zotero-db/storage/GTHQHCZ4/.zotero-ft-cache

THE EVOLUTION
OF SPACE AND TIME
Paul Langevin
The attention of physicists has of late been directed baok to the [undo.mental concepts of spaoo and time, which they ar~ being forced to r~bape in the light of new experimental facts. Nothing demonstrates the empirical origin of these concepts more clearly than their cont.i1ming adaptation to the increasingly refined data of human experience.
1 should like to show tbat the form i111 wbiob these concepts have hitherto been presented, which as a rule is not analysed with sufficient care, waa determined ancl conditioned by a specific anl(] provisional synthesis of tho world, m\mel,1•, by the mooharustic theory. Ou.r space and our time have in fact been thoi;o devised to suit the neods of rational mechanics,_
The new and increasingly authoritative synthesis of physical phenomena that is ropr"1!ontod by the eleetromngne&fo theory introduces a space and a ti me {and pa!'ticularly a Umc) which are different irolll those of lllecharucs and which 11re supported by the methocla of eitperimentru investigation now available to us. It is particularly remarkable that even today we 1ue still being compelled by the increasing refinem,eot of our methods of measurement, the accuracy of which ha& in some casea been pushed beyond one part in a thousand million, to contiu ue the adapta.tion to establi.!!hod fact of the most fundamental categories of our thought. This surely coustitutos, for the philosopher, an excellent opportunity of penetrating the innermost nature of these cat-egori~, in that he ean see them .still in the course of evolution, alive and changing bMore his very eyes.
Neither space nor time exists a vr-wri: for every moment in time and for every degree of refinement of our theories about the physical world, there is a correspon(ling conception of space a.nd time. The mechaniatie theory intl'od uced the old conception, and the eloetromagt1etio theory is now demanding a new one, but there is nothing to justify our aa-ying that tbis will be the deftn.itive one.
Furth0rmore, it is difficult for our bn,in to become accustomed to these new form.a of thought: their aai,im.ilatioo presents particular problems, anti can be aided only by the formation of an adequate language.
This is the task in which, to facilitate. the evolutio.u of tho human apeciea,
. ... tho philol!ophera and pbysfoillta of tod!\y must collabor.ate.

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All living bcings havo 1i capacity for internal and spontaneous expansion that inoreal!CII wi th I.heir degree of adaptation to the environ ment into which they have been born. "'ben, as a result of this expansion, an encounter takea place between indivill uala 01· spooios, tho outcome is either mutual adaptation or, il ag:reeroOJJt is impossible, conflict ending Jn sun·ival of the fittest, which usually assimilates the substance of the other and imposes upon ii, a now form that life appears to have judged to be b ettor.
It is tho same with our physical theories: some will have been particularly well formulat-od and will have succeoded brilJiantly io the interpretation anti ordering of one category of experimental facts which i:epresenJ matter llpon whicl1 they impose a form; they then dovclop spontanoo1111ly in aooorclance
with this form and rhythm of their own, using as mat-Oria.1$ for the edifice that
they construct firstly facts which aro nlreai.ly k11 own but not yet ordorod, thon faote to whose dillcovcry tbey load tho way, an,t finally facts tbat have already boon incorporated into syntheses in the form of other theorie11 which the new theory absorbs after entering into conflict with bbem.
Just aa the process of constructing living beiugs is aided by tho orga11ic syntheses already pr()8ent in the other beings on which they food, so the new theory retains and uses t-o diffcri.og degrees the orderings of foots nlread,I' accomplished by the theories that it has sup_plaote,J.
At the present time, we are witnessing n coofilct of this kind between two p&rliculady important and elegant conceptions of th,• world, namely. the rational mechanics oi Galileo and :Newton and the electromagnetic theory in the mnture form given it by Maxwell, Hertz a.nil Lorentz.
Rational meobanics wns created to interpret tho pheno1Mnn of visible
ruction, and sucMOds admirably in doing tbjs_ Throughout the eighteenth century and for much of the nin&toou tb, all acientiflo effort was devoted to extending this interpretntivo capacity to cover all physical phenomena, by applying these same laws to the invisible motions of material particles or or fluids of dilterent kinds.
It wM in this way that the doctrine kuown as mechanism developed, by a fusion or rational mechanics with the hypotheses of atomic theory. It wae highly suoocsdul in some fields, such aa the kinetic theo ry of Ouida, for example, l>ut IC88 80 in others, sr1cb na elasticity and optics.
It must not bo forgotten that tho fnilurCA of mechanism are often blametl entirely upon tho atomistic concept-ion, yet this has now been dofiniti-vcly estnbliahetl on th o ba11ia ofiorlillputab lc experimental facts, and its combinatioo with the olcotromagnetie tboory bas proved remarkably fruitful over the last 6Jteon years. What really seems to have been the unreliable factor involved is the application to invisible motions of tho laws of mechaoics, which were originally formulated for visible motfons. and represent even for tbeso nothing more than a first approximation, albeit an oxcelleot one.
The theory of electromagnetic phenomena. ai, we know it today is certainly independent of the lnws imposed upon tho motion o-f matter by rational mechanics, even though the latter theory apl)eats to contribute to certain fundamental de6.nition11. The best proof of thia independenceia furnished by the contradictions that nre now arising between the two syntheses.
Electromagnetism ill os closely adapted to it.fl primary field aa rational mechanics waa to ita field. With ita specialized conco_pt-s of a medium which
trn.nsmits actions .atop by step and ot electric and magnetic fields which characterize tho state of this medium, and with the highly specific form of the relation&

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that it clefhtes between the simultaneous variations of those f,elds in space a.nd in tim e, el(lOtroma.gnetism constitute~ a discipl~e or a wa,y of thought which is quite scpa.rato and quite distinct from mechanics and posscssea an a$tonisbing capacity for expana.ion, in that it hns effortlessly aljlji:milatoil tho vast fiold of optics ancl radiant heat, in th-El face of which mechanism remained powerless, and is constantly leacli.ng the way to now discoveries in this field. &lectroma.gnetism hall conquered the greater pa-rt of physic.a, inva-ded chemistry, and or<lered a vast array of faots formerly lacking any form OF coherence.
Of our two opposing theories, the first boasts the titles of an already ancient past and possesses the authority of hiwing seen its laws verified by both the most distant stitrs ancl the most minute 01oleculos of gases, while tbo Gccond, whiob is younger and -moro a-li'l"o,. is inftuitoly better adapted to physics as a whole aucl possesses an intern.al capacity foi· gtowtb that the other
seems to have lost. MaX\voll believed it possible to reconcile the two theori.cs and to show
that electromagnetic phenomena allow of mech1micalinterp1·0tationa. Howqver, bis demonstration of this, which was anyway bas11d on tho special case of the phenomena dfaplayed by closed currentR, proves merely that the two syntheses ha.vo some featnres in common and share the property of giving certnin inl;egrals stationary values; they mtty 1·0.mni11 irreconcilable with respect to other foaturea.

