October 29, 2023 • 21 mins
This content was created in partnership and with the help of Artificial Intelligence AI
Mark as Played
Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
(00:01):
This is a LibriVox recording. AllLibriVox 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
(00:21):
of Relativity, Sections twenty seven totwenty nine. Section twenty seven. The
space time continuum of the General Theoryof Relativity is not a Euclidean continuum.
In the first part of this bookwe were able to make use of space
time coordinates, which allowed of asimple and direct physical interpretation, and which,
(00:47):
according to section twenty six, canbe regarded as four dimensional Cartesian coordinates.
This was possible on the basis ofthe law of the constancy of the
velocity of light, but according tosection twenty one, the general theory of
relativity cannot retain this law. Onthe contrary, we arrived at the result
(01:08):
that, according to this latter theory, the velocity of light must always depend
on the coordinates. When a gravitationalfield 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 coordinatesand the time, which led us to
(01:30):
our objective in the special theory ofrelativity. In view of the results of
these considerations, we are led tothe conviction that, according to the general
principle of relativity, the space timecontinuum cannot be regarded as a euclidian one,
but that here we have the generalcase corresponding to the marble slab with
(01:53):
local variations of temperature, and withwhich we made acquaintance as an example of
a two dimmes dimensional continuum. Justas it was there impossible to construct a
Cartesian coordinate system from equal rods,so here it is impossible to build up
a system or reference body from rigidbodies and clocks, which shall be of
(02:16):
such a nature that measuring rods andclocks 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 twentythree, But the considerations of section twenty
five and twenty six show us theway to surmount this difficulty. We refer
(02:40):
the four dimensional space time continuum inan arbitrary manner to Gauss coordinates. We
assigned to every point of the continuumor event four numbers x sub one,
x sub two, x sub three, and x sub four coordinates, which
(03:00):
have not the least direct physical significance, but only serve the purpose of numbering
the points of the continuum in adefinite but arbitrary manner. This arrangement does
not even need to be of sucha kind that we must regard x sub
one, x sub two, andx sub three as space coordinates and x
(03:21):
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 subone, x sub two, x sub
three, and x sub four,if in themselves these coordinates have no significance.
(03:44):
More careful consideration shows, however,that this anxiety is unfounded. Let
us consider, for instance, amaterial point with any kind of motion.
If this point had only a momentaryexistence without duration, then it would be
described in space time by a singlesystem of values x sub one, x
(04:06):
sub two, x sub three,and x sub four. Thus, its
permanent existence must be characterized by aninfinitely large number of such systems of values,
the coordinate values of which are soclose together as to give continuity corresponding
to the material point. We thushave a unidimensional line in the four dimensional
(04:30):
continuum. In the same way,any such lines in our continuum correspond to
many points in motion. The onlystatements having regard to these points which can
claim a physical existence are, inreality, the statements about their encounters.
In our mathematical treatment, such anencounter is expressed in the fact that the
(04:56):
two lines which represent the motions ofthe 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, in reality,such encounters constitute the only actual evidence of
(05:18):
a time space nature with which wemeet in physical statements. When we were
describing the motion of a material pointrelative to a body of reference, we
stated nothing more than the encounters ofthis point with particular points of the reference
body. We can also determine thecorresponding values of the time by the observation
(05:44):
of encounters of the body with clocks, in conjunction with the observation of the
encounter of the hands of clocks withparticular points on the dials. It is
just the same in the case ofspace measurements by means of measuring rods.
As a little consideration will show thefollowing statements Hauld. Generally, every physical
(06:08):
description resolves itself into a number ofstatements, each of which refers to the
space time coincidence of two events Aand B. In terms of Gaussian coordinates,
every such statement is expressed by theagreement of their four coordinates x sub
one, x sub two, xsub three, and x sub four.
(06:31):
Thus, in reality, the descriptionof the time space continuum by means of
Gauss coordinates completely replaces the description withthe aid of a body of reference,
without suffering from the defects of thelatter mode of description. It is not
tied down to the Euclidean character ofthe continuum, which has to be represented
(06:56):
Section twenty eight Exact four formulation ofthe General principle of relativity. We are
now in a position to replace theprovisional formulation of the general principle of relativity
given in section eighteen by an exactformulation the form they are used quote.
