H.A. Wilson- Gravitation and the Ether

8/3/2019 H.A. Wilson- Gravitation and the Ether

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G R A V I T A T I O N AND THE E T H E RINSTEINS theory o f g rav i t a t ion may be comparedE with thermodynamics. Both s ta r t with a few funda-

mental principles or axioms based on experience and pro-ceed by logical deductions without further appeal to facts.N eit he r at tem pts any explanation of the natu re of thephenomena considered.

T h e kinetic theory of gases is an example of a differenttype of theory. A definite mechanism is assumed for a gasand the propert ies of the mechanism are worked out andcompared with th e know n properties of gases.If the axioms of the first type of theory are true, the

theory itself must be true, unless the reasoning is at fault;both types of theory ar e to be tested by comparison of theresults with observation.

T h e principles on which Einsteins theory depends a re hisprinciple of rela tivit y and his principle of equivalence. Ac-cording to the f irs t , the laws of nature must be such thatthe differential equations which express them are independ-ent in form of the coordinate system or frame of referenceused, and, according to the second, a gravitational f ieldcannot be distinguished from an apparent f ield due to anacceleration of the fr am e of reference. F ro m these prin-ciples he shows how the form of the paths or orbi ts de-scribed by bodies moving in a gravitational f ield may bededuced.

T h e theory is mainly geometrical. I t gives the geometri-cal fo rm of the orbits . In the absence of a gravitational

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24 Gravi tat ion and the Etherfield a body moves in a straight line, provided the frame ofreference is suitably chosen, and in the field surrounding aheavy particle a small body describes an ellipse, as in New-tons theory, again provided the frame of reference is suit-ably chosen. I n New tons theo ry the ell ipse remains sta-tionary , while in Einsteins it slowly rotates in its own plane.

W h a t causes the moving part icle to move round an ellipseinstead of a long a s t ra ight l ine? According to New ton,there is an attractio n between the particles, a force tendingto pull them together. Bu t this is merely another way ofsaying th at they tend to move tog eth er; i t is no explanation.If we reg ard Einsteins geom etry of orbits as a geom etry ofspace, we may say th a t the body describes an ellipse becausethe space and time aroun d a heavy par t ic le a re not s t ra igh tbut curved. T h e path of the par tic le is the natu ral path inthe curved space-time: the path of maximum intervallength. T h is does not seem to be an explanation any moretha n New tons force. W h y should a particle describe acurve in a curved space, and, anyhow, what is the meaningof curved space?

T h e idea of space is obtained by experience; it cannot beexplained. W e express ou r experience of space by sayingth at bodies occupy p ar ts of space and can move about in i t ;between bodies there is w h a t is usually said to be emptyspace, o r a vacuum. Such statem ents seem to be intelligiblebecause of our experience of bodies and their motions; theywould mean nothing to a being without experience similarto ou r own. T o explain what is meant by curved space ornon-Euclidean space i t is customary to take the case of asurface which may be flat or curved. If we consider asphere on which a particle: is constrained to move, then wesee that this particle will not move in straight lines, butalong g reat circles of the sphere. In the same way, a pa r-


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Gravi ta t ion and the Ether 25t icle in curved space of three or four dimensions, i t is said,will move along a curve. T h e object ion to this i llustrat ionis obvious. T h e sphere must be a ma terial sphere, other-wise i t could not keep the particle on its surface . Theremust be som ething curved to m ake a curved space. If, then,the space between bodies is empty, there is nothing in i t tobe curved, so i t cannot be curved.

Suppose th a t a large number of cubical blocks were m adeat a certain place, all exactly equal when tested by placingany face of one against any face of the o thers . T he n sup-pose these blocks were taken into the gravitational fieldnear a heavy particle and were built up by placing themclose together so as to fi l l up the space around the heavyparticle . Suppose i t was then foun d th at they would notfit together exactly, so that the space could not be fi l led upcompletely with them. Oug ht we to conclude th at the spacewas curved or tha t the shape of the b locks had changed?If the shape of the blocks h ad n ot changed, then they ough tto fit together. If the blocks would not fi t , the proper con-clusion to draw would be that the gravi tat ional f ield haddistorted them. T h e experiment could no t give any infor-mat ion about the geometry of the space itself. Em ptyspace cannot be measured; we can only measure bodies andtheir distances apart . In empty space there is nothing tofix the sha pe o r position of geom etrical figures. T h e y canbe constructed in any way desired, and measurements madeof them relate t o the shape of the figures and give no infor-mation about the space in which they exist .

