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(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, recorded by Laurie Ann Walden, Part
two, The General Theory of Relativity, Sections eighteen through twenty. Section eighteen
(00:29):
Special and General principle of relativity.The basal principle, which was the pivot
of all our previous considerations, wasthe special principle of relativity, i e.
The principle of the physical relativity ofall uniform motion. Let us once
more analyze its meaning carefully. Itwas at all times clear that, from
(00:51):
the point of view of the ideait conveys to us, every motion must
be considered only as a relative motion. Returning to the illustration we have frequently
used of the embankment and the railwaycarriage, we can express the fact of
the motion here taking place in thefollowing two forms, both of which are
equally justifiable. A. The carriageis in motion relative to the embankment.
(01:15):
B the embankment is in motion relativeto the carriage in A the embankment in
B the carriage serves as the bodyof reference in our statement of the motion
taking place. If it is simplya question of detecting or of describing the
motion involved, it is in principleimmaterial to what reference body we refer the
(01:36):
motion. As already mentioned, thisis self evident, but it must not
be confused with the much more comprehensivestatement called the principle of relativity, which
we have taken as the basis ofour investigations. The principle we have made
use of not only maintains that wemay equally well choose the carriage or the
embankment as our reference body for thedescription of any event, for this too
(02:00):
is self evident. Our principle ratherasserts what follows. If we formulate the
general laws of nature as they areobtained from experience by making use of a
the embankment as reference body, bthe railway carriage is reference body, then
these general laws of nature e g. The laws of mechanics or the law
(02:23):
of the propagation of light in vacuohave exactly the same form in both cases.
This can also be expressed as follows. For the physical description of natural
processes. Neither of the reference bodiesK K prime is unique literally specially marked
out as compared with the other.Unlike the first, this latter statement need
(02:46):
not of necessity hold a priori.It is not contained in the conceptions of
motion and reference body, and arrivablefrom them. Only experience can decide as
to its correctness or incorrectness. Upto the present, however, we have
by no means maintained the equivalents ofall bodies of reference K in connection with
(03:07):
the formulation of natural laws. Ourcourse was more on the following lines.
In the first place, we startedout from the assumption that there exists a
reference body K, whose condition ofmotion is such that the Galilean law holds
with respect to it. A particleleft to itself and sufficiently far removed from
all other particles, moves uniformly ina straight line with reference to K Galileyan
(03:31):
reference body. The laws of naturewere to be as simple as possible,
but in addition to K, allbodies of reference K prime should be given
preference in this sense, and theyshould be exactly equivalent to K for the
formulation of natural laws, provided thatthey are in a state of uniform,
rectilinear and non rotary motion with respectto K. All these bodies of reference
(03:55):
are to be regarded as Galilean referencebodies. The validity of the principle of
relativity was assumed only for these referencebodies, but not for others, e
g. Those possessing motion of adifferent kind. In this sense we speak
of the special principle of relativity orspecial theory of relativity. In contrast to
(04:18):
this, we wish to understand bythe general principle of relativity the following statement,
all bodies of reference K, K, Prime, et cetera. Are
equivalent for the description of natural phenomenaor formulation of the general laws of nature,
whatever may be their state of motion. But before proceeding farther, it
(04:40):
ought to be pointed out that thisformulation must be replaced later by a more
abstract one, for reasons which willbecome evident at a later stage. Since
the introduction of the special principle ofrelativity has been justified, every intellect which
strives after generalization must feel the temptationto venture the step towards the su general
(05:00):
principle of relativity. But a simpleand apparently quite reliable consideration seems to suggest
that for the present, at anyrate, there is little hope of success
in such an attempt. Let usimagine ourselves transferred to our old friend,
the railway carriage, which is travelingat a uniform rate. As long as
it is moving uniformly, the occupantof the carriage is not sensible of its
(05:24):
motion, and it is for thisreason that he can, without reluctance,
interpret the facts of the case asindicating that the carriage is at rest,
but the embankment in motion. Moreover, according to the special principle of relativity,
this interpretation is quite justified also froma physical point of view. If
the motion of the carriage is nowchanged into a non uniform motion, as
(05:47):
for instance, by a powerful applicationof the brakes, then the occupant of
the carriage experiences a correspondingly powerful jerkforwards. The retarded motion is manifested in
the mechanical behaveavior of bodies. Relativeto the person in the railway carriage.
