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Speaker 1 (00:01):
This is a LibriVox recording. All LibriVox recordings are in
the public domain. For more information or to volunteer, please
visit LibriVox dot org. Relativity The Special and General Theory
by Albert Einstein, Continuing Part two, The General Theory of Relativity,
(00:22):
Sections twenty seven to twenty nine. Section twenty seven. The
space time continuum of the General Theory of Relativity is
not a Euclidean continuum. In the first part of this
book we were able to make use of space time coordinates,
which allowed of a simple and direct physical interpretation, and which,
(00:47):
according to section twenty six, can be regarded as four
dimensional Cartesian coordinates. This was possible on the basis of
the law of the constancy of the velocity of light,
but according to section twenty one, the general theory of
relativity cannot retain this law. On the contrary, we arrived
(01:08):
at the result that, according to this latter theory, the
velocity of light must always depend on the coordinates. When
a gravitational field is present. In connection with a specific
illustration in section twenty three, we found that the presence
of a gravitational field invalidates the definition of the coordinates
(01:28):
and the time, which led us to our objective in
the special theory of relativity. In view of the results
of these considerations, we are led to the conviction that,
according to the general principle of relativity, the space time
continuum cannot be regarded as a euclidian one, but that
(01:49):
here we have the general case corresponding to the marble
slab with local variations of temperature, and with which we
made acquaintance as an example of a two dimmes dimensional continuum.
Just as it was there impossible to construct a Cartesian
coordinate system from equal rods, so here it is impossible
(02:11):
to build up a system or reference body from rigid
bodies and clocks, which shall be of such a nature
that measuring rods and clocks arranged rigidly with respect to
one another shall indicate position and time directly. Such was
the essence of the difficulty with which we were confronted
in section twenty three, But the considerations of section twenty
(02:35):
five and twenty six show us the way to surmount
this difficulty. We refer the four dimensional space time continuum
in an arbitrary manner to Gauss coordinates. We assigned to
every point of the continuum or event four numbers x
sub one, x sub two, x sub three, and x
(02:57):
sub four coordinates, which have not the least direct physical significance,
but only serve the purpose of numbering the points of
the continuum in a definite but arbitrary manner. This arrangement
does not even need to be of such a kind
that we must regard x sub one, x sub two,
(03:18):
and x sub three as space coordinates and x sub
four as a time coordinate. The reader may think that
such a description of the world would be quite inadequate.
What does it mean to assign to an event the
particular coordinates x sub one, x sub two, x sub three,
and x sub four, if in themselves these coordinates have
(03:42):
no significance. More careful consideration shows, however, that this anxiety
is unfounded. Let us consider, for instance, a material point
with any kind of motion. If this point had only
a momentary existence without duration, then it would be described
in space time by a single system of values x
(04:06):
sub one, x sub two, x sub three, and x
sub four. Thus, its permanent existence must be characterized by
an infinitely large number of such systems of values, the
coordinate values of which are so close together as to
give continuity corresponding to the material point. We thus have
(04:27):
a unidimensional line in the four dimensional continuum. In the
same way, any such lines in our continuum correspond to
many points in motion. The only statements having regard to
these points which can claim a physical existence are, in reality,
the statements about their encounters. In our mathematical treatment, such
(04:53):
an encounter is expressed in the fact that the two
lines which represent the motions of the points in question
have a particular system of co ordinate values x sub one,
x sub two, x sub three, and x sub four
in common. After mature consideration, the reader will doubtless admit that,
(05:13):
in reality, such encounters constitute the only actual evidence of
a time space nature with which we meet in physical statements.