* * ,.,

These divergent featul'es lmve recently boon emphasized by new o:J.perimental faetll. namely. by the lack of auocess encountered ill all the experiments (some of them of an e:s:traordinary degree of reftnemel) t) that have been undertaken in an attempt to demonstrate.the collective u11iform translational motion of a material system by means of exp.eri1nents made within this system, that is. to define absolute translational rnoti,on.
It waa already known , and i.r:td<lO<.t rational mechanics accounts quite adequately for this fact, that mechanical e:xperimenta on visible motion, that are catried out within a material system cl o not make it possible to demonstrate a collective uniform translational motioo of this system, but they do make it possible to show rotational motion by means of Foucault's pendulum or the gyroscope. In other words. from the moohnttics point of view colleo.tive uniform translation baa no absolute meaning. whereas rotation iloes.
Howevor, it ia possible to carry out ,vithin a material system other experiments which in vol\"e oleotromagnetfo or op tical phenomena. In its explan~tions, the electromagnetic theory assumes the existence of a metl.ium, the ether, which transmits electric and magnetic actions an<l in which electromagnetic perturbations, an\l light in part.icular, are propagated at a specified velocity.
It was hoped that, if a material system ill moving in uniform translation relative to this medinm, electrom~gneti-o or optical experiments ca.med out within the ayatem conld make it p-ossil>le to determine and to demonstrate
this trM.slation. Since the Earth, iu its annual moti.<>n, po$seases a translational velocity
that v-M'iea constantly by amounts ranging up to sixty kilometres per second for the relative velocity corresponding to two diametrically opposite positions of the globe in its orbit, it was hoped that, at leMt at certain moment.s in the

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year, observers and their instru.menla on the Earth would be moving with respect to the ether at a velocity of this order and would be able to demonstrate their motion.
The grounds for upccting this wero that when the fundamental cquatione of electromagnetism, which aro assumod to be valid for stationary observeni in the ether, were combinod with the ordinary concepta of space and time as stipulated by rational mechanics, it was found that these equations should undergo a change of form for observora in motion in the ether, and that the ui:Jierenccs, for ,·elocitios of the order o'f that of the Earth in its orbit. should be visible in certain highly relined ex-periment<&.
Tho result. of such oxporimont~ luwo, howe v1Jr, always been negative, and independently of any interpretation we can state as nn experimental fad tho content of the following principle, known aa the principle or relativity:
If varioua groups of obsorvers are in uniform motion relative to one another (for instance, oliservers on the Earth for various positions of the latter i.u its orbit), all m0chtutical and physical phenomena will obey the same Jaws for all of these groups of observers. None oi them will be able to demonstrate, on tho basis of oxperimeuts oani.ed 011.t within tho material system to which ho belongs, the colleeLive uniform motion ol this system.
From the l'Jectromagnetics point of viow, it can also be sai,1 that the fundarnontal equations, in their ordinary form, are verified for all of theso groups of observe.rs simultaneously, and that everything happens for each of them R6 if he were motionless with respect to tho ether.

• ••

Thus, it is an exporimental fact that the equations between physical quantities that we uso to express tho laws of the external worltl necessarily have exactly the same form for different gToup11 of observers, or for di.llerent r&Ierence systems that are in unifor m translational motion relative t,o one another.
This .requ.irea, in the language of mathemaUos, that these equations should allow of a group of tranaformati.ons corresponding to the transition from one reference system to another that is in motion relative to it. Tho equations of physics must remain valid for all the transformations in this group. In a tranllformation of this kind, when a. tranaition is made from one reference syst-em t,o another, moa11urements of the various quantities, particularly those conesponding to space and time, Me modified in a way that correspondt1 to the very structure of these concept.a.
'.("he equat,ions of rational moohanics effectively allow of a group of transformations correepondiug lo the change ot reference syet.em, and the part of this group that concertl.8 me8.81lrement,s of spaeo nnd time is in agreement with the or hnary form of these concepte.
H will be Lorentz's main olaim to fame that he demom,trateJ thaL the (undomental equations of electromagootism aleo allow of a group of transformations that enables them to resume the samo .form when a transition is macle from one reference system to another. Thill grQU,p diQt!TB j,undament-0Uy /rcnn
1M abo~ grou,p (Ill rtgarm lrans/ormatiinlB of B'pace and time. We have to ohooao. Jfwowiah to retain au a)Jsolute va.luofor the equations
of rational mechanica, that is, for mechanism, and hence for the epaoe and

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time that correspond to them, then wo have to regard those of eleotromagnetism as false and renounce the admirable synthesis that we discussed above, returning in the fiel<l. of optics, for example, to a theory of emission with all the aasociated difficulties that caused it t9 be rejected more than fifty yoars ago. If, on the other hand, we wish to retain electromagoetism, then we have to adapt our way of thinking to the new conceptions of space ancl time that it demands, and regard rational mechanica as being no more than a first appro.:t-imatiou, although one that is moro than a.dequ.ate in tho case of motions whose velocity 1loes not exceed some thousands of kilom,et.res per second. Only electrnma.g. netism (and those laws of mechanics thi~t allow of the same grQup of transformations as electromagnetism) would make i.t po.ssible to go farthor. and it would then a11~ume the leading position that mechanism aasignod to rational mecba.nios.