The mechanical behavior is different from thatof the case previously considered, and for
(06:08):
this reason it would appear to beimpossible that the same mechanical laws hold relatively
to the non uniformly moving carriage ashold with reference to the carriage when at
rest or in uniform motion at allevents, it is clear that the Galilean
law does not hold with respect tothe non uniformly moving carriage. Because of
(06:29):
this, we feel compelled at thepresent juncture to grant a kind of absolute
physical reality to non uniform motion,in opposition to the general principle of relativity.
But in what follows we shall soonsee that this conclusion cannot be maintained
Section nineteen. The gravitational field.If we pick up a stone and then
(06:53):
let it go, why does itfall to the ground. The usual answer
to this question is because it isattracted by the Earth. Modern physics formulates
the answer rather differently, for thefollowing reason. As a result of the
more careful study of electromagnetic phenomena,we have come to regard action at a
distance as a process impossible without theintervention of some intermediary medium. If,
(07:18):
for instance, a magnet attracts apiece of iron, we cannot be content
to regard this as meaning that themagnet acts directly on the iron through the
intermediate empty space. But we areconstrained to imagine, after the manner of
Faraday, that the magnet always callsinto being something physically real in the space
around it, that something being whatwe call a magnetic field. In its
(07:43):
turn, this magnetic field operates onthe piece of iron, so that the
latter strives to move towards the magnet. We shall not discuss here the justification
for this incidental conception, which isindeed a somewhat arbitrary one. We shall
only mention that with its aid,electromagnetic phenomena can be theoretically represented much more
(08:03):
satisfactorily than without it, and thisapplies particularly to the transmission of electromagnetic waves.
The effects of gravitation also are regardedin an analogous manner. The action
of the Earth on the stone takesplace indirectly. The Earth produces in its
surroundings a gravitational field, which actson the stone and produces its motion of
(08:26):
fall. As we know from experience, the intensity of the action on a
body diminishes according to a quite definitelaw as we proceed farther and farther away
from the Earth from our point ofview. This means the law governing the
properties of the gravitational field in spacemust be a perfectly definite one in order
(08:48):
correctly to represent the diminution of gravitationalaction with the distance from operative bodies.
It is something like this. Thebody e g. The Earth produces a
field in its its immediate neighborhood directly. The intensity and direction of the field
at points farther removed from the bodyare thence determined by the law which governs
(09:09):
the properties in space of the gravitationalfields themselves. In contrast to electric and
magnetic fields, the gravitational field exhibitsa most remarkable property which is of fundamental
importance for what follows. Bodies whichare moving under the sole influence of a
gravitational field receive an acceleration which doesnot in the least depend either on the
(09:33):
material or on the physical state ofthe body. For instance, a piece
of lead and a piece of woodfall in exactly the same manner in a
gravitational field in vacuo when they startoff from rest or with the same initial
velocity. This law, which holdsmost accurately, can be expressed in a
different form in the light of thefollowing consideration. According to Newton's law of
(09:58):
motion, we have force equals inertialmass times acceleration, where the inertial mass
is a characteristic constant of the acceleratedbody. If now gravitation is the cause
of the acceleration, we then haveforce equals gravitational mass times intensity of the
(10:20):
gravitational field. Where the gravitational massis likewise a characteristic constant for the body.
From these two relations follows acceleration equalsthe fraction gravitational mass over inertial mass
times intensity of the gravitational field.If now, as we find from experience,
(10:43):
the acceleration is to be independent ofthe nature and the condition of the
body, and always the same fora given gravitational field, then the ratio
of the gravitational to the inertial massmust likewise be the same for all bodies.
