WEBVTT

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<v Speaker 1>Correction for this chapter in mathematical formulae instead of I

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<v Speaker 1>here one. This is a LibriVox recording. All LibriVox recordings

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<v Speaker 1>are in the public domain. For more information or to volunteer,

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<v Speaker 1>please visit LibriVox dot org. Recording by mL Cullen, Cleveland, Ohio,

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<v Speaker 1>March two thousand and seven. Relativity the Special and General

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<v Speaker 1>Theory by Albert Einstein, Appendix three The experimental confirmation of

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<v Speaker 1>the general theory of relativity. From a systematic theoretical point

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<v Speaker 1>of view, we may imagine the process of evolution of

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<v Speaker 1>an empirical science to be a continuous process of induction.

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<v Speaker 1>Theories are evolved and are expressed in short compass as

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<v Speaker 1>statements of a large number of individual object in the

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<v Speaker 1>form of empirical laws from which the general laws can

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<v Speaker 1>be ascertained by comparison. Regarded in this way, the development

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<v Speaker 1>of a science bears some resemblance to the compilation of

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<v Speaker 1>a classified catalog. It is, as it were, a purely

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<v Speaker 1>empirical enterprise. But this point of view by no means

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<v Speaker 1>embraces the whole of the actual process, for it slurs

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<v Speaker 1>over the important part played by intuition and deductive thought

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<v Speaker 1>in the development of an exact science. As soon as

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<v Speaker 1>a science has emerged from its initial stages, theoretical advances

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<v Speaker 1>are no longer achieved merely by a process of arrangement

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<v Speaker 1>guided by empirical data. The investigator rather develops a system

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<v Speaker 1>of thought which in general is built up logically from

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<v Speaker 1>a small number of fundamental assumptions, the so called axioms.

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<v Speaker 1>We call such a system of thought a theory. The

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<v Speaker 1>theory finds the justification for its existence in the fact

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<v Speaker 1>that it correlates a large number of single observations, and

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<v Speaker 1>it is just here that the truth of the theory

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<v Speaker 1>lies corresponding to the same complex of empirical data. There

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<v Speaker 1>may be several theories which differ from one another to

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<v Speaker 1>a considerable extent, but as regards the deduction from the

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<v Speaker 1>theories which are capable of being tested, the agreement between

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<v Speaker 1>the theories may be so complete that it becomes difficult to

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<v Speaker 1>find such deductions in which the two theories differ from

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<v Speaker 1>each other. As an example, a case of general interest

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<v Speaker 1>is available in the province of biology, in the Darwinian

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<v Speaker 1>theory of the development of species by selection, in the

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<v Speaker 1>struggle for existence, and in the theory of development which

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<v Speaker 1>is based on the hypothesis of the hereditary transmission of

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<v Speaker 1>acquired characters. We have another instance of far reaching agreement

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<v Speaker 1>between the deductions from the two theories and Newtonian mechanics

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<v Speaker 1>on the one hand, and the general theory of relativity

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<v Speaker 1>on the other. This agreement goes so far that up

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<v Speaker 1>to the present we have been able to find only

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<v Speaker 1>a few deductions from the general theory of relativity which

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<v Speaker 1>are capable of investigation and to which the physics of

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<v Speaker 1>pre relativity days does not also lead, and this despite

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<v Speaker 1>the profound difference in the fundamental assumption of the two theories.

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<v Speaker 1>In what follows, we shall again consider these important deductions,

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<v Speaker 1>and we shall also discuss the empirical evidence appertaining to them,

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<v Speaker 1>which has hitherto been obtained. A motion of the perihelion

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<v Speaker 1>of Mercury. According to Newtonian mechanics and Newton's law of gravitation,

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<v Speaker 1>a planet which is revolving around the Sun would describe

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<v Speaker 1>an ellipse around the latter, or more correct, around the

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<v Speaker 1>common center of gravity of the Sun and the planet.