When we were describing the motion of a material point
relative to a body of reference, we stated nothing more
than the encounters of this point with particular points of
(05:37):
the reference body. We can also determine the corresponding values
of the time by the observation of encounters of the
body with clocks, in conjunction with the observation of the
encounter of the hands of clocks with particular points on
the dials. It is just the same in the case
of space measurements by means of measuring rods. As a
(06:00):
little consideration will show the following statements Hauld. Generally, every
physical description resolves itself into a number of statements, each
of which refers to the space time coincidence of two
events A and B. In terms of Gaussian coordinates, every
(06:22):
such statement is expressed by the agreement of their four
coordinates x sub one, x sub two, x sub three,
and x sub four. Thus, in reality, the description of
the time space continuum by means of Gauss coordinates completely
replaces the description with the aid of a body of reference,
(06:43):
without suffering from the defects of the latter mode of description.
It is not tied down to the Euclidean character of
the continuum, which has to be represented Section twenty eight
Exact fourmulation of the general principle of relativity. We are
(07:05):
now in a position to replace the provisional formulation of
the general principle of relativity given in section eighteen by
an exact formulation the form they are used quote. All
bodies of reference, K, K, prime, etc. Are equivalent for
the description of natural phenomena or formulation of the general
(07:29):
laws of nature, whatever may be, their state of motion
cannot be maintained. Because the use of rigid reference bodies
in the sense of the method followed in the Special
theory of relativity is in general not possible. In space
time description, the Gauss coordinate system has to take the
(07:50):
place of the body of reference. The following statement corresponds
to the fundamental idea of the general principle of relativity.
All Gaussian coordinate systems are essentially equivalent for the formulation
of the general laws of nature. We can state this
general principle of relativity in still another form, which renders
(08:14):
it yet more clearly intelligible than it is when in
the form of the natural extension of the special principle
of relativity. According to the special theory of relativity, the
equations which express the general laws of nature pass over
into equations of the same form when, by making use
of the Lorentz transformation, we replace the space time variables x, y, z,
(08:40):
and t of a Galilean reference body K by the
space time variables x prime, y prime, z prime, and
t prime of a new reference body K prime. According
to the general theory of relativity, on the other hand,
by application of arbitrary substitutions of the Gauss variables x
(09:05):
sub one, x sub two, x sub three, and x
sub four. The equations must pass over into equations of
the same form for every transformation. Not only the Lorentz
transformation corresponds to the transition of one Gaus coordinate system
into another. If we desire to adhere to our old
(09:28):
time three dimensional view of things, then we can characterize
the development which is being undergone by the fundamental idea
of the general theory of relativity as follows. The special
theory of relativity has reference to Galilean domains i e.
To those in which no gravitational field exists. In this connection,
(09:52):
a Galilean reference body serves as body of reference i e.
A rigid body, the state of motion of which is
so chosen that the Galilean law of the uniform rectilinear
motion of isolated material points holds relatively to it. Certain
considerations suggest that we should refer the same Galilean domains
(10:15):
to non Galilean reference bodies. Also, a gravitational field of
a special kind is then present with respect to these
bodies c F Sections twenty and twenty three. In gravitational fields,
there are no such things as rigid bodies with Euclidean properties.
(10:37):
Thus the fictitious rigid body of reference is of no avail.
In the general theory of relativity, the motion of clocks
is also influenced by gravitational fields, and in such a
way that a physical definition of time which is made
directly with the aid of clocks has by no means
the same degree of plausibility as in the special theory
(10:59):
of relatives. For this reason, non rigid reference bodies are used,
which are as a whole not only moving in any
way whatsoever, but which also suffer alterations in form ad
lib during their motion. Clocks for which the law of
motion is of any kind, however irregular, serve for the
(11:21):
definition of time. We have to imagine each of these
clocks fixed at a point on the non rigid reference body.
These clocks satisfy only the one condition that the readings
which are observed simultaneously on adjacent clocks in space differ
from each other by an indefinitely small amount. This non
(11:43):
rigid reference body, which might appropriately be termed a reference mollusc,
is in the main equivalent to a Gaussian four dimensional
coordinate system chosen arbitrarily. That which gives the mollusk a
certain comprehensibility, as can compaired with the Gauss coordinate system,
is the really unjustified formal retention of the separate existence
(12:07):
of the space coordinates as opposed to the time coordinate.