By a suitable choice of units,we can thus make this ratio equal
to unity. We then have thefollowing law, The gravitational mass of a
(11:07):
body is equal to its inertial mass. It is true that this important law
had hitherto been recorded in mechanics,but it had not been interpreted. A
satisfactory interpretation can be obtained only ifwe recognize the following fact. The same
quality of a body manifests itself accordingto the circumstances as inertia or as weight
(11:31):
literally heaviness. In the following sectionwe shall show to what extent this is
actually the case, and how thisquestion is connected with the general postulate of
relativity. Section twenty the equality ofinertial and gravitational mass. As an argument
for the general postulate of relativity.We imagine a large portion of empty space,
(11:56):
so far removed from stars and otherappreciable masses, that we have before
us approximately the conditions required by thefundamental law of galilee. It is then
possible to choose a Galilean reference bodyfor this part of space world, relative
to which points at rest remain atrest and points in motion continue permanently in
(12:18):
uniform rectilinear motion. As reference body, Let us imagine a spacious chest resembling
a room with an observer inside whois equipped with apparatus. Gravitation naturally does
not exist for this observer. Hemust fasten himself with strings to the floor,
otherwise the slightest impact against the floorwill cause him to rise slowly toward
(12:39):
the ceiling of the room. Tothe middle of the lid of the chest
is fixed externally a hook with ropeattached. And now a being, what
kind of a being is immaterial tous begins pulling at this with a constant
force. The chest, together withthe observer, then begin to move upwards
with the uniformly accelerated motion. Incourse of time, their velocity will reach
(13:05):
unheard of values, provided that weare viewing all this from another reference body,
which is not being pulled with arope. But how does the man
in the chest regard the process.The acceleration of the chest will be transmitted
to him by the reaction of thefloor of the chest. He must therefore
take up this pressure by means ofhis legs, if he does not wish
to be laid out full length onthe floor. He is then standing in
(13:28):
the chest in exactly the same wayas any one stands in a room of
a house on our earth. Ifhe release a body which he previously had
in his hand, the acceleration ofthe chest will no longer be transmitted to
this body, and for this reasonthe body will approach the floor of the
chest with an accelerated relative motion.The observer will further convince himself that the
(13:52):
acceleration of the body towards the floorof the chest is always of the same
magnitude. Whatever kind of body hemay happen to use for the experiment,
relying on his knowledge of the gravitationalfield as it was discussed in the preceding
section. The man in the chestwill thus come to the conclusion that he
and the chest are in a gravitationalfield which is constant with regard to time.
(14:16):
Of course, he will be puzzledfor a moment as to why the
chest does not fall in this gravitationalfield. Just then, however, he
discovers the hook in the middle ofthe lid of the chest and the rope
which is attached to it, andhe consequently comes to the conclusion that the
chest is suspended at rest in thegravitational field. Ought we to smile at
(14:37):
the man and say that he errsin his conclusion. I do not believe
we ought to. If we wishto remain consistent, we must rather admit
that his mode of grasping the situationviolates neither reason nor known mechanical laws,
even though it is being accelerated withrespect to the Galilean space. First considered,
(14:58):
we can nevertheless regard the chess asbeing at rest. We have thus
good grounds for extending the principle ofrelativity to include bodies of reference which are
accelerated with respect to each other,and as a result we have gained a
powerful argument for a generalized postulate ofrelativity. We must note carefully that the
(15:18):
possibility of this mode of interpretation restson the fundamental property of the gravitational field
of giving all bodies the same accelerationor what comes to the same thing,
on the law of the equality ofinertial and gravitational mass. If this natural
law did not exist, the manin the accelerated chest would not be able
(15:41):
to interpret the behavior of the bodiesaround him on the supposition of a gravitational
field, and he would not bejustified on the grounds of experience in supposing
his reference body to be at rest. Suppose that the man in the chest
fixes a rope to the inner sideof the lid, and that he attaches
a body to the free end ofthe rope. The result of this will
(16:03):
be to stretch the rope so thatit will hang vertically downwards. If we
ask for an opinion of the causeof tension in the rope, the man
in the chest will say the suspendedbody experiences a downward force in the gravitational
field, and this is neutralized bythe tension of the rope. What determines
the magnitude of the tension of therope is the gravitational mass of the suspended
(16:26):
body. On the other hand,an observer who is poised freely in space
will interpret the condition of things.Thus, the rope must perforce take part
in the accelerated motion of the chest, and it transmits this motion to the
body attached to it. The tensionof the rope is just large enough to
effect the acceleration of the body.That which determines the magnitude of the tension
(16:51):
of the rope is the inertial massof the body. Guided by this example,
we see that our extension of theprinciple of relativity implies the necessity of
the law of the equality of inertialand gravitational mass. Thus we have obtained
a physical interpretation of this law.From our consideration of the accelerated chest,
(17:14):
we see that a general theory ofrelativity must yield important results on the laws
of gravitation. In point of fact, the systematic pursuit of the general idea
of relativity has supplied the laws satisfiedby the gravitational field. Before proceeding farther.
