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+ color: black; +} + +hr.noteseparator +{ + width: 25%; + height: 1em; + text-align: left; +} + +/* +// ol ul -- ordered list, unordered list +// +// class +// toc table of contents +*/ + + +/* +// li -- list item +// +// class +// toc_h1 table of contents h1 +// toc_h2 + +// table -- table +*/ + +table.navline +{ + font-size: 0.7em; + font-family: 'TITUS Cyberbit Basic', helvetica, sans-serif; + margin-top: 0em; + margin-bottom: 0em; + margin-top: 0em; + margin-bottom: 0em; +} + +</style> +</head> +<body> +<div>*** START OF THE PROJECT GUTENBERG EBOOK 11335 ***</div> + +<p> +<b>The Einstein Theory of Relativity</b> +</p> + +<p id="d0e112"> +<i>A Concise Statement</i> +</p> + +<p id="d0e118">by +</p> + +<p id="d0e121"> +<i>Prof</i>. H.A. Lorentz of the University of Leyden +<span id="d0e126" class="pageno"></span> +</p> + +<p id="d0e129">Copyright, 1920<span id="d0e131" class="pageno">page 5</span> +</p> + +<h1 id="d0e135">Note</h1> + +<p id="d0e140">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. +</p> + +<p id="d0e143">Professor Lorentz is credited by Einstein with sharing the development of his theory. He is doubtless <span id="d0e145" class="pageno">page 6</span>better able than any other man—except the author himself—to explain this scientific discovery. +</p> + +<p id="d0e148">The publishers wish to acknowledge their indebtedness to the New York <i>Times, The Review of Reviews</i> and <i>The Athenaeum</i> for courteous permission to reprint articles from their pages. Professor Lorentz's article appeared originally in <i>The Nieuwe Rotterdamsche Courant +</i> of November 19, 1919. +<span id="d0e162" class="pageno">page 7</span> +</p> + +<h1 id="d0e166">Introduction</h1> +<p id="d0e171">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. +</p> + +<p id="d0e174">The actual deflection of the rays that was discovered by the astronomers <span id="d0e176" class="pageno">page 8</span>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 <i>Times</i> at his home in Berlin. To this correspondent he expressed the difference between his conception and the law of gravitation +in the following terms: +</p> + +<p id="d0e182">“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 +<span id="d0e184" class="pageno">page 9</span>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. +</p> + +<p id="d0e187">“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 <span id="d0e189" class="pageno">page 10</span>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.” +</p> + +<p id="d0e192">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. +<span id="d0e194" class="pageno">page 11</span> +</p> + +<p id="d0e197">The question must have occurred to many, what has all this to do with relativity? When this query was propounded by the <i>Times</i> correspondent to Dr. Einstein he replied as follows: +</p> + +<p id="d0e203">“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. +</p> + +<p id="d0e206">“This led the Dutch professor, Lorentz, and myself to develop the <span id="d0e208" class="pageno">page 12</span>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. +</p> + +<p id="d0e211">“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. +</p> + +<p id="d0e214">“This special relativity, forming the first part of my theory, relates to all systems moving with uniform <span id="d0e216" class="pageno">page 13</span>motion; that is, moving in a straight line with equal velocity. +</p> + +<p id="d0e219">“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.” +</p> + +<p id="d0e222">As summarized by an American astronomer, Professor Henry Norris Russell, of Princeton, in the <i>Scientific American</i> for November 29, Einstein's contribution amounts to this: +</p> + +<p id="d0e228">“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 <span id="d0e230" class="pageno">page 14</span>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.” +</p> + +<p id="d0e233">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. +</p> + +<p id="d0e236">Clerk Maxwell had shown that light is electro-magnetic, and had reduced the whole theory of electro-magnetism <span id="d0e238" class="pageno">page 15</span>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 <span id="d0e240" class="pageno">page 16</span>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. +</p> + +<p id="d0e243">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. +<span id="d0e245" class="pageno">page 17</span> +</p> + +<p id="d0e248">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. +<span id="d0e250" class="pageno">page 18</span> +</p> + +<p id="d0e253">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 <span id="d0e255" class="pageno">page 19</span>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. +</p> + +<p id="d0e258">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. <span id="d0e260" class="pageno">page 20</span>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. +</p> + +<p id="d0e263">(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. +</p> + +<p id="d0e266">(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 <span id="d0e268" class="pageno">page 21</span>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 <span id="d0e270" class="pageno">page 22</span>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 <i>larger</i> 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. +</p> + +<p