Every point on the mollusc is treated as a space point,
and every material point which is at rest relatively to
it is at rest so long as the mollusc is
considered as reference body. The general principle of relativity requires
(12:28):
that all these molluks can be used as reference bodies
with equal right and equal success in the formulation of
the general laws of nature. The laws themselves must be
quite independent of the choice of mollusc. The great power
possessed by the general principle of relativity lies in the
(12:49):
comprehensive limitation which is imposed on the laws of nature.
In consequence of what we have seen above Section twenty
nine the solution of the problem of gravitation on the
basis of the general principle of relativity. If the reader
(13:10):
has followed all our previous considerations, he will have no
further difficulty in understanding the methods leading to the solution
of the problem of gravitation. We start off on a
consideration of a Galilean domain, i e. A domain in
which there is no gravitational field relative to the Galileyan
(13:30):
reference body K. The behavior of measuring rods and clocks
with reference to K is known from the special theory
of relativity. Likewise the behavior of isolated material points. The
latter move uniformly and in straight lines. Now let us
refer this domain to a random Gauss coordinate system or
(13:55):
to a Mollusk as reference body k prime. Then with
respect to k prime, there is a gravitational field G
of a particular kind. We learn the behavior of measuring
rods and clocks, and also of freely moving material points
with reference to K prime simply by mathematical transformation. We
(14:18):
interpret this behavior as the behavior of measuring rods, clocks,
and material points under the influence of the gravitational field G.
Hereupon we introduce a hypothesis that the influence of the
gravitational field on measuring rods, clocks, and freely moving material
points continues to take place according to the same laws
(14:43):
even in the case where the prevailing gravitational field is
not derivable from the Galilean special case simply by means
of a transformation of coordinates. The next step is to
investigate the space time behavior of the gravitational field, which
was derived from the Galilean special case simply by transformation
(15:06):
of the coordinates. This behaviour is formulated in a law
which is always valid no matter how the reference body
or mollusc used in the description may be chosen. This
law is not yet the general law of the gravitational field,
since the gravitational field under consideration is of a special kind.
(15:29):
In order to find out the general law of field
of gravitation, we still require to obtain a generalization of
the law as found above. This can be obtained without caprice, however,
by taking into consideration the following demands. A. The required
generalization must likewise satisfy the general postulate of relativity. B.
(15:54):
If there is any matter in the domain under consideration,
only its inertial mass, and thus, according to section fifteen,
only its energy is of importance for its effect in
exciting a field. C. Gravitational field and matter together must
satisfy the law of the conservation of energy and of impulse. Finally,
(16:20):
the general principle of relativity permits us to determine the
influence of the gravitational field on the course of all
those processes which take place according to known laws when
a gravitational field is absent i e. Which have already
been fitted into the frame of the special theory of relativity.
(16:41):
In this connection, we proceed in principle according to the
method which has already been explained for measuring rods, clocks,
and freely moving material points. The theory of gravitation, derived
in this way from the general postulate of relativity, excels
not only in its beauty, nor in removing the defect
(17:03):
attaching to classical mechanics which was brought to light in
section twenty one, nor in interpreting the empirical law of
the equality of inertial and gravitational mass. But it has
also already explained a result of observation in astronomy against
which classical mechanics is powerless. If we confine the application
(17:27):
of the theory to the case where the gravitational fields
can be regarded as being weak, and in which all
masses move with respect to the coordinate system with velocities
which are small compared with the velocity of light, we
then obtain as a first approximation the Newtonian theory. Thus,
the latter theory is obtained here without any particular assumption,
(17:51):
whereas Newton had to introduce the hypothesis that the force
of attraction between mutually attracting material points is inversely proportional
to the square of the distance between them. If we
increase the accuracy of the calculation, deviations from the theory of
Newton make their appearance practically, all of which must nevertheless
(18:13):
escape the test of observation owing to their smallness. We
must draw attention here to one of these deviations. According
to Newton's theory, a planet moves around the Sun in
an ellipse, which would permanently maintain its position with respect
to the fixed stars if we could disregard the motion
(18:36):
of the fixed stars themselves and the action of the
other planets under consideration. Thus, if we correct the observed
motion of the planets for these two influences, and if
Newton's theory be strictly correct, we ought to obtain for
the orbit of the planet an ellipse which is fixed
with reference to the fixed stars. This deduction, which can
(19:00):
be tested with great accuracy, has been confirmed for all
the planets save one with the precision that is capable
of being obtained by the delicacy of observation attainable at
the present time. The sole exception is Mercury, the planet
which lies nearest the Sun. Since the time of Leverrier,
(19:20):
it has been known that the eclipse corresponding to the
orbit of Mercury, after it has been corrected for the
influences mentioned above, is not stationary with respect to the
fixed stars, but that it rotates exceedingly slowly in the
plane of the orbit and in the sense of the
orbital motion. The value obtained for this rotary movement of
(19:43):
the orbital ellipse was forty three seconds of arc per century,
an amount ensured to be correct to within a few
seconds of arc. This effect can be explained by means
of classical mechanics only on the assumption of hypotheses which
have little probability and which were devised solely for this purpose.