The conception of a curvature or distort ion of emptyspace is meaningless, since only material bodies can bemeasured. Of course it is possible to t ry to deduce thegeometrical propert ies of space from observat ions on ma-terial bodies, but i t seems doubtful whether the results of


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26 Gravi ta t ion and the Ethersuch at tempts are anything but the geometr ical propert iesof the ma ter ial bodies . Einstein wri tes W e entirelyshun the vague word space, of which we must honestlyacknowledge we cannot form the s l ightes t conception, andwe replace it by m otion relative t o a practically rigid bodyof reference.

T h is difficulty ma y be remo ved by supposing tha t space isnot empty, but f i l led with a medium, the ether , and wemay suppose th a t the proper t ies of the e ther a re such tha tparticles (which m ay be merely modified ether o r singulari-t ies in i t ) move in i t a long paths which are s traight wherethe e ther i s un i form, and curved where the proper t ies of th eether vary f rom poin t to poin t. O r we may s imply say tha tthe e th er is space. Since it alw ays fills up space, we hav eno experience of space except when full of ether , and sowe may identify space with the ether . I t seems to the wri terbet ter t o retain the ethe r and not get r id of i t by supposingtha t space as such can have g eom etrical or oth er propert ies.A space in which a particle describes a curve must havesome degree of substantiality, and it seems more in accord-ance with experience to say that i t contains a medium hav-ing the necessary propert ies than to at tr ibute these prop-er t ies to a vacuum.It is admit ted t ha t in d i fferen t pa r ts of space bodies mov e

in different ways. I t is clear, then, th a t different p a rt s ofspace have different properties, and, therefore, physicalpropert ies ar e present in space. B u t the possession ofphysical properties is the only known at tr ibute of matter ,so th a t we ar e en ti t led , if we so choose, to re gar d space asfilled w ith a medium . If we d o n o t so choose, then we m ustregard space i tself as having propert ies , and we ought to

1 T h e T h e o r y of Relat ivi ty, authorized translat ion by R. W. Lawson,Page 9.


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Gravitat ion and the Eth er 27conclude that matter does not differ essentially from space,for matter merely has physical propert ies. If so, thenspace is full of matter, so t h a t w e get back to the ether inthis way also.

I n recent years m any physicists seem to have come to theconclusion t h at the ethe r d oes no t exist , because it is foundto be impossible to detect any kind of effect due to themot ion of t ransla t ion of the ear th through it. T h e o l darguments fo r the ether, however, are st il l valid. Gr avi ta -tional and electromagnetic actions take place across avacuum, and light t ravels thro ugh a vacuum and ha s al l theproperties to be expected of a wave mot ion through a me-dium. T o give up the ether merely because it fai ls t o mani-f es t its presence in one particular way is absurd and neveroug ht to have been suggested.

Einsteins principle of equivalence provides a good illus-tration of how something which is everywhere present mayfail to produce any observable effect. On a mater ia l sys-tem falling freely in a uniform gravitational field thereshould be no observable effect due to the field, although thesystem may move in it with ever-increasing velocity. T h eacceleration is pro duc ed by th e field, but is th e same f o r allpa rts of th e system and so does not change the relative mo-tion of the p ar ts of th e system, and there for e produces noobservable effects.It seems that the general principle that any action on amaterial system which is equal on all parts of the systemwill produce no effe ctobservable in the system, migh t be putfo rw ar d as p lausib le . It is only differential effects, due tovariations in the action over the volume of the system,which can be observed.If a system is moving with uniform velocity through the

ether which remains everywhere at rest , then i f all par t s of


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28 Gravitat ion and the Etherthe system are equally affected by the relative motion, i t isnot surprising that no effects observable in the system areproduced. T h e effects produce d exactly compensate theaction, just as in the case of a uniform gravitational f ield.N o observable effects should be expected and none arefound. I t is not a case of a surprising compensation ofeffects, but a perfectly natural state of things. Mo t io nthrough the air or through water gives observable effectsbecause the action is not uniformly distributed over all thep a r t s of the system.

