WEBVTT

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Appendix three, the experimental confirmation of
the general theory of relativity. From a

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systematic theoretical point of view, we
may imagine the process of evolution of an

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empirical science to be a continuous process
of induction. Theories are evolved and are

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expressed in short compass as statements of
a large number of individual observation in the

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form of empirical laws, from which
the general laws can be ascertained by comparison.

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Regarded in this way, the development
of a science bears some resemblance to

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the compilation of a classified catalog.
It is, as it were, a

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purely empirical enterprise. But this point
of view by no means embraces the whole

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of the actual process, for it
slurs over the important part played by intuition

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and deduction to thought and the development
of an exact science. As soon as

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a science has emerged from its initial
stages, theoretical advances are no longer achieved

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merely by a process of arrangement guided
by empirical data. The investigator rather develops

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a system of thought, which in
general is built up logically from a small

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number of fundamental assumptions, the so
called axioms. We call such a system

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of thought a theory. The theory
finds the justification for its existence in the

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fact that it correlates a large number
of single observations, and it is just

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here that the truth of the theory
lies corresponding to the same complex of empirical

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data. There may be several theories
which differ from one another to a considerable

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extent, but as regards the deduction
from the theories which are capable of being

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tested, the agreement between the theories
may be so complete that it becomes difficult

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to find such deduction in which the
two theories differ from each other. As

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an example, a case of general
interest is available in the province of biology,

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in the Darwinian theory of the development
of species by selection in the struggle

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for existence, and in the theory
of development, which is based on the

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hypothesis of the hereditary transmission of acquired
characters. We have another instance of far

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reaching agreement between the deductions from two
theories and Newtonian mechanics on the one hand,

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and the general theory of relativity on
the other. This agreement goes so

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far that up to the present we
have been able to find only a few

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deductions from the general theory of relativity
which are capable of investigation, and to

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which the physics of pre relativity days
does not also lead, and this despite

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the profound difference in the fundamental assumption
of the two theories. In what follows,

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we shall again consider these important deductions, and we shall also discuss the

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empirical evidence appertaining to them which has
hitherto been obtained. A motion of the

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perihelion of Mercury. According to Newtonian
mechanics and Newton's law of gravitation, a

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planet which is revolving round the Sun
would describe an ellipse round the latter,

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or more correctly, round the common
center of gravity of the Sun and the

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planet. In such a system,
the Sun or the common center of gravity

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lies in one of the foci of
the orbit ellipse, in such a manner

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that in the course of a planet
year, the distant sun planet grows from

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a minimum to a maximum, and
then decreases again to a minimum. If

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instead of Newton's law, we insert
a somewhat different law of attraction into the

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calculation, we find that according to
this new law, the motion would still

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take place in such a manner that
the distant Sun planet exhibits periodic variations.

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But in this case the angle described
by the line joining Sun and planet.

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During such a period princes from perihelian
closest proximity to the Sun to Perihelian and

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Princes would differ from three hundred and
sixty degrees. The line of the orbit

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would not then be a closed one, but in the course of time it

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would fill up an annular part of
the orbital plane, that is, between

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the circle of least and the circle
of greatest distance of the planet from the

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Sun. According also to the general
theory of relativity, which differs, of

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course from the theory of Newton,
a small variation from the Newton Kepler motion

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of a planet in its orbit should
take place, and in such a way

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that the angle described by the radius
Sun planet between one perihelian and the next

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should exceed that corresponding to one complete
revolution by an amount given by the formula

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plus twenty four pie cubed a square
divided by t squared c squared times The

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quantity one e squared n b one
complete revolution corresponds to the angle two to

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the pie power in the absolute angle
room measure customary in physics, and the

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above expression gives the amount by which
the radius Sun planet exceeds this angle during

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the interval between one perihelian and the
next close prends. In this expression,

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A represents the major semi axis of
the ellipse, e its eccentricity, c

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the velocity of light, and T
the period of revolution of the planet.