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<v Speaker 1>In such a system, the Sun or the common center

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<v Speaker 1>of gravity lies in one of the foci of the

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<v Speaker 1>orbital lips in such a manner as that, in the

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<v Speaker 1>course of a planet year, the distant Sun planet grows

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<v Speaker 1>from a minimum to a maximum and then decreases again

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<v Speaker 1>to a minimum. If instead of Newton's law, we insert

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<v Speaker 1>a somewhat different law of attraction into the calculation, we

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<v Speaker 1>find that according to this new law, the motion would

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<v Speaker 1>still take place in such a manner that the distant

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<v Speaker 1>Sun planet exhibits periodic variations. But in this case, the

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<v Speaker 1>angle described by the line joining Sun and planet during

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<v Speaker 1>such a period preentzes from perihelium closest proximity to the

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<v Speaker 1>Sun to perihelion, and prencees would differ from three hundred

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<v Speaker 1>and sixty degrees. The line of the orbit would not

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<v Speaker 1>then be a closed one, but in the course of

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<v Speaker 1>time it would fill up an an annular part of

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<v Speaker 1>the orbital plane, that is, between the circle of least

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<v Speaker 1>and the circle of greatest distance of the planet from

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<v Speaker 1>the Sun. According also to the general theory of relativity,

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<v Speaker 1>which differs, of course from the theory of Newton, a

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<v Speaker 1>small variation from the Newton Kepler motion of a planet

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<v Speaker 1>in its orbit should take place, and in such a

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<v Speaker 1>way that the angle described by the radius Sun planet

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<v Speaker 1>between one perihelion and the next should exceed that corresponding

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<v Speaker 1>to one complete revolution by an amount given by the

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<v Speaker 1>formula plus twenty four pi cubed a square divided by

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<v Speaker 1>t squared c squared times to quantity one minus e

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<v Speaker 1>squared nb. One complete revolution corresponds to the angle two

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<v Speaker 1>to the pie power in the absolute angle measure customary

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<v Speaker 1>in physics, and the above expression gives the amount by

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<v Speaker 1>which the radius un planet exceeds this angle during the

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<v Speaker 1>interval between one perihelium and the next close priens. In

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<v Speaker 1>this expression, A represents the major semi axis of the

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<v Speaker 1>ellipse e its eccentricity see the velocity of light, and

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<v Speaker 1>T the period of revolution of the planet. Our result

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<v Speaker 1>may also be stated as follows. According to the general

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<v Speaker 1>theory of relativity, the major axis of the ellipse rotates

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<v Speaker 1>around the Sun in the same sense as the orbital

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<v Speaker 1>motion of the planet. Theory requires that this rotation should

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<v Speaker 1>amount the forty three seconds of arc per century for

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<v Speaker 1>the planet Mercury, but for the other planets of our

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<v Speaker 1>solar system, its magnitude should be so small that it

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<v Speaker 1>would necessarily escape detection. Footnote, especially since the next planet

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<v Speaker 1>Venus has an orbit that is almost an exact circle,

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<v Speaker 1>which makes it more difficult to locate the perihelium with

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<v Speaker 1>precision end footnote. In point of fact, astronomers have found

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<v Speaker 1>that the theory of Newton does not suffice to calculate

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<v Speaker 1>the observed motion of Mercury with an exactness corresponding to

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<v Speaker 1>that of the delicacy of observation attainable at the present time.

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<v Speaker 1>After taking account of all the disturbing influences exerted on

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<v Speaker 1>Mercury by the remaining planets, it was found Prentzes Leverer

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<v Speaker 1>eighteen fifty nine. In Newcome eighteen ninety five close prenzes

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<v Speaker 1>that an unexplained perihelial movement of the orbit of Mercury

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<v Speaker 1>remained over the amount of which does not differ sensibly

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<v Speaker 1>from the above mentioned plus forty three seconds of arc

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<v Speaker 1>per century. The uncertainty of the empirical results amounts to

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<v Speaker 1>a few seconds only. B deflection of light by a

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<v Speaker 1>gravitational field. In section twenty two, it has been already

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<v Speaker 1>mentioned that according to the general theory of relativity, a

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<v Speaker 1>ray of light will experience the curvature of its path

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<v Speaker 1>when passing through a gravitational field, this curvature being similar

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<v Speaker 1>to that experience by the path of a body which

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<v Speaker 1>is projected through a gravitational field. As a result of

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<v Speaker 1>this theory, we should expect that a ray of light

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<v Speaker 1>which is passing close to a heavenly body would be

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<v Speaker 1>deviated towards the latter. For a ray of light which

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<v Speaker 1>passes the Sun at a distance of delta sun radii

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<v Speaker 1>from its center, the angle of deflection Prence's alpha closed

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<v Speaker 1>brend should amount to alpha equals one point seven seconds

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<v Speaker 1>of arc divided by delta. It may be added that,

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<v Speaker 1>according to the theory, half of this deflection is produced

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<v Speaker 1>by the Newtonian field of attraction of the Sun and

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<v Speaker 1>the other half by the geometrical modification prences quote curvature

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<v Speaker 1>end quote end preentheses of space caused by the Sun.