However, I must warn the readeragainst a misconception suggested by these considerations.
(17:37):
A gravitational field exists for the manin the chest, despite the fact
that there was no such field forthe co ordinate system first chosen. Now
we might easily suppose that the existenceof a gravitational field is always only an
apparent one. We might also thinkthat, regardless of the kind of gravitational
field which may be present, wecould always choose another reference body such that
(18:03):
no gravitational field exists with reference toit. This is by no means true
for all gravitational fields, but onlyfor those of quite special form. It
is, for instance, impossible tochoose a body of reference such that,
as judged from it, the gravitationalfield of the Earth in its entirety vanishes.
(18:25):
We can now appreciate why that argumentis not convincing, which we brought
forward against the general principle of relativityat the end of section eighteen. It
is certainly true that the observer inthe railway carriage experiences a jerk forwards as
a result of the application of thebreak, and that he recognizes in this
the non uniformity of motion or retardationof the carriage. But he is compelled
(18:51):
by nobody to refer this jerk toa real acceleration or retardation of the carriage.
He might also interpret his experience thusmy body of reference. The carriage
remains permanently at rest with reference toit. However, there exists, during
the period of application of the brakesa gravitational field which is directed forwards,
(19:14):
and which is variable with respect totime. Under the influence of this field,
the embankment, together with the Earth, moves non uniformly in such a
manner that their original velocity in thebackwards direction is continuously reduced. End of Section twenty
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, recorded by Laurie Ann Walden, Part
two, The General Theory of Relativity, Sections eighteen through twenty. Section eighteen
(00:29):
Special and General principle of relativity.The basal principle, which was the pivot
of all our previous considerations, wasthe special principle of relativity, i e.
The principle of the physical relativity ofall uniform motion. Let us once
more analyze its meaning carefully. Itwas at all times clear that, from
(00:51):
the point of view of the ideait conveys to us, every motion must
be considered only as a relative motion. Returning to the illustration we have frequently
used of the embankment and the railwaycarriage, we can express the fact of
the motion here taking place in thefollowing two forms, both of which are
equally justifiable. A. The carriageis in motion relative to the embankment.
(01:15):
B the embankment is in motion relativeto the carriage in A the embankment in
B the carriage serves as the bodyof reference in our statement of the motion
taking place. If it is simplya question of detecting or of describing the
motion involved, it is in principleimmaterial to what reference body we refer the
(01:36):
motion. As already mentioned, thisis self evident, but it must not
be confused with the much more comprehensivestatement called the principle of relativity, which
we have taken as the basis ofour investigations. The principle we have made
use of not only maintains that wemay equally well choose the carriage or the
embankment as our reference body for thedescription of any event, for this too
(02:00):
is self evident. Our principle ratherasserts what follows. If we formulate the
general laws of nature as they areobtained from experience by making use of a
the embankment as reference body, bthe railway carriage is reference body, then
these general laws of nature e g. The laws of mechanics or the law
(02:23):
of the propagation of light in vacuohave exactly the same form in both cases.
This can also be expressed as follows. For the physical description of natural
processes. Neither of the reference bodiesK K prime is unique literally specially marked
out as compared with the other.Unlike the first, this latter statement need
(02:46):
not of necessity hold a priori.It is not contained in the conceptions of
motion and reference body, and arrivablefrom them. Only experience can decide as
to its correctness or incorrectness. Upto the present, however, we have
by no means maintained the equivalents ofall bodies of reference K in connection with
(03:07):
the formulation of natural laws. Ourcourse was more on the following lines.