(07:18):
All bodies of reference, K,K, prime, etc. Are equivalent
for the description of natural phenomena orformulation of the general laws of nature,
whatever may be, their state ofmotion cannot be maintained. Because the use
of rigid reference bodies in the senseof the method followed in the Special theory
(07:42):
of relativity is in general not possible. In space time description, the Gauss
coordinate system has to take the placeof the body of reference. The following
statement corresponds to the fundamental idea ofthe general principle of relativity. All Gaussian
coordinate systems are essentially equivalent for theformulation of the general laws of nature.
(08:09):
We can state this general principle ofrelativity in still another form, which renders
it yet more clearly intelligible than itis 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 lawsof nature pass over into equations of
(08:31):
the same form when, by makinguse of the Lorentz transformation, we replace
the space time variables x, y, z, and t of a Galilean
reference body K by the space timevariables x prime, y prime, z
prime, and t prime of anew reference body K prime. According to
(08:56):
the general theory of relativity, onthe other hand, by application of arbitrary
substitutions of the Gauss variables x subone, 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
(09:20):
transition of one Gaus coordinate system intoanother. If we desire to adhere to
our old time three dimensional view ofthings, then we can characterize the development
which is being undergone by the fundamentalidea of the general theory of relativity as
follows. The special theory of relativityhas reference to Galilean domains i e.
(09:46):
To those in which no gravitational fieldexists. In this connection, a Galilean
reference body serves as body of referencei e. A rigid body, the
state of motion of which is sochosen that the Galilean law of the uniform
rectilinear motion of isolated material points holdsrelatively to it. Certain considerations suggest that
(10:11):
we should refer the same Galilean domainsto non Galilean reference bodies. Also,
a gravitational field of a special kindis 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 Euclideanproperties. Thus the fictitious rigid body of
(10:39):
reference is of no avail. Inthe general theory of relativity, the motion
of clocks is also influenced by gravitationalfields, and in such a way that
a physical definition of time which ismade directly with the aid of clocks has
by no means the same degree ofplausibility as in the special theory of relatives.
(11:01):
For this reason, non rigid referencebodies are used, which are as
a whole not only moving in anyway 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 definition of time.
(11:22):
We have to imagine each of theseclocks fixed at a point on the non
rigid reference body. These clocks satisfyonly the one condition that the readings which
are observed simultaneously on adjacent clocks inspace differ from each other by an indefinitely
small amount. This non rigid referencebody, which might appropriately be termed a
(11:46):
reference mollusc, is in the mainequivalent to a Gaussian four dimensional coordinate system
chosen arbitrarily. That which gives themollusk a certain comprehensibility, as can compaired
with the Gauss coordinate system, isthe really unjustified formal retention of the separate
(12:07):
existence of the space coordinates as opposedto the time coordinate. Every point on
the mollusc is treated as a spacepoint, and every material point which is
at rest relatively to it is atrest so long as the mollusc is considered
as reference body. The general principleof relativity requires that all these molluks can
(12:30):
be used as reference bodies with equalright and equal success in the formulation of
the general laws of nature. Thelaws themselves must be quite independent of the
choice of mollusc. The great powerpossessed by the general principle of relativity lies
in the comprehensive limitation which is imposedon the laws of nature. In consequence
(12:54):
of what we have seen above Sectiontwenty nine the solution of the problem of
gravitation on the basis of the generalprinciple of relativity. If the reader has
followed all our previous considerations, hewill have no further difficulty in understanding the
(13:16):
methods leading to the solution of theproblem 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 theGalileyan reference body K. The behavior of
measuring rods and clocks with reference toK is known from the special theory of
(13:39):
relativity. Likewise the behavior of isolatedmaterial points. The latter move uniformly and
in straight lines. Now let usrefer this domain to a random Gauss coordinate
system or to a Mollusk as referencebody k prime. Then with respect to
(14:00):
k prime, there is a gravitationalfield G of a particular kind. We
learn the behavior of measuring rods andclocks, and also of freely moving material
points with reference to K prime simplyby mathematical transformation. We interpret this behavior
as the behavior of measuring rods,clocks, and material points under the influence
(14:24):
of the gravitational field G. Hereuponwe 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 samelaws even in the case where the prevailing
gravitational field is not derivable from theGalilean special case simply by means of a
(14:50):
transformation of coordinates. The next stepis to investigate the space time behavior of
the gravitational field, which was derivedfrom the Galilean special case simply by transformation
of the coordinates. This behaviour isformulated in a law which is always valid
(15:11):
no matter how the reference body ormollusc used in the description may be chosen.
