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This is a LibriVox recording. AllLibriVox recordings are in the public domain.
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Peter Eastman, July thirty, twothousand six. Relativity the Special and General
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Theory by Albert Einstein, Continuing partone, section seven. The apparent incompatibility
of the law of propagation of lightwith the principle of relativity. There is
hardly a simpler law in physics thanthat according to which light is propagated in
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empty space. Every child at schoolknows or believes he knows that this propagation
takes place in straight lines with thevelocity C equals three hundred thousand kilometers per
second at all events. We knowwith great exactness that this velocity is the
same for all colors, because ifthis were not the case, the minimum
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of emission would not be observed simultaneouslyfor different colors during the eclipse of a
fixed star by its dark neighbor.By means of similar considerations based on observations
of double stars, the Dutch astronomerDeserter was also able to show that the
velocity of propagation of light cannot dependon the velocity of motion of the body
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emitting the light. The assumption thatthis velocity of propagation is dependent on the
direction in space is in itself improbable. In short, let us assume that
the simple law of the constancy ofthe velocity of light see in vacuum is
justifiably believed by the child at school, who would imagine that this simple law
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has plunged the kind, conscientiously thoughtfulphysicist into the greatest intellectual difficulties. Let
us consider how these difficulties arise.Of course, we must refer the process
of the propagation of light, andindeed every other process, to a rigid
reference body coordinate system. As sucha system, let us again choose our
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embankment. We shall imagine the airabove it to have been removed. If
a ray of light be sent alongthe embankment. We see from the above
that the tip of the ray willbe transmitted with the velocity C relative to
the embankment. Now, let ussuppose that our railway carriage is again traveling
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along the railway lines with the velocityV, and that its direction is the
same as that of the ray oflight, but its velocity of course much
less. Let us inquire about thevelocity of propagation of the ray of light
relative to the carriage. It isobvious that we can here apply the consideration
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of the previous section. Since theray of light plays the part of the
man walking along relatively to the carriage. The velocity capital W of the man
relative to the embankment is here replacedby the velocity of light relative to the
embankment. W is the required velocityof light with respect to the carriage,
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and we have W equals C minusV. The velocity of propagation of a
ray of light relative to the carriagethus comes out smaller than C. But
this result comes into conflict with theprinciple of relativity set forth in section five.
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For like every other general law ofnature, the law of the transmission
of light in vacuo must, accordingto the principle of right relativity, be
the same for the railway carriage asreference body as when the rails are the
body of reference. But from ourabove consideration this would appear to be impossible.
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If every ray of light is propagatedrelative to the embankment with the velocity
C, then for this reason itwould appear that another law of propagation of
light must necessarily hold with respect tothe carriage, a result contradictory to the
principle of relativity. In view ofthis dilemma, there appears to be nothing
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else for it than to abandon eitherthe principle of relativity or the simple law
of the propagation of light in vacuo. Those of you who have carefully followed
the preceding discussion are almost sure toexpect that we should retain the principle of
relativity, which appeals so convincingly tothe intellect because it is so natural and
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simple. The law of the propagationof light in vacuo would then have to
be replaced by a more complicated lawconformable to the principle of relativity. The
development of theoretical physics shows, however, that we cannot pursue this course.
The epoch making theoretical investigations of H. A. Lorentz on the electrodynamical and
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optical phenomena connected with moving bodies showthat experience in this domain leads conclusively to
a theory of electromagnetic phenomena, ofwhich the law of the constancy of the
velocity of light in vacuo is anecessary consequence. Prominent theoretical physicists were therefore
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more inclined to reject the principle ofrelativity, in spite of the fact that
no empirical data had been found whichwere contradictory to this principle. At this
juncture, the theory of relativity enteredthe arena. As a result of an
analysis of the physical conceptions of timeand space. It became evident that in
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reality there is not the least incompatibilitybetween the principle of relativity and the law
of propagation of light, and thatby systematically holding fast to both these laws,
a logically rigid theory could be arrivedat This theory has been called the
special theory of relativity, to distinguishit from the extended theory with which we
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shall deal later. In the followingpages, we shall present the fundamental ideas
of the special theory of relativity.End of section seven. Section eight on
the idea of time in physics.Lightning has struck the rails on our railway
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and bank at two places A andB far distant from each other. I
make the additional assertion that these twolightning flashes occurred simultaneously. If I ask
you whether there is sense in thisstatement, you will answer my question with
a decided yes. But if Inow approach you with the request to explain
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to me the sense of the statementmore precisely, you find after some consideration
that the answer to this question isnot so easy as it appears at first
sight. After some time, perhapsthe following answer would occur to you.