(20:07):
On the basis of the general theory of relativity, it
is found that the ellipse of every planet round the
Sun must necessarily rotate in the manner indicated above, that
for all the planets with the exception of Mercury, this
rotation is too small to be detected with the delicacy
of observation possible at the present time, but that in
(20:29):
the case of mercury it must amount to forty three
seconds of arc per century, a result which is strictly
in agreement with observation. Apart from this one, it has
hitherto been possible to make only two deductions from the
theory which admit of being tested by observation, to wit,
(20:49):
the curvature of light rays by the gravitational field of
the Sun first observed by Eddington and others in nineteen nineteen,
and placement of the spectral lines of light reaching us
from large stars as compared with the corresponding lines for
light produced in an analogous manner terrestrially i e. By
(21:12):
the same kind of atom established by atoms in nineteen
twenty four. These two deductions from the theory have both
been confirmed. End of Section twenty nine.
This is a LibriVox recording. All LibriVox recordings are in
the public domain. For more information or to volunteer, please
visit LibriVox dot org. Relativity The Special and General Theory
by Albert Einstein, Continuing Part two, The General Theory of Relativity,
(00:22):
Sections twenty seven to twenty nine. Section twenty seven. The
space time continuum of the General Theory of Relativity is
not a Euclidean continuum. In the first part of this
book we were able to make use of space time coordinates,
which allowed of a simple and direct physical interpretation, and which,
(00:47):
according to section twenty six, can be regarded as four
dimensional Cartesian coordinates. This was possible on the basis of
the law of the constancy of the velocity of light,
but according to section twenty one, the general theory of
relativity cannot retain this law. On the contrary, we arrived
(01:08):
at the result that, according to this latter theory, the
velocity of light must always depend on the coordinates. When
a gravitational field is present. In connection with a specific
illustration in section twenty three, we found that the presence
of a gravitational field invalidates the definition of the coordinates
(01:28):
and the time, which led us to our objective in
the special theory of relativity. In view of the results
of these considerations, we are led to the conviction that,
according to the general principle of relativity, the space time
continuum cannot be regarded as a euclidian one, but that
(01:49):
here we have the general case corresponding to the marble
slab with local variations of temperature, and with which we
made acquaintance as an example of a two dimmes dimensional continuum.
Just as it was there impossible to construct a Cartesian
coordinate system from equal rods, so here it is impossible
(02:11):
to build up a system or reference body from rigid
bodies and clocks, which shall be of such a nature
that measuring rods and clocks arranged rigidly with respect to
one another shall indicate position and time directly. Such was
the essence of the difficulty with which we were confronted
in section twenty three, But the considerations of section twenty
(02:35):
five and twenty six show us the way to surmount
this difficulty. We refer the four dimensional space time continuum
in an arbitrary manner to Gauss coordinates. We assigned to
every point of the continuum or event four numbers x
sub one, x sub two, x sub three, and x
(02:57):
sub four coordinates, which have not the least direct physical significance,
but only serve the purpose of numbering the points of
the continuum in a definite but arbitrary manner. This arrangement
does not even need to be of such a kind
that we must regard x sub one, x sub two,
(03:18):
and x sub three as space coordinates and x sub
four as a time coordinate. The reader may think that
such a description of the world would be quite inadequate.
