07. The Apparent Incompatability of the Law of Propagation of Light with the Principle of Relativity08. On the Idea of Time in Physics09. Th

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Episode Transcript

Speaker 1 (00:01):
This is a LibriVox recording. All LibriVox recordings are in
the public domain. For more information or to volunteer, please
visit LibriVox dot org. Recording by Peter Eastman, July thirty,
two thousand six. Relativity the Special and General Theory by

(00:24):
Albert Einstein, Continuing part one, section seven. The apparent incompatibility
of the law of propagation of light with the principle
of relativity. There is hardly a simpler law in physics
than that according to which light is propagated in empty space.

(00:48):
Every child at school knows or believes he knows that
this propagation takes place in straight lines with the velocity
C equals three hundred thousand kilometers per second at all events.
We know with great exactness that this velocity is the
same for all colors, because if this were not the case,

(01:09):
the minimum of emission would not be observed simultaneously for
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 astronomer Deserter was also
able to show that the velocity of propagation of light

(01:29):
cannot depend on the velocity of motion of the body
emitting the light. The assumption that this 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 of the velocity of light see in vacuum

(01:52):
is justifiably believed by the child at school, who would
imagine that this simple law has plunged the kind, conscientiously
thoughtful physicist into the greatest intellectual difficulties. Let us consider
how these difficulties arise. Of course, we must refer the
process of the propagation of light, and indeed every other process,

(02:17):
to a rigid reference body coordinate system. As such a system,
let us again choose our embankment. We shall imagine the
air above it to have been removed. If a ray
of light be sent along the embankment. We see from
the above that the tip of the ray will be
transmitted with the velocity C relative to the embankment. Now,

(02:42):
let us suppose that our railway carriage is again traveling
along the railway lines with the velocity V, and that
its direction is the same as that of the ray
of light, but its velocity of course much less. Let
us inquire about the velocity of propagation of the ray
of light relative to the carriage. It is obvious that

(03:05):
we can here apply the consideration of the previous section.
Since the ray 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
replaced by the velocity of light relative to the embankment.
W is the required velocity of light with respect to

(03:28):
the carriage, and we have W equals C minus V.
The velocity of propagation of a ray of light relative
to the carriage thus comes out smaller than C. But
this result comes into conflict with the principle of relativity

(03:49):
set forth in section five. For like every other general
law of nature, the law of the transmission of light
in vacuo must, according to the principle of right relativity,
be the same for the railway carriage as reference body
as when the rails are the body of reference. But
from our above consideration this would appear to be impossible.

(04:13):
If every ray of light is propagated relative to the
embankment with the velocity C, then for this reason it
would appear that another law of propagation of light must
necessarily hold with respect to the carriage, a result contradictory
to the principle of relativity. In view of this dilemma,

(04:35):
there appears to be nothing else for it than to
abandon either the 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
to expect that we should retain the principle of relativity,
which appeals so convincingly to the intellect because it is

(04:58):
so natural and simple. The law of the propagation of
light in vacuo would then have to be replaced by
a more complicated law conformable 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.

(05:22):
Lorentz on the electrodynamical and optical phenomena connected with moving
bodies show that experience in this domain leads conclusively to
a theory of electromagnetic phenomena, of which the law of
the constancy of the velocity of light in vacuo is
a necessary consequence. Prominent theoretical physicists were therefore more inclined

(05:45):
to reject the principle of relativity, in spite of the
fact that no empirical data had been found which were
contradictory to this principle. At this juncture, the theory of
relativity entered the arena. As a result of an analysis
of the physical conceptions of time and space. It became

(06:08):
evident that in reality there is not the least incompatibility
between the principle of relativity and the law of propagation
of light, and that by systematically holding fast to both
these laws, a logically rigid theory could be arrived at
This theory has been called the special theory of relativity,

(06:30):
to distinguish it from the extended theory with which we
shall deal later. In the following pages, we shall present
the fundamental ideas of the special theory of relativity. End
of section seven. Section eight on the idea of time

(06:53):
in physics. Lightning has struck the rails on our railway
and bank at two places A and B far distant
from each other. I make the additional assertion that these
two lightning flashes occurred simultaneously. If I ask you whether

(07:15):
there is sense in this statement, you will answer my
question with a decided yes. But if I now approach
you with the request to explain to me the sense
of the statement more precisely, you find after some consideration
that the answer to this question is not so easy
as it appears at first sight. After some time, perhaps

(07:40):
the following answer would occur to you. The significance of
the statement is clear in itself and needs no further explanation.
Of course, it would require some consideration if I were
to be commissioned to determine my observations whether, in the
actual case the two events to play simultaneously or not.

(08:03):
I cannot be satisfied with this answer for the following reason.
Supposing that, as a result of ingenious considerations, an able
meteorologist or to discover that the lightning must always strike
the places A and B simultaneously, then we should be
faced with the task of testing whether or not this

(08:26):
theoretical result is in accordance with the reality. We encounter
the same difficulty with all physical statements in which the
conception simultaneous plays a part. The concept does not exist
for the physicist until he has the possibility of discovering
whether or not it is fulfilled in an actual case.

(08:51):
We thus require a definition of simultaneity such that this
definition supplies us with the method by means of which,
in the present case he can decide by experiment whether
or not both the lightning strokes occurred simultaneously. As long
as this requirement is not satisfied, I allow myself to

(09:12):
be deceived as a physicist, And of course the same
applies if I am not a physicist. When I imagine
that I am able to attach a meaning to the
statement of simultaneity, I would ask the reader not to
proceed farther until he is fully convinced on this point.