id="d0e276">(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 <span id="d0e278" class="pageno">page 23</span>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 <i>may</i> 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. +</p> + +<p id="d0e284">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 <span id="d0e286" class="pageno">page 24</span>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. +</p> + +<span id="d0e291" class="pageno">page 25</span> + +<h1 id="d0e295">The Einstein Theory of Relativity</h1> + +<p id="d0e300"> +<i>A Concise Statement by Prof. H. A. Lorentz, of the University of Leyden</i> +</p> + +<p id="d0e306">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 <span id="d0e308" class="pageno">page 26</span>general appreciation in the following lines. +</p> + +<p id="d0e311">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. +</p> + +<p id="d0e314">But, while the skill of the mathematicians was devoted to making <span id="d0e316" class="pageno">page 27</span>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 <span id="d0e318" class="pageno">page 28</span>unchangeable, without any connection, apparently, with other phenomena of natural philosophy. +</p> + +<p id="d0e321">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. +<span id="d0e323" class="pageno">page 29</span> +</p> + +<p id="d0e326">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. +<span id="d0e328" class="pageno">page 30</span> +</p> + +<h1 id="d0e332">The Earth as a Moving Car</h1> + +<p id="d0e337">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 <span id="d0e339" class="pageno">page 31</span>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 <span id="d0e341" class="pageno">page 32</span>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. +</p> + +<p id="d0e344">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 <span id="d0e346" class="pageno">page 33</span>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 <span id="d0e348" class="pageno">page 34</span>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. +</p> + +<p id="d0e351">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 <span id="d0e353" class="pageno">page 35</span>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. +<span id="d0e355" class="pageno">page 36</span> +</p> + +<h1 id="d0e359">Einstein's Departure</h1> + +<p id="d0e364">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. +</p> + +<p id="d0e367">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 <span id="d0e369" class="pageno">page 37</span>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 <span id="d0e371" class="pageno">page 38</span>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. +</p> + +<p id="d0e374">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 <span id="d0e376" class="pageno">page 39</span>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. +</p> + +<p id="d0e379">Thus we see that we, also when the measure is not attached to the earth, disregarding its displacement, <span id="d0e381" class="pageno">page 40</span>may describe the motion of the body in respect to the measure always in the same way—<i>i.e.</i>, 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. +</p> + +<p id="d0e387">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 <span id="d0e389" class="pageno">page 41</span>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. +<span id="d0e391" class="pageno">page 42</span> +</p> + +<h1 id="d0e395">New System or Co-Ordinates</h1> + +<p id="d0e400">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<span id="d0e402" class="pageno">page 43</span>—<i>i.e.</i>, 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.) +</p> + +<p id="d0e408">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 <span id="d0e410" class="pageno">page 44</span>space to introduce no fewer than ten quantities in the place of the one that occurred in the example mentioned above. +</p> + +<p id="d0e413">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 <span id="d0e415" class="pageno">page 45</span>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. +</p> + +<p id="d0e418">Now, there was a difficulty in the movement of the planet Mercury which could not be solved. Even after all the disturbances +<span id="d0e420" class="pageno">page 46</span>caused by the attraction of other planets had been taken into account, there remained an inexplicable phenomenon—<i>i.e.</i>, 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. +</p> + +<p id="d0e426">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 <span id="d0e428" class="pageno">page 47</span>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, <i>A</i>, stand still somewhere in open space. A projectile, <i>B</i>, can travel with constant speed along a horizontal line, without varying from it in the slightest. +</p> + +<p id="d0e437">A ray of light can do the same; everybody will admit that in each case, if there is no gravitation, light <span id="d0e439" class="pageno">page 48</span>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, <i>C</i>, of a ray of light arises, or if we fix our attention upon a single vibration of light, <i>C</i>, while we on the other hand give to the projectile, <i>B</i>, a speed equal to that of light, then we can conclude that <i>B</i> and <i>C</i> 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 <i>A</i>, which shows us that we have to deal with a sphere of gravitation. The