• • •
To clcmonatrate the opposition betwe.e1i the two synth0$ea more clearly, it is simpler to fuse the two concepts of space ancl time toge.ther in tho more general concept of world, as w11..s suggested by Minko,vski.
Tho world is the ensemble of all events: an ovont consists il\ ~omethi11g taking place or existing in a certain placo at a certain moment in time. With a givon reference system, that is, a syetern of ax:cs associated with a certain group of observers, any event is d.otermined from the point of view ofits position in space and time by four coortlina.tc11 related to tbia reference system, three
for space apd on8 (or timo.
Any two events rel.atod to any one, reference system will gonera1ly diffor both in space and in time, that ii,, they 'Will take place at different points at different moments in time. Thus, for any pair of events there will be a corresponding distance in space (that between the points at W'hi.oh the two events tnlce place) and interval in time.
Thus, timo cn.i1 be defined a1; the ensem,blo of events t,hat t&ke plaoo successively at, any one point. as, for example, in any one port.ion of matter rolated 1,o the reforenl)e system, and spaC0 can bo def1Dod as the ensemble of simultaneous events. This deftn.it.ion of space is equivalent to saying that the form of a body in motion L~ defined by the e11semble o[ the simultaneous positions of tho various portions of matter of which it consists, or of its various material points, an<l by the ensemble of events 1·opresonted by tbe simultaneous prOBcncca of these various material points. If we follow Minkowski in calling tho ensemble Qf events that take place r,mcCOl!sively in a portion of matter that can be in motion relative to the reference system tho world litt~ of toia vortiou of matter, the form of a body at ·any given moment in time is determined by Lhe ensemble of the simultaneous positions 011 their world lines of the various material points Lhat make up this body.
The concept of simultaneity of event,1, that take place at different points is therefore fundamental to the ,ory clefrnition of space when we ar-e concerned with bodies in motion, ancl this is the g<lneral case.
!11 the u.maL co-1tc11ptum of tinie, a·n absol.ute meaning is attribtded to this sintulta.11.eiiy, that is, it i8 amwied to /Je i-n<wpendimt of tl1e reference sy8te1n . Wo need, however, to analyse the content of this gilner11lly tacit assumption more closoly.
Why nxo we usually anablo to aooopt that two events that are simultaneous for any one group of observers may not be so for another group that is in motion

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relative to the llrat, or, what amounts to the same thiog, why do we not aooept that a change of reference system makes it possible for tho order of succession in time of two events to bo reversed t
Tho reason for this is, obviously, that we assume implicitly that if two eventa follow oacb other in a certain order for a given reference system, it is po88ible for the one that took place first to ha.v o aote<l as on.use and llltered tho conditions in wbioh the second took place, whatever the distance separating them in space.
In thege conditions, it is absurd io suggest that for other observers, or
for another reference system, the second event, or effect, can precede ita cause. The absolute nature that is normally attril>uted to the eoncopt of aimu-1-
taneity is therefore based on the implicit hypothesc,. of a causality that can travel at an infinite velocity, i.e. the b ypotheai8 that an event can act instantaneously ns cause at any clistance.
This hypothesis conforms with lbe mechaniatic conception and is required by it, since a porfect !!olid of rationa.J mechanics, or, for exrunpfo, on inelastic bell-pull stretchod between the two points at which tho events take place, would mako it possible to signal the occurrenco o! the first e\·ont instantaneously at the point where the second is lo orcur, and would ronscquently make it possible to take the flrat into account an,! make it a.ct as cause in the conditions that govern t,bo seco11d. There is. thoreforo, mutual Mlaptation of rational mechanics and of tho normal conceptions of space and time in which tho Bimnltancity of two events that are aoparated in space possesses no absolute meaning.
lt is therefore in no wny surprising to observe that, in tho transformation gcou_p which retains t-he equations or mecbnnics, t.M i11tcn•oL o/ tim~ beticce,1 two e11011t, 1'tmaine constant and is n,cmnired in IM sam~ ,oay by all groups of observers, whatootl1' their ,-olative niotions.
This is not so i•i the case of their rlistance i11 ~pace: it i11 a quite plain fact, and ono that is incorporated in thenoirmal cono-0pti!, that the distance 8Cparal:ing two events in space does not genera.Uy havo nn absolute meaning and varies with Lh-0 reference ayl!t.om that is uaed.
A concrete example wilJ serve to clemoustro.te how the distance separating any two given eventa in space oan be different for various groups of observers that aro in motion relatJve to one .another. Suppose that two objects are dropped one after tho other through "' 11010 in the floor of a car th11t ia in motio11 relative lo tho ground ; the two 1>vo:ntl! represented by the emergence of tho two objects through the bole take J?laco at ono and the snmo point for observers in tho car, but at different points fo1· obse.rvel"1! on tho g1·ound. Tbo distance separiiting these two events in spaco is zero for the fir&t group of observers, whereas for the sooorrd group it is o qonl to tho pro.Jud of the speed oJ t.llu car by tho interval of time ijeparating the dropping of tbe two objects.
It is only in the caso where tho two oventa are simultaneoua that tlioir dilltan<.:e in spaco has an nbsolute meaning, that is, det>.s not vary with the reference system. l t follows direoMy from this that U1e dimensions o{ an object, such 1141 tho length of a rnlGT, have an absolute meaning and are the same for observers who are oither at- rest or in motion relative to this object. This ill because wo have observed that for all ob11erver& the length of a ruler is tho distance between two simultaneous positions of tho ends of the rulor, that is, tho distance in spaee separating two simultaneous presouces of the two ends of the ruler. We havoju.st soon that simultaneity, as also bbedistance

