Maudlin - Galilean Relativity and Lorenzian Contraction

7/23/2019 Maudlin - Galilean Relativity and Lorenzian Contraction

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Galilean Relativity and the LorentzContraction

Tim Maudlin, NYUSplit, July 7, !"#



$hat i% Galilean Relativity& 'n honor o( the #)!th anniver%ary o( Galileo*%

+irth, it %eem% appropriate to revie andappreciate the principle o( -Galilean Relativity.or -the e/uivalence o( all inertial (rame%.,%ince it i% a phy%ical principle o( endurin0importance1

't i% al%o %omehat o+%cure, and o(ten

mi%under%tood1



2ne $orry 't i% %ometime %aid that the Special Theory o(

Relativity can +e derived (rom to principle%3

"4 Galilean Relativity

4 The Con%tancy o( the Speed o( Li0ht

5ut i( %o, then General Relativity mu%t reject one o( the%e principle%, %ince it i% not SpecialRelativity1

$hich one&



6nother $orry '( the principle i% -all inertial (rame% are

e/uivalent., then e have to no hat aninertial (rame i%1

't i% al%o e%%ential to no hat %ort o(-e/uivalence. i% meant3 8u%t e/uivalence o(observable behavior or e/uivalence in %omedeeper %en%e1



9or :;ample 'n one %en%e, Netonian Mechanic% i%

%uppo%ed to e;empli(y Galilean Relativity1

'ndeed, Corollary < in the Principia i% %uppo%edto prove %ome %ort o( relativity principle, atlea%t (or impact (orce%1

5ut accordin0 to Neton, not all -inertial

(rame%. are phy%ically e/uivalent3 there i%e;actly one (rame at -a+%olute re%t.1



Symmetry =rinciple%2ne ay to characterize Galilean Relativity i%

a% an assertion of the existence of a space-time symmetry 1

The relevant %ymmetry ould +e %ymmetryunder a -+oo%t. o( %ome %ort1

Thi% approach %u00e%t% a characteri%tic that

could hold in Netonian 6+%olute Space and Time, in Neo>Netonian Space>Time, and inMino%i %pace>time1



Note 'n%o(ar a% the principle invoe% %ituation% that

are observationally indistinguishable, the%ymmetry need not +e a complete %ymmetry1

Thi% i% true in Netonian 6+%olute Space1 5uthatever i% not invariant under the %ymmetry?e101 6+%olute <elocity4 cannot +e o+%erva+le orhave o+%erva+le e@ect%1 So one ould +etempted to drop it, i( po%%i+le1

9or Neton, only relative di%tance% areo+%erva+le and only relative velocitie% appear inthe (orce la%, and the%e are pre%erved underthe +oo%t1



Cla%%ical 5oo%t

r

s



Relativi%tic 5oo%t

State SEQ

Light

Light

State S’



6ctive and =a%%ive

Tran%(ormation% 'n the Relativi%tic ca%e, the +oo%t create% hat Lorentz

called -corre%pondin0 %tate%., i1e1 %tate% that tae the%ame coordinate dependent form relative to di@erent

Lorentz (rame%1

$hen +oth %tate% are then re(erred to the %ame (rame,thi% called an -active tran%(ormation.1

Mathematically, thou0h, thi% %eem% to +e the %ameprocedure a% de%cri+in0 the same %ituation u%in0

dierent (rame% o( re(erence1

5ut i( %uch a pa%%ive tran%(ormation i% really e/uivalentto an active tran%(ormation ?'n %ome %en%e4, then it i%trivial that there are no o+%erva+le di@erence%1



Galileo*% :;periment9or a Anal indication o( the nullity o( the e;periment%

+rou0ht (orth, thi% %eem% to me a place to %ho you aay to te%t them all very ea%ily1 Shut your%el( up ith

%ome (riend in the main ca+in +elo dec% on %ome lar0e%hip, and have ith you there %ome Bie%, +utterBie%, andother %mall Byin0 animal%1 ave a lar0e +ol o( aterith %ome A%h in itD han0 up a +ottle that emptie% drop+y drop into a ide ve%%el +eneath it1 $ith the %hip%tandin0 %till, o+%erve care(ully ho the little animal% Byith e/ual %peed to all %ide% o( the ca+in1 The A%h %im

indi@erently in all direction%D the drop% (all in the ve%%el+eneathD and in throin0 %omethin0 to your (riend, youneed thro it no more %tron0ly in one direction thananother, the di%tance% +ein0 e/ualD 8umpin0 ith your(eet to0ether, you pa%% e/ual %pace% in every direction1