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Our result may also be stated as
follows. According to the general theory of

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relativity, the major axis of the
ellipse rotates round the Sun in the same

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sense as the orbital motion of the
planet. Theory requires that this rotation should

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amount the forty three seconds of arc
percentury for the planet Mercury, but for

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the other planets of our solar system, its magnitude should be so small that

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it would necessarily escape detection footnote,
especially since the next planet, Venus has

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an orbit that is almost an exact
circle, which makes it more difficult to

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locate the perihelium with precision. End
footnote, end point of fact. Astronomers

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have found that the theory of Newton
does not suffice to calculate the observed motion

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of Mercury with an exactness corresponding to
that of the delicacy of observation attainable at

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the present time. After taking account
of all the disturbing influences exerted on Mercury

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by the remaining planets, it was
found Prenzes Leverier eighteen fifty nine. In

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Newcome eighteen ninety five closed Prenzes that
an unexplained perihelium movement of the orbit of

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Mercury remained over the amount of which
does not differ sensibly from the above mentioned

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plus forty three seconds of art per
century. The uncertainty of the empirical results

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amounts to a few seconds only.
B deflection of light by a gravitational field.

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In section twenty two, it has
been already mentioned that, according to

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the general theory of relativity, a
ray of light will experience a curvature of

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its path when passing through a gravitational
field, this curvature being similar to that

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experience by the path of a body
which is projected through a gravitational field.

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As a result of this theory,
we should expect that a ray of light

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which is passing close to a heavenly
body would be deviated towards the latter.

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For a ray of light which passes
the Sun at a distance of delta Sun

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radii from its center. The angle
of deflection prens these alpha closed brand should

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amount to alpha equals one point seven
seconds of arc divided by delta. It

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may be added that, according to
the theory, half of this deflection is

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produced by the Newtonian field of attraction
of the Sun and the other half by

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the geometrical modification princes quote curvature end
quote end princes of space caused by the

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Sun. This result admits of an
experimental test by means of the photographic registration

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of stars during a total eclipse of
the Sun. The only reason why we

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must wait for a total eclipse is
because at every other time the atmosphere is

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so strongly illuminated by the light from
the Sun that the star is situated near

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the Sun's disc are invisible. The
predicted effect can be seen clearly from the

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accompanying diagram reader's annotation Fig. Five. The Earth is shown as a dot

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at the bottom of the diagram.
A straight line preceding from there, labeled

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d sub one, proceeds upward and
slightly to the right, passing the Sun

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00:09:07.919 --> 00:09:15.000
at a tangent Sun being represented by
a circle. A second line labeled D

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sub two starts at the Earth proceeds
at a relatively smaller angle, which results

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in its passing the Sun at a
greater distance than the initial line D one,

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which is signified by the symbol delta. After passing the Sun, the

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line becomes parallel to D sub one
end of Rena's annotation. If the Sun,

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prencees, s, and princes were
not present, a star which is

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practically infinitely distant would be seen in
the direction D sub one as observed from

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the Earth, but as a consequence
of the action of light from the star

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00:10:01.240 --> 00:10:05.080
by the Sun, the star will
be seen in the direction D sub two,

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00:10:05.360 --> 00:10:07.519
that is, at a somewhat greater
distance from the center of the Sun

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00:10:07.960 --> 00:10:16.200
than corresponds to its real position.
In practice, the question is tested in

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the following way. The stars in
the neighborhood of the Sun are photographed during

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a solar eclipse. In addition,
a second photograph of the same stars is

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taken when the Sun is situated at
another position in the sky that is a

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few months earlier or later. As
compared with the standard photograph, the positions

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00:10:37.919 --> 00:10:43.600
of the stars on the eclipse photograph
ought to appear displaced radially outwards. Pren

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00:10:43.679 --> 00:10:48.159
sees away from the center of the
sun close friends by an amount corresponding to

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the angle a. We are indebted
to the Royal Society and to Royal Astronomical

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00:10:54.759 --> 00:11:01.159
Society for the investigation of this important
deduction. Undaunted by the war and by

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difficulties of both a material and a
psychological nature aroused by the war, these

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societies equipped to expeditions to Sobral,
Brazil and to the island of Principe,

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West Africa, and sent several of
Britain's most celebrated astronomers Prinzes, Eddington,

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Cottingham, Cromelin, Davidson and Prinz, in order to obtain photographs of the

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solar eclipse of twenty ninth May nineteen
nineteen. The relative discrepancies to be expected

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between the stellar photographs observing during the
eclipse and a comparison photographs amounted to a

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few hundreds of a millimeter only.
Thus, great accuracy was necessary in making

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the adjustments required for taking of the
photographs and in their subsequent measurement. The

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results of the measurements confirmed the theory
in a thoroughly satisfactory manner. The rectangular

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components of the observed and of the
calculated deviation of the stars and seconds of

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an arc and pren. These are
set forth in the following table of results.