projectile <i>B</i> will, in a bent path, vary more and more from a horizontal straight line, and the light <span id="d0e462" class="pageno">page 49</span>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 <i>B</i> and <i>C</i>. +<span id="d0e470" class="pageno">page 50</span> +</p> + +<h1 id="d0e474">Deflection of Light</h1> + +<p id="d0e479">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 <span id="d0e481" class="pageno">page 51</span>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. +</p> + +<p id="d0e484">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 <span id="d0e486" class="pageno">page 52</span>that point the sought-for movement to one side may become apparent. +</p> + +<p id="d0e489">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. +</p> + +<p id="d0e492">The total eclipse lasted five minutes, during four of which it was perfectly clear, so that good photographs <span id="d0e494" class="pageno">page 53</span>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: +</p> + +<p id="d0e497">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. +</p> + +<p id="d0e500">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 <span id="d0e502" class="pageno">page 54</span>the observations together. As the last of the displacements given above—<i>i.e.,</i> 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. +</p> + +<p id="d0e508">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. +<span id="d0e510" class="pageno">page 55</span> +</p> + +<p id="d0e513">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 <span id="d0e515" class="pageno">page 56</span>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. +</p> + +<p id="d0e518">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 <span id="d0e520" class="pageno">page 57</span>above; it also appears from the final result to be 1.98 for the edge of the sun—<i>i.e.,</i> 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. +</p> + +<p id="d0e526">(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.) +<span id="d0e528" class="pageno">page 58</span> +</p> + +<h1 id="d0e532">Difficulty Exaggerated</h1> + +<p id="d0e537">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 <i>The Times</i> there should be so much complaint about the difficulty of understanding the new theory. It is evident that Einstein's little +book <span id="d0e542" class="pageno">page 59</span>“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. +</p> + +<p id="d0e545">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, <span id="d0e547" class="pageno">page 60</span>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. +</p> + +<p id="d0e550">It is not necessary to give up entirely even the ether. Many natural philosophers find satisfaction in the <span id="d0e552" class="pageno">page 61</span>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 <span id="d0e554" class="pageno">page 62</span>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. +</p> + +<p id="d0e557">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 <span id="d0e559" class="pageno">page 63</span>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. +</p> + +<p id="d0e562">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 <span id="d0e564" class="pageno">page 64</span>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. +</p> + +<div>*** END OF THE PROJECT GUTENBERG EBOOK 11335 ***</div> +</body> +</html> + diff --git a/11335-h/style/amazonia.css b/11335-h/style/amazonia.css new file mode 100644 index 0000000..f3a05a3 --- /dev/null +++ b/11335-h/style/amazonia.css @@ -0,0 +1,26 @@ +/* amazonia.css -- color scheme Amazonia, for use with Gutenberg stylesheet */ + +body +{ + background: #FFFFF5; /* #FFFFF5; very light green */ +} + +body, a.hidden +{ + color: black; +} + +h1, h2, h3, h4, h5, h6, .noteref, span.leftnote, p.legend, hr.noteseparator +{ + color: #880000; /* #880000; brownish red */ +} + +.navline, span.rightnote, span.pageno, span.lineno +{ + color: #808000; /* #808000; olive green */ +} + +a.navline:hover, a.hidden:hover, a.noteref:hover +{ + color: red; +} diff --git a/11335-h/style/arctic.css b/11335-h/style/arctic.css new file mode 100644 index 0000000..605eb46 --- /dev/null +++ b/11335-h/style/arctic.css @@ -0,0 +1,33 @@ +/* arctic.css -- color scheme Arctic, for use with Gutenberg stylesheet */ + +body +{ + background: #FFFFFF; + font-family: Times; +} + +body, a.hidden +{ + color: black; +} + +h1, h2, h3, h4, h5, h6 +{ + color: #001FA4; + font-family: Arial; +} + +.figureHead, .noteref, span.leftnote, p.legend +{ + color: #001FA4; +} + +.navline, span.rightnote, span.pageno, span.lineno +{ + color: #AAAAAA; +} + +a.navline:hover, a.hidden:hover, a.noteref:hover +{ + color: red; +} diff --git a/11335-h/style/borneo.css b/11335-h/style/borneo.css new file mode 100644 index 0000000..51cc9bc --- /dev/null +++ b/11335-h/style/borneo.css @@ -0,0 +1,26 @@ +/* borneo.css -- color scheme Borneo, for use with Gutenberg stylesheet */ + +body +{ + background: #FFFFEE; /* #FFFFEE; light yellowish brown */ +} + +body, a.hidden +{ + color: black; +} + +h1, h2, h3, h4, h5, h6, .noteref, span.leftnote, p.legend +{ + color: #880000; /* #880000; brownish red */ +} + +.navline, span.rightnote, span.pageno +{ + color: #AC8D70; /* #AC8D70; sepia */ +} + +a.navline:hover, a.hidden:hover, a.noteref:hover +{ + color: #D25C00; /* #D25C00; orange brown */ +}
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