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diff --git a/old/11335.txt b/old/11335.txt new file mode 100644 index 0000000..643436a --- /dev/null +++ b/old/11335.txt @@ -0,0 +1,1133 @@ +Project Gutenberg's The Einstein Theory of Relativity, by H.A. Lorentz + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: The Einstein Theory of Relativity + +Author: H.A. Lorentz + +Release Date: February 27, 2004 [EBook #11335] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK THE EINSTEIN THEORY OF RELATIVITY *** + + + + +Produced by Jeroen Hellingman and the Distributed Proofreaders Team + + + + + The Einstein Theory of Relativity + + A Concise Statement + + by + + Prof. H.A. Lorentz of the University of Leyden + + + + + +NOTE + +Whether it is true or not that not more than twelve persons in all the +world are able to understand Einstein's Theory, it is nevertheless +a fact that there is a constant demand for information about this +much-debated topic of relativity. The books published on the subject +are so technical that only a person trained in pure physics and +higher mathematics is able to fully understand them. In order to +make a popular explanation of this far-reaching theory available, +the present book is published. + +Professor Lorentz is credited by Einstein with sharing the development +of his theory. He is doubtless better able than any other man--except +the author himself--to explain this scientific discovery. + +The publishers wish to acknowledge their indebtedness to the New +York Times, The Review of Reviews and The Athenaeum for courteous +permission to reprint articles from their pages. Professor Lorentz's +article appeared originally in The Nieuwe Rotterdamsche Courant of +November 19, 1919. + + + +INTRODUCTION + +The action of the Royal Society at its meeting in London on November +6, in recognizing Dr. Albert Einstein's "theory of relativity" +has caused a great stir in scientific circles on both sides of the +Atlantic. Dr. Einstein propounded his theory nearly fifteen years +ago. The present revival of interest in it is due to the remarkable +confirmation which it received in the report of the observations +made during the sun's eclipse of last May to determine whether rays +of light passing close to the sun are deflected from their course. + +The actual deflection of the rays that was discovered by the +astronomers was precisely what had been predicted theoretically by +Einstein many years since. This striking confirmation has led certain +German scientists to assert that no scientific discovery of such +importance has been made since Newton's theory of gravitation was +promulgated. This suggestion, however, was put aside by Dr. Einstein +himself when he was interviewed by a correspondent of the New York +Times at his home in Berlin. To this correspondent he expressed the +difference between his conception and the law of gravitation in the +following terms: + +"Please imagine the earth removed, and in its place suspended a box as +big as a room or a whole house, and inside a man naturally floating +in the center, there being no force whatever pulling him. Imagine, +further, this box being, by a rope or other contrivance, suddenly +jerked to one side, which is scientifically termed 'difform motion', +as opposed to 'uniform motion.' The person would then naturally reach +bottom on the opposite side. The result would consequently be the +same as if he obeyed Newton's law of gravitation, while, in fact, +there is no gravitation exerted whatever, which proves that difform +motion will in every case produce the same effects as gravitation. + +"I have applied this new idea to every kind of difform motion and +have thus developed mathematical formulas which I am convinced give +more precise results than those based on Newton's theory. Newton's +formulas, however, are such close approximations that it was difficult +to find by observation any obvious disagreement with experience." + +Dr. Einstein, it must be remembered, is a physicist and not an +astronomer. He developed his theory as a mathematical formula. The +confirmation of it came from the astronomers. As he himself says, the +crucial test was supplied by the last total solar eclipse. Observations +then proved that the rays of fixed stars, having to pass close to +the sun to reach the earth, were deflected the exact amount demanded +by Einstein's formulas. The deflection was also in the direction +predicted by him. + +The question must have occurred to many, what has all this to do with +relativity? When this query was propounded by the Times correspondent +to Dr. Einstein he replied as follows: + +"The term relativity refers to time and space. According to Galileo and +Newton, time and space were absolute entities, and the moving systems +of the universe were dependent on this absolute time and space. On +this conception was built the science of mechanics. The resulting +formulas sufficed for all motions of a slow nature; it was found, +however, that they would not conform to the rapid motions apparent +in electrodynamics. + +"This led the Dutch professor, Lorentz, and myself