What does it mean to assign to an event the
particular coordinates x sub one, x sub two, x sub three,
and x sub four, if in themselves these coordinates have
(03:42):
no significance. More careful consideration shows, however, that this anxiety
is unfounded. Let us consider, for instance, a material point
with any kind of motion. If this point had only
a momentary existence without duration, then it would be described
in space time by a single system of values x
(04:06):
sub one, x sub two, x sub three, and x
sub four. Thus, its permanent existence must be characterized by
an infinitely large number of such systems of values, the
coordinate values of which are so close together as to
give continuity corresponding to the material point. We thus have
(04:27):
a unidimensional line in the four dimensional continuum. In the
same way, any such lines in our continuum correspond to
many points in motion. The only statements having regard to
these points which can claim a physical existence are, in reality,
the statements about their encounters. In our mathematical treatment, such
(04:53):
an encounter is expressed in the fact that the two
lines which represent the motions of the points in question
have a particular system of co ordinate values x sub one,
x sub two, x sub three, and x sub four
in common. After mature consideration, the reader will doubtless admit that,
(05:13):
in reality, such encounters constitute the only actual evidence of
a time space nature with which we meet in physical statements.
When we were describing the motion of a material point
relative to a body of reference, we stated nothing more
than the encounters of this point with particular points of
(05:37):
the reference body. We can also determine the corresponding values
of the time by the observation of encounters of the
body with clocks, in conjunction with the observation of the
encounter of the hands of clocks with particular points on
the dials. It is just the same in the case
of space measurements by means of measuring rods. As a
(06:00):
little consideration will show the following statements Hauld. Generally, every
physical description resolves itself into a number of statements, each
of which refers to the space time coincidence of two
events A and B. In terms of Gaussian coordinates, every
(06:22):
such statement is expressed by the agreement of their four
coordinates x sub one, x sub two, x sub three,
and x sub four. Thus, in reality, the description of
the time space continuum by means of Gauss coordinates completely
replaces the description with the aid of a body of reference,
(06:43):
without suffering from the defects of the latter mode of description.
It is not tied down to the Euclidean character of
the continuum, which has to be represented Section twenty eight
Exact fourmulation of the general principle of relativity. We are
(07:05):
now in a position to replace the provisional formulation of
the general principle of relativity given in section eighteen by
an exact formulation the form they are used quote. All
bodies of reference, K, K, prime, etc. Are equivalent for
the description of natural phenomena or formulation of the general
(07:29):
laws of nature, whatever may be, their state of motion
cannot be maintained. Because the use of rigid reference bodies
in the sense of the method followed in the Special
theory of relativity is in general not possible. In space
time description, the Gauss coordinate system has to take the
(07:50):
place of the body of reference. The following statement corresponds
to the fundamental idea of the general principle of relativity.
All Gaussian coordinate systems are essentially equivalent for the formulation
of the general laws of nature. We can state this
general principle of relativity in still another form, which renders
(08:14):
it yet more clearly intelligible than it is when in
the form of the natural extension of the special principle
of relativity. According to the special theory of relativity, the
equations which express the general laws of nature pass over
into equations of the same form when, by making use
of the Lorentz transformation, we replace the space time variables x, y, z,
(08:40):
and t of a Galilean reference body K by the
space time variables x prime, y prime, z prime, and
t prime of a new reference body K prime. According
to the general theory of relativity, on the other hand,
by application of arbitrary substitutions of the Gauss variables x
(09:05):
sub one, x sub two, x sub three, and x
sub four. The equations must pass over into equations of
the same form for every transformation. Not only the Lorentz
transformation corresponds to the transition of one Gaus coordinate system
into another. If we desire to adhere to our old
(09:28):
time three dimensional view of things, then we can characterize
the development which is being undergone by the fundamental idea
of the general theory of relativity as follows. The special
theory of relativity has reference to Galilean domains i e.
