Relativity - Part 04-06 Einstein

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This is a LibriVox recording. AllLibriVox recordings are in the public domain.
For more information or to volunteer,please visit LibriVox dot org. Recording by
Linda Leo. Relativity the Special andGeneral Theory by Albert Einstein, continuing Part

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one, sections four through six.Section four the Galilean system of coordinates.
As is well known, the fundamentallaw of the mechanics of Galilei Newton,
which is known as a law ofinertia, can be stated thus, a
body removed sufficiently far from other bodiescontinues in a state of rest or of

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uniform motion in a straight line.This law not only says something about the
motion of the bodies, but italso indicates the reference bodies or systems of
coordinates permissible in mechanics, which canbe used in mechanical description. The visible
fixed stars are bodies for which thelaw of inertia certainly holds to a high

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degree of approximation. Now, ifwe use a system of coordinates which is
rigidly attached to the Earth, thenrelative to this system, every fixed star
describes a circle of immense radius inthe course of an astronomical day, a
result which is opposed to the statementof the law of inertia, so that

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if we adhere to this law,we must refer these motions only to systems
of coordinates relative to which the fixedstars do not move in a circle.
A system of coordinates which the stateof motion is such that the law of
inertia holds relative to it, iscalled a Galilean system of coordinates. The

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laws of the mechanics of Galilee Newtoncan be regarded as valid only for a
Galilee system of coordinates, and ofsection four Section five the principle of relativity
in the restricted sense. In orderto attain the greatest possible clearness, let

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us return to our example of therailway carriage supposed to be traveling uniformly.
We call its motion a uniform translation. Uniform because it is of constant velocity
and direction, translation because although thecarriage changes its position relative to the embankment,

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yet it does not rotate. Inso doing, let us imagine a
raven flying through the air in sucha manner that its motion, as observed
from the embankment, is uniform andin a straight line. We were to
observe the flying raven from the movingrailway carriage, we should find that the
motion of the raven will be oneof different velocity and direction, but that

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it would still be uniform and ina straight line. Expressed in an abstract
manner, we may say, ifa mass M is moving uniformly in a
straight line with respect to a coordinatesystem K, then it will also be
moving uniformly and in a straight linerelative to a second coordinate system K prime,

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provided that the latter is executing auniform translatory motion with respect to K.
In accordance with the discussion contained inthe preceding section, it follows that
if K is a Galilean coordinate system, then every other coordinate system K prime
is a Galilean one when in relationto K, it is in a condition

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of uniform motion of translation. Relativeto K prime, mechanical laws of Galilee
Newton hold good exactly as they dowith respect to K. We advance a
step farther in our generalization when weexpressed the tenet. Thus, if relative
to K, k prime is auniformly moving coordinate system devoid of rotation,

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then natural phenomena run their course withrespect to K prime according to exactly the
same general laws as with respect toK. This statement is called the principle
of relativity in the restricted sense.As long as one was convinced that all
natural phenomena were capable of representation withthe help of classical mechanics, there was

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no need to doubt the validity ofthis principle of relativity. But in view
of the more recent development of electrodynamicsand optics, it became more and more
evident that classical mechanics affords an insufficientfoundation for the physical description of all natural
phenomena. At this juncture, thequestion of the validity of the principle of

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relativity became ripe for discussion, andit did not appear impossible that the answer
to this question might be in thenegative. Nevertheless, there are two general
facts which at the outset speak verymuch in favor of the validity of the
principle of relativity. Even though classicalmechanics does not supply us with a sufficiently

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broad basis for the theoretical presentation ofall physical phenomena, still we must grant
it a considerable measure of truth,since it supplies us with the actual motions
of the heavenly bodies, with thedelicacy of detail. Little short and wonderful.
The principle of relativity must therefore applywith great accuracy in the domain of

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mechanics. But that a principle ofsuch broad generality mold with such exactness in
one domain of phenomena and yet shouldbe invalid for another is a priori not
very probable. We now proceed tothe second argument, to which moreover we
shall return later. If the principleof relativity in the restricted sense does not

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hold, then the Galilean coordinate systemsk k prime, k double prime,
et cetera, which are moving uniformlyrelative to each other, will not be
equivalent for the description of natural phenomena. In this case, we should be
constrained to believe that natural laws arecapable of being formulated in a particularly simple

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manner, and of course, onlyon condition that from amongst all possible Galilean
coordinate systems we should have chosen onek sub zero of a particular state of
motion as our body of reference.We should then be justified because of its
merits for the description of natural phenomenain calling this system absolutely at rest,

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and all other Galilean systems k inmotion. If, for instance, our
embankment were the system k sub zero, Then our railway carriage would be a
system K, relative to which lesssimple loss would hold than with the respect
to k some zero. This diminishedsimplicity would be due to the fact that

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the carriage K would be in motioni e. Really, with respect to
k s zero. In the generallaws of nature which had been formulated with
reference to K, the magnitude anddirection of the velocity of the carriage would
necessarily play a part. We shouldexpect, for instance, that the note

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emitted by an organ pipe placed withits axis parallel to the direction of travel,
would be different from that emitted ifthe axis of the pipe were placed
perpendicular to this direction. Now,in virtue of its motion in an orbit
round the Sun, our Earth iscomparable with a railway carriage traveling with a

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velocity of about thirty kilometers per second. If the principle of relativity were not
valid, we should therefore expect thatthe direction of motion of the Earth at
any moment would enter into the lawsof nature, and also that physical systems,
in their behavior would be dependent onthe orientation in space with respect to

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the Earth. For owing to thealteration and direction of the velocity revolution of
the Earth in the course of ayear. The Earth cannot be at rest
relative to the hypothetical system case ofzero throughout the whole year. However,
the most careful observations have never revealedsuch anisotropic properties in terrestrial physical space,

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i e. A physical non equivalenceof different directions. This is very powerful
argument in favor of the principle relativity. End of section five. Section six.
The theorem of the addition of velocitiesemployed in classical mechanics. Let us

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suppose our old friend the railway carectto be traveling along the rails with a
constant velocity V, and that aman traverses the length of the carriage in
the direction of travel with a velocityW. How quickly, or in other
words, with what velocity capital Wdoes a man advance relative to the embankment

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during the process. The only possibleanswer seems to result from the following consideration.
If the man were to stand stillfor a second, he would advance
relative to the embankment through a distanceV equal numerically to the velocity of the
carriage. As a consequence of hiswalking. However, he traverses an additional

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distance W relative to the carriage,and hence also relative to the embankment in
the second, the distance W beingnumerically equal to the velocity with which he
is walking. Thus, in totalhe covers distance capital W equals V plus

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W relative to the embankment in thesecond considered. We shall see later that
this result, which expresses the theoremof the addition of velocities employed in classical
mechanics, cannot be maintained. Inother words, the law that we have
just written down does not hold inreality for the time being. However,

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we shall assume its correctness end ofSection six