In the first place, we startedout from the assumption that there exists a
reference body K, whose condition ofmotion is such that the Galilean law holds
with respect to it. A particleleft to itself and sufficiently far removed from
all other particles, moves uniformly ina straight line with reference to K Galileyan
(03:31):
reference body. The laws of naturewere to be as simple as possible,
but in addition to K, allbodies of reference K prime should be given
preference in this sense, and theyshould be exactly equivalent to K for the
formulation of natural laws, provided thatthey are in a state of uniform,
rectilinear and non rotary motion with respectto K. All these bodies of reference
(03:55):
are to be regarded as Galilean referencebodies. The validity of the principle of
relativity was assumed only for these referencebodies, but not for others, e
g. Those possessing motion of adifferent kind. In this sense we speak
of the special principle of relativity orspecial theory of relativity. In contrast to
(04:18):
this, we wish to understand bythe general principle of relativity the following statement,
all bodies of reference K, K, Prime, et cetera. Are
equivalent for the description of natural phenomenaor formulation of the general laws of nature,
whatever may be their state of motion. But before proceeding farther, it
(04:40):
ought to be pointed out that thisformulation must be replaced later by a more
abstract one, for reasons which willbecome evident at a later stage. Since
the introduction of the special principle ofrelativity has been justified, every intellect which
strives after generalization must feel the temptationto venture the step towards the su general
(05:00):
principle of relativity. But a simpleand apparently quite reliable consideration seems to suggest
that for the present, at anyrate, there is little hope of success
in such an attempt. Let usimagine ourselves transferred to our old friend,
the railway carriage, which is travelingat a uniform rate. As long as
it is moving uniformly, the occupantof the carriage is not sensible of its
(05:24):
motion, and it is for thisreason that he can, without reluctance,
interpret the facts of the case asindicating that the carriage is at rest,
but the embankment in motion. Moreover, according to the special principle of relativity,
this interpretation is quite justified also froma physical point of view. If
the motion of the carriage is nowchanged into a non uniform motion, as
(05:47):
for instance, by a powerful applicationof the brakes, then the occupant of
the carriage experiences a correspondingly powerful jerkforwards. The retarded motion is manifested in
the mechanical behaveavior of bodies. Relativeto the person in the railway carriage.
The mechanical behavior is different from thatof the case previously considered, and for
(06:08):
this reason it would appear to beimpossible that the same mechanical laws hold relatively
to the non uniformly moving carriage ashold with reference to the carriage when at
rest or in uniform motion at allevents, it is clear that the Galilean
law does not hold with respect tothe non uniformly moving carriage. Because of
(06:29):
this, we feel compelled at thepresent juncture to grant a kind of absolute
physical reality to non uniform motion,in opposition to the general principle of relativity.
But in what follows we shall soonsee that this conclusion cannot be maintained
Section nineteen. The gravitational field.If we pick up a stone and then
(06:53):
let it go, why does itfall to the ground. The usual answer
to this question is because it isattracted by the Earth. Modern physics formulates
the answer rather differently, for thefollowing reason. As a result of the
more careful study of electromagnetic phenomena,we have come to regard action at a
distance as a process impossible without theintervention of some intermediary medium. If,
(07:18):
for instance, a magnet attracts apiece of iron, we cannot be content
to regard this as meaning that themagnet acts directly on the iron through the
intermediate empty space. But we areconstrained to imagine, after the manner of
Faraday, that the magnet always callsinto being something physically real in the space
around it, that something being whatwe call a magnetic field. In its
(07:43):
turn, this magnetic field operates onthe piece of iron, so that the
latter strives to move towards the magnet. We shall not discuss here the justification
for this incidental conception, which isindeed a somewhat arbitrary one. We shall
only mention that with its aid,electromagnetic phenomena can be theoretically represented much more
(08:03):
satisfactorily than without it, and thisapplies particularly to the transmission of electromagnetic waves.