to develop +the theory of special relativity. Briefly, it discards absolute +time and space and makes them in every instance relative to moving +systems. By this theory all phenomena in electrodynamics, as well as +mechanics, hitherto irreducible by the old formulae--and there are +multitudes--were satisfactorily explained. + +"Till now it was believed that time and space existed by themselves, +even if there was nothing else--no sun, no earth, no stars--while +now we know that time and space are not the vessel for the universe, +but could not exist at all if there were no contents, namely, no sun, +earth and other celestial bodies. + +"This special relativity, forming the first part of my theory, +relates to all systems moving with uniform motion; that is, moving +in a straight line with equal velocity. + +"Gradually I was led to the idea, seeming a very paradox in science, +that it might apply equally to all moving systems, even of difform +motion, and thus I developed the conception of general relativity +which forms the second part of my theory." + +As summarized by an American astronomer, Professor Henry Norris +Russell, of Princeton, in the Scientific American for November 29, +Einstein's contribution amounts to this: + +"The central fact which has been proved--and which is of great interest +and importance--is that the natural phenomena involving gravitation +and inertia (such as the motions of the planets) and the phenomena +involving electricity and magnetism (including the motion of light) +are not independent of one another, but are intimately related, so +that both sets of phenomena should be regarded as parts of one vast +system, embracing all Nature. The relation of the two is, however, of +such a character that it is perceptible only in a very few instances, +and then only to refined observations." + +Already before the war, Einstein had immense fame among physicists, +and among all who are interested in the philosophy of science, +because of his principle of relativity. + +Clerk Maxwell had shown that light is electro-magnetic, and had reduced +the whole theory of electro-magnetism to a small number of equations, +which are fundamental in all subsequent work. But these equations +were entangled with the hypothesis of the ether, and with the notion +of motion relative to the ether. Since the ether was supposed to be +at rest, such motion was indistinguishable from absolute motion. The +motion of the earth relatively to the ether should have been different +at different points of its orbit, and measurable phenomena should +have resulted from this difference. But none did, and all attempts to +detect effects of motions relative to the ether failed. The theory of +relativity succeeded in accounting for this fact. But it was necessary +incidentally to throw over the one universal time, and substitute +local times attached to moving bodies and varying according to their +motion. The equations on which the theory of relativity is based are +due to Lorentz, but Einstein connected them with his general principle, +namely, that there must be nothing, in observable phenomena, which +could be attributed to absolute motion of the observer. + +In orthodox Newtonian dynamics the principle of relativity had a +simpler form, which did not require the substitution of local time +for general time. But it now appeared that Newtonian dynamics is only +valid when we confine ourselves to velocities much less than that +of light. The whole Galileo-Newton system thus sank to the level +of a first approximation, becoming progressively less exact as the +velocities concerned approached that of light. + +Einstein's extension of his principle so as to account for gravitation +was made during the war, and for a considerable period our astronomers +were unable to become acquainted with it, owing to the difficulty +of obtaining German printed matter. However, copies of his work +ultimately reached the outside world and enabled people to learn more +about it. Gravitation, ever since Newton, had remained isolated from +other forces in nature; various attempts had been made to account +for it, but without success. The immense unification effected by +electro-magnetism apparently left gravitation out of its scope. It +seemed that nature had presented a challenge to the physicists which +none of them were able to meet. + +At this point Einstein intervened with a hypothesis which, apart +altogether from subsequent verification, deserves to rank as one +of the great monuments of human genius. After correcting Newton, +it remained to correct Euclid, and it was in terms of non-Euclidean +geometry that he stated his new theory. Non-Euclidean geometry is +a study of which the primary motive was logical and philosophical; +few of its promoters ever dreamed that it would come to be applied +in physics. Some of Euclid's axioms were felt to be not "necessary +truths," but mere empirical laws; in order to establish this view, +self-consistent geometries were constructed upon assumptions other +than those of Euclid. In these geometries the sum of the angles of +a triangle is not two right