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in space separating two simultaneous events. ba.i an a-bsolutc mea.ning iJl the
normal conceptions of time and space. Given any two successive evcnt.s, that is. two events that are 6eparal-Od
in time, it will always be possible to ·fi.n<l a reference SJ6tem with respect to which tbeso two events coincide in 11pace, or observers for whom these two ovents tako place at one and tho same 11>oint. All that we Deed to do is to aasigD to these observers a motion 1·clative to the original referMce system such that, having witnessed the first eve:ut, they then witn()ss the secon(l, tl1~
two events thus taking place for tb.om a.t any one giv.en point near to tllim1:
we ne<id only assign to Urnse observera a velecity eq_ual to the guotie-nt o[ the 1listanco in spaoo sepa1·ating tbe two events rola-ted to tho original rofer-enec syi.tem by tho iute-rval of·time between t hem, and this will always be possible if this in to1·va l of time is not 1-ero, that is, ii t-he two events are itot simultanoou$.
,vo have seen that t:his posl!ibilit,y of engineering tho coincidence of two (went$ in space by a imitable choice of r-efer~nee system does not exist io the ease of time. ,;inoe tho interval of tin1P, soparnt.ing two ovent& baa an al>aolute moaning, that is, it is meast1rccl in t,he isiune way i11 all rnfcrcnce systems,
This eorn;.titutc8 a la(',k of s.vmmctr~" between the Mrmally acccepte<l spnce a,11Cl time which fa cl.i.mii111,ted in the new conceptions: with these,, tho
interval in time, like the distance in spac,e. becomes v!4·iable with the r(lferet1ce system, or -,,i th the motion of tho observer.
ln the now co11coptions, only one ,case remains. and has to remain, in which tho change of reference system haa no effect. and this ia !,he case in which the two C'Vents coincide both in space a.-n(l in t.i.me. This double coincidence has lo have an absolute meru,ing. ~iuoo it;, corresponds to an encounter lietwcen
tho tw.o e,,cn~, a,ncl this encounter·cau give rise to ti phenomenon, or a. new event, which ncccssa.rily has an absolntll meaning. Retnming to the cxo,mple used abo..,e, if the two objects t hat are <ll.·opped from tbe car through the same hole are droppod simultanepusly, th.at is, if their droppi11g coincides both in spaco aml in time, the result may be a collision and broakago of the objecta,
:.incl tl1is collision phenomenon h!l-8 an ab.solute 1neaning. This means that in no conception of thn wo1·1<1, wbctho1· that of elcotromagnetics or tl1ai, of meohanios, can coincideocc both in space and in time, if it exists for one group of obser..era, be ileniea by another group, whatever its motion relath0 e to the first. Both for those wbo see the oar going by aud for those who aro in ~he car, the two objects wm hiwe been br.okon rcoiprocitlly because thoy were
dropped at the same time and at the same point. With the excoption of th.is very special oai,e. it is eosy to see tl1a.t the
electromagnetic conception reqllires a fw1damental reshaping of lhe -world concept, Iu their usual [Orm, the equations of eloctromagnetiam st.ipuliito tba,t an eleotromaguetie perturbation snch as a Hgl1t wave. for example, trnvels i11, vacuo at a velooity that is constant in all directions and eq11al to a1>proxi-
Jt1ately three hunclred thousand kilomot,l'()(I per second. Siuce experimental faets tl1at have rf',eently been establish.eel have show11
t hat, if these equations are valid for one grou1> of observers, they must alao be so for a.ii others, whatover their motion relative to the first group, tbii; leaves us with the pa.re.<_loxioal fact that any givon light WllVC must travel at the same velooity for different groups of observers in motion relative to one another. Onegroup of observers secs a light ,v1we tra,velling in a. certain direction at a velocity of three bu.ndre<l thousand kilometres per second and secs 1\ second group of observers running aft.or thil! wa'Ve at a velocity that cnn be

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solccted 1\l'bitrnrily; notwithstanding this, tor this second group of observers the light w1we will still be moving with respect t-0 thorn at this samo velocity of threo hundred thousand kilometres per socond.
Einstein wni; the first to demonstrnto how this ncecss11ry consoquence or lbc electromagnetic theory Mn by itself det0rmino tho nature ef the epace aud time chat are req uired by tho new world concept. lt can bo seen from wJ1at bns been said 11bove that tJ:ie velocity of ligh t must play an essential role in tbe new statcmenui of physical ph,onomena. [t is the only v<'locity that remains const1mtwhen there is n transition from one roforonce 11ystmn to another, 11nd in tbo 1miverse of olectromagnctics it pl(l;ys tho role plnyed by infinitt> ,·elocity in the uni"ert1e or moohnnies. 'rhiswill be shown ·clearly by tho resullR described below.
For any pa.ir of events, a change of reference system modi.fies both tho distance in space and the inten,aJ in timo separating 01em, but from tho poinb of view of the extent o! these modi.ficntions it seems advisable to clnasi!y pairA of events into two brond categories for which space nnd time play symmetric roles.
Tho first 1:ntogory consists of pail's of evonis such Uiat their distance in space is greater than the dista.noo tmvelled by light during their intervol in time. that is, such that if the occurrence of tbe two events is aecompnnicd h,v tho omission of light signals, oaeh of thc111 will tnko place beforo the a.rrivnl of the signal coming from tho other. A relationship of this kind has an ob11olute meaning, I.hat. is, it is \'alid for all reference BJ•stems if it is so for one of them .
The equations of trausformntiou that are required b,~· the electromagnetic
theory show that, in this case, tho order of 8UCC<'fl6ion of tho two ovenls in l,ime hM no absolute mMning. lf tho Lwo events follow each other in a given order for one roferenco system. this order will be rcvt>l'8Cd for obsen·crs moving with w pect to tbe first group of observers at a velocity le,i;s t.ban that of light, that is, at a physically attaiui,ble v olocity.
It is obviously impossible for two evont11 wbo~c order or suocC68ion can be reverscd in tbi& way to be linked by a relationship of cause an,l effeot; ii' a relationship of this kind existed b~twcen our two ev<mts. somo observers would be seeing the cnuse later than the effect, which is absurd.
Given that the distance in space of our two ovent-s is greater than the distance travelled by light clming tllcir interval in time, the first could not net as cause in the occurrence of the 1Second, and th<' second could be informed of the first, only iI tho causal link coulcl travel at a velocity greater than that of light. On tho basis of who.t hall' boon anid above, we have to eliminate Um Jl()l!3ibility: it must be imposaiblo fo_r cnUtllllity. whatever its nature, to travel at a velocil.y greater than thnt of light, that is, for there to exist either a mesaongor or a sigonl that oan traverse more than three bundJ'ed thousand kilometres per 11ecoud.
"'e tbereforo have to accept tltat an event can not act instantaneonel,y as eaulJO at a distanco, and thnt its reporcussion can mn.ke it.eel! felt immediately only lQoally, at the actual point where it occurs, and. then subsequently at iocrea.amg distances which increiise at most at t,he velocity o{ light. Tbus, oven from this point of view alone the velocity of light certainly p lays. in the new conceptio11s, the role played in the olu conceptions by innnite velocity, which in their t-0rms represents the maximum velocity at wbich causality can travel.