:;periment Con*t1$hen you have o+%erved all the%e thin0% care(ully ?thou0h there i% no dou+t that

hen the %hip i% %tandin0 %till everythin0 mu%t happen thi% ay4, have the %hipproceed ith any %peed you lie, %o lon0 a% the motion i% uni(orm and not Buctuatin0thi% ay and that1 You ill di%cover not the lea%t chan0e in all the e@ect% named, nor

could you tell (rom any o( them hether the %hip a% movin0 or %tandin0 %till1 'n 8umpin0 you ill pa%% on the Boor the %ame %pace% a% +e(ore, nor ill you maelar0er 8ump% toard the %tern than toard the pro, even thou0h the %hip i% movin0/uite rapidly, de%pite the (act that durin0 the time you are in the air the Boor underyou ill +e 0oin0 in a direction oppo%ite to your 8ump1 'n throin0 %omethin0 to yourcompanion, you ill need no more (orce to 0et it to him hether he i% in the directiono( the +o or the %tern, ith your%el( %ituated oppo%ite1 The droplet% ill (all a% +e(ore

into the ve%%el +eneath ithout droppin0 toard the %tern, althou0h hile the drop%are in the air the %hip run% many %pan%1 The A%h in their ater ill %im toard the(ront o( their +ol ith no more e@ort than toard the +ac, and ill 0o ith e/ualea%e to +ait placed anyhere around the ed0e% o( the +ol1 9inally the +utterBie% illcontinue their Bi0ht% indi@erently toard every %ide, nor ill it ever happen that theyare concentrated toard the %tern, a% i( tired out (rom eepin0 up ith the cour%e o(the %hip, (rom hich they ill have +een %eparated durin0 lon0 interval% +y eepin0them%elve% in the air1



Not a 5oo%t in 6+ove

Sen%eGalileo*% o+%ervation% do not compare a 0iven

%tate to a +oo%ted %tate in the %en%e e havedeAned1

Rather, Galileo di%cu%%e% o+%ervation% madeusing the same equipment +e(ore and a(ter itha% e;perienced an acceleration1

Nothin0 in our deAnition o( a +oo%t re/uire%any con%ideration o( the phy%ical e@ect% o(acceleratin0 a %y%temE



& & && &



$hat Fetermine% the

Tran%ition& The mathematical +oot operation determine% the

relation +eteen a 0iven global %tate and thecorre%pondin0 +oo%ted %tate1 5ut it i% rather the

physics of the material and the details of theacceleration that determine% hat the upper %tate ill+e 0iven the loer %tate1

Galileo*% a%%ertion i% that that phy%ical tran%(ormationill lead to an empirically indi%tin0ui%ha+le %ituation1

Note3 it need not +e indi%tin0ui%ha+le durin0 thetran%itionE

$hat mu%t the phy%ic% +e lie to achieve that&



Corollary <' 'n the Principia, a(ter provin0 Corollary <, Neton

prove% Corollary <'3 If bodies, any ho movedamong themselves, are urged in the direction of

parallel lines by equal accelerative forces! they illall continue to move among themselves, after thesame manner as if they had been urged by no such

forces"

'( Corollary <' hold%, then one could All in the 0ap

+eteen the to %tate% ith e/ual accelerative(orce%1

The re%ult ould +e a Galilean tran%(ormation+eteen %tate%, not a #orent$ transformation1



The Rocet =uzzle 'n hi% paper on ho to teach Relativity, 5ell

relate% a di%cu%%ion at C:RN a+out an oldpuzzle3 i( a %trin0 i% tied +eteen pro8ection%

comin0 o@ to identical rocet%, and therocet% are i0nited %imultaneou%ly ?in theirinitial re%t (rame4, %o their tra8ectorie% ill +eparallel ?i1e1 they maintain the %ame di%tanceapart in the ori0inal (rame4, ill the %trin0

+rea&

?$e could add lot% o( little rocet%, one (or eachlittle %tretch o( %trin01 Then it ould AtNeton*% condition14



The Set>up

Rocet " Rocet

Thread

:/ual>t %lice in theinitial re%t (rameo( the rocet%



The Up%hotSince Neton*% Corollary <' lead% to a Galilean

tran%(ormation a% a +oo%t %ymmetry, and theLorentz tran%(ormation i% not the Galilean

tran%(ormation, Neton*% Corollary <' had+etter +e +roen +y the Relativi%tic dynamic%implementin0 Galileo*% e;periment1

'n %hort, the particle% in the %trin0 mu%t not

continue to move amon0 them%elve% in the%ame ay hen accelerated a% henunaccelerated i( Galileo*% phenomenolo0y i%pre%erved1



The Lorentz>9itzGerald

Contraction The phy%ical e@ect o( acceleration needed to 0et

the ri0ht re%ult (or Galileo i% produced +y thephy%ical (orce% that maintain a -ri0id. %olid in it%

e/uili+rium conA0uration1

9or e;ample, in order (or the pair o( rocet% toend up in the proper Lorentz>tran%(ormed %tatea(ter the rocet% %top Arin0, they mu%t +e dran

closer together" '( the %trin0 ere a very %tron0ca+le, the rocet% ould +e dran to0ether +yten%ion in the ca+le1 '( the (orce needed to eepthe rocet% to0ether i% 0reater than the ten%ile%tren0th, the ca+le ill +rea1