angles, and the departure from two right +angles increases as the size of the triangle increases. It is often +said that in non-Euclidean geometry space has a curvature, but this +way of stating the matter is misleading, since it seems to imply a +fourth dimension, which is not implied by these systems. + +Einstein supposes that space is Euclidean where it is sufficiently +remote from matter, but that the presence of matter causes it +to become slightly non-Euclidean--the more matter there is in the +neighborhood, the more space will depart from Euclid. By the help of +this hypothesis, together with his previous theory of relativity, he +deduces gravitation--very approximately, but not exactly, according +to the Newtonian law of the inverse square. The minute differences +between the effects deduced from his theory and those deduced from +Newton are measurable in certain cases. There are, so far, three +crucial tests of the relative accuracy of the new theory and the old. + +(1) The perihelion of Mercury shows a discrepancy which has long +puzzled astronomers. This discrepancy is fully accounted for by +Einstein. At the time when he published his theory, this was its only +experimental verification. + +(2) Modern physicists were willing to suppose that light might be +subject to gravitation--i.e., that a ray of light passing near a +great mass like the sun might be deflected to the extent to which a +particle moving with the same velocity would be deflected according +to the orthodox theory of gravitation. But Einstein's theory required +that the light should be deflected just twice as much as this. The +matter could only be tested during an eclipse among a number of +bright stars. Fortunately a peculiarly favourable eclipse occurred +last year. The results of the observations have now been published, +and are found to verify Einstein's prediction. The verification is not, +of course, quite exact; with such delicate observations that was not to +be expected. In some cases the departure is considerable. But taking +the average of the best series of observations, the deflection at +the sun's limb is found to be 1.98'', with a probable error of about +6 per cent., whereas the deflection calculated by Einstein's theory +should be 1.75''. It will be noticed that Einstein's theory gave a +deflection twice as large as that predicted by the orthodox theory, +and that the observed deflection is slightly larger than Einstein +predicted. The discrepancy is well within what might be expected in +view of the minuteness of the measurements. It is therefore generally +acknowledged by astronomers that the outcome is a triumph for Einstein. + +(3) In the excitement of this sensational verification, there has +been a tendency to overlook the third experimental test to which +Einstein's theory was to be subjected. If his theory is correct as it +stands, there ought, in a gravitational field, to be a displacement +of the lines of the spectrum towards the red. No such effect has +been discovered. Spectroscopists maintain that, so far as can be +seen at present, there is no way of accounting for this failure if +Einstein's theory in its present form is assumed. They admit that some +compensating cause may be discovered to explain the discrepancy, but +they think it far more probable that Einstein's theory requires some +essential modification. Meanwhile, a certain suspense of judgment +is called for. The new law has been so amazingly successful in two +of the three tests that there must be some thing valid about it, +even if it is not exactly right as yet. + +Einstein's theory has the very highest degree of aesthetic merit: +every lover of the beautiful must wish it to be true. It gives a +vast unified survey of the operations of nature, with a technical +simplicity in the critical assumptions which makes the wealth of +deductions astonishing. It is a case of an advance arrived at by +pure theory: the whole effect of Einstein's work is to make physics +more philosophical (in a good sense), and to restore some of that +intellectual unity which belonged to the great scientific systems of +the seventeenth and eighteenth centuries, but which was lost through +increasing specialization and the overwhelming mass of detailed +knowledge. In some ways our age is not a good one to live in, but +for those who are interested in physics there are great compensations. + + + + + +THE EINSTEIN THEORY OF RELATIVITY + +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 the new theory of the universal attractive power +of gravitation developed by Albert Einstein, and thus reinforced +the conviction that the defining of this theory is one of the most +important steps ever taken in the domain of natural science. In +response to a request by the editor, I will attempt to contribute +something to its general appreciation in the following lines. + +For centuries Newton's doctrine of the attraction of gravitation has +been the most prominent example of a theory of natural science. Through +the simplicity of its basic idea, an attraction between two bodies +proportionate to their mass and also