This law is not yet the generallaw of the gravitational field, since
the gravitational field under consideration is ofa special kind. In order to find
out the general law of field ofgravitation, we still require to obtain a
(15:35):
generalization of the law as found above. This can be obtained without caprice,
however, by taking into consideration thefollowing demands. A. The required generalization
must likewise satisfy the general postulate ofrelativity. B. If there is any
matter in the domain under consideration,only its inertial mass, and thus,
(16:00):
according to section fifteen, only itsenergy is of importance for its effect in
exciting a field. C. Gravitationalfield and matter together must satisfy the law
of the conservation of energy and ofimpulse. Finally, the general principle of
(16:21):
relativity permits us to determine the influenceof the gravitational field on the course of
all those processes which take place accordingto known laws when a gravitational field is
absent i e. Which have alreadybeen fitted into the frame of the special
theory of relativity. In this connection, we proceed in principle according to the
(16:45):
method which has already been explained formeasuring rods, clocks, and freely moving
material points. The theory of gravitation, derived in this way from the general
postulate of relativity, excels not onlyin its beauty, nor in removing the
defect attaching to classical mechanics which wasbrought to light in section twenty one,
(17:08):
nor in interpreting the empirical law ofthe equality of inertial and gravitational mass.
But it has also already explained aresult of observation in astronomy against which classical
mechanics is powerless. If we confinethe application of the theory to the case
where the gravitational fields can be regardedas being weak, and in which all
(17:33):
masses move with respect to the coordinatesystem with velocities which are small compared with
the velocity of light, we thenobtain as a first approximation the Newtonian theory.
Thus, the latter theory is obtainedhere without any particular assumption, whereas
Newton had to introduce the hypothesis thatthe force of attraction between mutually attracting material
(17:57):
points is inversely proportional to the squareof 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 mustnevertheless escape the test of observation owing to
their smallness. We must draw attentionhere to one of these deviations. According
(18:22):
to Newton's theory, a planet movesaround the Sun in an ellipse, which
would permanently maintain its position with respectto the fixed stars if we could disregard
the motion of the fixed stars themselvesand the action of the other planets under
consideration. Thus, if we correctthe observed motion of the planets for these
(18:45):
two influences, and if Newton's theorybe strictly correct, we ought to obtain
for the orbit of the planet anellipse which is fixed with reference to the
fixed stars. This deduction, whichcan be tested with great accuracy, has
been confirmed for all the planets saveone with the precision that is capable of
(19:07):
being obtained by the delicacy of observationattainable at the present time. The sole
exception is Mercury, the planet whichlies nearest the Sun. Since the time
of Leverrier, it has been knownthat the eclipse corresponding to the orbit of
Mercury, after it has been correctedfor the influences mentioned above, is not
(19:29):
stationary with respect to the fixed stars, but that it rotates exceedingly slowly in
the plane of the orbit and inthe sense of the orbital motion. The
value obtained for this rotary movement ofthe orbital ellipse was forty three seconds of
arc per century, an amount ensuredto be correct to within a few seconds
(19:52):
of arc. This effect can beexplained by means of classical mechanics only on
the assumption of hypotheses which have littleprobability and which were devised solely for this
purpose. On the basis of thegeneral theory of relativity, it is found
that the ellipse of every planet roundthe Sun must necessarily rotate in the manner
(20:15):
indicated above, that for all theplanets with the exception of Mercury, this
rotation is too small to be detectedwith the delicacy of observation possible at the
present time, but that in thecase of mercury it must amount to forty
three seconds of arc per century,a result which is strictly in agreement with
(20:37):
observation. Apart from this one,it has hitherto been possible to make only
two deductions from the theory which admitof being tested by observation, to wit,
the curvature of light rays by thegravitational field of the Sun first observed
by Eddington and others in nineteen nineteen, and placement of the spectral lines of
(21:02):
light reaching us from large stars ascompared with the corresponding lines for light produced
in an analogous manner terrestrially i e. By 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 twentynine.
This is a LibriVox recording. AllLibriVox 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
(00:21):
of Relativity, Sections twenty seven totwenty nine. Section twenty seven. The
space time continuum of the General Theoryof Relativity is not a Euclidean continuum.
In the first part of this bookwe were able to make use of space
time coordinates, which allowed of asimple and direct physical interpretation, and which,
(00:47):
according to section twenty six, canbe regarded as four dimensional Cartesian coordinates.