The significance of the statement is clearin itself and needs no further explanation.
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Of course, it would require someconsideration if I were to be commissioned to
determine my observations whether, in theactual case the two events to play simultaneously
or not. I cannot be satisfiedwith this answer for the following reason.
Supposing that, as a result ofingenious considerations, an able meteorologist or to
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discover that the lightning must always strikethe places A and B simultaneously, then
we should be faced with the taskof testing whether or not this theoretical result
is in accordance with the reality.We encounter the same difficulty with all physical
statements in which the conception simultaneous playsa part. The concept does not exist
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for the physicist until he has thepossibility of discovering whether or not it is
fulfilled in an actual case. Wethus require a definition of simultaneity such that
this definition supplies us with the methodby means of which, in the present
case he can decide by experiment whetheror not both the lightning strokes occurred simultaneously.
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As long as this requirement is notsatisfied, I allow myself to be
deceived as a physicist, And ofcourse the same applies if I am not
a physicist. When I imagine thatI am able to attach a meaning to
the statement of simultaneity, I wouldask the reader not to proceed farther until
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he is fully convinced on this point. After thinking the matter over for some
time, you then offer the followingsuggestion with which to test simultaneity by measuring
along the rails. The connecting lineAB should be measured up and an observer
placed at the midpoint M of thedistance AB. This observer should be supplied
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with an arrangement e g. Twomirrors inclined at ninety degree, which allows
him visually to observe both places Aand B at the same time. If
the observer perceives the two flashes oflightning at the same time, then they
are simultaneous. I am very pleasedwith the suggestion, but for all that,
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I cannot regard the matter as quitesettled, because I feel constrained to
raise the following objection. Your definitionwould certainly be right if only I knew
that the light, by means ofwhich the observer at M perceives the lightning
flashes, travels along the length Ato M with the same velocity as along
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the length B to M. Butan examination of this supposition would only be
possible if we already had at ourdisposal the means of measuring time. It
would thus appear as though we weremoving here in a logical circle. After
further concent iteration, you cast asomewhat disdainful glance at me, and rightly
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so, and you declare, Imaintain my previous definition. Nevertheless, because
in reality it assumes absolutely nothing aboutlight, there is only one demand to
be made of the definition of simultaneity, namely that in every real case,
it must supply us with an empiricaldecision as to whether or not the conception
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that has to be defined is fulfilled. That my definition satisfies this demand is
indisputable that light requires the same timeto traverse the path A to M as
for the path B T M.Is in reality, neither a supposition nor
a hypothesis about the physical nature oflight, but a stipulation which I can
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make of my own free will inorder to arrive at a definition of simultaneity.
It is clear that this definition canbe used to give an exact meaning
not only to two events, butto as many events as we care to
choose, and independently of the positionsof the scenes of the events with respect
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to the body of reference here therailway embankment footnote. We suppose further that
when three events A, B,and C occur in different places in such
a manner that A is simultaneous withB, and B is simultaneous with C
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simultaneous in the sense of the abovedefinition, then the criterion for the simultaneity
of the pair of events A Cis also satisfied. This assumption is a
physical hypothesis about the propagation of light. It must certainly be fulfilled if we
are to maintain the law of theconstantcy of the velocity of light. In
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vacuo end a footnote. We arethus led also to a definition of time
in physics. For this purpose,we suppose that clocks of identical construction are
placed at the points A, B, and C of the railway line coordinate
system, and that they are setin such a manner that the positions of
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their pointers are simultaneously in the abovesense the same. Under these conditions,
we understand by the time of anevent the reading position of the hands of
that one of these clocks which isin the immediate vicinity in space of the
event. In this manner, atime value is associated with every event which
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is essentially capable of observation. Thisstipulation contains a further physical hypothesis, the
validity of which will hardly be doubtedwithout empirical evidence. To the contrary,
it has been assumed that all theseclocks go at the same rate if they
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are of identical construction. Stated moreexactly, when two clocks arranged at rest
in different places of a reference bodyare set in such a manner that a
particular position of the pointers of theone clock is simultaneous in the above sense
with the same position of the pointersof the other clock, then identical settings
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are always simultaneous in the sense ofthe above definition end of Section eight.