proportionate to the square +of the distance; through the completeness with which it explained +so many of the peculiarities in the movement of the bodies making +up the solar system; and, finally, through its universal validity, +even in the case of the far-distant planetary systems, it compelled +the admiration of all. + +But, while the skill of the mathematicians was devoted to making +more exact calculations of the consequences to which it led, no +real progress was made in the science of gravitation. It is true +that the inquiry was transferred to the field of physics, following +Cavendish's success in demonstrating the common attraction between +bodies with which laboratory work can be done, but it always was +evident that natural philosophy had no grip on the universal power +of attraction. While in electric effects an influence exercised +by the matter placed between bodies was speedily observed--the +starting-point of a new and fertile doctrine of electricity--in +the case of gravitation not a trace of an influence exercised by +intermediate matter could ever be discovered. It was, and remained, +inaccessible and unchangeable, without any connection, apparently, +with other phenomena of natural philosophy. + +Einstein has put an end to this isolation; it is now well established +that gravitation affects not only matter, but also light. Thus +strengthened in the faith that his theory already has inspired, +we may assume with him that there is not a single physical or +chemical phenomenon--which does not feel, although very probably in +an unnoticeable degree, the influence of gravitation, and that, on the +other side, the attraction exercised by a body is limited in the first +place by the quantity of matter it contains and also, to some degree, +by motion and by the physical and chemical condition in which it moves. + +It is comprehensible that a person could not have arrived at such a +far-reaching change of view by continuing to follow the old beaten +paths, but only by introducing some sort of new idea. Indeed, +Einstein arrived at his theory through a train of thought of great +originality. Let me try to restate it in concise terms. + + + +THE EARTH AS A MOVING CAR + +Everyone knows that a person may be sitting in any kind of a vehicle +without noticing its progress, so long as the movement does not vary +in direction or speed; in a car of a fast express train objects fall +in just the same way as in a coach that is standing still. Only when +we look at objects outside the train, or when the air can enter the +car, do we notice indications of the motion. We may compare the earth +with such a moving vehicle, which in its course around the sun has +a remarkable speed, of which the direction and velocity during a +considerable period of time may be regarded as constant. In place +of the air now comes, so it was reasoned formerly, the ether which +fills the spaces of the universe and is the carrier of light and of +electro-magnetic phenomena; there were good reasons to assume that the +earth was entirely permeable for the ether and could travel through it +without setting it in motion. So here was a case comparable with that +of a railroad coach open on all sides. There certainly should have +been a powerful "ether wind" blowing through the earth and all our +instruments, and it was to have been expected that some signs of it +would be noticed in connection with some experiment or other. Every +attempt along that line, however, has remained fruitless; all the +phenomena examined were evidently independent of the motion of the +earth. That this is the way they do function was brought to the front +by Einstein in his first or "special" theory of relativity. For him +the ether does not function and in the sketch that he draws of natural +phenomena there is no mention of that intermediate matter. + +If the spaces of the universe are filled with an ether, let us suppose +with a substance, in which, aside from eventual vibrations and other +slight movements, there is never any crowding or flowing of one part +alongside of another, then we can imagine fixed points existing in it; +for example, points in a straight line, located one meter apart, points +in a level plain, like the angles or squares on a chess board extending +out into infinity, and finally, points in space as they are obtained +by repeatedly shifting that level spot a distance of a meter in the +direction perpendicular to it. If, consequently, one of the points +is chosen as an "original point" we can, proceeding from that point, +reach any other point through three steps in the common perpendicular +directions in which the points are arranged. The figures showing how +many meters are comprized in each of the steps may serve to indicate +the place reached and to distinguish it from any other; these are, as +is said, the "co-ordinates" of these places, comparable, for example, +with the numbers on a map giving the longitude and latitude. Let +us imagine that each point has noted upon it the three numbers that +give its position, then we have something comparable with a measure +with numbered