The =hy%ic%$hat 5ell %ho% in hi% paper i% that the

electroma0netic (orce% in %uch a -ri0id. %olid ?inhi% analy%i%, a %in0le atom4 ill produce %uch a

-contraction.1 6+%ent %uch (orce%, the end %tatea(ter the acceleration ould not +e the-corre%pondin0 %tate., and Galileo*%phenomenolo0y ill (ail1

Suppo%e, (or e;ample, the rocet% are %endin0radar %i0nal% +ac and (orth1 '( the ca+le +rea%,and the rocet% are not dran to0ether, thena(ter the acceleration the timin0 o( the %i0nal%ill chan0e, contrary to Galileo*% prediction1



Solid% and :/uili+rium 't i% e;actly +ecau%e the e;perimental apparatu%

i% a solid that one doe% not have to concernone%el( ith the detail% o( the acceleration

pha%e3 any part o( the in%trument can +e actedon directly to produce the acceleration, and theinternal dynamic% o( the %olid to yield a uni/ue%tate once the acceleration is over and thesystem relaxes bac% into equilibrium1

'( the e;perimental apparatu% ere not %olid,then the Anal %tate ould depend %en%itively onho the acceleration i% carried out, and acorre%pondin0 %tate ould not, in 0eneral, re%ult1



Michel%on>Morley The Michel%on>Morley e;periment centrally

involve% an acceleration3 the rotation o( thein%trument (rom one orientation to another1

The apparatu% a% an ela%tic %olid, %o the end%tate ould +e a corre%pondin0 %tate, and theinter(erence +and% ould not %hi(t1

Thi% prediction depends critically on the#orent$-&it$'erald (contraction) as e havede*ned it , i1e1 on the internal electro>ma0netic(orce% in the apparatu%1



2n -Contraction. The internal dynamic% o( the %trin0 ?+reain04

or the ca+le ?deBectin0 the rocet%4 or theMichel%on>Morley apparatu% hen rotated mu%t

+e taen into account hen main0phenomenolo0ical prediction%1 In some framesof reference the%e e@ect% ould +e de%cri+eda% a -contraction.1 'n other%, that ord ouldnot +e u%e(ul1 5ut in every (rame, the internal

dynamic% mae% a di@erence1

$ithout it, the Galilean phenomenolo0y ouldnot occur1



Galilean Relativity and the-Con%tancy o( the Speed o(

Li0ht. The (act that certain phenomena ill +e

invariant +e(ore and a(ter an acceleration,to0ether ith the e;i%tence o( a li0ht>cone

%tructure, account% (or -the con%tancy o( the%peed o( li0ht.1

6ny e;perimental method de%i0ned to +e%en%itive to the -%peed o( li0ht. mu%t +e

%en%itive to the tra8ectory o( a li0ht ray throu0h%pace>time1

Such a method need not even attempt toquantify the -%peed o( li0ht.1



9or :;ample

Li0htSource

Screen



Corre%pondin0 State%

StateS:

StateS*

Li0htRay

Li0htRay



There(ore '( the machine i% tuned to allo the li0ht ray

throu0h hen oriented in one direction, thenrotated or linearly accelerated and alloed to

return to e/uili+rium, the li0ht ray ill %till 0othrou0h1

'n thi% e;ample the li0ht %ource it%el( i% part o(the apparatu%, and 0et% accelerated to a ne

%tate1



'n 6dditionH1 The e;i%tence o( a li0ht>cone %tructure entail%

that the tra8ectory o( a li0ht ray i% independento( the %tate o( motion o( the %ource, %o one

ould 0et the %ame re%ult (or li0ht (rom any%ource1

Thi% i% all e mean +y -the %peed o( li0ht i%con%tant.1

Galilean Relativity plu% the li0ht>cone %tructureyield% all the phenomena e a%%ociate ith-the con%tancy o( the %peed o( li0ht., evenhen no %peed i% a%%i0ned to li0ht at all1



'n Conclu%ion 'n Relativity, unlie Netonian phy%ic%, the

phenomenon o( Galilean Relativity depend% oncertain dynamical (eature% o( the (orce% that

mae -ri0id. +odie% -ri0id.1

The%e internal (orce% create chan0e% in the%tate o( an accelerated +ody that can +erea%ona+ly called a Lorentz contraction1

So the Lorentz contraction, a% a physical e@ect,i% indeed e%%ential to e;plain the +a%icphenomenolo0y o( Relativi%tic phy%ic%1

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Maudlin - Galilean Relativity and Lorenzian Contraction

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