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<v Speaker 1>This result admits of an experimental test by means of

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<v Speaker 1>the photographic registration of stars during a total eclipse of

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<v Speaker 1>the Sun. The reason why we must wait for a

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<v Speaker 1>total eclipse is because at every other time the atmosphere

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<v Speaker 1>is so strongly illuminated by the light from the Sun

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<v Speaker 1>that the stars situated near the Sun's disc are invisible,

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<v Speaker 1>the predicted effect can be seen clearly from the accompanying

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<v Speaker 1>diagram Reader's annotation Fig. Five. The Earth is shown as

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<v Speaker 1>a dot at the bottom of the diagram. A straight

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<v Speaker 1>line proceeding from there, labeled D sub one, proceeds upward

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<v Speaker 1>and slightly to the right, passing the Sun at a

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<v Speaker 1>tangent Sun being represented by a circle. A second line,

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<v Speaker 1>label D sub two, starts at the Earth proceeds at

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<v Speaker 1>a relatively smaller angle, which results in its passing the

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<v Speaker 1>Sun at a greater distance than the the initial line

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<v Speaker 1>D one, which is signified by the symbol delta. After

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<v Speaker 1>passing the Sun, the line becomes parallel to D sub

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<v Speaker 1>one end of Reader's annotation. If the Sun prencees, s,

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<v Speaker 1>and preentzes were not present, a star which is practically

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<v Speaker 1>infinitely distant would be seen in the direction D sub

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<v Speaker 1>one as observed from the Earth, but as a consequence

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<v Speaker 1>of the deflection of light from the star by the Sun,

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<v Speaker 1>the star will be seen in the direction D sub two,

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<v Speaker 1>that is, at a somewhat greater distance from the center

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<v Speaker 1>of the Sun, then corresponds to its real position. In practice,

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<v Speaker 1>the question is tested in the following way. The stars

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<v Speaker 1>in the neighborhood of the Sun are photographed during a

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<v Speaker 1>solar eclipse. In addition, a second photograph of the same

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<v Speaker 1>stars is taken when the Sun is situated at another

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<v Speaker 1>position in the sky, that is a few months earlier

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<v Speaker 1>or later. As compared with the standard photograph, the positions

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<v Speaker 1>of the stars on the eclipse photograph ought to appear

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<v Speaker 1>displaced radially outwards prenzes away from the center of the

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<v Speaker 1>Sun close friends by an amount corresponding to the angle a.

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<v Speaker 1>We are indebted to the Royal Society and to Royal

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<v Speaker 1>Astronomical Society for the investigation of this important deduction. Undaunted

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<v Speaker 1>by the war and by difficulties of both the material

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<v Speaker 1>and a psychological nature aroused by the war, these societies

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<v Speaker 1>equipped two expeditions to Sobral, Brazil and to the island

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<v Speaker 1>of princeip West Africa, and sent several of Britain's most

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<v Speaker 1>celebrated astronomers Prenzies Eddington, Cottingham, Crommelin, Davidson and Prinz in

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<v Speaker 1>order to obtain photographs of the solar eclipse of twenty

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<v Speaker 1>ninth May nineteen nineteen. The relative discrepancies to be expected

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<v Speaker 1>between the stellar photographs of jeting during the eclipse, and

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<v Speaker 1>the comparison photographs amounted to a few hundreds of a

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<v Speaker 1>millimeter only. Thus, great accuracy was necessary in making the

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<v Speaker 1>adjustments required for taking of the photographs and in their

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<v Speaker 1>subsequent measurement. The results of the measurements confirmed the theory

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<v Speaker 1>in a thoroughly satisfactory manner. The rectangular components of the

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<v Speaker 1>observed and of the calculated deviation of the stars, prenzes

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<v Speaker 1>and seconds of an arc and prenzes are set forth

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<v Speaker 1>in the following table of results Reader's annotation. The table

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<v Speaker 1>consists of measurements on seven stars, which are then tabulated

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<v Speaker 1>in four additional columns, which are entitled first coordinate and

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<v Speaker 1>second coordinate, and then for each of those the observed

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<v Speaker 1>and calculated measurements are given end reader's annotation. Number of

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<v Speaker 1>the star eleven first coordinate observed minus zero point one

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<v Speaker 1>nine calculated minus zero point two two. Second coordinate observed

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<v Speaker 1>plus zero point one six, calculated plus zero point zero two.