This was possible on the basis ofthe law of the constancy of the
velocity of light, but according tosection twenty one, the general theory of
relativity cannot retain this law. Onthe contrary, we arrived at the result
(01:08):
that, according to this latter theory, the velocity of light must always depend
on the coordinates. When a gravitationalfield 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 coordinatesand the time, which led us to
(01:30):
our objective in the special theory ofrelativity. In view of the results of
these considerations, we are led tothe conviction that, according to the general
principle of relativity, the space timecontinuum cannot be regarded as a euclidian one,
but that here we have the generalcase corresponding to the marble slab with
(01:53):
local variations of temperature, and withwhich we made acquaintance as an example of
a two dimmes dimensional continuum. Justas it was there impossible to construct a
Cartesian coordinate system from equal rods,so here it is impossible to build up
a system or reference body from rigidbodies and clocks, which shall be of
(02:16):
such a nature that measuring rods andclocks 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 twentythree, But the considerations of section twenty
five and twenty six show us theway to surmount this difficulty. We refer
(02:40):
the four dimensional space time continuum inan arbitrary manner to Gauss coordinates. We
assigned to every point of the continuumor event four numbers x sub one,
x sub two, x sub three, and x sub four coordinates, which
(03:00):
have not the least direct physical significance, but only serve the purpose of numbering
the points of the continuum in adefinite but arbitrary manner. This arrangement does
not even need to be of sucha kind that we must regard x sub
one, x sub two, andx sub three as space coordinates and x
(03:21):
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 subone, x sub two, x sub
three, and x sub four,if in themselves these coordinates have no significance.
(03:44):
More careful consideration shows, however,that this anxiety is unfounded. Let
us consider, for instance, amaterial point with any kind of motion.
If this point had only a momentaryexistence without duration, then it would be
described in space time by a singlesystem of values x sub one, x
(04:06):
sub two, x sub three,and x sub four. Thus, its
permanent existence must be characterized by aninfinitely large number of such systems of values,
the coordinate values of which are soclose together as to give continuity corresponding
to the material point. We thushave a unidimensional line in the four dimensional
(04:30):
continuum. In the same way,any such lines in our continuum correspond to
many points in motion. The onlystatements having regard to these points which can
claim a physical existence are, inreality, the statements about their encounters.
In our mathematical treatment, such anencounter is expressed in the fact that the
(04:56):
two lines which represent the motions ofthe 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, in reality,such encounters constitute the only actual evidence of
(05:18):
a time space nature with which wemeet in physical statements. When we were
describing the motion of a material pointrelative to a body of reference, we
stated nothing more than the encounters ofthis point with particular points of the reference
body. We can also determine thecorresponding values of the time by the observation
(05:44):
of encounters of the body with clocks, in conjunction with the observation of the
encounter of the hands of clocks withparticular points on the dials. It is
just the same in the case ofspace measurements by means of measuring rods.
As a little consideration will show thefollowing statements Hauld. Generally, every physical
(06:08):
description resolves itself into a number ofstatements, each of which refers to the
space time coincidence of two events Aand B. In terms of Gaussian coordinates,
every such statement is expressed by theagreement of their four coordinates x sub
one, x sub two, xsub three, and x sub four.
(06:31):
Thus, in reality, the descriptionof the time space continuum by means of
Gauss coordinates completely replaces the description withthe aid of a body of reference,
without suffering from the defects of thelatter mode of description. It is not
tied down to the Euclidean character ofthe continuum, which has to be represented
(06:56):
Section twenty eight Exact four formulation ofthe General principle of relativity. We are
now in a position to replace theprovisional formulation of the general principle of relativity
given in section eighteen by an exactformulation the form they are used quote.
(07:18):
All bodies of reference, K,K, prime, etc. Are equivalent
for the description of natural phenomena orformulation of the general laws of nature,
whatever may be, their state ofmotion cannot be maintained. Because the use
of rigid reference bodies in the senseof the method followed in the Special theory
(07:42):
of relativity is in general not possible. In space time description, the Gauss
coordinate system has to take the placeof the body of reference. The following
statement corresponds to the fundamental idea ofthe general principle of relativity. All Gaussian
coordinate systems are essentially equivalent for theformulation of the general laws of nature.
(08:09):
We can state this general principle ofrelativity in still another form, which renders
it yet more clearly intelligible than itis 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 lawsof nature pass over into equations of
(08:31):
the same form when, by makinguse of the Lorentz transformation, we replace
the space time variables x, y, z, and t of a Galilean
reference body K by the space timevariables x prime, y prime, z
prime, and t prime of anew reference body K prime. According to
(08:56):
the general theory of relativity, onthe other hand, by application of arbitrary
substitutions of the Gauss variables x subone, 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
(09:20):
transition of one Gaus coordinate system intoanother. If we desire to adhere to
our old time three dimensional view ofthings, then we can characterize the development
which is being undergone by the fundamentalidea of the general theory of relativity as
follows. The special theory of relativityhas reference to Galilean domains i e.