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It can be seen from this that the present ant;,gonism between meohauism and electromagnetism merely expresses im a new form tho opposition betwe-en the two conceptions which succootlod ea.di other in tho development of the eJectrical theories: that of instnntaueous :action a.t a dista.noo. which was compatible with meehanlsm, and that of traJ;Jamu;sion via a mecliwu !Jy stop-1,ystep a.ction. which was introduced by Fru-adny. Nowada.ys, this ancient opposition is having repercussions on the most fun<lamontal concepl:4!° tbemselve11.
Thero are various inferencet! to be drawn from wh:1t has been sa.iil e.bove. Firstly, fo is impossible for a portion of matter to move relative to another at, a velocity greater thatt that of light. This paradoxical r1>,ault is contained in the formulae introduced. by the new kinematics for the composit.ion of velocities: the composition of any numl>er of velocities t hat are less than the velocity of light alwa-ys gives 11. n loci,ty that is l~s than that of ligbL. Jn tho samo way, tile usual conception specifies thllt tho oompolrition of any number of finite velocities always givos a finite vclooity.
Secoudly, we can state that it rnus.t be irnpo11.~fble for nny action at a distance, such aa gravitation, t-0 travel faster than light. and we kno,v that
this is in no way contradicted by the rcaults that arc now being obtained in tho field of astronomy.
Lastly, the perfect solid of mechrulics. wllich 1·eprei;euted a means of signalli ng instan taneously at a dista1tcc and o( establishing a Cl'lus11l link able to t ravel faster than light, ba~ to be rejected. There is not.bing in what we know of real solids t-0 indicate otherwise than th:tt every action or every wave must travel at a velocity less than that or light. Eloatio waves in the most rigid bodies trn,,el, in fact-, at a velocity much low()r than this. The important
thing is that; we have to reject tbe en-tim conception of the perfoot solid, tl1at
is, of a body which could be set in 1notion simultaneously at all its points. The reasoning given above can be su.mmarized as follows: if there existed
a signal able to travel at a velocity great-er than that of light, there could be observer&for whom th.is signal woulcl ha,ve al'rived before ha.ving been trani,mitted, that is, for whom tho causal link that t-his signal makes it possible to eatabliah would be inverted. As Einstein says, it would be po&1ible to send a telegram into the paat, and this wottltl patently bo absurd.
Thus, it is neeea.sarily impossible for the two eyents of the pair in question, ,.,hieh have no clearly defined order of i,11cccssiQn in t ime, to have any mutual influence; they are truly independent events. I t is clear that, since there is no causal link between them, they can not follow ea-0h other in one and the same portion of matt.er. that is, they can not belong to one and the same world line or to the lifetime of one and tho same being. This impossibility also conforms with the fad that, to bfl the site of these two events one after the other. this portion ofmattilr would have to move, at a velocity greater tba.n that oflight.
There is, therefore, no choice of reiercnc-0 system by which the two events can be made to coincide in sp!IC<l, butt.bey can be made to coinciue in time, since their order of succession can be inv,erted, there do exiat reference systems for which the two events arc simultaneous.
'l'he pairs of events that, we have jull't examinc,d, whose order of succession in time boa no 1>baolutc mcn.ning but bctw-ocn whioh there .is abaolut-0 8PpMation in epa:oe, can be called pairs i1t 8Pace..
It is not.a,ble that, aUhougl1 the distQ,n.:;e 'i1t space of IM two events can not be recluced to zero, it passes tlm:,ugh a 1ninimu~,i for those reftrrence eystents relative
to which the two 61Jents are simultane01~.

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This leads us to the following statement. The di8ta11ce in 311ace of two tvenu that are aimulta>teou.i, /oT a 9fre11 gro14p of obserocTB is ~l&orteT for /hem tha,i f or nil o-th.er obsor11er11 fa 01111 kin<1 of motion
rrlative lo the111.
This statem('nt contains. 011 o sp'1cial case, wbatl1as been named the l,orcnh: contraction, tbn.t is. tbo fact that ono and t.ho sa1nc ruler t hat is oxmninod by vario1111 groupR of observe!'I', 11omo at r~t antl otbor~ in motion relative to it. is shorter for those who see it paSII b;v than for thoeo who are attached to it. 'fl1i1, is bocanse, as we h11,ve socn. tho lengt h of a rulor for observers ,vho seo it pass by is cl(l8ned by tho distance in space of two simultaneous (for the8o
observ(lrs) positions of the two ends or the ruler. And on the b88is of whnt
has be.en stated 1~bovo. this distnnoo will bo shorter ror theao observers tban ror all others, and in particulnr shorter than for thoso who arc attacbed to the ruler.
Thus, it can rcll(lily be seon how th is Lorentz contraction oan be reciprocal, thnt is. how lilvo rulers that nre of <'qurll longfh -when at rest relative to Pach other ar<' mutnnlly shortened wh()n they slide against each otber, with ODl!orvorR attached to ono of tho two rulors seoi11g the other a11 t<horter than theirs. 1'bi~ reciprocity is based on tho facl that the observe?'$ attached lo tho two rulers in motion relative to ono another do not define simultaneity i11 t4e 11a,me waJ·.
For llairs of events belonging to the second category, we ftnd propertiCI' that are exactly correlative to thol!e stated above if we interohango space and time. Tbese pair~, which we shall call p11irs in t-i1ne, 1~ro defined by the following condition, which has nn absolut-0 meaning: the distance in space of the two o,,ent& is smaller thno tho distanu trtwclled by light during their interval in i ime. ln othor words. the second cvo11t takes plnco ci/1-er the arrivat of tho light signal whose emission ooincideA in Fpacc and in time with tho first event. This introduces a lack of symmetry from tho point of view llf time between t.lie two events; the first occurs befoi·o t he osrival of tho light sign11,L whose omission coincides in space and in time with Lhc second event, wbi!Q tho l!eilontl OCCUI'tl after tlu.1 arrival of tho light signal whose emission accompanies tho first event. It is poSISiblo for 11, link of causality to exist between the two e,,ents. at Least lhrough the agency of light. that is. for the sccoocl e~eot to have been informed of the first, and this moans that the order of t111CC01!sion bas to have ao n.bsoluto meaning an1 I can not be rovers()() by any change of reference system. It can be seen immediately that such an invel'8ion would require a velocity greater than that of light for tho second rofercnco system relative to tho first.
_<\!though two eve11ls brLween wbich there thus rx:ist-s a real pos,;ibilitr of influence e,an uot bo made to coincide in thne, tboy can nlwaye bo ma.de to coincidl' in space by a, suitable choico of 1·oJ:ereocc system. ln particular, if the two events belong to ono and lbo samo world line, that is. follow each other in an absolute order in the lifetime of one and tho same portion of mattoi-, they coincide in a;pace for observers at,t,ached to tl1is portion of maU.or.
Co-rrrlativ~ly w what tel1-8 tM case above, although the i 11terval in limo of th~
two cvenl-8 can not be redt,ce<l to zero, it i>asseB through n m-ini1111,11i /or lhnt rq,ference
~ystem relative w ~nhich the ttro iwents ooincide in -,act.
This leatl8 us to the following statement.
'TIW! interval of time separafo19 two event8 that coincide in spact. that iB,

