{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_70272/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_70272","id":"gutenberg_70272","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/70272","summary":null,"tags":["Category: Science - Physics","Relativity (Physics)","Science -- Philosophy"],"text":"THE ROMANES LECTURE\n\n                                1922\n\n\n\n\n\n                                _THE_\n\n                        _THEORY OF RELATIVITY_\n\n\n                              _and its_\n\n                  _Influence on Scientific Thought_\n\n\n\n\n\n                                  BY\n\n                       ARTHUR STANLEY EDDINGTON\n\n                             M.A., F.R.S.\n\n           _Plumian Professor of Astronomy, Cambridge_\n          _President of the Royal Astronomical Society_\n\n\n                              DELIVERED\n                      IN THE SHELDONIAN THEATRE\n                             24 MAY, 1922\n\n\n\n\n                                OXFORD\n                        AT THE CLARENDON PRESS\n                                 1922\n\n\n\n\nHas not a deeper meditation taught certain of every climate and\nage, that the where and the when so mysteriously inseparable\nfrom all our thoughts, are but superficial terrestrial adhesions to\nthought?\n\n                             CARLYLE, _Sartor Resartus_.\n\n\n\n\n                        Oxford University Press\n\n\n\n\nTHE THEORY OF RELATIVITY\n\n\nIn the days before Copernicus the earth was, so it seemed, an immovable\nfoundation on which the whole structure of the heavens was reared. Man,\nfavourably situated at the hub of the universe, might well expect that\nto him the scheme of nature would unfold itself in its simplest aspect.\nBut the behaviour of the heavenly bodies was not at all simple; and the\nplanets literally looped the loop in fantastic curves called epicycles.\nThe cosmogonist had to fill the skies with spheres revolving upon\nspheres to bear the planets in their appointed orbits; and wheels were\nadded to wheels until the music of the spheres seemed well-nigh drowned\nin a discord of whirling machinery. Then came one of the great\nrevolutions of scientific thought, which swept aside the Ptolemaic\nsystem of spheres and epicycles, and revealed the simple plan of the\nsolar system which has endured to this day.\n\nThe revolution consisted in changing the view-point from which the\nphenomena were regarded. As presented to the earth the track of a planet\nis an elaborate epicycle; but Copernicus bade us transfer ourselves to\nthe sun and look again. Instead of a path with loops and nodes, the\norbit is now seen to be one of the most elementary curves--an ellipse.\nWe have to realize that the little planet on which we stand is of no\ngreat account in the general scheme of nature; to unravel that scheme we\nmust first disembarrass nature of the distortions arising from the local\npoint of view from which we observe it. The sun, not the earth, is the\nreal centre of the scheme of things--at least of those things in which\nastronomers at that time had interested themselves--and by transferring\nour view-point to the sun the simplicity of the planetary system becomes\napparent. The need for a cumbrous machinery of spheres and wheels has\ndisappeared.\n\nEvery one now admits that the Ptolemaic system, which regarded the earth\nas the centre of all things, belongs to the dark ages. But to our dismay\nwe have discovered that the same _geocentric_ outlook still permeates\nmodern physics through and through, unsuspected until recently. It has\nbeen left to Einstein to carry forward the revolution begun by\nCopernicus--to free our conception of nature from the terrestrial bias\nimported into it by the limitations of our earthbound experience. To\nachieve a more neutral point of view we have to imagine a visit to some\nother heavenly body. That is a theme which has attracted the popular\nnovelist, and we often smile at his mistakes when sooner or later he\nforgets where he is supposed to be and endows his voyagers with some\npurely terrestrial appanage impossible on the star they are visiting.\nBut scientific men, who have not the novelist's licence, have made the\nsame blunder. When, following Copernicus, they station themselves on the\nsun, they do not realize that they must leave behind a certain purely\nterrestrial appanage, namely, _the frame of space and time_ in which men\non this earth are accustomed to locate the events that happen. It is\ntrue that the observer on the sun will still locate his experiences in a\nframe of space and time, if he uses the same faculties of perception and\nthe same methods of scientific measurement as on the earth; but the\nsolar frame of space and time is not precisely the same as the\nterrestrial frame, as we shall presently see.\n\nI think you will readily understand what is meant by a _frame_ of space\nand time. It is the system of location to which we appeal when we state,\nfor example, that one event is 100 miles distant from and 10 hours later\nthan another. The terms space and time have not only a vague descriptive\nreference to a boundless void and an ever-rolling stream, but denote an\nexact quantitative system of reckoning distances and time-intervals.\nEinstein's first great discovery was that there are many such systems of\nreckoning--many possible frames of space and time--exactly on all fours\nwith one another. No one of these can be distinguished as more\nfundamental than the rest; no one frame rather than another can be\nidentified as the scaffolding used in the construction of the world. And\nyet one of them does present itself to us as being the actual space and\ntime of our experience; and we recoil from the other equivalent frames\nwhich seem to us artificial systems in which distance and duration are\nmixed up in an extraordinary way. What is the cause of this invidious\nselection? It is not determined by anything distinctive in the frame; it\nis determined by something distinctive in us--by the fact that our\nexistence is bound to a particular planet and our motion is the motion\nof that planet. _Nature_ offers an infinite choice of frames; we select\nthe one in which we and our petty terrestrial concerns take the most\ndistinguished position. Our mischievous geocentric outlook has cropped\nout again unsuspected, persuading us to insist on this terrestrial\nspace-time frame which in the general scheme of nature is in no way\nsuperior to other frames.\n\nThe more closely we examine the processes by which events are assigned\nto their positions in space and time, the more clearly do we see that\nour local circumstances play a considerable part in it. We have no more\nright to expect that the space-time frame on the sun will be identical\nwith our frame on the earth than to expect that the force of gravity\nwill be the same there as here. If there were no experimental evidence\nin support of Einstein's theory, it would nevertheless have made a\nnotable advance by exposing a fallacy underlying the older mode of\nthought--the fallacy of attributing unquestioningly a more than local\nsignificance to our terrestrial reckoning of space and time. But there\nis abundant experimental evidence for detecting and determining the\ndifference between the frames of differently circumstanced observers.