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00:12:07.960 --> 00:12:18.519
Reader's annotation detable consists of measurements on
seven stars, which are then tabulated

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in four additional columns, which are
entitled first coordinate and second coordinate, and

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then for each of those, the
observed and calculated measurements are given end reader's

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annotation number of the star eleven first
coordinate observed zero point one nine, calculated

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minus zero point two two. Second
coordinate observed plus zero point one six calculated

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plus zero point zero two. Star
number to five. First coordinate observed plus

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00:12:58.799 --> 00:13:05.759
zero point two nine calculated plus zero
point three one. Second coordinate observed negative

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00:13:05.840 --> 00:13:11.440
zero point four six, calculated minus
zero point four three. Star number four

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observed zero point one one, calculated
zero point one zero. Second coordinate observed

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00:13:20.240 --> 00:13:24.759
zero point eight three, calculated plus
zero point seven four. Star number three

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00:13:26.320 --> 00:13:31.519
observed plus zero point two zero,
calculated plus zero point one two. Second

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00:13:31.519 --> 00:13:39.039
coordinate observed plus one point zero zero
calculated plus zero point eight seven. Star

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00:13:39.159 --> 00:13:46.120
number six observed at the first coordinate
plus zero point one zero calculated plus zero

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00:13:46.120 --> 00:13:54.200
point zero four second coordinate observed plus
zero point five seven calculated plus zero point

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00:13:54.200 --> 00:14:03.320
four zero number the star ten observed
minus zero point zero eight, calculated plus

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00:14:03.440 --> 00:14:11.200
zero point zero nine, second coordinate
observed plus zero point three five calculated plus

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00:14:11.240 --> 00:14:18.960
zero point three two number of the
star two observed plus zero point nine five

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00:14:18.600 --> 00:14:26.080
calculated plus zero point eight five.
And at the second coordinate observed point two

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00:14:26.120 --> 00:14:37.759
seven calculated point zero nine c displacement
of the spectral line towards the red.

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00:14:39.600 --> 00:14:45.120
In section twenty three, it has
been shown that in a system k prime

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00:14:45.639 --> 00:14:48.879
which is in rotation with regard to
a Galilean system, K, clocks of

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00:14:48.919 --> 00:14:54.000
identicals construction and which are considered at
rest with respect to the rotating reference body

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go at rates which are dependent on
the position of the clocks. We shall

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00:15:00.159 --> 00:15:07.399
now examine this dependence quantitatively. A
clock which is situated at a distance R

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00:15:07.519 --> 00:15:11.240
from the center of the disc has
a velocity relative K, which is given

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00:15:11.320 --> 00:15:16.879
by v equals omega r, where
omega represents the angle of velocity of rotation

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00:15:16.919 --> 00:15:20.559
of the disc k prime with respect
to K. If v sub zero represents

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the number of ticks of a clock
per unit time prints ces quote rate end

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00:15:24.039 --> 00:15:28.919
quote of the clock closed brands relative
decay. When the clock is at rest,

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00:15:28.480 --> 00:15:33.840
then the quote rate end quote of
the clock prints c v close brands.

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00:15:33.200 --> 00:15:37.159
When it is moving relative to k
with a velocity V, but at

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00:15:37.159 --> 00:15:39.919
rest with respect at a disc will, in accordance with Section twelve, be

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00:15:41.000 --> 00:15:48.480
given by V equals v sub zero
times the square root of one V squared

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00:15:48.519 --> 00:15:54.919
over C squared, or with sufficient
accurately, by V equals v zero times

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00:15:54.679 --> 00:16:02.840
the quantity one one half V squared
over C squared. This expression may be

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00:16:02.919 --> 00:16:07.879
also stated in the following form V
equals v sub zero times to quantity one

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00:16:08.399 --> 00:16:15.600
one oversea squared times omega squared are
squared over two. If we represent the

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00:16:15.639 --> 00:16:19.840
difference of potential of the centrifical force
between the position of the clock and the

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00:16:19.919 --> 00:16:25.840
center of the disc by fi,
that is, the work considered negatively which

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00:16:25.919 --> 00:16:30.039
must be performed on the unit of
mass against the centrifical force in order to

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00:16:30.080 --> 00:16:33.080
transport it from the position of the
clock on the rotating disc to the center

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00:16:33.080 --> 00:16:41.559
of the disc, then we have
five equals omega squared are squared divided by

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00:16:41.600 --> 00:16:47.120
two. From this, it follows
that V equals v sub zero times to

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00:16:47.240 --> 00:16:53.759
quantity one plus five over c squared
in the first place. We see from

