurement method is reliable, in the sense that it gives the true'.alue of the measured quantity. The question of reliability becomesnuch more interesting and troublesome for concepis that do not have:recise delinitions, as there would be no unambiguous true values:here to be found. That has deeper implications than it seems at first:1ance; what is being undermined is the basic notion of measurement:s.rn activity of discovering an objectively existing value (or even the.,biectively existing probabilities that various possible values will ob-:rin). Let rne illustrate this point by going back to the case of kinetic:nergv in quantum physics, at the same time tying together some of:re ihemes that have emerged earlier

The first point I want to make about kinetic energy in quantum:hvsics is that it did not have a clear theoretical definition. In classical:h\.sics, kinetic energy was defined by the formula mv2,/2, which inr'irn lyas an expression of the equivalence of energy to rvork, which is:re integral of force over distance. This theoretical definition cannot.asilv be transferred to quantum mechanics, which has no place for:he concept of force in its equations. The only candidate I can see for: rheoretical definition of kinetic energy in quantum physics would be::.ed on the kinetic energy operator, P2/2IJ,.lt would certainly do for-..n abstract descripllor of kinetic energy to say that it is the eigenvalue-.i the kinetic energy operator, but the practices of laboratory measure-::'.ent proceeded without regard to this description. The electrostatic:.:ardation and the magnetic deflection methods relied wholly on clas-

Perspectiv€s on Scien<e

168 Cir(ularity and Reliability in Measurement

sical theory. The material retardation method relied on particular phe-nomenological laws, making few references to any kind of high-leveltheory Hence, at least in the laboratory, the quantum-mechanical ki-netic energy operator did not serve as an effective definiiion, since itwas almost entirely powerless in regulating the uses of the concept.

It is more difficult to say whether kinetic energy in quantum physicshad an operational definition. In the absence of a clear theoreticaldefinition, the correctness or cogency of statements about kinetic en-ergy was often judged on the basis of their consistency with measure-ment results. Hence one could say that kinetic ene.gy in effect, hadan operational definition in quantum physics. However, this putativeoperational definition was by no means a simple and precise one.There were at least three major independent methods of measuringkinetic energy and there was no one method that regulated all others.We can only say that all of the approved measurement methods collec-tively defined kinetic energy; if they gave mutually conflicting results,there was no clear and convincing way of judging which wai correct.That is to say in many instances there existed no precise value of ki-netic energy,23 and questions about the reliability of its measurementdid not have unequivocäl dnswerc.

There is notl.ring wrong with leaving concepts without precisedefinitions and dispensing with the question of the stdct retiability ofrneäsurement methods. The web of measurement methods held to,gether by mutual grounding can be a perfectly good source of a mean-ingful concept. However, it should be recognized that the mutualgrounding can almost never be perfect. First of all, it cannot be thor-ough, because different measurement methods have different domainsof application; as Bridgman noted, it is only in the "overlapping,, do-mains that mutuäl grounding can be carried out. And then, in thoseoverlapping regions, we can only do so many experiments; it is impos-sible to check the agreement between measurement methods in all pos-sible situations. The historical practice was to have results obtaineä inlimited domains serve as a check for a wider range of cases. There wassome nervousness about this practice, but attempts at double-checkingcould not be complete. Finall), when the mutual grounding is actuallycarried out, it is most likely that the result will not be periect. That isto sa), any measurement method is likely to be slightly unreliable if itis judged against another method. I believe suclr imperfect webs of

23. This pojnt has no direct relationship to quantum mechanical indeterminacy. Thelack of a prccise definiLion would mean that kinetic energy did not even have a preciseprubdbilrly diriribulion over il5 po,.ible \.rlu"-.

PerspectiYes on Science

:.r.:1:urement methods have provided operational definitions for some.:r'.Flrrtant concepts in quantum physics, including kinetic energy,:::ss, \'elociq, momentum, and angular momentum, all of which lost:reir classical theoretical definitions rvith the advent of quantum me-:ianics.r'It seems that quantum physics developed cluite well in rnany.enses rvhile leaving many of its fundamental concepts unclefined or-.'oselv deäned.

Ii should also be recognized, hor,rever, that there are some important:.rnsequences of leaving concepts without precise definitions and thuseaving their quantitative values imprecise ("l,tzzy"). For instance,

:,iFpo-se, as I think is the case in quantum physics, that energy does:,.: har-e precise values, even apart from all considerations of the un-,:::aintv principle. This threatens the conceptual basis for one of the:-.-.>t important principles in all of rnodern pl.rvsics, namel_v, the conser':::Lrn of energy. In general, any quantitative relation would be ren-::::d imprecise25 if the concepts involved in it did not have precise-'. ritions. Often experiments are quite imprecise for practical rea-. :.. and the inherent imprecision of meaning is masked. Hou'ever, if:.-. :recision of experiments gets pushed ever higher, the imprecision: reaning is bound to manifest iiself. I do not mean to imply that

: . .ics ah,vays has to be ertremelv exact. I think a good deal of good:' ..ics can be done and l.Las been done r'r'ithout high cluantitative pre: :: -.r. \\Ihat I do want to argue is that we should know what kind of: ..:c' is being practiced in a given situation-exact with precisely:...:.ed concepts, or more qualitative with concepts with loose mean-

:. The imprecision of meaning is easilv concealed by the exact- --n-,rtic.)l forrn- ot our eqlr,rtion'.

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-, ;"r!s ()f t/rr Roy, I Soc ie ty ol Lond o n, ser. A, 102:294-318.. 1923. "Tlre Studv of Forked c-Ray Tracks." Proceedings of fhc

: . .,t1 Sctcietrl of Londor, ser. A, 103:62-78.:.: : \iels. 1913. "On ihe Theorv of the Decrease of Velocity of Mov-

::r Electrified Particles on Passing ihrough Matter." Phllosophicnl'.1.;-;.u:lrc 25:10 31.

. 191r. "On the Decrease of Velocitv of Swiftly Moving Electri-:'=: Particles in Passing through Matter." Philosophical Magazirci:rii-o12.l- l::r has to do \\'ith thc climination of definite trajecto es and the concept of

::. :. ,_irantun1 nlechanics.::- lr.re.ise" herc should not be taken b mean "inaccuraie."

169

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Perspeclivcs on 5cien<€

of Radium B and Radium C;' Proceerlings ot' the Royal Society of Lon-dor, ser. A, 109:540-61.

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