\nMuch of the evidence is too technical to be discussed here, and I can\nonly refer to the Michelson-Morley experiment. I fear that some of you\nmust be getting rather tired of the Michelson-Morley experiment; but\nthose who go to a performance of Hamlet have to put up with the Prince\nof Denmark.\n\nThis famous experiment is a simple test whether light travels at the\nsame speed in two different directions. For this purpose an apparatus is\nconstructed with two equal arms at right angles, providing two equal\ntracks for the light. A beam of light is divided into two parts so that\none part travels along one arm and back, and the other along the other\narm and back. The two rays then re-unite, and by delicate interference\ntests it is possible to tell if one has been delayed more than the\nother; a delay of less than a thousand-billionth of a second could be\ndetected. The experiment is simply a race between two light-rays with\nequal tracks, but pointing in different directions; the result turns out\nto be a dead-heat. At first sight this is just what would be expected;\nand one almost wonders why it should have been thought worth while to\ntry the experiment. But Michelson, like a good Copernican, had stationed\nhimself on the sun to watch the race; accordingly he realized that the\napparatus was being borne along by the earth's orbital motion with a\nspeed of 20 miles a second. Consequently the light does not travel\nexactly the double length of the arm; starting at one end it has to go\nto the turning-mark at the other end which has moved on a little in the\nmeantime; then it returns to the place which the starting-mark has\ntravelled to whilst the race is in progress. That does not add up to\nexactly the double-length of the arm. Making the calculations we easily\nfind that, although the two arms are equal, the two light-journeys are\nunequal; the competitor whose track lies in the line of the earth's\nmotion has the longer journey, and is at a disadvantage. And yet\naccording to the experiment he does not suffer the expected delay. From\nour standpoint on the sun, the experiment seems to have gone wrong;\nCopernicus has met with a rebuff, and Ptolemy is triumphant.\n\nBut that is because we have not admitted the full consequences of\ntransferring our standpoint to the sun. We have all the while been\nkeeping one foot on earth. Of course, the whole experiment turns on the\ntwo arms having been first adjusted to perfect equality. This could only\nbe ascertained by experiment; and the test applied was to rotate the\napparatus through a right angle, so that if, for example, the journey in\nthe line of the earth's motion had had the advantage of the shorter arm\non one occasion, the transverse journey would have had it on the\nrepetition. That is a perfectly satisfactory test for a terrestrial\nobserver; to turn a rod from one direction to another is the simple and\ndirect way of marking out equal lengths. But the test is not\nsatisfactory to an observer on the sun; he would not think of attempting\nto partition equal lengths of space by means of rods travelling at 20\nmiles a second. His frame of space--the space not only of refined\nmeasurement, but also of the cruder measurements made with the\nsense-organs of his body which determine his perception of space--is\npartitioned by appliances at rest relatively to him, e.g. his own eyes\nand limbs. Lengths of objects carried on the earth must be judged by him\naccording to the room they occupy in his own frame. In the space of the\nterrestrial observer the two arms of the apparatus were adjusted to\nequal length; but in the re-partitioned space of the solar observer they\nmay quite well occupy unequal lengths, and when we take the view-point\nof an observer on the sun we must not overlook this inequality. This\ninequality is not so much an hypothesis proposed to account for\nMichelson's result as a direct deduction from it. The two light-journeys\nwere found to occupy equal times; this clearly shows that the arm in the\nless favoured direction is shorter than the other so as to\ncounterbalance the handicap to which I have referred.[1]\n\nWhen the apparatus is turned through a right angle, the experiment still\ngives the same result. It does not matter which of the two arms we place\nin the line of the earth's motion; that arm must be shorter than the\nother. In other words each arm must automatically contract when it is\nturned from the transverse to the longitudinal position with respect to\nits line of motion. This is the famous FitzGerald contraction of a\nmoving rod. It is of the same amount whatever the material of the rod,\nand depends only on the speed of its motion. For the earth's orbital\nmotion the contraction amounts to one part in 200 million; in fact the\nearth's diameter in the direction of its motion is always shortened by\n2\u00bd inches, the transverse diameter being unaffected.\n\nThis contraction of a moving material object was first revealed to us by\nthe Michelson-Morley experiment; but it is not at all disagreeable to\ntheoretical anticipations. We have to remember that a rod consists of a\nlarge number of molecules kept in position by their mutual forces. The\nchief force is the force of cohesion, and there is little doubt that\nthis is of electrical nature. But when the rod is set in motion, the\nelectrical forces inside it must change. For example, each electric\ncharge when put in motion becomes an _electric current_; and the\ncurrents will exert magnetic attractions on each other which did not\noccur in the system at rest. Under the new system of forces the\nmolecules will have to find new positions of equilibrium; they become\ndifferently spaced; and it is therefore not surprising that the form of\nthe rod changes. Without going beyond the classical laws of Maxwell we\ncan anticipate theoretically what will be the new equilibrium state of\nthe rod, and it turns out to be contracted to the exact amount required\nby the Michelson-Morley result.\n\nThe contraction of the moving rod ought not to surprise us; it would be\nmuch more surprising if the rod were to maintain the same form in spite\nof the alteration of the electrical forces which determine the spacing\nof the molecules. But the remarkable thing is that the contraction is\nonly apparent according to the outlook of the solar observer; and we on\nthe earth, who travel with the rod, cannot appreciate it. The fact that\nthe contraction happens to be very small is irrelevant. For convenience\nsuppose that the earth's velocity is 8,000 times faster, so that the\ncontraction amounts to something like a half the original, length. We\nshould still fail to notice it in everyday life. Let us say that the\ndirection of the earth's motion is vertically upwards.\n\nI turn my arm from horizontal to vertical and it contracts to half its\nlength. No, you cannot convince me I am wrong; I am not afraid of a\nyard-measure. Bring one and measure my arm; first horizontally, the\nresult is 30 inches; now vertically, the result is 30--half-inches!\nBecause you must remember that you have turned the scale into the line\nof the earth's motion so that each inch-division contracts to half an\ninch. 