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that follow each othe-r at mw mul the same point fo-r a given refe-re1we ayst6m, i s
smalle-r for this sytt.em tha.n for aU othet· •11st#)1,11 i·11 anv k-ind of 1iniforni
tr1mslational niotion -relative to the frr$/..

*• *
In evei·ytbing that has been said al:)ove, the reforenc(l systems U$1.'d ate i.UlSumed to be endowed witb uni{or·m translal.ion:il motions: it is only for systems of t.bis kind that tbe obs(lrvers a;ttaehell to them are uuable to deteot cxperimeuta.Uy t heir collective motion, and that tho ec1nations of physics necessarily retain their form when there is a transition from on(I to another. Por syst-0ms of this kintl, everything happens as il they were motionless wHh respect to the oihor; tmiform translational motion in t.he ether has no experimental meeniug.
This, is however, no reason to coueluue, as has somotimcs been uone prem1\turely, that the concept, of other should be abandoned, and that the ether is Mn-existent and inaceosaible to llA"}>erimont. lt is only a velocii;:\' that is uniform ,vitb respect to tl1e ether that can not be demonstrated; a11y change of ,,etocity. or llCcelerat.\011. haij an absolute meaning. ln pn.rticular. ib is a fundamental poin t in the electromagnetic theory that any change of velocity or ncceloratiou of a chargeu pintiole is Mcompanied by th e emission of a wave that is propag11-tet1 in the me1l i1u11 at the velocity of light, aml the P.xistence of this wave l11u1 an absolute meaning; conversely. 11vei·y eleetrom,1g. netic wave, such. as n light wave, origu.1ates in the change of velocity of a
charged p!'lt tiele. Thu;;, we h:tvo idenhlfted the ethor through tho intermediary
of accelerations; acceleration has an at,solut.e meariing in that it detorminos t be production of waves from the matter which has UJ1dcrgo11e tbo change of velocity, and the ethel' rlolllonstratea its realit.y ns a voltlclc or carriel' of Lhe enm·gy traosportccl by these wavP,s.
The theory allows the posaibility of t1e1nonstrating, by means of electrourngnetic or opt,ical experiments. any acooler11,tion of the collective motion of
a. material eystem with the aid of ()lcperiiments carried out within this system,
even if only by verifying the emission ,of waves by chargell bodies attached to the system i~nd motionless with respect to it. WC> also know tha:t, if the acceleration of the collective motion is communicated to the systo111 by external forces which (ns opposctl to what happems in the caiie of gravitation) act only upon certain parts of the syatem, we have many other means of demonstrating it, such as deformations within the system wbich calll!e the acceleration lo be transmittecl from portions of the system that arc subjeetecl to the external forces to other portions that a.re not.
In a, uniform gravitational field, in which every portion of the system would be directly sul)jeet to the external for~e that would eomJnurucate to it the collective acceleration, as in Jules Verne's projectile, r•eo,otions oi this kind would not take plaee, but it would still be possible, as stated above, to carr,r out electromagnetic or optical experiments in order t.o !lemonstrate the change of velocity of th e collcctivo motion. '.I'ho laws of elootromagnetism wou.lcl not be the fame for axos attache<l to this material system as for axoa in eoUeetive uniform translational motion.

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We shall now see this absolute nature of acceleration pre11ent itself in another form.
Let us consider a portion of matter in any kind of mot-ion and the euooession of events that constitute the lifetime of tWs portion of matter, that is, ill! world line.
For two of these events tbat are aufficien tly close to each other, observerB in unilorm motion -wbo ·witness these two eveot.B successively may be regardod a.a being attached t-o ibe portion of matter, since the change of velocity of this portion of matter is imperceptible in the interval separnting the two events. For theae obson·ers, the interval of time between the two events, which will oonstit11te an element of wbnt we shall call the -proper ti·mo of the portion of matter, will be shortel' than lot any other group of observers atta-0hed to a reference syst-crn that is in any kind of unifonn motion.
H we now take any two events in the lifetime o{ our portion of matter, their intorval of time as measured by observel's itJ non-unilorm UlOtion who will bavo con11tautly followed the portion of matt-er will, by integration of the above result, be shorter thau for tho reference system in uniform motion,
In partiou.lar, this refernnce system can be such that th e two events in question take place within it at one and the same _point, and that with reapect to it tho portion o.f matter bill! tra.ve.lled through a closed cycle, or returned to its starting point as a result of i~ noet-uniform motion. And too cm1 state thal. for observna aUached IQ thia porlio11 of maUer, the time that -will have ela-p,ed bet111ee11, tM departure and the r~tum, or the pro1>er time of the portion of matter, ivilt bo shorter tlta·ll for observers tolw l1ai·e f'e11wi·11ed alllWhed to tl1e reference system, fa unifornl nu,lion. [n other words, t he portion of matter will have aged )etS between its cleparture a111l its return tlum if it l1ad not undergone any 11.-0<".nlP.r11tions. but had remained fb:ed with respect lo a rorerencc system in unifonu translational motion.
We can, in fact, sa.y that it is sufficient to be in non.uniform motion or Lo undergo accelerations in ol'det to nge 18811 quickly; we shall see in a moment jw.t how much time Mn be oxpect.ed to be gained in this way.
\Veshall take two concrote cxampfoa. Lot us imngine, firstly, a labora.tory atta-0hecl to the Earth, whose motion <mn be regarded as a uniform translation, and, in this labora.tory, two completely identical samples of radium. From our knowledge of the sponta110oua dceay of radioactive substances, we are 1\ble to atate tbat, if these samples romnin in the laboratory. they will both lose their activity at the same rat-e in time and wiU ha.ve equal activities a.t nll tiinGa, However, if we acncl one of these sa-mplos out on a journey at a high enough volocity and thon bring it back into the laboratory. this neceasa.rily implies lhat, l\t certain moments in time at least, this sample bas undergooo neceleraiions. We arc able to ~tate that, on its return, since its proper time between depMture and return is less than the intorval of time measured be• tween these same events by observers attached to tho laboratory, it will have decayed less than the other sample and will consequently be more active; it will ht1ve aged lea&, since it b.ns boon subjected to more non -uniform motion. Calculation shows that, in order to obtain a difference of one part in ten thousand between the variations in 11ctivity of tbe two aarnplos, it will have been oooe88ary to mulntain tbe travelling sample at a velocity of approximately
. . . four tboll8and kilometres por second (luring the separation.