To those in which no gravitational field exists. In this connection,
(09:52):
a Galilean reference body serves as body of reference i e.
A rigid body, the state of motion of which is
so chosen that the Galilean law of the uniform rectilinear
motion of isolated material points holds relatively to it. Certain
considerations suggest that we should refer the same Galilean domains
(10:15):
to non Galilean reference bodies. Also, a gravitational field of
a special kind is then present with respect to these
bodies c F Sections twenty and twenty three. In gravitational fields,
there are no such things as rigid bodies with Euclidean properties.
(10:37):
Thus the fictitious rigid body of reference is of no avail.
In the general theory of relativity, the motion of clocks
is also influenced by gravitational fields, and in such a
way that a physical definition of time which is made
directly with the aid of clocks has by no means
the same degree of plausibility as in the special theory
(10:59):
of relatives. For this reason, non rigid reference bodies are used,
which are as a whole not only moving in any
way whatsoever, but which also suffer alterations in form ad
lib during their motion. Clocks for which the law of
motion is of any kind, however irregular, serve for the
(11:21):
definition of time. We have to imagine each of these
clocks fixed at a point on the non rigid reference body.
These clocks satisfy only the one condition that the readings
which are observed simultaneously on adjacent clocks in space differ
from each other by an indefinitely small amount. This non
(11:43):
rigid reference body, which might appropriately be termed a reference mollusc,
is in the main equivalent to a Gaussian four dimensional
coordinate system chosen arbitrarily. That which gives the mollusk a
certain comprehensibility, as can compaired with the Gauss coordinate system,
is the really unjustified formal retention of the separate existence
(12:07):
of the space coordinates as opposed to the time coordinate.
Every point on the mollusc is treated as a space point,
and every material point which is at rest relatively to
it is at rest so long as the mollusc is
considered as reference body. The general principle of relativity requires
(12:28):
that all these molluks can be used as reference bodies
with equal right and equal success in the formulation of
the general laws of nature. The laws themselves must be
quite independent of the choice of mollusc. The great power
possessed by the general principle of relativity lies in the
(12:49):
comprehensive limitation which is imposed on the laws of nature.
In consequence of what we have seen above Section twenty
nine the solution of the problem of gravitation on the
basis of the general principle of relativity. If the reader
(13:10):
has followed all our previous considerations, he will have no
further difficulty in understanding the methods leading to the solution
of the problem of gravitation. We start off on a
consideration of a Galilean domain, i e. A domain in
which there is no gravitational field relative to the Galileyan
(13:30):
reference body K. The behavior of measuring rods and clocks
with reference to K is known from the special theory
of relativity. Likewise the behavior of isolated material points. The
latter move uniformly and in straight lines. Now let us
refer this domain to a random Gauss coordinate system or
(13:55):
to a Mollusk as reference body k prime. Then with
respect to k prime, there is a gravitational field G
of a particular kind. We learn the behavior of measuring
rods and clocks, and also of freely moving material points
with reference to K prime simply by mathematical transformation. We
(14:18):
interpret this behavior as the behavior of measuring rods, clocks,
and material points under the influence of the gravitational field G.
Hereupon we introduce a hypothesis that the influence of the
gravitational field on measuring rods, clocks, and freely moving material
points continues to take place according to the same laws
(14:43):
even in the case where the prevailing gravitational field is
not derivable from the Galilean special case simply by means
of a transformation of coordinates. The next step is to
investigate the space time behavior of the gravitational field, which
was derived from the Galilean special case simply by transformation
(15:06):
of the coordinates. This behaviour is formulated in a law
which is always valid no matter how the reference body
or mollusc used in the description may be chosen. This
law is not yet the general law of the gravitational field,
since the gravitational field under consideration is of a special kind.