'But we can see that your arm does not contract. Are we not to\ntrust our eyes?' Certainly not, unless you first correct your visual\nimpressions for the contraction of the retina in the vertical direction,\nand for the effect of our rapid motion on the apparent direction of\npropagation of the waves of light. You will find, when you calculate\nthese corrections, that they just conceal the contraction. 'But if the\ncontraction takes place, ought one not to feel it happening to the arm?'\nNot necessarily; I am an observer on the earth, and my feelings like\nother sense-impressions belong to the geocentric outlook on nature,\nwhich Copernicus has persuaded us to abandon.\n\nTake a pair of compasses and twiddle them on a sheet of paper. Is the\nresulting curve a circle or an ellipse? Copernicus from his standpoint\non the sun declares that owing to the FitzGerald contraction the two\npoints drew nearer together when turned in the direction of the earth's\norbital motion; hence the curve is flattened into an ellipse. But here I\nthink Ptolemy has a right to be heard; he points out that from the\nbeginning of geometry circles have always been drawn with compasses in\nthis way, and that when the word 'circle' is mentioned every intelligent\nperson understands that this is the curve meant. The same pencil line is\nin fact a circle in the space of the terrestrial observer and an ellipse\nin the space of a solar observer. It is at the same time a moving\nellipse and a stationary circle. I think that illustrates as well as\npossible what we mean by _the relativity of space_.\n\nIt is sometimes complained that Einstein's conclusion that the frame of\nspace and time is different for observers with different motions tends\nto make a mystery of a phenomenon which is not after all intrinsically\nstrange. We have seen that it depends on a contraction of moving objects\nwhich turns out to be quite in accordance with Maxwell's classical\ntheory. But even if we have succeeded in explaining it to ourselves\nintelligibly, that does not make the statement any the less true! A new\nresult may often be expressed in various ways; one mode of statement may\nsound less mysterious; but another mode may show more clearly what will\nbe the consequences in amending and extending our knowledge. It is for\nthe latter reason that we emphasize the relativity of space--that\nlengths and distances differ according to the observer implied. Distance\nand duration are the most fundamental terms in physics; velocity,\nacceleration, force, energy, and so on, all depend on them; and we can\nscarcely make any statement in physics without direct or indirect\nreference to them. Surely then we can best indicate the revolutionary\nconsequences of what we have learnt by the statement that distance and\nduration, and all the physical quantities derived from them, do not as\nhitherto supposed refer to anything absolute in the external world, but\nare relative quantities which alter when we pass from one observer to\nanother with different motion. The consequence in physics of the\ndiscovery that a yard is not an absolute chunk of space, and that what\nis a yard for one observer may be eighteen inches for another observer,\nmay be compared with the consequences in economics of the discovery that\na pound sterling is not an absolute quantity of wealth, and in certain\ncircumstances may 'really' be seven and sixpence. The theorist may\ncomplain that this last statement tends to make a mystery of phenomena\nof currency which have really an intelligible explanation; but it is a\nstatement which commends itself to the man who has an eye to the\npractical applications of currency.\n\nPtolemy on the earth and Copernicus on the sun are both contemplating\nthe same external universe. But their experiences are different, and it\nis in the process of experiencing events that they become fitted into\nthe frame of space and time--the frame being different according to the\nlocal circumstances of the observer who is experiencing them. That, I\ntake it, is Kant's doctrine, 'Space and time are forms of experience.'\nThe frame then is not in the world; it is supplied by the observer and\ndepends on him. And those relations of simplicity, which we seek when we\ntry to obtain a comprehension of how the universe functions, must lie in\nthe events themselves before they have been arbitrarily fitted into the\nframe. The most we can hope for from any frame is that it will not have\ndistorted the simplicity which was originally present; whilst an\nill-chosen frame may play havoc with the natural simplicity of things.\nWe have seen that the simplicity of planetary motions was obscured in\nPtolemy's frame, and became apparent in Copernicus's frame. But for\nordinary terrestrial phenomena the position is reversed and Ptolemy's\nframe allows their natural simplicity to become apparent. In\nCopernicus's frame the most simple phenomena are brought about by highly\ncomplicated processes which mutually cancel one another. Ordinary\nobjects contract and expand as they are moved about, and the changes are\nconcealed by an elaborate conspiracy in which all the quantities of\nnature--electrical, optical, mechanical, gravitational--have joined. In\nCopernicus's frame we have a great complication of description which has\nno counterpart in anything occurring in the external world; because the\nterms of our description refer to the irrelevant process of fitting into\nthe selected frame of space and time. This elaborate Copernican scheme\nrather reminds one of the schemes of the White Knight--\n\n\n    But I was thinking of a plan\n      To dye one's whiskers green,\n    And always use so large a fan\n      That they could not be seen.\n\n\nWe do not deny the subtlety and the remarkable efficiency of the plan;\nbut we may be allowed to question whether it is the simplest\ninterpretation of the drab monotony of the face of nature presented to\nus. The simple fact is that a terrestrial or Ptolemaic frame fits\nnaturally the terrestrial phenomena, and a solar or Copernican frame\nfits the phenomena of the solar system; but we cannot make one frame\nserve for both without introducing irrelevant, complications.\n\nWe go beyond Copernicus nowadays, and are not content with a visit to\nthe sun. Why choose the sun rather than some other star in order to\nobtain an undistorted view of things? The astronomer now places himself\nso as to travel with the centre of gravity of the stellar universe, and\nis not even then quite satisfied. The physicist dreams of a land of\nWeissnichtwo, which shall be truly at rest in the ether. We realize the\ndistortion imported into the world of nature by the parochial standpoint\nfrom which we observe it, and we try to place ourselves so as to\neliminate this distortion--so as to observe that which actually is. But\nit is a vain pursuit. Wherever we pitch our camera, the photograph is\nnecessarily a two-dimensional picture distorted according to the laws of\nperspective; it is never a true semblance of the building itself.\n\nWe must try another plan. I do not think we can ever eliminate\naltogether the human element in our conception of nature; but we can\neliminate a particular human element, namely, this framework of space\nand time. If our thought must be anthropocentric, it need not be\ngeocentric. Nor are we permanently better off if we merely substitute\nthe space-time frame of some other star or standard of motion. We must\nleave the frame entirely indeterminate. When we do that, we find that\nthe world common to all observers--in which each observer traces a\ndifferent space-time frame according to his own outlook--is a world of\nfour dimensions. When we look at any object, say a chair, the impression\non our eyes is a two-dimensional picture depending on the position from\nwhich we are looking; but we have no difficulty in conceiving of the\nchair as a solid object, not to be identified with any one of our\ntwo-dimensional pictures of it, but giving rise them all as the position\nof the observer is varied. We must now realize that this solid chair in\nthree dimensions is itself only an appearance, which changes according\nto the motion of the observer, and that there is a super-object in\nfour-dimensions, not to be identified with the three-dimensional chair\nin Ptolemy's scheme, or the same chair in Copernicus's scheme, but\ngiving rise to both these appearances. The synthesis of a\nthree-dimensional chair from a number of flat pictures is easy to us\nbecause we are accustomed to assume different positions in rapid\nsuccession; indeed our two eyes give us slightly different points of\nview simultaneously. By sheer necessity our brains have been forced to\nconstruct the conception of the solid chair to combine these changing\nappearances. But we do not vary our motion to any appreciable extent and\nour brains have not hitherto been called upon to combine the appearances\nfor different motions; thus the effort which we now ask the brain to\nmake is a novel one. That explains why the result seems to transcend our\nordinary mode of thought.\n\nThe discovery, or one should rather say the rediscovery, of the world of\nfour dimensions is due to Minkowski. Einstein had worked out fully the\nrelations between the frames of space and time for observers with\ndifferent motions. To the genius of Minkowski we owe the realization\nthat these frames are merely systems of partitions arbitrarily drawn\nacross a four-dimensional world which is common to all observers.\n\nThere is a strange delusion that the fourth dimension must be something\nwholly beyond the conception of the ordinary man, and that only the\nmathematician can be initiated into its mysteries. It is true that the\nmathematician has the advantage of understanding the technical machinery\nfor solving the problems which may arise in studying the world of four\ndimensions; but as regards the conception of the four dimensions of the\nworld his point of view is the same as that of anybody else. Is it\nsupposed that by intense thought he throws himself into some state of\ntrance in which he perceives some hitherto unsuspected direction\nstretching away at right angles to length, breadth, and thickness? That\nwould not be much use. The world of four dimensions, of which we are now\nspeaking, is perfectly familiar to everybody. It is obvious to every\none--even to the mathematician--that the world of solid and permanent\n_objects_ has three dimensions and no more; that objects are arranged in\na threefold order, which for any particular individual may be analysed\ninto right-and-left, backwards-and-forwards, up-and-down. But it is no\nless obvious to every one that the world of _events_ is of four\ndimensions; that events are arranged in a fourfold order, which in the\nexperience of any particular individual will be analysed into\nright-and-left, backwards-and-forwards, up-and-down, _sooner-and-later_.\nThe subject of our study is external nature, which is a world of events,\ncommon to all observers but represented by them differently in their\nparochial frames of space and time; it is obvious to the most\ncommonplace experience that this absolute world contains a fourfold\norder.[2]\n\nThe news that the events around us form a world of four dimensions is as\nstale as the news that Queen Anne is dead. The reason why the relativist\nresurrects this ancient truism is because it is only in this undissected\ncombination of four dimensions that the experiences of all observers\nmeet. In our own experience one dimension is sharply separated from the\nother three and is distinguished as time; but our experience is solely\nterrestrial, and if we insist on building the scheme of nature on purely\nterrestrial experience we are limiting ourselves to the mediaeval\ngeocentric system of the world.\n\nWe have been accustomed to regard the enduring world as composed of a\ncontinuous succession of instantaneous states, as though the world of\nevents were _stratified_. Each event is supposed to lie in a definite\ninstant or stratum, and the orderly succession of these strata makes up\nthe whole of reality. The instant 'now' represents one such stratum\nrunning throughout the universe. Indeed we are accustomed to extend it\nbeyond the universe, and we even use the word 'now' with reference to\nthe existence of those who have passed away from the material world. The\ninvestigations of the relativity theory show incontrovertibly that this\nsupposed stratification is an illusion; there is not the slightest\nevidence for such a view of world-structure. The instantaneous state,\nwhich we have hitherto taken to be a natural stratum in the\nfour-dimensional world of events, is merely an arbitrary partition\ncreated by ourselves to correspond with our geocentric outlook. We can\ntake a differently inclined partition,[3] that is to say, a section\nwhich includes on the one side of us events which happened a little\nwhile ago and on the other side of us events which have not yet\nhappened; such a farcical combination is in every way equivalent to our\nso-called instantaneous state, and indeed it _is_ an instantaneous state\naccording to the outlook of some non-terrestrial observer with suitably\nassigned motion.\n\nIt is so contrary to our natural prejudices to recognize that the\nworld-wide instant now is created by ourselves and has no existence\napart from our geocentric outlook, that I will spend a few moments\ntrying to show its artificiality. When I say that I am conscious of an\ninstant now, I am only conscious of it in so far as it is HERE--inside\nme. What then has led me to imagine that there exists a continuation of\nit outside me? It is because I look out on the world and see various\nevents happening 'now', so that I jump to the conclusion that this\ninstant of which I am conscious has to be extended to include\nthem. But that idea is another inheritance from the dark ages,\noverthrown by R\u00f6mer in 1675. It is not the events themselves but the\nsense-impressions to which they give rise which are happening in the\ninstant now. So my justification for placing the events outside me in\nthe instants of which I am conscious has entirely disappeared.\nUnfortunately, however, the crude outlook was not abolished, but patched\nup; it was found that the immediate difficulties could be met by\nlocating the external events not in the instant of our visual perception\nof them but in an instant which we had experienced a little time\nback--allowing, as we say, for the time of propagation of light. Thus\nour instants were still made to extend through space; but they were\ncarried like partitions among the events by an artificial process of\ncomputation, and no longer by immediate intuition. The relativity theory\nrecognizes these _worldwide instants_ for what they are--artificial\npartitions constructed for purposes of calculation. I may add that it in\nno way tampers with the _local instants_ which form the stream of our\nconsciousness; it fully recognizes that the chain of events in such a\ntime-succession is a series of an entirely distinctive character from\nthe succession of points along a line in space. Those who suspect that\nEinstein's theory is playing unjustifiable tricks with time should\nrealize that it leaves entirely untouched that time-succession of which\nwe have intuitive knowledge, and confines itself to overhauling the\nartificial scheme of time which R\u00f6mer first introduced into physics.\n\nThe study of the four-dimensional world of events gives us a new insight\ninto the processes of nature because it removes the irrelevant\nstratification in a particular direction--the instantaneous\nstates--which we have so unnecessarily introduced in our customary\noutlook. When this stratification is ignored we are enabled to see the\nprocesses in their simplest aspect, though not, of course, in their most\nfamiliar aspect. We must distinguish between simplicity and familiarity;\na pig may be most familiar to us in the form of rashers, but the\n_unstratified_ pig is a simpler object of study to the biologist who\nwishes to understand how the animal functions.\n\nI will conclude this part of the argument with an experimental\napplication which illustrates the power of Einstein's method. Much study\nhas of late been given to electrons moving with very high speeds; for\nexample, the \u03b2 particles shot off from radioactive substances are\nnegative electrons which sometimes attain speeds of 100,000 miles a\nsecond. It is found by experiment that the rapid motion produces an\nincrease of mass of these particles. I want to show that the theory of\nrelativity gives a very simple explanation of just how this increase of\nmass occurs. But I must first remark that an explanation had been\npreviously given which had generally been accepted as satisfactory. The\nphenomenon was actually predicted by J. J. Thomson before relativity was\nthought of; because, assuming that the mass of a particle is of\nelectrical origin, an application of Maxwell's equations shows that it\nought to increase with velocity. But the precise law of increase cannot\nbe predicted on this basis, since various plausible assumptions lead to\nslightly different results. Moreover, Maxwell's equations are after all\nonly empirical laws, with a mystery of their own; it was a notable\nadvance to connect the change of mass at high speeds with other\nphenomena whose strangeness has disappeared by long familiarity, but\nthere is still scope for a more far-reaching explanation. Einstein takes\nus straight to the root of the mystery, and he clears up one point which\nwas misleading, if not actually wrong, in the older explanation. The\nchange of mass does not in any way depend on whether the mass is of\nelectrical origin or not; it arises simply from the fact that mass is a\n_relative_ quantity, depending by its definition on the relative\nquantities length and time. Let us look at the \u03b2 particle from its own\npoint of view; it is just an ordinary electron in no way different from\nany other. 'But it is travelling unusually rapidly?' 'That', says the\nelectron, 'is a matter of opinion. So far as I am aware I am at rest, if\nthe word \"rest\" has any meaning. In fact I was just contemplating with\namazement _your_ extraordinary speed of 100,000 miles a second with\nwhich you are shooting past me.' Of course our motion is of no\nparticular concern to the electron, and it will not modify its\nconstitution on our account; so it keeps its mass, radius, electric\nfield, &c., equal to the standard constants applying to electrons in\ngeneral. These terms are relative, and refer therefore to some\nparticular frame of space and time--clearly the frame appropriate to an\nelectron in self-contemplation, viz. the one with, respect to which it\nis at rest. But this frame is not the usual geocentric frame to which\n_we_ refer quantities such as length, time, and mass; there is a\ndifference of 100,000 miles a second between our station of observation\nand that of the \u03b2 particle in self-contemplation. It is a mere matter\nof geometry to discover what the \u03b2 particle's lengths and times become\nwhen referred to the partitions which we have drawn across the world.\nBut when we calculate the consequential change of mass resulting from\nthe changes of length and time, we find that it should be increased in\nprecisely the proportion indicated by the most refined experiments.\n\nThe point is that every electron, at rest or in motion, is a perfectly\nconstant structure; but we distort it by fitting it into the space-time\nframe appropriate to our own motion with which the electron has no\nconcern. The greater our motion with respect to the electron, the\ngreater will be the distortion. The distortion is not produced by any\nphysical agency at work in the electron; it is a purely subjective\ndistortion depending on our transformation of the reference frame of\nspace and time. This distortion involves a change in our physical\ndescription of the electron in terms of mass, shape, size; and in\nparticular the change of mass agrees precisely with that found\nexperimentally.\n\nYou see that it is not altogether idle discussing the natural space-time\nframes for observers moving with huge velocities. We know of no animate\nobservers with these speeds; but we do know of inanimate material\nobjects. Their common resemblance is obscured when we refer them\nindiscriminately to our irrelevant geocentric frame; we think they have\naltered their properties, varied in mass, and so on; but the resemblance\nis restored when we refer each individual to the frame appropriate to\nit, and so describe them all in comparable terms.\n\nOur measurements of distance in space are found to be subject to certain\nlaws--the laws of geometry. But it has now become impossible to regard\nthe subject of space-geometry as complete in itself. Consider a triangle\nformed by three points (or events) in the four-dimensional world; if we\nhappen to have drawn our instantaneous strata so that the three points\nlie in one stratum, then the triangle is a space-triangle and its\nproperties fall within the scope of our classical geometry. But another\nobserver will draw his strata in a different direction, and for him the\ntriangle would be partly in space and partly in time, so that it would\nnot be a fit subject for space-geometry. The subject of geometry is in a\ndesperate condition, because Copernicus and Ptolemy not merely disagree\nas to the geometry of a configuration; they even disagree as to whether\na given configuration is one to which space-geometry is applicable. It\nis clear that to save it we must extend our geometry so as to include\ntime as well as space. Let me give an illustration of this extension.\nThe terrestrial observer can have a space-triangle (formed by three\npoints or events at the same instant) whose sides he can measure with\nscales; he can also have a 'time-triangle', formed by three events on\ndifferent dates, whose sides he must measure with _clocks_.[4] You all\nknow the law of the space-triangle--that if you measure with a scale\nfrom _A_ to _B_ and from _B_ to _C_ the sum of the readings is always\n_greater_ than the measure from _A_ to _C_. It is not so well known that\nthere is a precisely analogous law for the time-triangle--that if you\nmeasure with a clock from _A_ to _B_ and from _B_ to _C_ the sum of the\nreadings is always _less_ than the reading of a clock measuring directly\nfrom _A_ to _C_. In the space-triangle any two sides are together\n_greater_ than the third side; in the time-triangle two sides are\ntogether _less_ than the third side.[5] Both these laws must be combined\nin our general geometry of four dimensions, so that it will not be quite\nso simple a geometry as that to which we are accustomed.[6]\n\nBut the point to which I would especially direct attention is this.\nEvidently the proposition which I have given you about time-triangles\ncannot be dissociated from the corresponding proposition about\nspace-triangles. When we give up the mediaeval geocentric standpoint, we\nmust recognize that they belong to one geometry, of which our ordinary\nspace-geometry is only a part or projection. But if you examine the\nproposition about time-triangles, you will see that it is a statement\nabout the behaviour of clocks when they move about, a subject which\nobviously comes under the heading of mechanics. When we deal with the\nfour-dimensional world we can no longer distinguish between geometry and\nmechanics. They become the same subject. When we have completely\nmastered the geometry of the world of events, we shall have inevitably\nlearnt the mechanics of it. That is why Einstein, studying the geometry\nof the world and discovering that it was strictly non-Euclidean, found\nthat he was at the same time studying the mechanical force of\ngravitation. And when he had made up his mind which of the possible\nvarieties of non-Euclidean geometry was obeyed, and so settled the laws\nof the new geometry, the same decision settled the law of gravitation--a\nlaw approximating to, but not identical with, the law which Newton had\ngiven.\n\nHere a wide vista opens before us. We see that two great divisions of\nmathematical physics, viz. geometry and mechanics, have met in the\nfour-dimensional world. It is not merely that mechanical problems can be\ntreated by formulae originally belonging to pure geometry; that device\nhas long been in use. Experimental geometry and mechanics actually\nrelate to the same subject-matter; and the young student who discovers\nexperimental laws with ruler and compasses and cardboard figures, and\nlater goes on to pendulums and spring-balances, is developing a single\nsubject which cannot be divided any more than the subject of magnetism\ncan be divided from electricity.\n\nIt is through this unification of geometry and mechanics that I should\nlike to approach the problem of gravitation, showing that a field of\nforce is a manifestation of the geometry of space and time. But I fear\nthat that would be too technical; so we will approach it from a\ndifferent angle.\n\nWe have shown that the contemplation of the world from the standpoint\nof a single observer is liable to distort its simplicity, and we have\ntried to obtain a juster idea by taking into account and combining\nother points of view. The more standpoints the better. Let us now\nconsider another point of view, which we have not previously thought\nabout--the point of view of an observer who has tumbled out of an\naeroplane and is falling headlong. In many respects his is an ideal\nsituation--temporarily. Unfortunately on _terra firma_ we are\ncontinually subjected to a very disturbing influence; we undergo a\nterrific bombardment by the molecules of the ground, which are hammering\non the soles of our boots with a total force of some ten stone weight\npressing us upwards. Now our bodies are the scientific appliances which\nwe use to make our common observations of the world. I am sure that no\nphysicist would permit any one to enter his laboratory and hammer on his\nclocks and galvanometers whilst he was observing with them; at any rate\nhe would think it necessary to apply some corrections for the effect of\nthe disturbance. Let us then allow ourselves to fall freely _in vacuo_;\nthen we shall be free from this disturbing bombardment and able to take\na much more natural view of what is going on around us.\n\nWhilst falling, we perform the experiment of letting go an apple held in\nthe hand. The apple is now free, but it cannot fall any more than it was\nfalling already; consequently it remains poised in contact with our\nhand. In our new outlook--in our new frame of space and time--an apple\ndoes not drop. There is no mysterious force accelerating it. And\nremember that this new frame of space and time is the natural frame of a\nfree observer; whereas the old frame, in which the mysterious\naccelerating force occurred, was the frame of a very much disturbed\nobserver. It is true that when we look down at the earth we see trees\nand houses rushing up to meet us; but there is no mystery about that.\nThere is an obvious cause for it; plainly they are being propelled\nupwards from below by that molecular bombardment which I have mentioned.\nYou see that the apple's view of things is simpler than Newton's. Newton\nhad to invent a mysterious force dragging the apple down; the apple\nobserves only a familiar physical agency propelling Newton up.\n\nIt is not my purpose to emphasize unduly the superiority of the apple's\nview over Newton's, but rather to regard both on an equal footing. I\nhave perhaps been a little unfair to Newton. His position on the surface\nof the earth was unfortunate, but he would have been perfectly content\nto be at the centre of the earth, where he could have remained without\nsupport, i.e. without disturbance by molecular bombardment. From there\nhe would still have observed the well-known acceleration of the apple;\nand the apple would have observed a corresponding acceleration of Newton\nwithout any molecular bombardment causing it. From either point of view\nthere is a mysterious agent at work. How shall we picture to ourselves\nthis agent? Shall we picture it as a force--a tug of some kind? But if\nso, to which of them is the tug applied? If we take the standpoint of\nNewton the tug is applied to the apple, if the standpoint of the apple\nthe tug is applied to Newton; so that in our synthesis of all\nstandpoints we cannot decide which is being tugged, and the picture of\ngravitation as a tugging agent becomes impossible. Einstein replaces it\nby a different picture, which we shall perhaps better understand if we\ncompare it with a very similar revolution of scientific thought which\noccurred long ago.\n\nThe ancients believed that the earth was flat. The small portion of its\nsurface with which they were chiefly concerned could be represented\nwithout serious distortion on a flat map. As more distant countries were\nadded, it would be natural to think that they also could be included in\nthe flat map. You have all seen such maps of the world, e. g. Mercator's\nprojection, and you will remember how Greenland appears enormously\nexaggerated in size. Now those who adhered to the flat-earth theory must\nhold that the flat map gives the _true_ size of Greenland. How then\nwould they explain that travellers in that country reported that the\ndistances were much shorter? They would, I suppose, invent a theory that\na demon resided in that country who helped travellers on their way,\nmaking the journeys appear much shorter than they 'really' were. No\ndoubt the scientists would preserve their self-respect by using some\nGraeco-Latin polysyllable instead of the word 'demon', but that must not\ndisguise from us the fact that they were appealing to a _deus ex\nmachina_. The name demon is rather suitable, however, because he has the\nimpish characteristic that we cannot pin him down to any particular\nlocality. We might equally well start our flat map with its centre in\nGreenland; then it would be found that journeys there were quite normal,\nand that the activities of the demon were disturbing travellers in\nEurope. We now recognize that the true explanation is that the earth's\nsurface is curved; and the demoniacal complications appeared because we\nwere forcing the earth's surface into an inappropriate flat frame which\ndistorts the simplicity of things.\n\nWhat has happened in the case of the earth has happened also in the case\nof the world, and a similar revolution of thought is needed. An\nobserver, say at the centre of the earth, finds that there is a frame of\nspace and time--a flat or Euclidean frame--in which he can locate things\nhappening in his neighbourhood without distorting their natural\nsimplicity. There is no gravitation, no tendency of bodies to fall, so\nlong as the observer confines his observations to his immediate\nneighbourhood. He extends this frame of space and time to greater\ndistances, and ultimately to the earth's surface where he encounters the\nphenomenon of falling apples. This new phenomenon must be accounted for,\nso he invents a _deus ex machina_ which he calls gravitation to whose\nactivities the disturbance is attributed. But we have seen that we may\njust as well start with the falling apple. It has a flat frame of space\nand time into which phenomena in its neighbourhood fit without\ndistortion; and from its point of view bodies near it do not undergo any\nacceleration. But when it extends this frame farther afield, the\nsimplicity is lost; and it too has to postulate the demon force of\ngravitation existing in distant parts, and for example causing\nundisturbed objects at the centre of the earth to fall towards it. As we\nchange from one observer to another--from one flat space-time frame to\nanother--so we have to change the region of activity of this demon. Is\nnot the solution now apparent? The demon is simply the complication\nwhich arises when we force the world into a flat Euclidean space-time\nframe into which it does not fit without distortion. It does not fit the\nframe, because _it is not a Euclidean or flat world_. Admit a curvature\nof the world and the mysterious disturbance disappears. Einstein has\nexorcized the demon.\n\nEinstein, recognizing that in the phenomena of gravitation he was not\ndealing with a 'tug' but with a curvature of the world, had to\nreconsider the law of gravitation. He could not make any possible law of\ncurvature correspond exactly with the previously assumed law of tugging.\nThus he was led to propound a new law of gravitation--a law which in\nmost practical cases differs very little from that of Newton, although\nit has an essentially different foundation. I need not here dwell on the\nvery remarkable way in which Einstein's emendation of the law of\ngravitation has been confirmed both by the anomalous secular change in\nthe orbit of the planet Mercury, and by the observed displacement of the\nstars near the sun during the total eclipse of 1919. I might, however,\nremind you that in the latter observation the point at issue between\nNewton's and Einstein's theory was not the _existence_ of a deflexion of\nlight-rays passing near the sun but the amount of the deflexion,\nEinstein predicting twice the deflexion possible on the Newtonian\ntheory. The larger deflexion was quantitatively confirmed by the eclipse\nobservations. Einstein's main achievement is a new law, not a new\nexplanation, of gravitation. He attributes the gravitation of massive\nbodies to a curvature of the world in the region surrounding them and so\nthrows a flood of light on the whole problem; but he is not primarily\nconcerned to explain how material bodies produce (or are associated\nwith) this curvature of the world around them, nor how this curvature is\nmade subject to a law. Although it would be an entire misunderstanding\nof Einstein's attitude in propounding the general relativity theory to\nregard it as a search for an explanation of gravitation, nevertheless I\nthink that the further following up of his ideas has led to a genuine\nexplanation as complete as could be desired. But I am not going to give\nyou the explanation in this lecture; sometimes an explanation requires a\ngreat deal of explaining.[7]\n\nI think that we can without mathematics form a general idea of why\nEinstein found it necessary to amend Newton's law of gravitation. Let us\nreturn to the illustration of the pig, and imagine that we wish to\ndiscover the law governing the distribution of fat and lean in the\nanimal. From the breakfast-table standpoint a plausible type of law\nwould be that half of each rasher is fat and the other half lean; and if\nthis turned out to be confirmed very approximately by observation we\nmight well imagine that we had discovered the exact law of porcine\nstructure. But the case is altered if we give up the breakfast-table\nstandpoint and contemplate the animal in a more general way, remembering\nthat he has not been designed with any particular reference to the\nseries of rashers into which our grocer has chosen to slice him. We must\nnow look for a different type of law altogether. Two possibilities may\narise. We may find that our proposed law, although expressed in\nbreakfast-table parlance, is nevertheless equivalent to a possible\nbiological law; it may be immediately capable of translation into a more\ngeneral statement which makes no reference to a particular\nstratification. But on the other hand, it may happen that the suggested\nlaw cannot be freed from this reference to a particular system of\nslicing. In that case we can only regard it as approximate, perhaps\nholding fairly well for the slices of which we have most experience but\nbecoming less and less accurate in the more tortuous parts of the\nanimal. Both these cases are illustrated in Einstein's modifications of\nclassical theory. Newton's law of gravitation explicitly refers to a\nspace-time frame and therefore to a world stratified into instantaneous\nstates. It proves to be impossible to free it from this reference to a\nparticular stratification without modifying it. In fact if the crucial\nastronomical observations had shown that Newton's law and not Einstein's\nwas the exact law of gravitation, this would have been evidence of a\nreal stratification of the structure of the world--a stratification\nrevealed by no other phenomena. Einstein's law is the simpler law\nbecause it is consistent with what we now know of the general plan of\nworld-structure; Newton's law could only be made possible by introducing\na novel and specialized feature--a stratified arrangement of\nstructure--which is not revealed in any other phenomena.\n\nMaxwell's laws of electromagnetism afford an example of the other type.\nThese, it is true, are stated as relating to the particular slices of\nthe world of events, which are served up to us like rashers instant by\ninstant. But they can be restated, without alteration of effect, in a\nform making no reference to slices. This is a very remarkable property\nof Maxwell's equations which was quite unknown at the time they were\nfirst put forward. It was brought to light much later by the researches\nof Larmor and Lorentz. In consequence of this Einstein is able to take\nover the whole classical theory of electromagnetism unaltered; he\nrestates it so as to show how it applies generally and is not bound up\nwith the purely terrestrial point of view, but he does not amend the\nlaws. He metes out different treatment to the gravitational laws and\nelectromagnetic laws, because he finds the latter already adapted to his\nscheme.\n\nIf I have succeeded in my object, you will have realized that the\npresent revolution of scientific thought follows in natural sequence on\nthe great revolutions at earlier epochs in the history of science.\nEinstein's special theory of relativity, which explains the\nindeterminateness of the frame of space and time, crowns the work of\nCopernicus who first led us to give up our insistence on a geocentric\noutlook on nature; Einstein's general theory of relativity, which\nreveals the curvature or non-Euclidean geometry of space and time,\ncarries forward the rudimentary thought of those earlier astronomers who\nfirst contemplated the possibility that their existence lay on something\nwhich was not flat. These earlier revolutions are still a source of\nperplexity in childhood, which we soon outgrow; and a time will come\nwhen Einstein's amazing revelations have likewise sunk into the\ncommonplaces of educated thought.\n\nTo free our thought from the fetters of space and time is an aspiration\nof the poet and the mystic, viewed somewhat coldly by the scientist who\nhas too good reason to fear the confusion of loose ideas likely to\nensue. If others have had a suspicion of the end to be desired, it has\nbeen left to Einstein to show the way to rid ourselves of these\n'terrestrial adhesions to thought'. And in removing our fetters he\nleaves us, not (as might have been feared) vague generalities for the\necstatic contemplation of the mystic, but a precise scheme of\nworld-structure to engage the mathematical physicist.\n\n\n[Footnote 1: The only alternative is that (relatively to a solar\nobserver) the velocity of light differs in different directions, at\nleast in the region where the experiment is conducted. This would\npresumably be due to some influence of the moving earth on the\npropagation of light (convection of the ether). This explanation was at\none time favoured, but it could not be reconciled with the observed\nphenomena of the aberration of light.]\n\n[Footnote 2: The relativity theory does not suggest that there is such\na thing in nature as a four-dimensional space. The whole object of the\nrecognition of the four-dimensional world is to eliminate the harassing\nframe of space.]\n\n[Footnote 3: The inclination must not exceed a certain limit. This\nlimiting angle may be regarded as a fundamental constant of the\nworld-structure, and owing to its fundamental character it appears in\nmany kinds of phenomena; for example, it determines the velocity of\npropagation of light. The instant on the sun which is simultaneous with\na given instant on the earth is indeterminate (varying according to the\nspace and time frame employed) but only within a range of 16 minutes.\nAny event on the sun happening before this 16 minutes is _absolutely_ in\nthe past, all observers agreeing on this point; in fact it would be\npossible for us to have already received a wireless message announcing\nits occurrence. Events after the 16 minutes are in the _absolute_\nfuture. The neutral zone which is (absolutely) neither past nor future\nbecomes proportionately wider as the distance increases; at the nearest\nfixed star it extends to 8 years, and at the most distant stars yet\nknown it reaches 400,000 years.]\n\n[Footnote 4: The three events must not be at the same place since that\nwould give a time-_line_ not a triangle. The clock must move so that the\ntwo events whose time-distance is to be determined both happen where it\nis, just as the scale must be directed so that the two points fall on\nit. You are not allowed to 'bend' the clock, i. e. apply force so as to\nmake it move with other than uniform velocity, any more than you are\nallowed to bend the scale by applying force.]\n\n[Footnote 5: Of course, it is not true that _any_ two sides are less\nthan the third side. A clock, unlike a scale, can only measure in one\ndirection, viz. from past to future, so that the sides _AB_ + _BC_ and\n_AC_ can be chosen in only one way.]\n\n[Footnote 6: This involves only a comparatively trifling generalization\nof Euclidean geometry, not to be confused with the 'non-Euclidean'\ngeometry introduced later in the lecture.]\n\n[Footnote 7: The following brief outline will give a hint of the nature\nof the explanation. Einstein's law of gravitation is usually expressed\nas a set of ten very lengthy differential equations; these equations are\nexactly equivalent to the geometrical statement that 'the radius of\nspherical curvature of any 3-dimensional section of the 4-dimensional\nworld is a universal constant length, the same for all points of the\nworld and for all directions of the section'. The law therefore implies\nthat the world has a certain type of homogeneity and isotropy (not,\nhowever, the _complete_ homogeneity and isotropy of a sphere). To\nexplain the law of gravitation and the phenomena governed by it, we have\nto explain how this isotropy and homogeneity is secured. Our explanation\nis that the homogeneity and isotropy is not initially in the external\nworld, but _in the measurements which we make of it_. It is introduced\nin all our operations of measurement, because the appliances which we\nuse for measurement are themselves part of the world. In the earlier\npart of this lecture we saw that the contraction of the arm turned from\nhorizontal to vertical is not detected by measurements made with a\nyard-measure which shares the contraction; in the same way any\nanisotropy of the world does not appear in measurements of it by\nappliances which, being part of the world, share the same anisotropy.\nThe law of gravitation therefore arises from the fact that a certain\ntype of non-homogeneity and non-isotropy of the world cannot come into\nobservational experience, because it is necessarily eliminated in all\nobservations and measurements made with material appliances. The orderly\nphenomena of gravitation are due to the _absence_ of certain conceivable\neffects. We have been trying to find a key to the mystery; but the\nsecret of the lock lies not in the key but in the wards.]","title":"The theory of relativity and its influence on scientific thought","tradition":"philosophy-ethics","translated_text":null,"word_count":9632}