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00:16:53.759 --> 00:17:00.519
this expression that the two clocks of
identical construction will go at different rates when

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00:17:00.600 --> 00:17:04.680
situated at different distances from the center
of the disk. This result is also

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00:17:04.799 --> 00:17:11.000
valid from the standpoint of an observer
who is rotating with the disc. Now,

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00:17:11.039 --> 00:17:15.599
as judge from the disk, the
latter is in a gravitational field of

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00:17:15.640 --> 00:17:19.680
potential FI. Hence, the result
we have obtained will hold quite generally for

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00:17:19.759 --> 00:17:26.920
gravitational fields. Furthermore, we can
regard an atom which is emitting spectral lines

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00:17:26.960 --> 00:17:32.880
as a clock, so that the
following statement will hold. An atom absorbs

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00:17:33.039 --> 00:17:37.880
or amidst light of a frequency which
is dependent on the potential of the gravitational

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00:17:37.960 --> 00:17:42.039
field in which it is situated.
The frequency of an atom situated on the

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00:17:42.079 --> 00:17:45.640
surface of a heavenly body will be
somewhat less than the frequency of an atom

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00:17:45.680 --> 00:17:51.640
of the same element which is situated
in free space prencs or on the surface

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00:17:51.640 --> 00:17:59.559
of a smaller celestial body closed princes
period Now FI equals k times M over

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00:17:59.839 --> 00:18:03.960
R, where k is Newton's constant
gravitation and m is the mass of the

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00:18:03.960 --> 00:18:07.279
heavenly body. Thus, a displacement
towards the red all to take place for

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00:18:07.400 --> 00:18:11.759
spectral lines produced at the surface of
stars as compared with the spectral lines of

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00:18:11.799 --> 00:18:15.759
the same element produced at the surface
of the Earth, the amount of this

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00:18:15.839 --> 00:18:26.039
displacement being v subzero V divided by
V subzero equals K over C squared times

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00:18:26.240 --> 00:18:30.839
M over R. For the Sun, the displacement towards the red predicted by

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00:18:30.920 --> 00:18:37.599
theory amounts to about two millions of
the wavelength. A trustworthy calculation is not

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00:18:37.720 --> 00:18:41.880
possible in the case of the stars, because in general, neither the mass

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00:18:41.119 --> 00:18:48.759
M nor the radius R is known. It is an open question whether or

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00:18:48.839 --> 00:18:53.119
not this effect exists, and at
the present time astronomers are working with great

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00:18:53.200 --> 00:18:59.119
zeal towards the solution. Owing to
the smallness of the effect in the case

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00:18:59.160 --> 00:19:03.559
of the Sun, it is difficult
to form an opinion as to its existence.

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00:19:04.880 --> 00:19:10.839
Whereas Grebb and Bachum Prentz's bond and
prinds as a result of their own

197
00:19:10.880 --> 00:19:15.240
measurements and those of ever Shed and
schwartz Child on the cyanogen bands, have

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00:19:15.359 --> 00:19:21.680
placed the existence of the effect almost
beyond doubt, other investigators, particularly Saint

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00:19:21.759 --> 00:19:25.319
John, have been led to the
opposite opinion. In consequence of their measurements.

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00:19:26.359 --> 00:19:30.319
Mean displacements of lines towards the less
refrangible end of the spectrum are certainly

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00:19:30.319 --> 00:19:36.279
revealed by statistical investigation of the fixed
stars, but up to the present the

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00:19:36.319 --> 00:19:41.079
examination of the available data does not
allow of any definite decision being arrived at

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00:19:41.640 --> 00:19:45.400
as to whether or not these displacements
are to be referred in reality to the

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00:19:45.400 --> 00:19:52.960
effect of gravitation. The results of
observation have been collected together and discussed in

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detail from the standpoint of the question
which has been engaging our attention here in

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a paper by E. Feindlich and
Ti sirperfundur alamingun rabatats theory Princes die Exosenshaften,

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nineteen nineteen, number thirty five,
Page five twenty Julia Springer, Berlin,

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Close Prince period. At all events, a definite decision will be reached

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during the next few years. If
the displacement of spectral lines towards the red

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by the gravitational potential does not exist, then the general theory of relativity will

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be untenable. On the other hand, if the cause of the displacement of

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spectral lines be definitely traced to the
gravitational potential, then, the study of

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this displacement will furnish us with important
information as to the mass of the heavenly

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bodies. End of Appendix three.