WEBVTT

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Section seven. The apparent incompatibility of
the law of propagation of light with the

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principle of relativity. There is hardly
a simpler law in physics than that according

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to which light is propagated in empty
space. Every child a school knows or

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believes he knows that this propagation takes
place in straight lines with a velocity c

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equals three hundred thousand kilometers per second
at all events. We know with great

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exactness that this velocity is the same
for all colors, because if this were

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not the case, the minimum of
emission would not be observed simultaneously for different

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colors during the eclipse of a fixed
star by its dark neighbor. By means

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of similar considerations based on observations of
double stars, the Dutch astronomer to Zetter

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was also able to show that the
velocity of propagation of light cannot depend on

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the velocity of motion of the body
emitting the light. The assumption that this

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velocity of propagation is dependent on the
direction in space is in itself improbable.

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In short, let us assume that
the simple law of the constancy of the

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velocity of light see in vacuum is
justifiably believed by the child at school,

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who would imagine that this simple law
has plunged the conscientiously thoughtful physicist into the

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greatest intellectual difficulties. Let us consider
how these difficulties arise. Of course,

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we must refer the process of the
propagation of light, and indeed every other

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process, to a rigid reference body
coordinate system. As such a system,

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let us again choose our embankment.
We shall imagine the air above it to

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have been removed if a ray of
light be sent along the embankment. We

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see from the above that the tip
of the ray will be transmitted with the

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velocity C relative to the embankment.
Now, let us suppose that our railway

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carriage is again traveling along the railway
lines with the velocity V, and that

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its direction is the same as that
of the ray of light, but its

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velocity, of course much less.
Let us inquire about the velocity of propagation

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of the ray of light relative to
the carriage. It is obvious that we

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can here apply the consideration of the
previous section. Since the ray of light

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plays the part of the man walking
along relatively to the carriage, the velocity

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capital W of the man relative to
the embankment is here replaced by the velocity

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of light relative to the embankment.
W is the required velocity of light with

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respect to the carriage, and we
have W equals c fee. The velocity

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of propagation of a ray of light
relative to the carriage thus comes out smaller

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than C. But this result comes
into conflict with the principle of relativity set

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forth in section five. For,
like every other general law of nature,

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the law of the transmission of light
in vacuo must, according to the principle

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of relativity, be the same for
the railway carriage as reference body as when

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the rails are the body of reference. But from our above consideration, this

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would appear to be impossible. If
every ray of light is propagated relative to

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the embankment with the velocity C,
then for this reason it would appear that

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another law of propagation of light must
necessarily hold with respect to the carriage,

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a result contradictory to the principle of
relativity. In view of this dilemma,

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there appears to be nothing else for
it than to abandon either the principle of

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relativity or the simple law of the
propagation of light invacuo. Those of you

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who have carefully followed the preceding discussion
are almost sure to expect that we should

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retain the principle of relativity, which
appeals so convincingly to the intellect because it

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is so natural and simple. The
law of the propagation of light invacuo would

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then have to be replaced by a
more complicated law conformable to the principle of

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relativity. The development of theoretical physics
shows, however, that we cannot pursue

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this course. The epoch making theoretical
investigations of H. A. Lorentz on

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the electrodynamical and optical phenomena connected with
moving bodies show that experience in this domain

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leads conclusively to a theory of electromagnetic
phenomena, of which the law of the

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constancy of the velocity of light in
vacuo is a necessary consequence. Prominent theoretical

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physicists were therefore more inclined to reject
the principle of relativity, in spite of

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the fact that no empirical data had
been found which were contradictory to this principle.

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At this juncture, the theory of
relativity entered the arena. As a

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result of an analysis of the physical
conceptions of time and space, it became

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evident that in reality there is not
the least incompatibility between the principle of relativity

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and the law of propagation of light, and that by systematically holding fast to

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both these laws, a logically rigid
theory could be arrived at. This theory

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has been called the special theory of
relativity, to distinguish it from the extended

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theory with which we shall deal later. In the following pages. We shall

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present the fundamental ideas of the special
theory of relativity. End of section seven.