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<v Speaker 1>Star number five first coordinate observed plus zero point twenty

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<v Speaker 1>nine calculated plus zero point three to one. Second coordinate

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<v Speaker 1>observed negative zero point four to six calculated minus zero

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<v Speaker 1>point four to three. Star number four observed zero point

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<v Speaker 1>one one calculated zero point one zero. Second coordinate observed

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<v Speaker 1>zero point eight three calculated plus zero point seven four.

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<v Speaker 1>Star number three observed plus zero point two zero calculated

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<v Speaker 1>plus zero point one two, second coordinate observed plus one

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<v Speaker 1>point zero zero calculated plus zero point eight seven. Star

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<v Speaker 1>number six observed at the first coordinate plus zero point

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<v Speaker 1>one zero calculated plus zero point zero four, second coordinate

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<v Speaker 1>observed plus zero point five seven calculated plus zero point

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<v Speaker 1>four zero. Number the star ten observed minus zero point

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<v Speaker 1>zero eight calculated plus zero point zero nine, second coordinate

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<v Speaker 1>observed plus zero point three five calculated plus zero point

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<v Speaker 1>three two number of the star two observed plus zero

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<v Speaker 1>point nine five calculated plus zero point eight five, and

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<v Speaker 1>at the second coordinate observed minus point two seven calculated

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<v Speaker 1>minus zero point zero nine c displacement of the spectral

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<v Speaker 1>line towards the red. In section twenty three, it has

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<v Speaker 1>been shown that in a system K prime which is

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<v Speaker 1>in rotation with regard to a Galalian system K clocks

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<v Speaker 1>of identical construction and which are considered at rest with

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<v Speaker 1>respect to the rotating reference body, go at rates which

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<v Speaker 1>are dependent on the position of the clocks. We shall

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<v Speaker 1>now examine this dependence quantitatively. A clock which is situated

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<v Speaker 1>at a distance R from the center of the disc

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<v Speaker 1>has a velocity relative k, which is given by V

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<v Speaker 1>equals omega R, where omega represents the angle of velocity

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<v Speaker 1>of rotation of the disc k prime with respect to k.

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<v Speaker 1>If the sub zero represents the number of ticks of

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<v Speaker 1>a clock per unit time prints these quote rate end

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<v Speaker 1>quote of the clock close brands relative to k. When

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<v Speaker 1>the clock is at rest, then the quote rate end

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<v Speaker 1>quote of the clock prince thes v close priends when

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<v Speaker 1>it is moving relative to kay with a velocity v

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<v Speaker 1>but at rest with respect to the disc, will, in

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<v Speaker 1>accordance with section twelve, be given by V equals v

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<v Speaker 1>sub zero times the square root of one minus V

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<v Speaker 1>squared over C squared, or with sufficient accuracy, buy v

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<v Speaker 1>equals v zero times the quantity one minus one half

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<v Speaker 1>V squared over C squared. This expression may be also

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<v Speaker 1>stated in the following form V equals v sub zero

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<v Speaker 1>times the quantity one minus one over C squared times

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<v Speaker 1>omega squared are squared over two. If we represent a

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<v Speaker 1>difference of potential of the centrifugal force between the position

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<v Speaker 1>of the clock and the center of the disc y five.

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<v Speaker 1>That is, the work considered negatively which must be performed

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<v Speaker 1>on the unit of mass against this trifical force in

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<v Speaker 1>order to transport it from the position of the clock

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<v Speaker 1>on the rotating disc to the center of the disc.

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<v Speaker 1>Then we have Pi equals minus omega squared r square

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<v Speaker 1>divided by two. From this, it follows that v equals

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<v Speaker 1>v sub zero times to quantity one plus five overse squared.