The effects of gravitation also are regardedin an analogous manner. The action
of the Earth on the stone takesplace indirectly. The Earth produces in its
surroundings a gravitational field, which actson the stone and produces its motion of
(08:26):
fall. As we know from experience, the intensity of the action on a
body diminishes according to a quite definitelaw as we proceed farther and farther away
from the Earth from our point ofview. This means the law governing the
properties of the gravitational field in spacemust be a perfectly definite one in order
(08:48):
correctly to represent the diminution of gravitationalaction with the distance from operative bodies.
It is something like this. Thebody e g. The Earth produces a
field in its its immediate neighborhood directly. The intensity and direction of the field
at points farther removed from the bodyare thence determined by the law which governs
(09:09):
the properties in space of the gravitationalfields themselves. In contrast to electric and
magnetic fields, the gravitational field exhibitsa most remarkable property which is of fundamental
importance for what follows. Bodies whichare moving under the sole influence of a
gravitational field receive an acceleration which doesnot in the least depend either on the
(09:33):
material or on the physical state ofthe body. For instance, a piece
of lead and a piece of woodfall in exactly the same manner in a
gravitational field in vacuo when they startoff from rest or with the same initial
velocity. This law, which holdsmost accurately, can be expressed in a
different form in the light of thefollowing consideration. According to Newton's law of
(09:58):
motion, we have force equals inertialmass times acceleration, where the inertial mass
is a characteristic constant of the acceleratedbody. If now gravitation is the cause
of the acceleration, we then haveforce equals gravitational mass times intensity of the
(10:20):
gravitational field. Where the gravitational massis likewise a characteristic constant for the body.
From these two relations follows acceleration equalsthe fraction gravitational mass over inertial mass
times intensity of the gravitational field.If now, as we find from experience,
(10:43):
the acceleration is to be independent ofthe nature and the condition of the
body, and always the same fora given gravitational field, then the ratio
of the gravitational to the inertial massmust likewise be the same for all bodies.
By a suitable choice of units,we can thus make this ratio equal
to unity. We then have thefollowing law, The gravitational mass of a
(11:07):
body is equal to its inertial mass. It is true that this important law
had hitherto been recorded in mechanics,but it had not been interpreted. A
satisfactory interpretation can be obtained only ifwe recognize the following fact. The same
quality of a body manifests itself accordingto the circumstances as inertia or as weight
(11:31):
literally heaviness. In the following sectionwe shall show to what extent this is
actually the case, and how thisquestion is connected with the general postulate of
relativity. Section twenty the equality ofinertial and gravitational mass. As an argument
for the general postulate of relativity.We imagine a large portion of empty space,
(11:56):
so far removed from stars and otherappreciable masses, that we have before
us approximately the conditions required by thefundamental law of galilee. It is then
possible to choose a Galilean reference bodyfor this part of space world, relative
to which points at rest remain atrest and points in motion continue permanently in
(12:18):
uniform rectilinear motion. As reference body, Let us imagine a spacious chest resembling
a room with an observer inside whois equipped with apparatus. Gravitation naturally does
not exist for this observer. Hemust fasten himself with strings to the floor,
otherwise the slightest impact against the floorwill cause him to rise slowly toward
(12:39):
the ceiling of the room. Tothe middle of the lid of the chest
is fixed externally a hook with ropeattached. And now a being, what
kind of a being is immaterial tous begins pulling at this with a constant
force. The chest, together withthe observer, then begin to move upwards
with the uniformly accelerated motion. Incourse of time, their velocity will reach
(13:05):
unheard of values, provided that weare viewing all this from another reference body,
which is not being pulled with arope. But how does the man
in the chest regard the process.The acceleration of the chest will be transmitted
to him by the reaction of thefloor of the chest. He must therefore
take up this pressure by means ofhis legs, if he does not wish
to be laid out full length onthe floor. He is then standing in
(13:28):
the chest in exactly the same wayas any one stands in a room of
a house on our earth. Ifhe release a body which he previously had
in his hand, the acceleration ofthe chest will no longer be transmitted to
this body, and for this reasonthe body will approach the floor of the
chest with an accelerated relative motion.The observer will further convince himself that the
(13:52):
acceleration of the body towards the floorof the chest is always of the same
magnitude. Whatever kind of body hemay happen to use for the experiment,
relying on his knowledge of the gravitationalfield as it was discussed in the preceding
section. The man in the chestwill thus come to the conclusion that he
and the chest are in a gravitationalfield which is constant with regard to time.