According to the principle of equivalence, the visible uni-verse may, for al l we know, be moving with an enormousacceleration due to a uniform gravitational f ield producedby eno rm ous ma sses outside. Such a field can prod uce noobservable effects, and so its presence or absence cannot bede te rmined. W e may say , i f we like, that i t does not existfo r us.

In the case of the e ther , no effect due to un iform m otionthrou gh it can be detected, but its presence is manifested inother ways independent of uniform motion which have beenmentioned. I t s presence and impo rtant functions need notbe doubted. W e have gravitat ional electr ic and magneticfields which can exist together in so-called empty space,and it seems much more reasonable to say that such fieldsare modifications of a single medium, th e e ther , than to sup-pose t h at they exis t in em pty space or ar e due t o modifica-tions of empty space.

In wh at fol lows i t wil l be supposed tha t there is a me-dium , the e ther, f il ling up all space, and a theo ry of gravita-t ion recently put fo rw ar d by the wri ter1 and based on thisidea an d on the electrical theo ry of m att er will be described.

The a toms of mat ter , accord ing to Ruther ford , cons is tPhysical Review, January, 1921.


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Gravitat ion and the Ether 29of a minute positively charged nucleus surrounded by anumber of negative electrons, the positive charge on thenucleus being equal to th e tot al negative charge on th e elec-t rons . T hi s theory is confirmed in many ways and will beado pted here. A n electrically neutral body is , therefore , asystem of electrical charges, and its mass is probablywholly electromagnetic.

T h e facts which a theory of gravi tat ion h as to explain a rethree :

( I ) New tons law of gravi tation.( 2 ) The deflection of l ight by the gravitational field of( 3 ) T h e change of frequency of th e spectral lines( I ) I s not absolutely exact, according to Einstein.( 2 ) W a s predicted by Einstein and verified by observa -

tions during the solar eclipse of 1919.( 3 ) W a s predicted by Einstein and its existence is sti l lin doubt , but the mos t recent results ar e fa vor ableto i t, so i ts tr ut h will be assumed here.

the sun.em itted by atom s in the sun.

If we assume matter to consist of electrical charges im-m erse d in a medium, then, t o explain New ton s law of g ravi-tation , we mu st consider under w ha t circumstances a neutralelectrical system tends t o mov e thro ug h a medium in whichit is immersed.

It is well known that an electrostatic system immersedin a medium the specific inductive capacity ( K ) of whichvaries fro m point to point tends to move in the direction inwhich K increases mo st rapidly. I t is natural , therefore, t otest the suggestion th at grav i tat ion may be due to variat ionsof the specific inductive capacity of the ether. If we findthat the three facts given above can all be explained on


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30 G r a v i t a t i o n a n d t h e E th e rsuch a theory, we shall have good reason to consider thethe ory to be a possible one.

The observed deflection of light passing by the sun re-quires th at the refractive index ( n ) of the ether be equal t oI + 2 m/r , where m denotes the sun's m ass and r the distancefro m his center. T h e distance r is expressed in units oflength equal to the distance traveled by light in unit time,an d th e mass m is expressed in units of mass which produceunit gravitational acceleration at unit distance. If theunit of time is one second, then t he unit of leng th is 3 x I O ~ Ocms. and the unit of mass is about 4 x 103* grams. Therefra ctive index of the e the r is equal to 2/Kwhere p is itsmagnetic permeability and K its specific inductive capacity.H en ce , if we assume n = I + 2 m/r, we have (pK ) =I t m/r. T h e ratio m /r is always very small. I ts great-est value in the s ola r system is about z x 10-6 at the surfaceof the sun. T h e equation (p K ) 4 = I + 2 m/r can be satis-fied by taking p = I + 2 m/r and K = I + 2 m/r.