Section nine the relativity of simultaneity.Up to now our considerations have been referred
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to a particular Miller body of reference, which we have styled a railway embankment.
We suppose a very long train travelingalong the rails with the constant velocity
V and in the direction indicated inFig. One. People traveling in this
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train will, with advantage view thetrain as a rigid reference body coordinate system.
They regard all events in reference tothe train. Then every event which
takes place along the line also takesplace at a particular point of the train.
Also, the definition of simultaneity canbe given relative to the train in
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exactly the same way as with respectto the embankment. As a natural consequence,
however, the following question arises rtwo events e g. The two
strokes of lightning A and B,which are simultaneous with reference to the railway
embankment also simultaneous relatively to the train. We shall show directly that the answer
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must be in the negative. Whenwe say that the lightning strokes A and
B are simultaneous with respect to theembankment, we mean the rays of light
emitted at the places A and Bwhere the lightning occurs meet each other at
the midpoint M of the length Ato B of the embankment. But the
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events A and B also correspond topositions A and B on the train.
Let M prime be the midpoint ofthe distance A to B on the traveling
train just when the flashes, asjudged from the embankment of lightning occur.
This point M prime naturally coincides withthe point M, but it moves toward
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the right ear the diagram with thevelocity V of the train. If an
observer sitting at the position M primein the train did not possess this velocity,
then he would remain permanently at Mand the light rays emitted by the
flashes of lightning A and B wouldreach him simultaneously i e. They would
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meet just where he is situated now. In reality, considered with reference to
the railway embankment, he is hasteningtowards the beam of light coming from B
whilst he is riding on ahead ofthe beam of light coming from A.
Hence, the observer will see thebeam of light emitted from B earlier than
he will see that emitted from A. Observers who take the railway train as
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their reference body must therefore come tothe conclusion that the lightning flash B took
place earlier than the lightning flash A. We thus arrive at an important result.
Events which are simultaneous with reference tothe embankment are not simultaneous with respect
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to the train, and vice versa. Relativity of simultaneity. Every reference body
coordinate system has its own particular time. Unless we are told the reference body
to which the statement of time refers, there is no meaning in a statement
of the time of an event.Now, before the advent of the theory
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of relativity, it had always tacitlybeen assumed in physics that the statement of
time had an absolute significance, ie. That it is independent of the
state of motion of the body ofreference. But we have just seen that
this assumption is incompatible with the mostnatural definition of simultaneity. If we discard
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this assumption, then the conflict betweenthe law of the propagation of light in
vacuo and the principle of relativity developedin section seven disappears. We were led
to that conflict by the considerations ofSection six, which are now no longer
tenable. In that section we concludedthat the man in the carriage who traverses
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the distance W per second relative tothe carriage, traverses the same distance also
with respect to the embankment in eachsecond of time. But according to the
foregoing considerations, the time required bya particular occurrence with respect to the carriage
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must not be considered equal to theduration of the same occurrence as judged from
the embankment as reference body. Hence, it cannot be contended that the man
in walking travels the distance W relativeto the railway law in a time which
is equal to one second as judgedfrom the embankment. Moreover, the considerations
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of Section six are based on yeta second assumption, which, in the
light of a strict consideration, appearsto be arbitrary, although it was always
tacitly made even before the introduction ofthe theory of relativity. End of Section nine