(14:16):
Of course, he will be puzzledfor a moment as to why the
chest does not fall in this gravitationalfield. Just then, however, he
discovers the hook in the middle ofthe lid of the chest and the rope
which is attached to it, andhe consequently comes to the conclusion that the
chest is suspended at rest in thegravitational field. Ought we to smile at
(14:37):
the man and say that he errsin his conclusion. I do not believe
we ought to. If we wishto remain consistent, we must rather admit
that his mode of grasping the situationviolates neither reason nor known mechanical laws,
even though it is being accelerated withrespect to the Galilean space. First considered,
(14:58):
we can nevertheless regard the chess asbeing at rest. We have thus
good grounds for extending the principle ofrelativity to include bodies of reference which are
accelerated with respect to each other,and as a result we have gained a
powerful argument for a generalized postulate ofrelativity. We must note carefully that the
(15:18):
possibility of this mode of interpretation restson the fundamental property of the gravitational field
of giving all bodies the same accelerationor what comes to the same thing,
on the law of the equality ofinertial and gravitational mass. If this natural
law did not exist, the manin the accelerated chest would not be able
(15:41):
to interpret the behavior of the bodiesaround him on the supposition of a gravitational
field, and he would not bejustified on the grounds of experience in supposing
his reference body to be at rest. Suppose that the man in the chest
fixes a rope to the inner sideof the lid, and that he attaches
a body to the free end ofthe rope. The result of this will
(16:03):
be to stretch the rope so thatit will hang vertically downwards. If we
ask for an opinion of the causeof tension in the rope, the man
in the chest will say the suspendedbody experiences a downward force in the gravitational
field, and this is neutralized bythe tension of the rope. What determines
the magnitude of the tension of therope is the gravitational mass of the suspended
(16:26):
body. On the other hand,an observer who is poised freely in space
will interpret the condition of things.Thus, the rope must perforce take part
in the accelerated motion of the chest, and it transmits this motion to the
body attached to it. The tensionof the rope is just large enough to
effect the acceleration of the body.That which determines the magnitude of the tension
(16:51):
of the rope is the inertial massof the body. Guided by this example,
we see that our extension of theprinciple of relativity implies the necessity of
the law of the equality of inertialand gravitational mass. Thus we have obtained
a physical interpretation of this law.From our consideration of the accelerated chest,
(17:14):
we see that a general theory ofrelativity must yield important results on the laws
of gravitation. In point of fact, the systematic pursuit of the general idea
of relativity has supplied the laws satisfiedby the gravitational field. Before proceeding farther.
However, I must warn the readeragainst a misconception suggested by these considerations.
(17:37):
A gravitational field exists for the manin the chest, despite the fact
that there was no such field forthe co ordinate system first chosen. Now
we might easily suppose that the existenceof a gravitational field is always only an
apparent one. We might also thinkthat, regardless of the kind of gravitational
field which may be present, wecould always choose another reference body such that
(18:03):
no gravitational field exists with reference toit. This is by no means true
for all gravitational fields, but onlyfor those of quite special form. It
is, for instance, impossible tochoose a body of reference such that,
as judged from it, the gravitationalfield of the Earth in its entirety vanishes.
(18:25):
We can now appreciate why that argumentis not convincing, which we brought
forward against the general principle of relativityat the end of section eighteen. It
is certainly true that the observer inthe railway carriage experiences a jerk forwards as
a result of the application of thebreak, and that he recognizes in this
the non uniformity of motion or retardationof the carriage. But he is compelled
(18:51):
by nobody to refer this jerk toa real acceleration or retardation of the carriage.
He might also interpret his experience thusmy body of reference. The carriage
remains permanently at rest with reference toit. However, there exists, during
the period of application of the brakesa gravitational field which is directed forwards,
(19:14):
and which is variable with respect totime. Under the influence of this field,
the embankment, together with the Earth, moves non uniformly in such a
manner that their original velocity in thebackwards direction is continuously reduced. End of Section twenty
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