T h e force on a neutral electromagnetic system in a me-dium in which it can move freely due t o var iation s in K andp is equal to { E V K + HVp} per unit volume. H e r eE is the electric intensity and H the magnetic intensity.The electrical energy per unit volume is KE2/8n, and themagn etic energy is pH2/8rr. L e t W denote the electricalenergy an d W1 the magnetic energy per unit volume. T h e nthe expression fo r th e fo rce becomes

8n

F = W V K / K +W I V p / p= WV log K +W1V log p.If p = I + 2 m/r and K = I + 2 m/r, then neglecting squares

of m /r log K = z m/r andF= - 2 m ( W + W l ) / r 2 .The electromagnetic mass m1 of the system in the units we


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Gravitation and the Ether 31are using is equal to / ( W t W1)da, where da denotes anelement of volume, so that for a small system, in which rcan be regar ded as constant,

Fr =- 2 mml/rzwhere Fr is now the tota l force on the system. T h is is justtwice the Newtonian attraction -mm1/r2.I t appears tha t i f we assume for p and K values whichgive the o bserved deflection of lig ht, then we get the gravi-tation al a ttractio n twice too big.

So f a r we have supposed th at t he electromagnetic systemremains unchanged in size when p and K va ry, but since theforces between the parts of the system depend on p and K,we should expect the size to vary.If 1 is a quantity propor tional t o th e linear dimensions of

the system a nd equal to unity when K = p = I , then the elec-trical energy of the system can easily be shown to be in-versely as K1 and the magnetic energy inversely as pl, sotha t the force on the system, per unit volume, is given byF =W V log K1 t W1 V lo g pl.Hence t o get the observed gravitational attraction, we must

have p1= K1= I + m/r or 1= I - m/r.W e should expect the dimensions of such a system t o bedetermined by the dimensions of the electrons it contains.The size of an electron may be regarded as determined byan equilibrium between t he tension inside it an d th e stress inthe electric field outside it. The internal tension may beregarded as a sort of elastic reaction against the electricdisplacement a t its surface. W e should there fore expectthe tension to be proportional t o the displacement. T h isgives

I IKa4 c2


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32 Gravitat ion and the Etherwhe re a is the rad ius of the electron, so tha t aK * is cons tant .If K = I + 2 m/r, this gives a a I - m / r .If the linear dimensions of the system are prop ortion al to

a , we get , therefore , 1= I -m /r , which, as we have jus tseen, is the value required to give the observed gravita-t ional at t ract ion.

T h u s it appears tha t i f we assume p = I t m/r , andK = I + 2 m/r, then we can explain the deflection of light bythe sun and the gravitat ional at t ract ion. T h e cont rac tiongiven by 1= I -m/r is in agreement with Einsteins theory.T h e third fa ct , tha t the frequency of the l ight emit ted byan atom on the sun should be diminished by the gravita-tional field, can also be easily deduced from the presenttheory.

According to Bohrs theory of spectral l ines, the fre-quency is proportional to the energy emitted when the atompasses f rom one s tat ionary s tate to another . If the a tomis in ether for which K = I + 2 m/r ins tead of K = I , itsenergy in each of its stationary states will be diminished inthe ra t io I - m / r , a n d so the frequency of any line which itemits will be diminished in the same ratio exactly as pre-dicted by Einstein.

T h u s it appears tha t the theory proposed leads to a sim-ple explanation of all the three facts of gravitation, and somust be regarded as a possible theory.

T h e squares and h igher powers of the ra t io m/r havebeen neglected, so that the results obtained are only accu-ra te to the f i r s t o rder of m/r. To th is order the resu l tsobtained agree with Einsteins theory, so tha t the theoryhere proposed may be regarded as a physical interpretationof his theory.

The only sort of physical theory which seems possible isone depending on the physical properties of the ether, and


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Gravitat ion and the Ether 33p and K ar e the only propert ies of the ether w ith which wear e acquainted. T h e nature of these propert ies is unknown,so th at we have only explained the facts of gravitat ion interms of unknown quanti t ies , and we do not know why pand K should be changed nea r m atter in the way assumed.

Einsteins theory has the very great advantage that i t isbased on general principles derived f ro m experience, where-as the theo ry jus t descr ibed depends on the assumption of avar iat ion of K and p, chosen so as to give results in agree-ment wi th the facts . T h e present theory has the advantageth a t it is very s imple and requires no elabo rate analysis ; itmay prove useful by enabling new phenomena to be pre-dicted.

H. A. WILSON.

H.A. Wilson- Gravitation and the Ether

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