(09:46):
To those in which no gravitational fieldexists. In this connection, a Galilean
reference body serves as body of referencei e. A rigid body, the
state of motion of which is sochosen that the Galilean law of the uniform
rectilinear motion of isolated material points holdsrelatively to it. Certain considerations suggest that
(10:11):
we should refer the same Galilean domainsto non Galilean reference bodies. Also,
a gravitational field of a special kindis 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 Euclideanproperties. Thus the fictitious rigid body of
(10:39):
reference is of no avail. Inthe general theory of relativity, the motion
of clocks is also influenced by gravitationalfields, and in such a way that
a physical definition of time which ismade directly with the aid of clocks has
by no means the same degree ofplausibility as in the special theory of relatives.
(11:01):
For this reason, non rigid referencebodies are used, which are as
a whole not only moving in anyway 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 definition of time.
(11:22):
We have to imagine each of theseclocks fixed at a point on the non
rigid reference body. These clocks satisfyonly the one condition that the readings which
are observed simultaneously on adjacent clocks inspace differ from each other by an indefinitely
small amount. This non rigid referencebody, which might appropriately be termed a
(11:46):
reference mollusc, is in the mainequivalent to a Gaussian four dimensional coordinate system
chosen arbitrarily. That which gives themollusk a certain comprehensibility, as can compaired
with the Gauss coordinate system, isthe really unjustified formal retention of the separate
(12:07):
existence of the space coordinates as opposedto the time coordinate. Every point on
the mollusc is treated as a spacepoint, and every material point which is
at rest relatively to it is atrest so long as the mollusc is considered
as reference body. The general principleof relativity requires that all these molluks can
(12:30):
be used as reference bodies with equalright and equal success in the formulation of
the general laws of nature. Thelaws themselves must be quite independent of the
choice of mollusc. The great powerpossessed by the general principle of relativity lies
in the comprehensive limitation which is imposedon the laws of nature. In consequence
(12:54):
of what we have seen above Sectiontwenty nine the solution of the problem of
gravitation on the basis of the generalprinciple of relativity. If the reader has
followed all our previous considerations, hewill have no further difficulty in understanding the
(13:16):
methods leading to the solution of theproblem 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 theGalileyan reference body K. The behavior of
measuring rods and clocks with reference toK is known from the special theory of
(13:39):
relativity. Likewise the behavior of isolatedmaterial points. The latter move uniformly and
in straight lines. Now let usrefer this domain to a random Gauss coordinate
system or to a Mollusk as referencebody k prime. Then with respect to
(14:00):
k prime, there is a gravitationalfield G of a particular kind. We
learn the behavior of measuring rods andclocks, and also of freely moving material
points with reference to K prime simplyby mathematical transformation. We interpret this behavior
as the behavior of measuring rods,clocks, and material points under the influence
(14:24):
of the gravitational field G. Hereuponwe 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 samelaws even in the case where the prevailing
gravitational field is not derivable from theGalilean special case simply by means of a
(14:50):
transformation of coordinates. The next stepis to investigate the space time behavior of
the gravitational field, which was derivedfrom the Galilean special case simply by transformation
of the coordinates. This behaviour isformulated in a law which is always valid
(15:11):
no matter how the reference body ormollusc used in the description may be chosen.
This law is not yet the generallaw of the gravitational field, since
the gravitational field under consideration is ofa special kind. In order to find
out the general law of field ofgravitation, we still require to obtain a
(15:35):
generalization of the law as found above. This can be obtained without caprice,
however, by taking into consideration thefollowing demands. A. The required generalization
must likewise satisfy the general postulate ofrelativity. B. If there is any
matter in the domain under consideration,only its inertial mass, and thus,
(16:00):
according to section fifteen, only itsenergy is of importance for its effect in
exciting a field. C. Gravitationalfield and matter together must satisfy the law
of the conservation of energy and ofimpulse. Finally, the general principle of
(16:21):
relativity permits us to determine the influenceof the gravitational field on the course of
all those processes which take place accordingto known laws when a gravitational field is
absent i e. Which have alreadybeen fitted into the frame of the special
theory of relativity. In this connection, we proceed in principle according to the
(16:45):
method which has already been explained formeasuring rods, clocks, and freely moving
material points. The theory of gravitation, derived in this way from the general
postulate of relativity, excels not onlyin its beauty, nor in removing the
defect attaching to classical mechanics which wasbrought to light in section twenty one,
(17:08):
nor in interpreting the empirical law ofthe equality of inertial and gravitational mass.