subdivisions; only we now have to do, one might say, +with a good many imaginary measures in three common perpendicular +directions. In this "system of co-ordinates" the numbers that fix +the position of one or the other of the bodies may now be read off +at any moment. + +This is the means which the astronomers and their mathematical +assistants have always used in dealing with the movement of the +heavenly bodies. At a determined moment the position of each body +is fixed by its three co-ordinates. If these are given, then one +knows also the common distances, as well as the angles formed by the +connecting lines, and the movement of a planet is to be known as soon +as one knows how its co-ordinates are changing from one moment to +the other. Thus the picture that one forms of the phenomena stands +there as if it were sketched on the canvas of the motionless ether. + + + +EINSTEIN'S DEPARTURE + +Since Einstein has cut loose from the ether, he lacks this canvas, and +therewith, at the first glance, also loses the possibility of fixing +the positions of the heavenly bodies and mathematically describing +their movement--i.e., by giving comparisons that define the positions +at every moment. How Einstein has overcome this difficulty may be +somewhat elucidated through a simple illustration. + +On the surface of the earth the attraction of gravitation causes +all bodies to fall along vertical lines, and, indeed, when one omits +the resistance of the air, with an equally accelerated movement; the +velocity increases in equal degrees in equal consecutive divisions of +time at a rate that in this country gives the velocity attained at +the end of a second as 981 centimeters (32.2 feet) per second. The +number 981 defines the "acceleration in the field of gravitation," +and this field is fully characterized by that single number; with its +help we can also calculate the movement of an object hurled out in an +arbitrary direction. In order to measure the acceleration we let the +body drop alongside of a vertical measure set solidly on the ground; +on this scale we read at every moment the figure that indicates the +height, the only co-ordinate that is of importance in this rectilinear +movement. Now we ask what would we be able to see if the measure were +not bound solidly to the earth, if it, let us suppose, moved down or +up with the place where it is located and where we are ourselves. If +in this case the speed were constant, then, and this is in accord with +the special theory of relativity, there would be no motion observed at +all; we should again find an acceleration of 981 for a falling body. It +would be different if the measure moved with changeable velocity. + +If it went down with a constant acceleration of 981 itself, then an +object could remain permanently at the same point on the measure, +or could move up or down itself alongside of it, with constant +speed. The relative movement of the body with regard to the measure +should be without acceleration, and if we had to judge only by what +we observed in the spot where we were and which was falling itself, +then we should get the impression that there was no gravitation at +all. If the measure goes down with an acceleration equal to a half +or a third of what it just was, then the relative motion of the body +will, of course, be accelerated, but we should find the increase +in velocity per second one-half or two-thirds of 981. If, finally, +we let the measure rise with a uniformly accelerated movement, then +we shall find a greater acceleration than 981 for the body itself. + +Thus we see that we, also when the measure is not attached to the +earth, disregarding its displacement, may describe the motion of the +body in respect to the measure always in the same way--i.e., as one +uniformly accelerated, as we ascribe now and again a fixed value to +the acceleration of the sphere of gravitation, in a particular case +the value of zero. + +Of course, in the case here under consideration the use of a measure +fixed immovably upon the earth should merit all recommendation. But +in the spaces of the solar system we have, now that we have abandoned +the ether, no such support. We can no longer establish a system of +co-ordinates, like the one just mentioned, in a universal intermediate +matter, and if we were to arrive in one way or another at a definite +system of lines crossing each other in three directions, then we should +be able to use just as well another similar system that in respect to +the first moves this or that way. We should also be able to remodel the +system of co-ordinates in all kinds of ways, for example by extension +or compression. That in all these cases for fixed bodies that do not +participate in the movement or the remodelling of the system other +co-ordinates will be read off again and again is clear. + + + +NEW SYSTEM OR CO-ORDINATES + +What way Einstein had to follow is now apparent. He must--this +hardly needs to be said--in calculating definite, particular cases +make use of a chosen system of co-ordinates, but as he had no means +of limiting his choice beforehand and in general, he had to reserve +full liberty of action in this respect. Therefore he made it his aim +so to arrange the theory that, no matter how the choice was made, the +phenomena of gravitation, so far as its effects and its stimulation +by the attracting bodies are concerned, may always be described in +the same way--i.e., through comparisons of the same general form, +as we again and again give certain values to the numbers that mark +the sphere of gravitation. (For the sake of simplification I here +disregard the fact that Einstein desires that also the way in which +time is measured and represented by figures shall have no influence +upon the central value of the comparisons.) + +Whether this aim could be attained was a question of mathematical +inquiry. It really was attained, remarkably enough, and, we may say, to +the surprise of Einstein himself, although at the cost of considerable +simplicity in the mathematical form; it appeared necessary for the +fixation of the field of gravitation in one or the other point in +space to introduce no fewer than ten quantities in the place of the +one that occurred in the example mentioned above. + +In this connection it is of importance to note that when we exclude +certain possibilities that would give rise to still greater intricacy, +the form of comparison used by Einstein to present the theory is +the only possible one; the principle of the freedom of choice in +co-ordinates was the only one by which he needed to allow himself to +be guided. Although thus there was no special effort made to reach a +connection with the theory of Newton, it was evident, fortunately, +at the end of the experiment that the connection existed. If we +avail ourselves of the simplifying circumstance that the velocities +of the heavenly bodies are slight in comparison with that of light, +then we can deduce the theory of Newton from the new theory, the +"universal" relativity theory, as it is called by Einstein. Thus +all the conclusions based upon the Newtonian theory hold good, as +must naturally be required. But now we have got further along. The +Newtonian theory can no longer be regarded as absolutely correct in all +cases; there are slight deviations from it, which, although as a rule +unnoticeable, once in a while fall within the range of observation. + +Now, there was a difficulty in the movement of the planet Mercury +which could not be solved. Even after all the disturbances caused by +the attraction of other planets had been taken into account, there +remained an inexplicable phenomenon--i.e., an extremely slow turning +of the ellipsis described by Mercury on its own plane; Leverrier had +found that it amounted to forty-three seconds a century. Einstein +found that, according to his formulas, this movement must really +amount to just that much. Thus with a single blow he solved one of +the greatest puzzles of astronomy. + +Still more remarkable, because it has a bearing upon a phenomenon which +formerly could not be imagined, is the confirmation of Einstein's +prediction regarding the influence of gravitation upon the course +of the rays of light. That such an influence must exist is taught +by a simple examination; we have only to turn back for a moment to +the following comparison in which we were just imagining ourselves +to make our observations. It was noted that when the compartment is +falling with the acceleration of 981 the phenomena therein will occur +just as if there were no attraction of gravitation. We can then see +an object, A, stand still somewhere in open space. A projectile, +B, can travel with constant speed along a horizontal line, without +varying from it in the slightest. + +A ray of light can do the same; everybody will admit that in each case, +if there is no gravitation, light will certainly extend itself in a +rectilinear way. If we limit the light to a flicker of the slightest +duration, so that only a little bit, C, of a ray of light arises, +or if we fix our attention upon a single vibration of light, C, while +we on the other hand give to the projectile, B, a speed equal to that +of light, then we can conclude that B and C in their continued motion +can always remain next to each other. Now if we watch all this, not +from the movable compartment, but from a place on the earth, then we +shall note the usual falling movement of object A, which shows us that +we have to deal with a sphere of gravitation. The projectile B will, +in a bent path, vary more and more from a horizontal straight line, +and the light will do the same, because if we observe the movements +from another standpoint this can have no effect upon the remaining +next to each other of B and C. + + + +DEFLECTION OF LIGHT + +The bending of a ray of light thus described is much too light on the +surface of the earth to be observed. But the attraction of gravitation +exercised by the sun on its surface is, because of its great mass, more +than twenty-seven times stronger, and a ray of light that goes close by +the superficies of the sun must surely be noticeably bent. The rays of +a star that are seen at a short distance from the edge of the sun will, +going along the sun, deviate so much from the original direction that +they strike the eye of an observer as if they came in a straight line +from a point somewhat further removed than the real position of the +star from the sun. It is at that point that we think we see the star; +so here is a seeming displacement from the sun, which increases in the +measure in which the star is observed closer to the sun. The Einstein +theory teaches that the displacement is in inverse proportion to the +apparent distance of the star from the centre of the sun, and that for +a star just on its edge it will amount to 1'.75 (1.75 seconds). This is +approximately the thousandth part of the apparent diameter of the sun. + +Naturally, the phenomenon can only be observed when there is a total +eclipse of the sun; then one can take photographs of neighboring stars +and through comparing the plate with a picture of the same part of +the heavens taken at a time when the sun was far removed from that +point the sought-for movement to one side may become apparent. + +Thus to put the Einstein theory to the test was the principal aim of +the English expeditions sent out to observe the eclipse of May 29, +one to Prince's Island, off the coast of Guinea, and the other to +Sobral, Brazil. The first-named expedition's observers were Eddington +and Cottingham, those of the second, Crommelin and Davidson. The +conditions were especially favorable, for a very large number of +bright stars were shown on the photographic plate; the observers at +Sobral being particularly lucky in having good weather. + +The total eclipse lasted five minutes, during four of which it was +perfectly clear, so that good photographs could be taken. In the +report issued regarding the results the following figures, which are +the average of the measurements made from the seven plates, are given +for the displacements of seven stars: + +1''.02, 0''.92, 0''.84, 0''.58, 0''.54, 0''.36, 0''.24, whereas, +according to the theory, the displacements should have amounted to: +0''.88, 0''.80, 0''.75, 0''.40, 0''.52, 0''.33, 0''.20. + +If we consider that, according to the theory the displacements must +be in inverse ratio to the distance from the centre of the sun, then +we may deduce from each observed displacement how great the sideways +movement for a star at the edge of the sun should have been. As the +most probable result, therefore, the number 1''.98 was found from +all the observations together. As the last of the displacements given +above--i.e., 0''.24 is about one-eighth of this, we may say that the +influence of the attraction of the sun upon light made itself felt +upon the ray at a distance eight times removed from its centre. + +The displacements calculated according to the theory are, just because +of the way in which they are calculated, in inverse proportion to the +distance to the centre. Now that the observed deviations also accord +with the same rule, it follows that they are surely proportionate +with the calculated displacements. The proportion of the first and +the last observed sidewise movements is 4.2, and that of the two most +extreme of the calculated numbers is 4.4. + +This result is of importance, because thereby the theory is excluded, +or at least made extremely improbable, that the phenomenon of +refraction is to be ascribed to, a ring of vapor surrounding the +sun for a great distance. Indeed, such a refraction should cause a +deviation in the observed direction, and, in order to produce the +displacement of one of the stars under observation itself a slight +proximity of the vapor ring should be sufficient, but we have every +reason to expect that if it were merely a question of a mass of +gas around the sun the diminishing effect accompanying a removal +from the sun should manifest itself much faster than is really the +case. We cannot speak with perfect certainty here, as all the factors +that might be of influence upon the distribution of density in a sun +atmosphere are not well enough known, but we can surely demonstrate +that in case one of the gasses with which we are acquainted were held +in equilibrium solely by the influence of attraction of the sun the +phenomenon should become much less as soon as we got somewhat further +from the edge of the sun. If the displacement of the first star, which +amounts to 1.02-seconds were to be ascribed to such a mass of gas, then +the displacement of the second must already be entirely inappreciable. + +So far as the absolute extent of the displacements is concerned, it +was found somewhat too great, as has been shown by the figures given +above; it also appears from the final result to be 1.98 for the edge +of the sun--i.e., 13 per cent, greater than the theoretical value +of 1.75. It indeed seems that the discrepancies may be ascribed to +faults in observations, which supposition is supported by the fact +that the observations at Prince's Island, which, it is true, did not +turn out quite as well as those mentioned above, gave the result, +of 1.64, somewhat lower than Einstein's figure. + +(The observations made with a second instrument at Sobral gave a +result of 0.93, but the observers are of the opinion that because of +the shifting of the mirror which reflected the rays no value is to +be attached to it.) + + + +DIFFICULTY EXAGGERATED + +During a discussion of the results obtained at a joint meeting of +the Royal Society and the Royal Astronomical Society held especially +for that purpose recently in London, it was the general opinion that +Einstein's prediction might be regarded as justified, and warm tributes +to his genius were made on all sides. Nevertheless, I cannot refrain, +while I am mentioning it, from expressing my surprise that, according +to the report in The Times there should be so much complaint about +the difficulty of understanding the new theory. It is evident that +Einstein's little book "About the Special and the General Theory of +Relativity in Plain Terms," did not find its way into England during +wartime. Any one reading it will, in my opinion, come to the conclusion +that the basic ideas of the theory are really clear and simple; it is +only to be regretted that it was impossible to avoid clothing them in +pretty involved mathematical terms, but we must not worry about that. + +I allow myself to add that, as we follow Einstein, we may retain +much of what has been formerly gained. The Newtonian theory remains +in its full value as the first great step, without which one cannot +imagine the development of astronomy and without which the second +step, that has now been made, would hardly have been possible. It +remains, moreover, as the first, and in most cases, sufficient, +approximation. It is true that, according to Einstein's theory, +because it leaves us entirely free as to the way in which we wish to +represent the phenomena, we can imagine an idea of the solar system +in which the planets follow paths of peculiar form and the rays of +light shine along sharply bent lines--think of a twisted and distorted +planetarium--but in every case where we apply it to concrete questions +we shall so arrange it that the planets describe almost exact ellipses +and the rays of light almost straight lines. + +It is not necessary to give up entirely even the ether. Many natural +philosophers find satisfaction in the idea of a material intermediate +substance in which the vibrations of light take place, and they +will very probably be all the more inclined to imagine such a medium +when they learn that, according to the Einstein theory, gravitation +itself does not spread instantaneously, but with a velocity that at +the first estimate may be compared with that of light. Especially in +former years were such interpretations current and repeated attempts +were made by speculations about the nature of the ether and about +the mutations and movements that might take place in it to arrive +at a clear presentation of electro-magnetic phenomena, and also of +the functioning of gravitation. In my opinion it is not impossible +that in the future this road, indeed abandoned at present, will once +more be followed with good results, if only because it can lead to the +thinking out of new experimental tests. Einstein's theory need not keep +us from so doing; only the ideas about the ether must accord with it. + +Nevertheless, even without the color and clearness that the ether +theories and the other models may be able to give, and even, +we can feel it this way, just because of the soberness induced +by their absence, Einstein's work, we may now positively expect, +will remain a monument of science; his theory entirely fulfills +the first and principal demand that we may make, that of deducing +the course of phenomena from certain principles exactly and to the +smallest details. It was certainly fortunate that he himself put the +ether in the background; if he had not done so, he probably would +never have come upon the idea that has been the foundation of all +his examinations. + +Thanks to his indefatigable exertions and perseverance, for he had +great difficulties to overcome in his attempts, Einstein has attained +the results, which I have tried to sketch, while still young; he is +now 45 years old. He completed his first investigations in Switzerland, +where he first was engaged in the Patent Bureau at Berne and later as a +professor at the Polytechnic in Zurich. After having been a professor +for a short time at the University of Prague, he settled in Berlin, +where the Kaiser Wilhelm Institute afforded him the opportunity to +devote himself exclusively to his scientific work. He repeatedly +visited our country and made his Netherland colleagues, among whom he +counts many good friends, partners in his studies and his results. He +attended the last meeting of the department of natural philosophy of +the Royal Academy of Sciences, and the members then had the privilege +of hearing him explain, in his own fascinating, clear and simple way, +his interpretations of the fundamental questions to which his theory +gives rise. + + + + + +End of Project Gutenberg's The Einstein Theory of Relativity, by H.A. 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