(15:29):
In order to find out the general law of field
of gravitation, we still require to obtain a generalization of
the law as found above. This can be obtained without caprice, however,
by taking into consideration the following demands. A. The required
generalization must likewise satisfy the general postulate of relativity. B.
(15:54):
If there is any matter in the domain under consideration,
only its inertial mass, and thus, according to section fifteen,
only its energy is of importance for its effect in
exciting a field. C. Gravitational field and matter together must
satisfy the law of the conservation of energy and of impulse. Finally,
(16:20):
the general principle of relativity permits us to determine the
influence of the gravitational field on the course of all
those processes which take place according to known laws when
a gravitational field is absent i e. Which have already
been fitted into the frame of the special theory of relativity.
(16:41):
In this connection, we proceed in principle according to the
method which has already been explained for measuring rods, clocks,
and freely moving material points. The theory of gravitation, derived
in this way from the general postulate of relativity, excels
not only in its beauty, nor in removing the defect
(17:03):
attaching to classical mechanics which was brought to light in
section twenty one, nor in interpreting the empirical law of
the equality of inertial and gravitational mass. But it has
also already explained a result of observation in astronomy against
which classical mechanics is powerless. If we confine the application
(17:27):
of the theory to the case where the gravitational fields
can be regarded as being weak, and in which all
masses move with respect to the coordinate system with velocities
which are small compared with the velocity of light, we
then obtain as a first approximation the Newtonian theory. Thus,
the latter theory is obtained here without any particular assumption,
(17:51):
whereas Newton had to introduce the hypothesis that the force
of attraction between mutually attracting material points is inversely proportional
to the square of the distance between them. If we
increase the accuracy of the calculation, deviations from the theory of
Newton make their appearance practically, all of which must nevertheless
(18:13):
escape the test of observation owing to their smallness. We
must draw attention here to one of these deviations. According
to Newton's theory, a planet moves around the Sun in
an ellipse, which would permanently maintain its position with respect
to the fixed stars if we could disregard the motion
(18:36):
of the fixed stars themselves and the action of the
other planets under consideration. Thus, if we correct the observed
motion of the planets for these two influences, and if
Newton's theory be strictly correct, we ought to obtain for
the orbit of the planet an ellipse which is fixed
with reference to the fixed stars. This deduction, which can
(19:00):
be tested with great accuracy, has been confirmed for all
the planets save one with the precision that is capable
of being obtained by the delicacy of observation attainable at
the present time. The sole exception is Mercury, the planet
which lies nearest the Sun. Since the time of Leverrier,
(19:20):
it has been known that the eclipse corresponding to the
orbit of Mercury, after it has been corrected for the
influences mentioned above, is not stationary with respect to the
fixed stars, but that it rotates exceedingly slowly in the
plane of the orbit and in the sense of the
orbital motion. The value obtained for this rotary movement of
(19:43):
the orbital ellipse was forty three seconds of arc per century,
an amount ensured to be correct to within a few
seconds of arc. This effect can be explained by means
of classical mechanics only on the assumption of hypotheses which
have little probability and which were devised solely for this purpose.
(20:07):
On the basis of the general theory of relativity, it
is found that the ellipse of every planet round the
Sun must necessarily rotate in the manner indicated above, that
for all the planets with the exception of Mercury, this
rotation is too small to be detected with the delicacy
of observation possible at the present time, but that in
(20:29):
the case of mercury it must amount to forty three
seconds of arc per century, a result which is strictly
in agreement with observation. Apart from this one, it has
hitherto been possible to make only two deductions from the
theory which admit of being tested by observation, to wit,
(20:49):
the curvature of light rays by the gravitational field of
the Sun first observed by Eddington and others in nineteen nineteen,
and placement of the spectral lines of light reaching us
from large stars as compared with the corresponding lines for
light produced in an analogous manner terrestrially i e. By
(21:12):
the same kind of atom established by atoms in nineteen
twenty four. These two deductions from the theory have both
been confirmed. End of Section twenty nine.
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