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Section eight on the idea of time
in physics. Lightning has struck the

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rails on our railway embankment at two
places A and B, far distant from

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each other. I make the additional
assertion that these two lightning flashes occurred simultaneously.

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If I ask you whether there is
sense in this statement, you will

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answer my question with a decided yes. But if I now approach you with

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the request to explain to me the
sense of the statement more precisely, you

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find, after some consideration that the
answer to this question is not so easy

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as it appears at first sight.
After some time, perhaps the following answer

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would occur to you. The significance
of the statement is clear in itself and

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needs no further explanation. Of course, it would require some consideration if I

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were to be commissioned to determine by
observations whether, in the actual case the

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two events took place simultaneously or not. I cannot be satisfied with this answer

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for the following reason. Supposing that, as a result of ingenious considerations,

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an able meteorologist were to discover that
the lightning must always strike the places A

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and B simultaneously, then we should
be faced with the task of testing whether

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or not this theoretical result is in
accordance with the ready We encounter the same

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difficulty with all physical statements in which
the conception simultaneous plays apart. The concept

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does not exist for the physicist until
he has the possibility of discovering whether or

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not it is fulfilled in an actual
case. We thus require a definition of

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simultaneity such that this definition supplies us
with the method by means of which,

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in the present case he can decide
by experiment whether or not both the lightning

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strokes occurred simultaneously. As long as
this requirement is not satisfied, I allow

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myself to be deceived as a physicist, and of course the same applies if

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I am not a physicist. When
I imagine that I am able to attach

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a meaning to the statement of simultaneity, I would ask the reader not to

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proceed farther until he is fully convinced
on this point. After thinking the matter

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over for some time, you then
offer the following suggestion with which to test

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simultaneity by measuring along the rails.
The connecting line AB should be measured up

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and an observer placed at the midpoint
M of the distance AB. This observer

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should be supplied with an arrangement e
g. Two mirrors inclined at ninety degrees,

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which allows him visually to observe both
places A and B at the same

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time. If the observer perceives the
two flashes of lightning at the same time,

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then they are simultaneous. I am
very pleased with the suggestion, but

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for all that I cannot regard the
matter as quite settled because I feel constrained

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to raise the following objection. Your
definition would certainly be right if only I

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knew that the light by means of
which the observer at M perceives the lightning

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flashes travels along the length A to
M with the same velocity as along the

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length B to M. But an
examination of this supposition would only be possible

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if we already had at our disposal
the means of measuring time. It would

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thus appear as though we were moving
here in a logical circle. After further

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consideration, you cast a somewhat disdainful
glance at me, and rightly so,

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and you declare, I maintain my
previous definition. Nevertheless, because in reality

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it assumes absolutely nothing about light,
there is only one demand to be made

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of the definition of simultaneity, namely
that in every real case, it must

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supply us with an empirical decision as
to whether or not the conception that has

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to be defined is fulfilled. That
my definition satisfies this demand is indisputable.

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The light requires the same time to
traverse the path A to M as for

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the path B to M. Is, in reality, neither a supposition nor

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a hypothesis about the physical nature of
light, but a stipulation which I can

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make of my own free will in
order to arrive at a definition of simultaneity.

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It is clear that this definition can
be used to give an exact meaning

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not only to two events, but
to as many events as we care to

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choose, and independently of the positions
of the scenes of the events with respect

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to the body of reference here the
railway embankment footnote. We suppose further that

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when three events A, B,
and C occur in different places in such

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a manner that A is simultaneous with
B, and B is simultaneous with C

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simultaneous in the sense of the above
definition, then the criterion for the simultaneity

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of the pair of events A C
is also satisfied. This assumption is a

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physical hypothesis about the propagation of light. It must certainly be fulfilled if we

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are to maintain the law of the
constancy of the velocity of light in vacuo

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end a footnote. We are thus
led also to a definition of time in

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physics. For this purpose, we
suppose that clocks of identical construction are placed

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at the points A, B,
and C of the railway line coordinate system,

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and that they are set in such
a manner that the positions of their

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pointers are simultaneously in the sense the
same. Under these conditions, we understand

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by the time of an event the
reading position of the hands of that one

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of these clocks which is in the
immediate vicinity in space of the event.