(09:34):
After thinking the matter over for some time, you then
offer the following suggestion with which to test simultaneity by
measuring along the rails. The connecting line AB should be
measured up and an observer placed at the midpoint M
of the distance AB. This observer should be supplied with

(09:56):
an arrangement e g. Two mirrors inclined at ninety degree,
which allows him visually to observe both places A and
B at the same time. If the observer perceives the
two flashes of lightning at the same time, then they
are simultaneous. I am very pleased with the suggestion, but

(10:18):
for all that, I cannot regard the matter as quite settled,
because I feel constrained to raise the following objection. Your
definition would certainly be right if only I knew that
the light, by means of which the observer at M
perceives the lightning flashes, travels along the length A to

(10:38):
M with the same velocity as along the length B
to M. But an examination of this supposition would only
be possible if we already had at our disposal the
means of measuring time. It would thus appear as though
we were moving here in a logical circle. After further

(10:59):
concent iteration, you cast a somewhat disdainful glance at me,
and rightly so, and you declare, I maintain my previous definition. Nevertheless,
because in reality it assumes absolutely nothing about light, there
is only one demand to be made of the definition

(11:21):
of simultaneity, namely that in every real case, it must
supply us with an empirical decision as to whether or
not the conception that has to be defined is fulfilled.
That my definition satisfies this demand is indisputable that light
requires the same time to traverse the path A to

(11:43):
M as for the path B T M. Is in reality,
neither a supposition nor a hypothesis about the physical nature
of light, but a stipulation which I can make of
my own free will in order to arrive at a
definition of simultaneity. It is clear that this definition can

(12:07):
be used to give an exact meaning not only to
two events, but to as many events as we care
to choose, and independently of the positions of the scenes
of the events with respect to the body of reference
here the railway embankment footnote. We suppose further that when

(12:27):
three events A, B, and C occur in different places
in such a manner that A is simultaneous with B,
and B is simultaneous with C simultaneous in the sense
of the above definition, then the criterion for the simultaneity
of the pair of events A C is also satisfied.

(12:50):
This assumption is a physical hypothesis about the propagation of light.
It must certainly be fulfilled if we are to maintain
the law of the constantcy of the velocity of light.
In vacuo end a footnote. We are thus led also
to a definition of time in physics. For this purpose,

(13:13):
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 set in such a
manner that the positions of their pointers are simultaneously in
the above sense the same. Under these conditions, we understand

(13:34):
by the time of an event the reading position of
the hands of that one of these clocks which is
in the immediate vicinity in space of the event. In
this manner, a time value is associated with every event
which is essentially capable of observation. This stipulation contains a

(13:59):
further physical hypothesis, the validity of which will hardly be
doubted without empirical evidence. To the contrary, it has been
assumed that all these clocks go at the same rate
if they are of identical construction. Stated more exactly, when

(14:19):
two clocks arranged at rest in different places of a
reference body are set in such a manner that a
particular position of the pointers of the one clock is
simultaneous in the above sense with the same position of
the pointers of the other clock, then identical settings are
always simultaneous in the sense of the above definition end

(14:45):
of Section eight. Section nine the relativity of simultaneity. Up
to now our considerations have been referred to a particular
Miller body of reference, which we have styled a railway embankment.

(15:05):
We suppose a very long train traveling along the rails
with the constant velocity V and in the direction indicated
in Fig. One. People traveling in this train will, with
advantage view the train as a rigid reference body coordinate system.

(15:26):
They regard all events in reference to the train. Then
every event which takes place along the line also takes
place at a particular point of the train. Also, the
definition of simultaneity can be given relative to the train
in exactly the same way as with respect to the embankment.

(15:49):
As a natural consequence, however, the following question arises r
two 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 must be in the negative. When

(16:14):
we say that the lightning strokes A and B are
simultaneous with respect to the embankment, we mean the rays
of light emitted at the places A and B where
the lightning occurs meet each other at the midpoint M
of the length A to B of the embankment. But

(16:34):
the events A and B also correspond to positions A
and B on the train. Let M prime be the
midpoint of the distance A to B on the traveling
train just when the flashes, as judged from the embankment
of lightning occur. This point M prime naturally coincides with

(16:56):
the point M, but it moves toward the right ear
the diagram with the velocity V of the train. If
an observer sitting at the position M prime in the
train did not possess this velocity, then he would remain
permanently at M and the light rays emitted by the
flashes of lightning A and B would reach him simultaneously

(17:20):
i e. They would meet just where he is situated now.
In reality, considered with reference to the railway embankment, he
is hastening towards the beam of light coming from B
whilst he is riding on ahead of the beam of
light coming from A. Hence, the observer will see the
beam of light emitted from B earlier than he will

(17:42):
see that emitted from A. Observers who take the railway
train as their reference body must therefore come to the
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 to the embankment are

(18:05):
not simultaneous with respect 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,

(18:31):
before the advent of the theory of relativity, it had
always tacitly been assumed in physics that the statement of
time had an absolute significance, i e. That it is
independent of the state of motion of the body of reference.
But we have just seen that this assumption is incompatible

(18:53):
with the most natural definition of simultaneity. If we discard
this assumption, then the conflict between the law of the
propagation of light in vacuo and the principle of relativity
developed in section seven disappears. We were led to that
conflict by the considerations of Section six, which are now

(19:17):
no longer tenable. In that section we concluded that the
man in the carriage who traverses the distance W per
second relative to the carriage, traverses the same distance also
with respect to the embankment in each second of time.
But according to the foregoing considerations, the time required by

(19:41):
a particular occurrence with respect to the carriage must not
be considered equal to the duration 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 relative to the railway law in a time

(20:01):
which is equal to one second as judged from the embankment. Moreover,
the considerations of Section six are based on yet a
second assumption, which, in the light of a strict consideration,
appears to be arbitrary, although it was always tacitly made
even before the introduction of the theory of relativity. End

(20:28):
of Section nine