8i6 



NATURE 



[August 25, 192 1 



cause of, and in proportion to, its mass-acceleration, 

 until friction and other obvious extras have to be 

 taken into account. 



The Principle of Equivalence. 



In returning from this, I hope pardonable, 

 elementary digression to more general considera- 

 tions, let me quote and amplify a sentence from a 

 sort of summary which vi^ill appear in the Fort- 

 nightly Review for September : — 



To ignore or deny or supersede the gravita- 

 tional stress, merely because we do not yet 

 understand the particular configuration of the 

 aether which is responsible for it and which 

 renders it possible, is to blind our eyes danger- 

 ously to dynamical reality, and to rest satisfied 

 with a mere geometrical specification of the 

 motion as if it were a peculiarity of space. 

 The " principle of equivalence " formulated by 

 Einstein claims that the inertia reaction of a 

 revolving body, to the centripetal force responsible 

 for the curvature of its path, is of the same char- 

 acter as what we call the force of gravity, due to 

 the neighbourhood of a large mass ; that this 

 inertia reaction is indistinguishable from weight ; 

 and, generally, that no distinction can be drawn 

 between an artificial field of force, such as that 

 representing the effect of a carefully defined revo- 

 lution round a centre, and what we are accustomed 

 to think of as a real field of force, such as that 

 surrounding the earth. 



We are told that by referring motion to rotat- 

 ing axes it is possible to abolish revolution and to 

 replace it by a centrifugal force acting outwards 

 on the body, thereby enabling the body to be 

 treated as if in static equilibrium. We do this 

 when we draw a static diagram of a revolving 

 body, say a conical pendulum or pair of governor 

 balls, and when a spurious and non-existent force 

 is supplied, to represent the inertia reaction, and 

 to balance the centripetal-force component which 

 in reality is curving the path. I called this 

 " unpardonable " in an elementary text-book, and 

 also wrong as a philosophic representation of fact, 

 but as a mathematical device it seems to be permis- 

 sible ; at any rate, it is quite consistent with the 

 principle of relativity. In fact, it is part of the 

 foundation of Einstein's principle of equivalence. 



Now it is true that the most careful experi- 

 mentation (first Newton, and now Eotvos) has 

 shown that weight and inertia are accurately pro- 

 portional. So it is possible to balance weight 

 precisely by inertia reaction, and, for calculation 

 purposes, to treat centrifugal force as if it were 

 an artificial kind of gravity, obedient to the same 

 laws. But this can only be done with due caution 

 and limitation, for it does not represent reality, 

 and the laws are not in all respects the same. 



We are also told that, by choosing accelerated 

 axes as our frame of reference, weight can be 

 abolished too. Passengers in an unsupported, 

 and therefore freely falling, enclosure, such as a 

 cage or lift, would experience no force of gravity ; 

 for nothing would require any support, and 

 nothing would tend to move out of its place as 

 NO. 2704, VOL. 107] 



defined by the walls of the room, which constitutes 

 the passenger's natural frame of reference. 



We are told still further that the behaviour of 

 things inside an enclosure or cage in free space, 

 dragged along by a hook with an acceleration of 

 32 ft. per sec. per sec, would be indistimguishable 

 from the behaviour of things inside a stationary 

 or equilibrated cage slung by the same hook above 

 the earth. These examples are instructive, for in 

 many respects the behaviour would be just the 

 same. But such illustrations must not be pressed 

 to philosophic extremes, as if there were really no 

 discrimination. For one of the two cages, after 

 the lapse of about a year, would attain the velocity 

 of light; and surely something noticeable must 

 happen then, even if only the invisibility of the 

 floor. Moreover, force is not really evaded ; for 

 something must be dragging at the hook — some- 

 thing quite gratuitous — whereas the influence of 

 the neiehbourhood of the earth is a manifest 

 vera causa, however little we may as yet under- 

 stand about its setherial mechanism. It must not 

 be supposed that we have no criterion for what is 

 true in all these cases ; we need not allow that we 

 have no means of discrimination, and that we are 

 really subject to all the uncertainties and 

 ignorances about absolute truth which tend to be 

 grafted on to us by the doctrine of relativity in 

 general and by the principle of equivalence in 

 particular. 



The fact is that the passengers-in-a-Iift argu- 

 ment, like others that we encounter round about 

 this subject, is of very limited application. It 

 can be well used to illustrate certain non-obvious 

 and interesting facts, but innumerable considera- 

 tions contradict the idea that the force of gravity 

 is really nothing else than a fanciful name for the 

 mass-acceleration which can be written in equa- 

 tions as equivalent to it. After all, distinction Is 

 quite feasible between the reaction of a heavy 

 body on the earth to its centripetal diurnal 

 acceleration, and any corresponding fraction of 

 the force of gravitation. The two do not even act 

 in the same direction, save at the equator ; and 

 at the poles one vanishes. What is true is that 

 the resultant between the pressure of the ground 

 on a stone or man, and the real weight of the stone 

 or man, is an unbalanced force which causes that 

 stone or man to rotate round the earth once a 

 day, and (if we allow for complete weight) round 

 the sun once a year. Attachment to the earth has 

 nothing to do with astronomical motions of our 

 human body ; for we are not attached. Each of us, 

 and each loose pebble, is as much a planet as the 

 earth, and nearly as much a satellite as the moon. 



To say — if anyone doea — that the force exerted 

 by a gravitational field, such as might be due to 

 a heavy mass at the centre of a wheel, is indis- 

 tinguishable from any other constraint needed to 

 curb the Inertia reaction of a particle attached to 

 the rim of the wheel when it is revolving, is false. 

 For the way the force is applied Is not the same, 

 and the law of force is different. The one 

 increases with distance from centre, the other 

 diminishes with the inverse square. 



