February 17, 192 1] 



NATURE 



805 



beings have smoked, or, if the doctrines of rela- 

 tivity are true, ever will smoke, cigars — let alone 

 make accurate measurements — in such aeroplanes, 

 and afterwards compared their exj>eriences. If 

 we pretend to talk about experiments, let us be 

 sure that we do talk about experiments, and not 

 about something that cannot possibly happen. 



However, it may not be useless to ask what 

 would happen if we did find our spatial laws un- 

 true, in the manner suggested, at speeds that can 

 be realised. I suggest that we should make our 

 laws true once more by changing slightly the 

 meaning of the terms in them. The technical terms 

 of science are labels attached to collections of 

 observations that can be grouped into laws, which 

 those terms are used to describe. If we find that 

 the supposed laws are not true, the terms become 

 meaningless ; we might abandon them altogether ; 

 but generally we discover that, by a slight re- 

 grouping of the facts according to the new laws, 

 we can make once more a collection of the facts 

 to which the old term may be applied appropri- 

 ately to state the new laws in almost precisely the 

 old form. 



Consider, for example, the term "simultane- 

 ous." Primarily, two events were judged to be 

 simultaneous by direct perception. Using this 

 test and examining a limited range of experience, 

 we found the law that events that arc simultane- 

 ous to one observer are simultaneous to another. 

 But later we found that the law was not valid 

 for more extended experience, including the sound 

 and flash from a gun. That discovery made 

 "simultaneous" meaningless, and with it all the 

 temporal magnitudes ; there was no longer any 

 way of assigning uniquely a numeral to repre- 

 sent the time-interval between two events. So 

 we changed the meaning of "simultaneous," and 

 introduced a "correction" (very complicated, as 

 sound-rangers know); by this means we made 

 " simultaneous " once more the expression of a 

 law, and reproduced our specifications for measur- 

 ing time-intervals in exactly the old form. but. 

 of course, with rather different content. If we 

 encountered new difficulties when we extended 

 our observations to events in systems moving 

 with great relative speeds, we could, I think, 

 intrwluce a new "correction" for speed, and re- 

 produce once more the form of our old laws an<l 

 our old mcthcKJs of measurement. At any rate, 

 the resulting change of form need not be so great 

 as to cause anv appearance of paradox. 



I conclude, therefore, that nothing that the most 

 extravagant imagination has suggested so far 

 could make us diverge appreciably from our 

 present spatial and temporal laws. Hut it is other- 

 wise with our theories. The experimental 

 physicist has a theory of time and space, although 

 he mav not be con.scious of it. It is based on 

 Cartesian geometry.* It likens "space" to an 

 array of black dots in a cubical lattice, and 



* ll U intervvlinc to notice thuf, iHoagh (he theory i« «<Mn«l-m«-« failed 

 Kndidean, KucliH had ■«v«v h«anl of it. No Oteek geom'ter wcmld ha¥e 

 known whr t you meant il yoa bad lold htm that tpAce wai Ibre*- 

 (liaentional. 



NO. 2677, VOL. 106] 



"time" to a series of ticks from a metronome. 

 It connects the position of a body with the in- 

 dividual characteristics of the dots that it "occu- 

 pies," and the magnitudes length, area, volume 

 with the number of those dots. The time of an 

 event it connects with the individual character- 

 istics of the ticks. The theory explains well some 

 spatial laws, but in some directions it is mis- 

 leading. Thus it fails to make a distinction 

 between lengths and areas, which (in the last 

 resort) must be measured by the superposition of 

 rigid bodies,^ and volumes, which cannot be 

 measured by such superposition. It should be 

 noted that the dots and ticks, the " points " and 

 "instants " of mathematically minded philo- 

 sophers, are purely theoretical ideas. They have 

 no meaning apart from the theory, and, like the 

 position of a hydrogen molecule, cannot be deter- 

 mined by experiment. 



Prof. Fiinstein has altered and expanded this 

 theory. In conjunction with Minkowski, he has 

 altered it by merging the dots and ticks, formerly 

 independent, into a single array of world-points, 

 and by making the arrangement of these points 

 quite different from that of a cubic (or Euclidean) 

 lattice. He has expanded it by introducing the 

 idea of the " natural path " of a body among the 

 points, which enables him to explain the laws of 

 dynamics without the (theoretical) idea of forces. 

 But his propositions still form a theory, and they 

 still contain purely theoretical ideas, which cannot 

 be determined by experiment — the world-point or 

 the infinitesimal "interval," which must be inte- 

 grated before it can be related to measured mag- 

 nitudes. 



These changes are very disturbing to the ex- 

 perimenter. He wants theories to explain laws. 

 Explanation involves not only the possibility of 

 deducing the laws (for that is easily attained), but 

 also the introduction of satisfactory ideas. In 

 the older types of physical theory this "satis- 

 factoriness " was obtained by means of an analogy 

 between the ideas of the theory and the concepts 

 of some experimental laws. Thus in the older 

 theory of space the points were related in a way 

 analogous to that in which small material bodies 

 can be related. In the new theory this analogy 

 fails. For the mathematician the passage from 

 flat three-dimensional space to curved four- 

 dimensional space is trivial ; for the experimenter 

 it is vital, because we do not actually experience 

 anv arrangements at all analogous to those of 

 points in such a space. The satisfactorincss of the 

 theory, for those who press if on our attention, is 

 derived, not from material analogy, but from the 

 intrinsic elegance and beauty of the relations in- 

 volved, the faculty for appreciating which distin- 

 guishes the pure mathematician from his fellows. 



It is not surprisin^r. therefore, that experi- 

 menters have found difficulty in accepting the 

 theory as an ultimate solution of their problem. 

 The old thcorie.1 explained, bccau.sc they inter- 



' "R1(H hmlia* " U a lahal a-iached to a (•lleeiian of fact* fioupMl In 

 law*, the law« that make poa^iblc the tneaurtmenl of lenilhl and arta«. 