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In this manner, a time value
is associated with every event which is essentially

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capable of observation. This stipulation contains
a further physical hypothesis, the validity of

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which will hardly be doubted without empirical
evidence. To the contrary, it has

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been assumed that all these clocks go
at the same rate if they are of

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identical construction. Stated more exactly,
when two clocks arranged at rest in different

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places of a reference body are set
in such a manner that a particular position

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of the pointers of the one clock
is simultaneous in the above sense with the

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same position of the pointers of the
other clock, then identical settings are always

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simultaneous in the sense of the above
definition. End of Section eight. Section

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nine the relativity of simultaneity. Up
to now our considerations have been referred to

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a particular body of reference, which
we have styled a railway embankment. We

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suppose a very long train traveling along
the rails with the constant velocity V and

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in the direction indicated in Figure one. People traveling in this train will with

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advantage view the train as a rigid
reference body coordinate system. They regard all

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events in reference to the train,
Then every event which takes place along the

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line also takes place at a particular
point of the train. Also, the

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definition of simultaneity can be given relative
to the train in exactly the same way

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as with respect to the embankment.
As a natural consequence, however, the

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following question arises. Are two events
e g. The two strokes of lightning

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A and B, which are simultaneous
with reference to the railway embankment, also

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simultaneous relatively to the train. We
shall show directly that the answer must be

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in the negative. When we say
that the lightning strokes A and B are

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simultaneous with respect to the embankment,
we mean the rays of light emitted at

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the places A and B where the
lightning occurs meet each other at the midpoint

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M of the length A to B
of the embankment. But the events A

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and B also correspond to positions A
and B on the train. Let M

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prime be the midpoint of the distance
A to B on the traveling train.

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Just when the flashes as judged from
the embankment of lightning occur. This point

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M prime naturally coincides with the point
M, but it moves toward the right

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in the diagram with the velocity V
of the train. If an observer sitting

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at the position M prime in the
train did not possess this velocity, then

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he would remain permanently at M,
and the light rays emitted by the flashes

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of lightning A and B would reach
him simultaneously, i e. They would

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meet just where he is situated now. In reality, considered with reference to

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the railway embankment, he is hastening
towards the beam of light coming from B,

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whilst he is riding on ahead of
the beam of light coming from A.

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Hence, the observer will see the
beam of light emitted from B earlier

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than he will see that emitted from
A. Observers who take the railway train

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as the reference body must therefore come
to the conclusion that the lightning flash B

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took place earlier than the lightning flash
A. We thus arrive at an important

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result. Events which are simultaneous with
reference to the embankment are not simultaneous with

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respect to the train, and vice
versa. Relativity of simultaneity every reference body

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coordinate system has its own particular time. Unless we are told the reference body

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to which the statement of time refers, there is no meaning in a statement

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of the time of an event.
Now, before the advent of the theory

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of relativity, it had always tacitly
been assumed in physics that the statement of

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time had an absolute significance, ie
that it is independent of the state of

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motion of the body of reference.
But we have just seen that this assumption

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is incompatible with the most natural definition
of simultaneity. If we've discard this assumption,

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then the conflict between the law of
the propagation of light invacuo and the

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principle of relativity developed in section seven
disappears. We were led to that conflict

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by the considerations of section six,
which are now no longer tenable. In

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that section, we concluded that the
man in the carriage who traverses the distance

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w per second relative to the carriage, traverses the same distance also with respect

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to the embankment in each second of
time. But according to the foregoing considerations,

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the time required by a particular occurrence
with respect to the carriage must not

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be considered equal to the duration of
the same occurrence as judged from the embankment

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as reference body. Hence, it
cannot be contended that the man in walking

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travels the distance W relative to the
railway line in a time which is equal

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to one second as judged from the
embankment. Moreover, the considerations of Section

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six are based on yet a second
assumption, which, in the light of

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a strict consideration appears to be arbitrary, although it was always pacitly made even

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before the introduction of the theory of
relativity. End of Section nine