The Trouton Rankine Experiment and the End of the FitzGerald Contraction

Transcription

1 Th Trouton Rankin Exprimnt and th End of th FitzGrald Contraction Dr. Adrian Sfarti 1. Abstract Assuming that FitzGrald was right in his contraction hypothsis, Trouton sought for mor positiv vidnc of its truth. In 1908 with A.Rankin, Trouton mad an attmpt to masur th chang of rsistanc of a wir whn orintd from paralll to transvrs to th thr drift. Four rctangular coils wr wound, mountd on a common stand and connctd in such a way that thy formd a Whatston ntwork, th wirs forming opposit arms of th bridg bing paralll. Th bridg was balancd whn th wir in two of th coils was at right angls to th thr drift and thn th whol assmbly was rotatd through 90 dgrs and th chang of balanc was tstd. Evry ralizabl prcaution was takn only to lad to a ngativ rsult as rcordd in Proc. Roy. Soc. 80A, , In th following w will giv a dtaild dscription of th xprimnt that mant th nd of th FitzGrald Contraction Hypothsis. Kywords: Trouton-Rankin, FitzGrald contraction.. Stup Dscription A Whatston bridg is a clvr masuring stup usd to masur an unknown rsistanc by balancing two lgs of a ntwork circuit. Hr, R x is th unknown rsistanc to b masurd; R 1, R and R 3 ar rsistors of known rsistanc and th rsistanc of R is adjustabl. If th ratio of th two rsistancs in th known lg (R / R 1 ) is qual to th ratio of th two in th unknown lg (R x / R 3 ), thn th

2 voltag btwn th two midpoints will b zro. R is varid until this condition is rachd. Dtcting zro currnt can b don to xtrmly high accuracy via a dflction galvanomtr. If th bridg is balancd thn th quivalnt rsistanc of th circuit btwn th sourc voltag trminals is indpndnt of th galvanomtr rsistanc, i.. : R 1 + R in paralll with R 3 + R x rsulting into: R ( R1+ R)( R3+ Rx ) = R + R + R + R 1 3 x (1.1) 3. Th Exprimntal Rsults For th bridg at quilibrium as sn in Fig. 1 th quivalnt rsistanc is: R ( R1+ R)( R3+ R4) = R + R + R + R (.1) Aftr rotating th bridg by 90 0 (Fig ), Trouton and Rankin calculatd th quivalnt rsistanc by taking into considration th FitzGrald contraction. If th FitzGrald contraction xistd, sinc th rsistanc is dirctly proportional with th lngth, Trouton xpctd to s aftr th 90 0 rotation of th stup that R 1 and R 4 dcrasd with rspct to

3 thir prvious valus whil R and R 3 incrasd with rspct to thir prvious valus (sinc thy wr prviously contractd by th FitzGrald ffct). Fig. 3 Wir Distortion Th wir rsistanc, assuming an lliptic sction is (s fig 3): l l R = ρ = ρ (.) S π ab For th wirs sn at th top of fig.3, th lngth l contracts according to Lorntz bcoming:: l =l/γ (.3) a =aγ a uncontracts by turning prpndicular to th dirction of motion and b, bing transvrs to th motion, dos not chang. Th wir at th bottom of fig.3 : l =lγ a =a/ γ (.4)

4 Th wirs conncting to th powr supply bfor and aftr rotation hav th sam rsistanc du to thir carful initial orintation at 45 0 with rspct to th dirction of motion. In addition, thy wr chosn to hav nar zro rsistanc. From (.3) w infr: R 1 =R 1 /γ (.5) R 4 =R 4 /γ From (.3) (l rturns to its pr-contractd valu) and (.4) (a contracts) w infr that: R =γ R R 3 =γ R 3 (.6) 1 whr γ = 1 v c ( R ' + R ')( R ' + R ') ( R / γ + γ R )( γ R + R / γ ) R' = = R R R R R R R R R ' + ' + 3' + 4' 1/ γ + γ + γ 3+ 4 / γ (.7) In othr words, th xpctation was that aftr rotating th balancd bridg by 90 0, th bridg would bcom unbalancd (R can b qual to R only if γ=1.), so th galvanomtr would dtct a voltag drop. In rality, Trouton and Rankin obsrvd a nar-zro dflction, i.. a dflction svral ordrs of magnitud smallr than prdictd by thory. Th Trouton-Rankin xprimnt markd th nd of th Lorntz-FitzGrald contraction thory. Th xprimnt has bn r-nactd svral tims -6 with sam rsults and highr prcision. 4. Rfrncs 1) F.T. Trouton and A. Rankin, On th lctrical rsistanc of moving mattr, Proc- Roy Soc, 80, 40, (1908). ) C.T. Chas, Phys rv, 30, 516, (197). 3) R. Tomaschk (194). Th conduct of light of xtratrrstrial light sourcs. Annaln dr Physik 73: ) R. Tomaschk (195). Attmpt at th locating of th lctrodynamic ffct of arth movmnts at high altituds I. Annaln dr Physik 78: ) R. Tomaschk (196). Concrning an xprimnt on th location of lctrodynamic ffcts of th movmnt of th Earth at high altituds II. Annaln dr Physik 80:

5 6) R. Tomaschk (197). Commnts on my tsts on th dtction of lctrodynamic ffcts at high altituds. Annaln dr Physik 84: