+ All Categories
Home > Documents > The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Date post: 25-Oct-2015
Category:
Upload: abhishek-patil
View: 32 times
Download: 0 times
Share this document with a friend
Description:
The Einstein Theory of Relativity
Popular Tags:
75
Transcript
Page 1: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf
Page 2: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

The Einstein Theory ofRelativity

Hendrik Antoon Lorentz

Published: 1920Categorie(s): Non-Fiction, Science and Technics,ScienceSource: http://www.gutenberg.org

Page 3: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

About Lorentz:Hendrik Antoon Lorentz (18 July

1853 – 4 February 1928) was a Dutchphysicist who shared the 1902 NobelPrize in Physics with Pieter Zeeman forthe discovery and theoreticalexplanation of the Zeeman effect. Healso derived the transformationequations subsequently used by AlbertEinstein to describe space and time.

Copyright: This work is available forcountries where copyright is Life+70and in the USA.

Note: This book is brought to you byFeedbookshttp://www.feedbooks.comStrictly for personal use, do not use this

Page 4: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

file for commercial purposes.

Page 5: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Note

Whether it is true or not that not morethan twelve persons in all the world areable to understand Einstein's Theory, itis nevertheless a fact that there is aconstant demand for information aboutthis much-debated topic of relativity.The books published on the subject areso technical that only a person trained inpure physics and higher mathematics isable to fully understand them. In order tomake a popular explanation of this far-reaching theory available, the presentbook is published.

Professor Lorentz is credited byEinstein with sharing the development ofhis theory. He is doubtless better able

Page 6: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

than any other man—except the authorhimself—to explain this scientificdiscovery.

The publishers wish to acknowledgetheir indebtedness to the NewY o r k Times, The Review ofReviews andThe Athenaeum forcourteous permission to reprint articlesfrom their pages. Professor Lorentz'sarticle appeared originally in TheNieuwe Rotterdamsche Courant ofNovember 19, 1919.

Page 7: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Introduction

The action of the Royal Society at itsmeeting in London on November 6, inrecognizing Dr. Albert Einstein's “theoryof relativity” has caused a great stir inscientific circles on both sides of theAtlantic. Dr. Einstein propounded histheory nearly fifteen years ago. Thepresent revival of interest in it is due tothe remarkable confirmation which itreceived in the report of theobservations made during the sun'seclipse of last May to determine whetherrays of light passing close to the sun aredeflected from their course.

The actual deflection of the rays thatwas discovered by the astronomers was

Page 8: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

precisely what had been predictedtheoretically by Einstein many yearssince. This striking confirmation has ledcertain German scientists to assert thatno scientific discovery of suchimportance has been made sinceNewton's theory of gravitation waspromulgated. This suggestion, however,was put aside by Dr. Einstein himselfwhen he was interviewed by acorrespondent of the New York Times athis home in Berlin. To thiscorrespondent he expressed thedifference between his conception andthe law of gravitation in the followingterms:

“Please imagine the earth removed,and in its place suspended a box as big

Page 9: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

as a room or a whole house, and inside aman naturally floating in the center, therebeing no force whatever pulling him.Imagine, further, this box being, by arope or other contrivance, suddenlyjerked to one side, which isscientifically termed ‘difform motion’,as opposed to ‘uniform motion.’ Theperson would then naturally reachbottom on the opposite side. The resultwould consequently be the same as if heobeyed Newton's law of gravitation,while, in fact, there is no gravitationexerted whatever, which proves thatdifform motion will in every caseproduce the same effects as gravitation.

“I have applied this new idea to everykind of difform motion and have thus

Page 10: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

developed mathematical formulas whichI am convinced give more preciseresults than those based on Newton'stheory. Newton's formulas, however, aresuch close approximations that it wasdifficult to find by observation anyobvious disagreement with experience.”

Dr. Einstein, it must be remembered,is a physicist and not an astronomer. Hedeveloped his theory as a mathematicalformula. The confirmation of it camefrom the astronomers. As he himselfsays, the crucial test was supplied by thelast total solar eclipse. Observationsthen proved that the rays of fixed stars,having to pass close to the sun to reachthe earth, were deflected the exactamount demanded by Einstein's

Page 11: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

formulas. The deflection was also in thedirection predicted by him.

The question must have occurred tomany, what has all this to do withrelativity? When this query waspropounded by the Times correspondentto Dr. Einstein he replied as follows:

“The term relativity refers to time andspace. According to Galileo andNewton, time and space were absoluteentities, and the moving systems of theuniverse were dependent on thisabsolute time and space. On thisconception was built the science ofmechanics. The resulting formulassufficed for all motions of a slow nature;it was found, however, that they wouldnot conform to the rapid motions

Page 12: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

apparent in electrodynamics.“This led the Dutch professor,

Lorentz, and myself to develop thetheory of special relativity. Briefly, itdiscards absolute time and space andmakes them in every instance relative tomoving systems. By this theory allphenomena in electrodynamics, as wellas mechanics, hitherto irreducible by theold formulae—and there are multitudes—were satisfactorily explained.

“Till now it was believed that timeand space existed by themselves, even ifthere was nothing else—no sun, no earth,no stars—while now we know that timeand space are not the vessel for theuniverse, but could not exist at all ifthere were no contents, namely, no sun,

Page 13: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

earth and other celestial bodies.“This special relativity, forming the

first part of my theory, relates to allsystems moving with uniform motion;that is, moving in a straight line withequal velocity.

“Gradually I was led to the idea,seeming a very paradox in science, thatit might apply equally to all movingsystems, even of difform motion, andthus I developed the conception ofgeneral relativity which forms thesecond part of my theory.”

As summarized by an Americanastronomer, Professor Henry NorrisRussell, of Princeton, in the ScientificAmerican for November 29, Einstein'scontribution amounts to this:

Page 14: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

“The central fact which has beenproved—and which is of great interestand importance—is that the naturalphenomena involving gravitation andinertia (such as the motions of theplanets) and the phenomena involvingelectricity and magnetism (including themotion of light) are not independent ofone another, but are intimately related,so that both sets of phenomena should beregarded as parts of one vast system,embracing all Nature. The relation of thetwo is, however, of such a character thatit is perceptible only in a very fewinstances, and then only to refinedobservations.”

Already before the war, Einstein hadimmense fame among physicists, and

Page 15: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

among all who are interested in thephilosophy of science, because of hisprinciple of relativity.

Clerk Maxwell had shown that light iselectro-magnetic, and had reduced thewhole theory of electro-magnetism to asmall number of equations, which arefundamental in all subsequent work. Butthese equations were entangled with thehypothesis of the ether, and with thenotion of motion relative to the ether.Since the ether was supposed to be atrest, such motion was indistinguishablefrom absolute motion. The motion of theearth relatively to the ether should havebeen different at different points of itsorbit, and measurable phenomena shouldhave resulted from this difference. But

Page 16: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

none did, and all attempts to detecteffects of motions relative to the etherfailed. The theory of relativitysucceeded in accounting for this fact. Butit was necessary incidentally to throwover the one universal time, andsubstitute local times attached to movingbodies and varying according to theirmotion. The equations on which thetheory of relativity is based are due toLorentz, but Einstein connected themwith his general principle, namely, thatthere must be nothing, in observablephenomena, which could be attributed toabsolute motion of the observer.

In orthodox Newtonian dynamics theprinciple of relativity had a simplerform, which did not require the

Page 17: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

substitution of local time for generaltime. But it now appeared thatNewtonian dynamics is only valid whenwe confine ourselves to velocities muchless than that of light. The wholeGalileo-Newton system thus sank to thelevel of a first approximation, becomingprogressively less exact as the velocitiesconcerned approached that of light.

Einstein's extension of his principleso as to account for gravitation wasmade during the war, and for aconsiderable period our astronomerswere unable to become acquainted withit, owing to the difficulty of obtainingGerman printed matter. However, copiesof his work ultimately reached theoutside world and enabled people to

Page 18: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

learn more about it. Gravitation, eversince Newton, had remained isolatedfrom other forces in nature; variousattempts had been made to account for it,but without success. The immenseunification effected by electro-magnetism apparently left gravitation outof its scope. It seemed that nature hadpresented a challenge to the physicistswhich none of them were able to meet.

At this point Einstein intervened witha hypothesis which, apart altogetherfrom subsequent verification, deservesto rank as one of the great monuments ofhuman genius. After correcting Newton,it remained to correct Euclid, and it wasin terms of non-Euclidean geometry thathe stated his new theory. Non-Euclidean

Page 19: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

geometry is a study of which the primarymotive was logical and philosophical;few of its promoters ever dreamed that itwould come to be applied in physics.Some of Euclid's axioms were felt to benot “necessary truths,” but mereempirical laws; in order to establish thisview, self-consistent geometries wereconstructed upon assumptions other thanthose of Euclid. In these geometries thesum of the angles of a triangle is not tworight angles, and the departure from tworight angles increases as the size of thetriangle increases. It is often said that innon-Euclidean geometry space has acurvature, but this way of stating thematter is misleading, since it seems toimply a fourth dimension, which is not

Page 20: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

implied by these systems.Einstein supposes that space is

Euclidean where it is sufficiently remotefrom matter, but that the presence ofmatter causes it to become slightly non-Euclidean—the more matter there is inthe neighborhood, the more space willdepart from Euclid. By the help of thishypothesis, together with his previoustheory of relativity, he deducesgravitation—very approximately, but notexactly, according to the Newtonian lawof the inverse square. The minutedifferences between the effects deducedfrom his theory and those deduced fromNewton are measurable in certain cases.There are, so far, three crucial tests ofthe relative accuracy of the new theory

Page 21: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

and the old.(1) The perihelion of Mercury shows

a discrepancy which has long puzzledastronomers. This discrepancy is fullyaccounted for by Einstein. At the timewhen he published his theory, this wasits only experimental verification.

(2) Modern physicists were willing tosuppose that light might be subject togravitation—i.e., that a ray of lightpassing near a great mass like the sunmight be deflected to the extent to whicha particle moving with the same velocitywould be deflected according to theorthodox theory of gravitation. ButEinstein's theory required that the lightshould be deflected just twice as muchas this. The matter could only be tested

Page 22: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

during an eclipse among a number ofbright stars. Fortunately a peculiarlyfavourable eclipse occurred last year.The results of the observations have nowbeen published, and are found to verifyEinstein's prediction. The verification isnot, of course, quite exact; with suchdelicate observations that was not to beexpected. In some cases the departure isconsiderable. But taking the average ofthe best series of observations, thedeflection at the sun's limb is found to be1.98″, with a probable error of about 6per cent., whereas the deflectioncalculated by Einstein's theory should be1.75″. It will be noticed that Einstein'stheory gave a deflection twice as largeas that predicted by the orthodox theory,

Page 23: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

and that the observed deflection isslightly larger than Einstein predicted.The discrepancy is well within whatmight be expected in view of theminuteness of the measurements. It istherefore generally acknowledged byastronomers that the outcome is atriumph for Einstein.

(3) In the excitement of thissensational verification, there has been atendency to overlook the thirdexperimental test to which Einstein'stheory was to be subjected. If his theoryis correct as it stands, there ought, in agravitational field, to be a displacementof the lines of the spectrum towards thered. No such effect has been discovered.Spectroscopists maintain that, so far as

Page 24: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

can be seen at present, there is no way ofaccounting for this failure if Einstein'stheory in its present form is assumed.They admit that some compensatingcause may be discovered to explain thediscrepancy, but they think it far moreprobable that Einstein's theory requiressome essential modification.Meanwhile, a certain suspense ofjudgment is called for. The new law hasbeen so amazingly successful in two ofthe three tests that there must be something valid about it, even if it is notexactly right as yet.

Einstein's theory has the very highestdegree of aesthetic merit: every lover ofthe beautiful must wish it to be true. Itgives a vast unified survey of the

Page 25: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

operations of nature, with a technicalsimplicity in the critical assumptionswhich makes the wealth of deductionsastonishing. It is a case of an advancearrived at by pure theory: the wholeeffect of Einstein's work is to makephysics more philosophical (in a goodsense), and to restore some of thatintellectual unity which belonged to thegreat scientific systems of theseventeenth and eighteenth centuries, butwhich was lost through increasingspecialization and the overwhelmingmass of detailed knowledge. In someways our age is not a good one to livein, but for those who are interested inphysics there are great compensations.

Page 26: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

The Einstein Theory ofRelativity

A Concise Statement by Prof. H. A.Lorentz, of the University of Leyden

The total eclipse of the sun of May 29,resulted in a striking confirmation of thenew theory of the universal attractivepower of gravitation developed byAlbert Einstein, and thus reinforced theconviction that the defining of this theoryis one of the most important steps evertaken in the domain of natural science. Inresponse to a request by the editor, Iwill attempt to contribute something toits 6general appreciation in thefollowing lines.

Page 27: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

For centuries Newton's doctrine of theattraction of gravitation has been themost prominent example of a theory ofnatural science. Through the simplicityof its basic idea, an attraction betweentwo bodies proportionate to their massand also proportionate to the square ofthe distance; through the completenesswith which it explained so many of thepeculiarities in the movement of thebodies making up the solar system; and,finally, through its universal validity,even in the case of the far-distantplanetary systems, it compelled theadmiration of all.

But, while the skill of themathematicians was devoted to makingmore exact calculations of the

Page 28: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

consequences to which it led, no realprogress was made in the science ofgravitation. It is true that the inquiry wastransferred to the field of physics,following Cavendish's success indemonstrating the common attractionbetween bodies with which laboratorywork can be done, but it always wasevident that natural philosophy had nogrip on the universal power of attraction.While in electric effects an influenceexercised by the matter placed betweenbodies was speedily observed—thestarting-point of a new and fertiledoctrine of electricity—in the case ofgravitation not a trace of an influenceexercised by intermediate matter couldever be discovered. It was, and

Page 29: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

remained, inaccessible andunchangeable, without any connection,apparently, with other phenomena ofnatural philosophy.

Einstein has put an end to thisisolation; it is now well established thatgravitation affects not only matter, butalso light. Thus strengthened in the faiththat his theory already has inspired, wemay assume with him that there is not asingle physical or chemical phenomenon—which does not feel, although veryprobably in an unnoticeable degree, theinfluence of gravitation, and that, on theother side, the attraction exercised by abody is limited in the first place by thequantity of matter it contains and also, tosome degree, by motion and by the

Page 30: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

physical and chemical condition inwhich it moves.

It is comprehensible that a personcould not have arrived at such a far-reaching change of view by continuing tofollow the old beaten paths, but only byintroducing some sort of new idea.Indeed, Einstein arrived at his theorythrough a train of thought of greatoriginality. Let me try to restate it inconcise terms.

Page 31: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

The Earth as a Moving Car

Everyone knows that a person may besitting in any kind of a vehicle withoutnoticing its progress, so long as themovement does not vary in direction orspeed; in a car of a fast express trainobjects fall in just the same way as in acoach that is standing still. Only whenwe look at objects outside the train, orwhen the air can enter the car, do wenotice indications of the motion. We maycompare the earth with such a movingvehicle, which in its course around thesun has a remarkable speed, of which thedirection and velocity during aconsiderable period of time may beregarded as constant. In place of the air

Page 32: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

now comes, so it was reasonedformerly, the ether which fills the spacesof the universe and is the carrier of lightand of electro-magnetic phenomena;there were good reasons to assume thatthe earth was entirely permeable for theether and could travel through it withoutsetting it in motion. So here was a casecomparable with that of a railroad coachopen on all sides. There certainly shouldhave been a powerful “ether wind”blowing through the earth and all ourinstruments, and it was to have beenexpected that some signs of it would benoticed in connection with someexperiment or other. Every attempt alongthat line, however, has remainedfruitless; all the phenomena examined

Page 33: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

were evidently independent of themotion of the earth. That this is the waythey do function was brought to the frontby Einstein in his first or “special”theory of relativity. For him the etherdoes not function and in the sketch thathe draws of natural phenomena there isno mention of that intermediate matter.

If the spaces of the universe are filledwith an ether, let us suppose with asubstance, in which, aside from eventualvibrations and other slight movements,there is never any crowding or flowingof one part alongside of another, then wecan imagine fixed points existing in it;for example, points in a straight line,located one meter apart, points in a levelplain, like the angles or squares on a

Page 34: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

chess board extending out into infinity,and finally, points in space as they areobtained by repeatedly shifting that levelspot a distance of a meter in thedirection perpendicular to it. If,consequently, one of the points is chosenas an “original point” we can,proceeding from that point, reach anyother point through three steps in thecommon perpendicular directions inwhich the points are arranged. Thefigures showing how many meters arecomprized in each of the steps may serveto indicate the place reached and todistinguish it from any other; these are,as is said, the “co-ordinates” of theseplaces, comparable, for example, withthe numbers on a map giving the

Page 35: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

longitude and latitude. Let us imaginethat each point has noted upon it thethree numbers that give its position, thenwe have something comparable with ameasure with numbered subdivisions;only we now have to do, one might say,with a good many imaginary measures inthree common perpendicular directions.In this “system of co-ordinates” thenumbers that fix the position of one orthe other of the bodies may now be readoff at any moment.

This is the means which theastronomers and their mathematicalassistants have always used in dealingwith the movement of the heavenlybodies. At a determined moment theposition of each body is fixed by its

Page 36: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

three co-ordinates. If these are given,then one knows also the commondistances, as well as the angles formedby the connecting lines, and themovement of a planet is to be known assoon as one knows how its co-ordinatesare changing from one moment to theother. Thus the picture that one forms ofthe phenomena stands there as if it weresketched on the canvas of the motionlessether.

Page 37: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Einstein's Departure

Since Einstein has cut loose from theether, he lacks this canvas, andtherewith, at the first glance, also losesthe possibility of fixing the positions ofthe heavenly bodies and mathematicallydescribing their movement—i.e., bygiving comparisons that define thepositions at every moment. HowEinstein has overcome this difficultymay be somewhat elucidated through asimple illustration.

On the surface of the earth theattraction of gravitation causes allbodies to fall along vertical lines, and,indeed, when one omits the resistance ofthe air, with an equally accelerated

Page 38: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

movement; the velocity increases inequal degrees in equal consecutivedivisions of time at a rate that in thiscountry gives the velocity attained at theend of a second as 981 centimeters (32.2feet) per second. The number 981defines the “acceleration in the field ofgravitation,” and this field is fullycharacterized by that single number; withits help we can also calculate themovement of an object hurled out in anarbitrary direction. In order to measurethe acceleration we let the body dropalongside of a vertical measure setsolidly on the ground; on this scale weread at every moment the figure thatindicates the height, the only co-ordinatethat is of importance in this rectilinear

Page 39: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

movement. Now we ask what would webe able to see if the measure were notbound solidly to the earth, if it, let ussuppose, moved down or up with theplace where it is located and where weare ourselves. If in this case the speedwere constant, then, and this is in accordwith the special theory of relativity,there would be no motion observed atall; we should again find an accelerationof 981 for a falling body. It would bedifferent if the measure moved withchangeable velocity.

If it went down with a constantacceleration of 981 itself, then an objectcould remain permanently at the samepoint on the measure, or could move upor down itself alongside of it, with

Page 40: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

constant speed. The relative movementof the body with regard to the measureshould be without acceleration, and ifwe had to judge only by what weobserved in the spot where we were andwhich was falling itself, then we shouldget the impression that there was nogravitation at all. If the measure goesdown with an acceleration equal to ahalf or a third of what it just was, thenthe relative motion of the body will, ofcourse, be accelerated, but we shouldfind the increase in velocity per secondone-half or two-thirds of 981. If, finally,we let the measure rise with a uniformlyaccelerated movement, then we shallfind a greater acceleration than 981 forthe body itself.

Page 41: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Thus we see that we, also when themeasure is not attached to the earth,disregarding its displacement, maydescribe the motion of the body inrespect to the measure always in thesame way—i.e., as one uniformlyaccelerated, as we ascribe now andagain a fixed value to the acceleration ofthe sphere of gravitation, in a particularcase the value of zero.

Of course, in the case here underconsideration the use of a measure fixedimmovably upon the earth should meritall recommendation. But in the spaces ofthe solar system we have, now that wehave abandoned the ether, no suchsupport. We can no longer establish asystem of co-ordinates, like the one just

Page 42: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

mentioned, in a universal intermediatematter, and if we were to arrive in oneway or another at a definite system oflines crossing each other in threedirections, then we should be able to usejust as well another similar system thatin respect to the first moves this or thatway. We should also be able to remodelthe system of co-ordinates in all kinds ofways, for example by extension orcompression. That in all these cases forfixed bodies that do not participate in themovement or the remodelling of thesystem other co-ordinates will be readoff again and again is clear.

Page 43: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

New System or Co-Ordinates

What way Einstein had to follow is nowapparent. He must—this hardly needs tobe said—in calculating definite,particular cases make use of a chosensystem of co-ordinates, but as he had nomeans of limiting his choice beforehandand in general, he had to reserve fullliberty of action in this respect.Therefore he made it his aim so toarrange the theory that, no matter howthe choice was made, the phenomena ofgravitation, so far as its effects and itsstimulation by the attracting bodies areconcerned, may always be described in

Page 44: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

the same way—i.e., throughcomparisons of the same general form,as we again and again give certainvalues to the numbers that mark thesphere of gravitation. (For the sake ofsimplification I here disregard the factthat Einstein desires that also the way inwhich time is measured and representedby figures shall have no influence uponthe central value of the comparisons.)

Whether this aim could be attainedwas a question of mathematical inquiry.It really was attained, remarkablyenough, and, we may say, to the surpriseof Einstein himself, although at the costof considerable simplicity in themathematical form; it appearednecessary for the fixation of the field of

Page 45: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

gravitation in one or the other point inspace to introduce no fewer than tenquantities in the place of the one thatoccurred in the example mentionedabove.

In this connection it is of importanceto note that when we exclude certainpossibilities that would give rise to stillgreater intricacy, the form of comparisonused by Einstein to present the theory isthe only possible one; the principle ofthe freedom of choice in co-ordinateswas the only one by which he needed toallow himself to be guided. Althoughthus there was no special effort made toreach a connection with the theory ofNewton, it was evident, fortunately, atthe end of the experiment that the

Page 46: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

connection existed. If we avail ourselvesof the simplifying circumstance that thevelocities of the heavenly bodies areslight in comparison with that of light,then we can deduce the theory ofNewton from the new theory, the“universal” relativity theory, as it iscalled by Einstein. Thus all theconclusions based upon the Newtoniantheory hold good, as must naturally berequired. But now we have got furtheralong. The Newtonian theory can nolonger be regarded as absolutely correctin all cases; there are slight deviationsfrom it, which, although as a ruleunnoticeable, once in a while fall withinthe range of observation.

Now, there was a difficulty in the

Page 47: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

movement of the planet Mercury whichcould not be solved. Even after all thedisturbances caused by the attraction ofother planets had been taken intoaccount, there remained an inexplicablephenomenon—i.e., an extremely slowturning of the ellipsis described byMercury on its own plane; Leverrier hadfound that it amounted to forty-threeseconds a century. Einstein found that,according to his formulas, this movementmust really amount to just that much.Thus with a single blow he solved oneof the greatest puzzles of astronomy.

Still more remarkable, because it hasa bearing upon a phenomenon whichformerly could not be imagined, is theconfirmation of Einstein's prediction

Page 48: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

regarding the influence of gravitationupon the course of the rays of light. Thatsuch an influence must exist is taught bya simple examination; we have only toturn back for a moment to the followingcomparison in which we were justimagining ourselves to make ourobservations. It was noted that when thecompartment is falling with theacceleration of 981 the phenomenatherein will occur just as if there wereno attraction of gravitation. We can thensee an object, A, stand still somewherein open space. A projectile, B, cantravel with constant speed along ahorizontal line, without varying from itin the slightest.

A ray of light can do the same;

Page 49: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

everybody will admit that in each case,if there is no gravitation, light willcertainly extend itself in a rectilinearway. If we limit the light to a flicker ofthe slightest duration, so that only a littlebit, C, of a ray of light arises, or if wefix our attention upon a single vibrationof light, C, while we on the other handgive to the projectile, B, a speed equalto that of light, then we can concludethat B and C in their continued motioncan always remain next to each other.Now if we watch all this, not from themovable compartment, but from a placeon the earth, then we shall note the usualfalling movement of object A, whichshows us that we have to deal with asphere of gravitation. The

Page 50: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

projectile B will, in a bent path, varymore and more from a horizontal straightline, and the light will do the same,because if we observe the movementsfrom another standpoint this can have noeffect upon the remaining next to eachother of B and C.

Page 51: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Deflection of Light

The bending of a ray of light thusdescribed is much too light on thesurface of the earth to be observed. Butthe attraction of gravitation exercised bythe sun on its surface is, because of itsgreat mass, more than twenty-seventimes stronger, and a ray of light thatgoes close by the superficies of the sunmust surely be noticeably bent. The raysof a star that are seen at a short distancefrom the edge of the sun will, goingalong the sun, deviate so much from theoriginal direction that they strike the eyeof an observer as if they came in astraight line from a point somewhatfurther removed than the real position of

Page 52: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

the star from the sun. It is at that pointthat we think we see the star; so here is aseeming displacement from the sun,which increases in the measure in whichthe star is observed closer to the sun.The Einstein theory teaches that thedisplacement is in inverse proportion tothe apparent distance of the star from thecentre of the sun, and that for a star juston its edge it will amount to 1′.75 (1.75seconds). This is approximately thethousandth part of the apparent diameterof the sun.

Naturally, the phenomenon can onlybe observed when there is a total eclipseof the sun; then one can take photographsof neighboring stars and throughcomparing the plate with a picture of the

Page 53: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

same part of the heavens taken at a timewhen the sun was far removed from thatpoint the sought-for movement to oneside may become apparent.

Thus to put the Einstein theory to thetest was the principal aim of the Englishexpeditions sent out to observe theeclipse of May 29, one to Prince'sIsland, off the coast of Guinea, and theother to Sobral, Brazil. The first-namedexpedition's observers were Eddingtonand Cottingham, those of the second,Crommelin and Davidson. Theconditions were especially favorable,for a very large number of bright starswere shown on the photographic plate;the observers at Sobral beingparticularly lucky in having good

Page 54: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

weather.The total eclipse lasted five minutes,

during four of which it was perfectlyclear, so that good photographs could betaken. In the report issued regarding theresults the following figures, which arethe average of the measurements madefrom the seven plates, are given for thedisplacements of seven stars:

1″.02, 0″.92, 0″.84, 0″.58, 0″.54,0″.36, 0″.24, whereas, according to thetheory, the displacements should haveamounted to: 0″.88, 0″.80, 0″.75, 0″.40,0″.52, 0″.33, 0″.20.

If we consider that, according to thetheory the displacements must be ininverse ratio to the distance from thecentre of the sun, then we may deduce

Page 55: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

from each observed displacement howgreat the sideways movement for a starat the edge of the sun should have been.As the most probable result, therefore,the number 1″.98 was found from all theobservations together. As the last of thedisplacements given above—i.e., 0″.24is about one-eighth of this, we may saythat the influence of the attraction of thesun upon light made itself felt upon theray at a distance eight times removedfrom its centre.

The displacements calculatedaccording to the theory are, just becauseof the way in which they are calculated,in inverse proportion to the distance tothe centre. Now that the observeddeviations also accord with the same

Page 56: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

rule, it follows that they are surelyproportionate with the calculateddisplacements. The proportion of thefirst and the last observed sidewisemovements is 4.2, and that of the twomost extreme of the calculated numbersis 4.4.

This result is of importance, becausethereby the theory is excluded, or at leastmade extremely improbable, that thephenomenon of refraction is to beascribed to, a ring of vapor surroundingthe sun for a great distance. Indeed, sucha refraction should cause a deviation inthe observed direction, and, in order toproduce the displacement of one of thestars under observation itself a slightproximity of the vapor ring should be

Page 57: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

sufficient, but we have every reason toexpect that if it were merely a questionof a mass of gas around the sun thediminishing effect accompanying aremoval from the sun should manifestitself much faster than is really the case.We cannot speak with perfect certaintyhere, as all the factors that might be ofinfluence upon the distribution of densityin a sun atmosphere are not well enoughknown, but we can surely demonstratethat in case one of the gasses with whichwe are acquainted were held inequilibrium solely by the influence ofattraction of the sun the phenomenonshould become much less as soon as wegot somewhat further from the edge ofthe sun. If the displacement of the first

Page 58: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

star, which amounts to 1.02-secondswere to be ascribed to such a mass ofgas, then the displacement of the secondmust already be entirely inappreciable.

So far as the absolute extent of thedisplacements is concerned, it wasfound somewhat too great, as has beenshown by the figures given above; it alsoappears from the final result to be 1.98for the edge of the sun—i.e., 13 per cent,greater than the theoretical value of 1.75.It indeed seems that the discrepanciesmay be ascribed to faults inobservations, which supposition issupported by the fact that theobservations at Prince's Island, which, itis true, did not turn out quite as well asthose mentioned above, gave the result,

Page 59: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

of 1.64, somewhat lower than Einstein'sfigure.

(The observations made with asecond instrument at Sobral gave a resultof 0.93, but the observers are of theopinion that because of the shifting of themirror which reflected the rays no valueis to be attached to it.)

Page 60: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Difficulty Exaggerated

During a discussion of the resultsobtained at a joint meeting of the RoyalSociety and the Royal AstronomicalSociety held especially for that purposerecently in London, it was the generalopinion that Einstein's prediction mightbe regarded as justified, and warmtributes to his genius were made on allsides. Nevertheless, I cannot refrain,while I am mentioning it, fromexpressing my surprise that, according tothe report in The Times there should beso much complaint about the difficulty ofunderstanding the new theory. It isevident that Einstein's little book “Aboutthe Special and the General Theory of

Page 61: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Relativity in Plain Terms,” did not findits way into England during wartime.Any one reading it will, in my opinion,come to the conclusion that the basicideas of the theory are really clear andsimple; it is only to be regretted that itwas impossible to avoid clothing themin pretty involved mathematical terms,but we must not worry about that.

I allow myself to add that, as wefollow Einstein, we may retain much ofwhat has been formerly gained. TheNewtonian theory remains in its fullvalue as the first great step, withoutwhich one cannot imagine thedevelopment of astronomy and withoutwhich the second step, that has now beenmade, would hardly have been possible.

Page 62: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

It remains, moreover, as the first, and inmost cases, sufficient, approximation. Itis true that, according to Einstein'stheory, because it leaves us entirely freeas to the way in which we wish torepresent the phenomena, we canimagine an idea of the solar system inwhich the planets follow paths ofpeculiar form and the rays of light shinealong sharply bent lines—think of atwisted and distorted planetarium—butin every case where we apply it toconcrete questions we shall so arrange itthat the planets describe almost exactellipses and the rays of light almoststraight lines.

It is not necessary to give up entirelyeven the ether. Many natural

Page 63: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

philosophers find satisfaction in the ideaof a material intermediate substance inwhich the vibrations of light take place,and they will very probably be all themore inclined to imagine such a mediumwhen they learn that, according to theEinstein theory, gravitation itself doesnot spread instantaneously, but with avelocity that at the first estimate may becompared with that of light. Especiallyin former years were suchinterpretations current and repeatedattempts were made by speculationsabout the nature of the ether and aboutthe mutations and movements that mighttake place in it to arrive at a clearpresentation of electro-magneticphenomena, and also of the functioning

Page 64: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

of gravitation. In my opinion it is notimpossible that in the future this road,indeed abandoned at present, will oncemore be followed with good results, ifonly because it can lead to the thinkingout of new experimental tests. Einstein'stheory need not keep us from so doing;only the ideas about the ether mustaccord with it.

Nevertheless, even without the colorand clearness that the ether theories andthe other models may be able to give,and even, we can feel it this way, justbecause of the soberness induced bytheir absence, Einstein's work, we maynow positively expect, will remain amonument of science; his theory entirelyfulfills the first and principal demand

Page 65: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

that we may make, that of deducing thecourse of phenomena from certainprinciples exactly and to the smallestdetails. It was certainly fortunate that hehimself put the ether in the background;if he had not done so, he probably wouldnever have come upon the idea that hasbeen the foundation of all hisexaminations.

Thanks to his indefatigable exertionsand perseverance, for he had greatdifficulties to overcome in his attempts,Einstein has attained the results, which Ihave tried to sketch, while still young; heis now 45 years old. He completed hisfirst investigations in Switzerland,where he first was engaged in the PatentBureau at Berne and later as a professor

Page 66: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

at the Polytechnic in Zurich. After havingbeen a professor for a short time at theUniversity of Prague, he settled inBerlin, where the Kaiser WilhelmInstitute afforded him the opportunity todevote himself exclusively to hisscientific work. He repeatedly visitedour country and made his Netherlandcolleagues, among whom he counts manygood friends, partners in his studies andhis results. He attended the last meetingof the department of natural philosophyof the Royal Academy of Sciences, andthe members then had the privilege ofhearing him explain, in his ownfascinating, clear and simple way, hisinterpretations of the fundamentalquestions to which his theory gives rise.

Page 67: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Loved this book ?Similar users also

downloaded

Dante AlighieriThe Divine ComedyDante Alighieri's poetic masterpiece, The DivineComedy, is a moving human drama, an unforgettablevisionary journey through the infinite torment of Hell,up the arduous slopes of Purgatory, and on to theglorious realm of Paradise-the sphere of universalharmony and eternal salvation.

Friedrich Wilhelm NietzscheBeyond Good and EvilBeyond Good and Evil (German: Jenseits von Gut undBöse), subtitled "Prelude to a Philosophy of the Future"(Vorspiel einer Philosophie der Zukunft), is a book by

Page 68: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

the German philosopher Friedrich Nietzsche, firstpublished in 1886.It takes up and expands on the ideas of his previouswork, Thus Spoke Zarathustra, but approached from amore critical, polemical direction.In Beyond Good and Evil, Nietzsche attacks pastphilosophers for their alleged lack of critical sense andtheir blind acceptance of Christian premises in theirconsideration of morality. The work moves into therealm "beyond good and evil" in the sense of leavingbehind the traditional morality which Nietzschesubjects to a destructive critique in favour of what heregards as an affirmative approach that fearlesslyconfronts the perspectival nature of knowledge and theperilous condition of the modern individual.

Dale Breckenridge CarnegieThe Art of Public SpeakingTraining in public speaking is not a matter of externals--primarily; it is not a matter of imitation--fundamentally; it is not a matter of conformity tostandards--at all. Public speaking is public utterance,

Page 69: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

public issuance, of the man himself; therefore the firstthing both in time and in importance is that the manshould be and think and feel things that are worthy ofbeing given forth. Unless there be something of valuewithin, no tricks of training can ever make of the talkeranything more than a machine--albeit a highlyperfected machine--for the delivery of other men'sgoods. So self-development is fundamental in our plan.

VatsyayanaThe Kama SutraThe Kama Sutra, is an ancient Indian text widelyconsidered to be the standard work on human sexualbehavior in Sanskrit literature written by the Indianscholar Vatsyayana. A portion of the work consists ofpractical advice on sex. Kāma means sensual orsexual pleasure, and sūtra are the guidlines of yoga, theword itself means thread in Sanskrit.The Kama Sutra is the oldest and most notable of agroup of texts known generically as Kama Shastra).Traditionally, the first transmission of Kama Shastra or"Discipline of Kama" is attributed to Nandi the sacred

Page 70: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

bull, Shiva's doorkeeper, who was moved to sacredutterance by overhearing the lovemaking of the godand his wife Parvati and later recorded his utterancesfor the benefit of mankind.

Arthur Conan DoyleThe Adventures of Sherlock HolmesThe Adventures of Sherlock Holmes is a collection oftwelve stories by Sir Arthur Conan Doyle, featuring hisfamous detective and illustrated by Sidney Paget.These are the first of the Sherlock Holmes shortstories, originally published as single stories in theStrand Magazine from July 1891 to June 1892. Thebook was published in England on October 14, 1892 byGeorge Newnes Ltd and in a US Edition on October15 by Harper. The initial combined print run was14,500 copies.

Sigmund FreudDream Psychology

Page 71: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

The Interpretation of Dreams is a book by SigmundFreud. The first edition was first published in Germanin November 1899 as Die Traumdeutung (though post-dated as 1900 by the publisher). The publicationinaugurated the theory of Freudian dream analysis,which activity Freud famously described as "the royalroad to the understanding of unconscious mentalprocesses".

Charles DarwinOn the Origin of Species, 6th EditionCharles Darwin's On the Origin of Species, in whichhe writes of his theories of evolution by naturalselection, is one of the most important works ofscientific study ever published.

Sun TzuThe Art of WarThe Art of War is a Chinese military treatise that waswritten during the 6th century BC by Sun Tzu.

Page 72: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

Composed of 13 chapters, each of which is devoted toone aspect of warfare, it has long been praised as thedefinitive work on military strategies and tactics of itstime.The Art of War is one of the oldest books on militarystrategy in the world. It is the first and one of the mostsuccessful works on strategy and has had a hugeinfluence on Eastern and Western military thinking,business tactics, and beyond. Sun Tzu was the first torecognize the importance of positioning in strategy andthat position is affected both by objective conditions inthe physical environment and the subjective opinions ofcompetitive actors in that environment. He taught thatstrategy was not planning in the sense of workingthrough a to-do list, but rather that it requires quick andappropriate responses to changing conditions. Planningworks in a controlled environment, but in a competitiveenvironment,

LaoziTao Te ChingThe Tao Te Ching is fundamental to the Taoist school

Page 73: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

of Chinese philosophy and strongly influenced otherschools, such as Legalism and Neo-Confucianism. Thisancient book is also central in Chinese religion, not onlyfor Taoism but Chinese Buddhism, which when firstintroduced into China was largely interpreted throughthe use of Taoist words and concepts. Many Chineseartists, including poets, painters, calligraphers, and evengardeners have used the Tao Te Ching as a source ofinspiration. Its influence has also spread widely outsideEast Asia, aided by hundreds of translations intoWestern languages.

Adam SmithAn Inquiry into the Nature and Causesof the Wealth of NationsAdam Smith's masterpiece, first published in 1776, isthe foundation of modern economic thought andremains the single most important account of the riseof, and the principles behind, modern capitalism.Written in clear and incisive prose, The Wealth ofNations articulates the concepts indispensable to an

Page 74: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

understanding of contemporary society.

Page 75: The Einstein Theory of Relativity - Hendrik Antoon Lorentz.pdf

www.feedbooks.comFood for the mind


Recommended