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<v Speaker 1>In the first place. We see from this expression that

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<v Speaker 1>the two clocks of identical construction will go at different

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<v Speaker 1>rates when situated at different distances from the center of

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<v Speaker 1>the disc. This result is also valid from the standpoint

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<v Speaker 1>of an observer who is rotating with the disc. Now,

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<v Speaker 1>as judge from the disc, the latter is in a

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<v Speaker 1>gravitational field of potential five. Hence, the result we have

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<v Speaker 1>obtained will hold quite generally for gravitational fields. Furthermore, we

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<v Speaker 1>can regard an atom which is emitting spectral lines as

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<v Speaker 1>a clock that the following statement will hold. An atom

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<v Speaker 1>absorbs or amidst light of a frequency which is dependent

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<v Speaker 1>on the potential of the gravitational field in which it

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<v Speaker 1>is situated. The frequency of an atom situated on the

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<v Speaker 1>surface of a heavenly body will be somewhat less than

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<v Speaker 1>the frequency of an atom of the same element which

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<v Speaker 1>is situated in free space prenzes or on the surface

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<v Speaker 1>of a smaller celestial body close Prentzes period now five

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<v Speaker 1>equals minus k times m over R, where K is

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<v Speaker 1>Newton's constant gravitation and M is the mass of the

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<v Speaker 1>heavenly body. Thus, a displacement towards the red ought to

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<v Speaker 1>take place for spectral lines produced at the surface of stars,

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<v Speaker 1>as compared with the spectral lines of the same element

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<v Speaker 1>produced at the surface of the Earth, the amount of

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<v Speaker 1>this displacement being v sub zero minus v divided by

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<v Speaker 1>v sub zero equals k over c squared times m

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<v Speaker 1>over R. For the Sun, the displacement towards the red

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<v Speaker 1>predicted by theory amounts to about two millions of the wavelength.

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<v Speaker 1>A trustworthy calculation is not possible in the case of

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<v Speaker 1>the stars, because in general, neither the mass M nor

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<v Speaker 1>the radius R is known. It is an open question

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<v Speaker 1>whether or not this effect exists, and at the present

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<v Speaker 1>time astronomers are working with great zeal towards the solution

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<v Speaker 1>owing to the smallness of the effect in the case

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<v Speaker 1>of the sun, it is difficult to form an opinion

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<v Speaker 1>as to its existence. Whereas Greb and Bacham, Prenzes, Bond

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<v Speaker 1>and Priends, as a result of their own measurements and

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<v Speaker 1>those of ever Sad and Schwartzchild on the cyanogen bands,

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<v Speaker 1>have placed the existence of the effect almost beyond doubt.

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<v Speaker 1>Other investigators, particularly Saint John, have been led to the

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<v Speaker 1>opposite opinion in consequence of their measurements. Mean displacements of

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<v Speaker 1>lines towards the less refrangible end of the spectrum are

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<v Speaker 1>certainly revealed by statistical investigation of the fixed stars, but

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<v Speaker 1>up to the present the examination of the available data

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<v Speaker 1>does not allow of any definite decision being arrived at

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<v Speaker 1>as to whether or not these displacements are to be

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<v Speaker 1>referred in reality to the effect of gravitation. The results

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<v Speaker 1>of observation have been collected together and discussed in detail

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<v Speaker 1>from the standpoint of the question which has been engaging

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<v Speaker 1>our attention here in a paper by E. Freundlich entitled

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<v Speaker 1>Sir Profunder alamingun rebtats Theori Prentzes dionito Zenshoften, nineteen nineteen,

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<v Speaker 1>Number thirty five, page five point twenty Julia Springer, Berlin,

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<v Speaker 1>Close Pranz period. At all events, a definite decision will

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<v Speaker 1>be reached during the next few years. If the displacement

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<v Speaker 1>of spectral lines towards the red by the gravitational potential

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<v Speaker 1>does not exist, then the general theory of relativity will

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<v Speaker 1>be untenable. On the other hand, if the cause of

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<v Speaker 1>the displacement of spectral lines be definitely traced to the

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<v Speaker 1>gravitational potential, then the study of this displacement will furnish

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<v Speaker 1>us with important information as to the mass of the

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<v Speaker 1>heavenly bodies. End of Appendix three