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Before looking at a second concrete example, we shall pres.ent our result again in a different light. Let ua a-ssmne that two portions of matter oncounter each other a first time, separn.te,, and tbe;n meet a.gain. We are able to state that observers attached to one and to t:he otbllr respectively du.ring the separation will uot bave made the siunc evaluation of the duration of tb.is separation an(l will not hn,,,e aged t,o tho sM:ne extent aa oach other. It follow-a
from what has been !1aid above that tb.e on.es .t.!Utt will have aged the leaat will be thos() whose motion du.l'iug the separation has been farthest from being uniform, or who have U11tlergone most nccelerat.io1ill.
Io this observation there .liell tbe moa.11~, (or any one of us willing to devote two years of his life to it, of l,.71owing-wh.at will have become of the Earth iu two hun,lrcd years, of exploring the futu:re of tha Earth liy taking a forward leap into its lifetitne that will last two centuries for the Earth and two years for him, a.lthough .it would have to be without any hope of returning 01· any pos.aib,ility of eorning back to ioforrn us oi the re-Sult of his joJ1rney, since any attempt to <lo this could only carry him farther and farther forwnrtl.
To clo thls, our traveller would neecl ,ooly to agree to boing shut up inside
a proje<ltile that the Earth would Jaunc.h at a velocity atuliciently close to
that of light, but still less than it, which is physically possible, nrraoging for nn encounter with, say, a star to take pliwe at the end of one year iIJ the life. time of the trnvellet and to send him ha.cl, townrJs the Earth at the same veloci ty. Having returnetl to Earth two yoara ol<lor, he will emerge from his ark to find that our globe haa aged tw,o hundred yoars, provided that h'is velocity has remllined within the rango c,f only one put in twenty thousan<I less thl\11 the velocity of light. The most reliably established experimentnl fact.a of physics enable us to state that this is indeed what wo uld happen.
It is diverting to picture l1ow our explorer and t.be Earth would watcl1 each other living if the.y could keep in constant r,0mmu11ication during their separation by meaus of light signa.ls or wi reless telegraphy, antl to understand in this way how it is possible for th.ore to be a lack of 1<ymmetr_y between th<• two measurement.s of the cl1uation of aepnratiou.
·wh.ile they are moving away from o,a.oh otl1or at a velocity closo to that. of light, en.ch of them will n.ppea1· to the o'ther to he fleeing in front of the oJp,e. tromagnctio or light signals sent to him, so that it will take a very long time to receive the sigun.18 emitted <luring a given peiio,l. Calculation. in (Mt, shows .that each of them will see tb<l other Jiving two hundred times more slowly Limn normal. During tbo yca;r for whicJ1 tbfa movement apart will last for him, the traveller will receive from the Rarth only news of tho first two days after his departmo; tluri.ng this year he will have 11een the Earth perform the actions of two days. In addition, for tbe ;Same reason arising from the Dopplei· principle, the radiations that ho will receive Irom the Earth during this timo will have, for him, a wavele1igth two hundretl times greater than for the Earth. What will appear to him as luminous rad i ation by which he will be able· to see the Earth wiU have been omitted by the Earth aa·e:xtrome ttl~ra.-violet radfatio11,
possibly close to X-rays. .Ancl if we wish .to maintain communication be-
tween them by Hertziim signals, that is, by wireless t.elegraphy, the e:s:.plo.rer having takeo with him roociving equipmeJlt ha-ving a oort11in antenna length, the transmitting equipment used by the Earth durir1g these two days following. his ,departure will need to have an .m1tenlla length two hundred time!\ aborter than his.
During the return journey, conditio,ns will be reversed. Each of them