But it has also already explained aresult of observation in astronomy against which classical
mechanics is powerless. If we confinethe application of the theory to the case
where the gravitational fields can be regardedas being weak, and in which all
(17:33):
masses move with respect to the coordinatesystem with velocities which are small compared with
the velocity of light, we thenobtain as a first approximation the Newtonian theory.
Thus, the latter theory is obtainedhere without any particular assumption, whereas
Newton had to introduce the hypothesis thatthe force of attraction between mutually attracting material
(17:57):
points is inversely proportional to the squareof 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 mustnevertheless escape the test of observation owing to
their smallness. We must draw attentionhere to one of these deviations. According
(18:22):
to Newton's theory, a planet movesaround the Sun in an ellipse, which
would permanently maintain its position with respectto the fixed stars if we could disregard
the motion of the fixed stars themselvesand the action of the other planets under
consideration. Thus, if we correctthe observed motion of the planets for these
(18:45):
two influences, and if Newton's theorybe strictly correct, we ought to obtain
for the orbit of the planet anellipse which is fixed with reference to the
fixed stars. This deduction, whichcan be tested with great accuracy, has
been confirmed for all the planets saveone with the precision that is capable of
(19:07):
being obtained by the delicacy of observationattainable at the present time. The sole
exception is Mercury, the planet whichlies nearest the Sun. Since the time
of Leverrier, it has been knownthat the eclipse corresponding to the orbit of
Mercury, after it has been correctedfor the influences mentioned above, is not
(19:29):
stationary with respect to the fixed stars, but that it rotates exceedingly slowly in
the plane of the orbit and inthe sense of the orbital motion. The
value obtained for this rotary movement ofthe orbital ellipse was forty three seconds of
arc per century, an amount ensuredto be correct to within a few seconds
(19:52):
of arc. This effect can beexplained by means of classical mechanics only on
the assumption of hypotheses which have littleprobability and which were devised solely for this
purpose. On the basis of thegeneral theory of relativity, it is found
that the ellipse of every planet roundthe Sun must necessarily rotate in the manner
(20:15):
indicated above, that for all theplanets with the exception of Mercury, this
rotation is too small to be detectedwith the delicacy of observation possible at the
present time, but that in thecase of mercury it must amount to forty
three seconds of arc per century,a result which is strictly in agreement with
(20:37):
observation. Apart from this one,it has hitherto been possible to make only
two deductions from the theory which admitof being tested by observation, to wit,
the curvature of light rays by thegravitational field of the Sun first observed
by Eddington and others in nineteen nineteen, and placement of the spectral lines of
(21:02):
light reaching us from large stars ascompared with the corresponding lines for light produced
in an analogous manner terrestrially i e. By 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 twentynine.
Popular Podcasts
CrimeLess: Hillbilly Heist
It’s 1996 in rural North Carolina, and an oddball crew makes history when they pull off America’s third largest cash heist. But it’s all downhill from there. Join host Johnny Knoxville as he unspools a wild and woolly tale about a group of regular ‘ol folks who risked it all for a chance at a better life. CrimeLess: Hillbilly Heist answers the question: what would you do with 17.3 million dollars? The answer includes diamond rings, mansions, velvet Elvis paintings, plus a run for the border, murder-for-hire-plots, and FBI busts.
Crime Junkie
Does hearing about a true crime case always leave you scouring the internet for the truth behind the story? Dive into your next mystery with Crime Junkie. Every Monday, join your host Ashley Flowers as she unravels all the details of infamous and underreported true crime cases with her best friend Brit Prawat. From cold cases to missing persons and heroes in our community who seek justice, Crime Junkie is your destination for theories and stories you won’t hear anywhere else. Whether you're a seasoned true crime enthusiast or new to the genre, you'll find yourself on the edge of your seat awaiting a new episode every Monday. If you can never get enough true crime... Congratulations, you’ve found your people. Follow to join a community of Crime Junkies! Crime Junkie is presented by audiochuck Media Company.
Stuff You Should Know
If you've ever wanted to know about champagne, satanism, the Stonewall Uprising, chaos theory, LSD, El Nino, true crime and Rosa Parks, then look no further. Josh and Chuck have you covered.