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1vill see the other living 11t a. singularly aooelerMed rat-e, two hundred times more quickly than normal, and during the yciir for whillh 1he Teturn journey will last for bim the explorer will !JOO the Earth pel'form the action(! of two centuries; it can thus 110 seen tllal on bis return lie wilJ find tbe EnrLh two hunclred years older. llo will also be able t.o see it during this poriotl with the aid of waves which for him will be light WI\VCS but 1vhich for the Earth will belong to the extromo infr,~-rod, with tho aid of the rn,vs or app·roximatel:..100-miorou wavelength that Rubens and Wood 1·ccently discovered in t-hc cmi88ion spectrum of t ho Wclsbach mantle. For him to continue lo receive llertzian signals from lho Earth, after the first two clays und throughout the following two centuries, tho Earth will ba.ve to 1\J!C a tr.ansmitting an1 enna two hundred times longer than that of the tmveller, l\lld Io1·t.v tlioussrnd time~ longer thnu tbnt used during the first two uoys.
To understand this lack of symmetry, it l!hould be noted that the Earth ,.,ill take two centuries to receive lhe siguals transmittod by tho orplorer 1luring his motion a-way from the Ea1·th, which for him lasts for a; year. Dw·ing this time tho Earth will see him Jivo in his 11rk at, a rate that is slowed down two hundred times; it will see him podonn tho nctfons of one year. During the two centuries for which tlrn F.nrlh will see him thu,; moving awny, in order to receive the llertzian signals that l1e emits it will need to use 11,n ant,ennn two hundred times longer tlHln bis. .At, the end of these two centuriC8, news will roach the Em·th o.f tlie projectile's encounter with the stm·, which marks tlte stnrt of the return journe,v. The travcller's arrival will then tako place two 1lays after thill. and during tliese tw o ,lay!\ 1,ho Earth will see him live two hundred times moro quickly than norma.i, Ulat is, it will sec him porform the actions o[ n second year ancl so find him aged bJ only two years on his return. During these lru1t two d1tys, in order to rccci..-e news of him tho Enrth will 11oe<l to u.se a receiving nulenna two hundrecl times sborlcr than tlmt of the traveller.
Tims, tho lack of symmetry arising from the fact that iL is only the traveller who has undergone, on his journey, an acceleration that changes tho direction of bis velocity and brings him back to bis starting point on the Earth, is re/looted by the fact that the traveller soos the F.1utb move away from him an<l then appronch him for poriocls of time that for him ai:e ench 0<1ual to one year, wb~ro,is tho Ea.rth, wltiob is iofo,.mod of thio ooceleraUou u11ly by tho arrival of light waves, sees the traveller move away from it for two oonturioa and t.bon return for two da)'S, that ;.i. for a perio1l of time Corty tbousan<I times shorter.
Now, if we seek to tletermino t he conditions in which a project of this kind cou.ld bo carried out in praotico. we naturally find ourselves faced with enormous material dimoulties.
[t is possible to oaloulate theoretically tho work that the Earth would need to expend Ju order to launch til:te projectilo and communicate to it the kinetic energy corroopon<liug to it11 eno.rmouely high velocity. lf we a11,111me the mass of the projectile to be ouly one ton, it oan readily 'be ealoulated that if we wish to take only ono year to launch it, by whirling it at the end of a sling before roleaaing it, for instaooo, it would be necessary to apply four hundred thoUB&nd million horse power continuously throughout this year, and to burn at least a thousand ou.bic kilometres of oil to produce thi& power.
These difficulties at the start would theu be followed by diftioulties that would be ao less daunting at the atages of reflection and atoppnge of the projec-

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tile. First o.f all, it would be ncce~ary. for its reflection, to find 1t system capable of storing the enormous kinetic energy of the projectile a.nd then 1-estoring it in ordeJ" to la,1mch it back in the opposite clirecticm at thesamo velocity. For stopping t·be projectile, it would be neceasar)T to dissipate this same energy gradually without allowing there to occur at any time either acceleration or a rise in temperature that woultl be harmfll.l to the projeotile, even though the- amount of heat equivalent to il:a kinetic energy would be sufficient to tl\ke it to 1\ tompern,tu.ro o.f ,1,t lea.st 10" degrees.
In acldition, wo hiwe good reason to think that. ii 11. projectile a,rrived back at tho Earth at a ve.looity of this order. the .Eartll woulcl not even be aware of its t\rrival, and that the projectile would come to a stop only when it llacl reached a OOl'tain depth in tlle eal'th, without even leaving n hole at the point oo the SUl'face through which it w<>u.ld have passod. It would scarcely proiluce ove11 a slight inerea1;e in the oloctri<lai conductivity of tho air on its trajectory through the atmosphere. For wo know from l;he o.xamplo of the ix-particles of radium that helium material atoms, wlloso velocity is barely twenty thousitntl kilometrca per scsioncl, oan follow ,i perfectly rectilinear tmjcotory through matter and pnss tlnough other atoms without leaving any t.rnce of their passage otllor than an increase in conductivity, an(l our projectile ,voulcl have, per unjt mass, a kinetic e.nergs one hundred tboW1aud times gi:eater than that of o:-particles. It would consHtute an extraordinarily penotratiog ra<lintion. To avoid these 1ii.fficulties, it wou.ld be nec-essary to tlnd a rne1tns of slowing down its rnotion gntdually ns it :i.pproaeheJ the
En.rth. Nor would it seem in this cnso pos.~iblo to attempt to apply the prin•
eiple of thn rocket that my collea.gue M. Perrin hM i,ugg<',sto1l should be used for intorplanoh1-y tr;wol.
,. ...

My .sole purpose in developing tl1ese speculations has been to tlomoo.strate, with tho aid of a. striking e,,i:ample, the kind of conaoq_uencea, far removed from tho usual conceptions, to which tho now form of the eoneepts of apace o.nd time leacls us. It tnUJ!t be rnmembenltl tbat this reprcseuta the p!lrfectly valid extrapolation of conclusions that are det<\rmined h~- indisputable ex• perimental facts of which ow· forbeara hacl no knowledge when tl\ey formulated, on the bru,is of their experience relating to mooha.n.ism. the categories of space ,ind time that we bave inhoritc(l from them. It is now our turn to carry on their work by J)w'suing, in more minute detail, and in keeping with the means that ,ve hiwo at our disposal, tho adrqrtation or man's thinking to the
faots. lt is not only in the field of space and tilllo that we are being forced to
reshape the most fundamental conception,a of the mechanistic synthesis. Ma,,is, which was used to meallure ioertia, a pr.ime attribute of matter, was once consiclered to be an essentially unvarying element charaoteristio of a given portion o! matter. This concept is now disappea,ring and is being fused with tllat of energy: tho mass of a portion of matter varies with ittl internal energy, increasing and decreai!ing with it. A por tion of matter th.at ia 1·acliat.ing losoii its inertia in a quantity proportional to the energy being -radiated. It is the energy that is inert; matt-er rosists a change in its velocity only in proportion to the energy that it contains.

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The concept of energy itsoli ill lu~ing it.a ab!lolute meaning: its meaaurement
variM 'with the reference s,ystem !.-, which the phenon,ena a:re related, and
physicisw are at present seeking ho cletermine which arc the true elements in the expres.aion of frhe laws of the 1utiverse wh~eh possess a.n abl!olute mea11ing. that is, the elements whioh remain constant when there is s iraneition from one reference syetom to an other and whioh will pla.y, in Lhu olcctro·mngnetic conception of the universe, the part pln.yeil by Limo, mass and energy in t,he mool1anist,ie eyntheei8.

•rrallBlnUon: J, D. S;yJtee • Stonneon, Abln1rdon